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the individual systems is not enough to reconstruct the state of the composite system. Just as density matrices specify the state of a subsystem of a larger system, analogously, positive operator-valued measures (POVMs) describe the effect on a subsystem of a measurement performed on a larger system. POVMs are extensively used in quantum information theory. As described above, entanglement is a key feature of models of measurement processes in which an apparatus becomes entangled with the system being measured. Systems interacting with the environment in which they reside generally become entangled with that environment, a phenomenon known as quantum decoherence. This can explain why, in practice, quantum effects are difficult to observe in systems larger than microscopic. Equivalence between formulations There are many mathematically equivalent formulations of quantum mechanics. One of the oldest and most common is the "transformation theory" proposed by Paul Dirac, which unifies and generalizes the two earliest formulations of quantum mechanics – matrix mechanics (invented by Werner Heisenberg) and wave mechanics (invented by Erwin Schrödinger). An alternative formulation of quantum mechanics is Feynman's path integral formulation, in which a quantum-mechanical amplitude is considered as a sum over all possible classical and non-classical paths between the initial and final states. This is the quantum-mechanical counterpart of the action principle in classical mechanics. Symmetries and conservation laws The Hamiltonian is known as the generator of time evolution, since it defines a unitary time-evolution operator for each value of . From this relation between and , it follows that any observable that commutes with will be conserved: its expectation value will not change over time. This statement generalizes, as mathematically, any Hermitian operator can generate a family of unitary operators parameterized by a variable . Under the evolution generated by , any observable that commutes with will be conserved. Moreover, if is conserved by evolution under , then is conserved under the evolution generated by . This implies a quantum version of the result proven by Emmy Noether in classical (Lagrangian) mechanics: for every differentiable symmetry of a Hamiltonian, there exists a corresponding conservation law. Examples Free particle The simplest example of quantum system with a position degree of freedom is a free particle in a single spatial dimension. A free particle is one which is not subject to external influences, so that its Hamiltonian consists only of its kinetic energy: The general solution of the Schrödinger equation is given by which is a superposition of all possible plane waves , which are eigenstates of the momentum operator with momentum . The coefficients of the superposition are , which is the Fourier transform of the initial quantum state . It is not possible for the solution to be a single momentum eigenstate, or a single position eigenstate, as these are not normalizable quantum states. Instead, we can consider a Gaussian wave packet: which has Fourier transform, and therefore momentum distribution We see that as we make smaller the spread in position gets smaller, but the spread in momentum gets larger. Conversely, by making larger we make the spread in momentum smaller, but the spread in position gets larger. This illustrates the uncertainty principle. As we let the Gaussian wave packet evolve in time, we see that its center moves through space at a constant velocity (like a classical particle with no forces acting on it). However, the wave packet will also spread out as time progresses, which means that the position becomes more and more uncertain. The uncertainty in momentum, however, stays constant. Particle in a box The particle in a one-dimensional potential energy box is the most mathematically simple example where restraints lead to the quantization of energy levels. The box is defined as having zero potential energy everywhere inside a certain region, and therefore infinite potential energy everywhere outside that region. For the one-dimensional case in the direction, the time-independent Schrödinger equation may be written With the differential operator defined by the previous equation is evocative of the classic kinetic energy analogue, with state in this case having energy coincident with the kinetic energy of the particle. The general solutions of the Schrödinger equation for the particle in a box are or, from Euler's formula, The infinite potential walls of the box determine the values of and at and where must be zero. Thus, at , and . At , in which cannot be zero as this would conflict with the postulate that has norm 1. Therefore, since , must be an integer multiple of , This constraint on implies a constraint on the energy levels, yielding A finite potential well is the generalization of the infinite potential well problem to potential wells having finite depth. The finite potential well problem is mathematically more complicated than the infinite particle-in-a-box problem as the wave function is not pinned to zero at the walls of the well. Instead, the wave function must satisfy more complicated mathematical boundary conditions as it is nonzero in regions outside the well. Another related problem is that of the rectangular potential barrier, which furnishes a model for the quantum tunneling effect that plays an important role in the performance of modern technologies such as flash memory and scanning tunneling microscopy. Harmonic oscillator As in the classical case, the potential for the quantum harmonic oscillator is given by This problem can either be treated by directly solving the Schrödinger equation, which is not trivial, or by using the more elegant "ladder method" first proposed by Paul Dirac. The eigenstates are given by where Hn are the Hermite polynomials and the corresponding energy levels are This is another example illustrating the discretization of energy for bound states. Mach–Zehnder interferometer The Mach–Zehnder interferometer (MZI) illustrates the concepts of superposition and interference with linear algebra in dimension 2, rather than differential equations. It can be seen as a simplified version of the double-slit experiment, but it is of interest in its own right, for example in the delayed choice quantum eraser, the Elitzur–Vaidman bomb tester, and in studies of quantum entanglement. We can model a photon going through the interferometer by considering that at each point it can be in a superposition of only two paths: the "lower" path which starts from the left, goes straight through both beam splitters, and ends at the top, and the "upper" path which starts from the bottom, goes straight through both beam splitters, and ends at the right. The quantum state of the photon is therefore a vector that is a superposition of the "lower" path and the "upper" path , that is, for complex . In order to respect the postulate that we require that . Both beam splitters are modelled as the unitary matrix , which means that when a photon meets the beam splitter it will either stay on the same path with a probability amplitude of , or be reflected to the other path with a probability amplitude of . The phase shifter on the upper arm is modelled as the unitary matrix , which means that if the photon is on the "upper" path it will gain a relative phase of , and it will stay unchanged if it is in the lower path. A photon that enters the interferometer from the left will then be acted upon with a beam splitter , a phase shifter , and another beam splitter , and so end up in the state and the probabilities that it will be detected at the right or at the top are given respectively by One can therefore use the Mach–Zehnder interferometer to estimate the phase shift by estimating these probabilities. It is interesting to consider what would happen if the photon were definitely in either the "lower" or "upper" paths between the beam splitters. This can be accomplished by blocking one of the paths, or equivalently by removing the first beam splitter (and feeding the photon from the left or the bottom, as desired). In both cases there will be no interference between the paths anymore, and the probabilities are given by , independently of the phase . From this we can conclude that the photon does not take one path or another after the first beam splitter, but rather that it is in a genuine quantum superposition of the two paths. Applications Quantum mechanics has had enormous success in explaining many of the features of our universe, with regards to small-scale and discrete quantities and interactions which cannot be explained by classical methods. Quantum mechanics is often the only theory that can reveal the individual behaviors of the subatomic particles that make up all forms of matter (electrons, protons, neutrons, photons, and others). Solid-state physics and materials science are dependent upon quantum mechanics. In many aspects modern technology operates at a scale where quantum effects are significant. Important applications of quantum theory include quantum chemistry, quantum optics, quantum computing, superconducting magnets, light-emitting diodes, the optical amplifier and the laser, the transistor and semiconductors such as the microprocessor, medical and research imaging such as magnetic resonance imaging and electron microscopy. Explanations for many biological and physical phenomena are rooted in the nature of the chemical bond, most notably the macro-molecule DNA. Relation to other scientific theories Classical mechanics The rules of quantum mechanics assert that the state space of a system is a Hilbert space and that observables of the system are Hermitian operators acting on vectors in that space – although they do not tell us which Hilbert space or which operators. These can be chosen appropriately in order to obtain a quantitative description of a quantum system, a necessary step in making physical predictions. An important guide for making these choices is the correspondence principle, a heuristic which states that the predictions of quantum mechanics reduce to those of classical mechanics in the regime of large quantum numbers. One can also start from an established classical model of a particular system, and then try to guess the underlying quantum model that would give rise to the classical model in the correspondence limit. This approach is known as quantization. When quantum mechanics was originally formulated, it was applied to models whose correspondence limit was non-relativistic classical mechanics. For instance, the well-known model of the quantum harmonic oscillator uses an explicitly non-relativistic expression for the kinetic energy of the oscillator, and is thus a quantum version of the classical harmonic oscillator. Complications arise with chaotic systems, which do not have good quantum numbers, and quantum chaos studies the relationship between classical and quantum descriptions in these systems. Quantum decoherence is a mechanism through which quantum systems lose coherence, and thus become incapable of displaying many typically quantum effects: quantum superpositions become simply probabilistic mixtures, and quantum entanglement becomes simply classical correlations. Quantum coherence is not typically evident at macroscopic scales, except maybe at temperatures approaching absolute zero at which quantum behavior may manifest macroscopically. Many macroscopic properties of a classical system are a direct consequence of the quantum behavior of its parts. For example, the stability of bulk matter (consisting of atoms and molecules which would quickly collapse under electric forces alone), the rigidity of solids, and the mechanical, thermal, chemical, optical and magnetic properties of matter are all results of the interaction of electric charges under the rules of quantum mechanics. Special relativity and electrodynamics Early attempts to merge quantum mechanics with special relativity involved the replacement of the Schrödinger equation with a covariant equation such as the Klein–Gordon equation or the Dirac equation. While these theories were successful in explaining many experimental results, they had certain unsatisfactory qualities stemming from their neglect of the relativistic creation and annihilation of particles. A fully relativistic quantum theory required the development of quantum field theory, which applies quantization to a field (rather than a fixed set of particles). The first complete quantum field theory, quantum electrodynamics, provides a fully quantum description of the electromagnetic interaction. Quantum electrodynamics is, along with general relativity, one of the most accurate physical theories ever devised. The full apparatus of quantum field theory is often unnecessary for describing electrodynamic systems. A simpler approach, one that has been used since the inception of quantum mechanics, is to treat charged particles as quantum mechanical objects being acted on by a classical electromagnetic field. For example, the elementary quantum model of the hydrogen atom describes the electric field of the hydrogen atom using a classical Coulomb potential. This "semi-classical" approach fails if quantum fluctuations in the electromagnetic field play an important role, such as in the emission of photons by charged particles. Quantum field theories for the strong nuclear force and the weak nuclear force have also been developed. The quantum field theory of the strong nuclear force is called quantum chromodynamics, and describes the interactions of subnuclear particles such as quarks and gluons. The weak nuclear force and the electromagnetic force were unified, in their quantized forms, into a single quantum field theory (known as electroweak theory), by the physicists Abdus Salam, Sheldon Glashow and Steven Weinberg. Relation to general relativity Even though the predictions of both quantum theory and general relativity have been supported by rigorous and repeated empirical evidence, their abstract formalisms contradict each other and they have proven extremely difficult to incorporate into one consistent, cohesive model. Gravity is negligible in many areas of particle physics, so that unification between general relativity and quantum mechanics is not an urgent issue in those particular applications. However, the lack of a correct theory of quantum gravity is an important issue in physical cosmology and the search by physicists for an elegant "Theory of Everything" (TOE). Consequently, resolving the inconsistencies between both theories has been a major goal of 20th- and 21st-century physics. This TOE would combine not only the models of subatomic physics but also derive the four fundamental forces of nature from a single force or phenomenon. One proposal for doing so is string theory, which posits that the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string. In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries gravitational force. Another popular theory is loop quantum gravity (LQG), which describes quantum properties of gravity and is thus a theory of quantum spacetime. LQG is an attempt to merge and adapt standard quantum mechanics and standard general relativity. This theory describes space as an extremely fine fabric "woven" of finite loops called spin networks. The evolution of a spin network over time is called a spin foam. The characteristic length scale of a spin foam is the Planck length, approximately 1.616×10−35 m, and so lengths shorter than the Planck length are not physically meaningful in LQG. Philosophical implications Since its inception, the many counter-intuitive aspects and results of quantum mechanics have provoked strong philosophical debates and many interpretations. The arguments centre on the probabilistic nature of quantum mechanics, the difficulties with wavefunction collapse and the related measurement problem, and quantum nonlocality. Perhaps the only consensus that exists about these issues is that there is no consensus. Richard Feynman once said, "I think I can safely say that nobody understands quantum mechanics." According to Steven Weinberg, "There is now in my opinion no entirely satisfactory interpretation of quantum mechanics." The views of Niels Bohr, Werner Heisenberg and other physicists are often grouped together as the "Copenhagen interpretation". According to these views, the probabilistic nature of quantum mechanics is not a temporary feature which will eventually be replaced by a deterministic theory, but is instead a final renunciation of the classical idea of "causality". Bohr in particular emphasized that any well-defined application of the quantum mechanical formalism must always make reference to the experimental arrangement, due to the complementary nature of evidence obtained under different experimental situations. Copenhagen-type interpretations remain popular in the 21st century. Albert Einstein, himself one of the founders of quantum theory, was troubled by its apparent failure to respect some cherished metaphysical principles, such as determinism and locality. Einstein's long-running exchanges with Bohr about the meaning and status of quantum mechanics are now known as the Bohr–Einstein debates. Einstein believed that underlying quantum mechanics must be a theory that explicitly forbids action at a distance. He argued that quantum mechanics was incomplete, a theory that was valid but not fundamental, analogous to how thermodynamics is valid, but the fundamental theory behind it is statistical mechanics. In 1935, Einstein and his collaborators Boris Podolsky and Nathan Rosen published an argument that the principle of locality implies the incompleteness of quantum mechanics, a thought experiment later termed the Einstein–Podolsky–Rosen paradox. In 1964, John Bell showed that EPR's principle of locality, together with determinism, was actually incompatible with quantum mechanics: they implied constraints on the correlations produced by distance systems, now known as Bell inequalities, that can be violated by entangled particles. Since then several experiments have been performed to obtain these correlations, with the result that they do in fact violate Bell inequalities, and thus falsify the conjunction of locality with determinism. Bohmian mechanics shows that it is possible to reformulate quantum mechanics to make it deterministic, at the price of making it explicitly nonlocal. It attributes not only a wave function to a physical system, but in addition a real position, that evolves deterministically under a nonlocal guiding equation. The evolution of a physical system is given at all times by the Schrödinger equation together with the guiding equation; there is never a collapse of the wave function. This solves the measurement problem. Everett's many-worlds interpretation, formulated in 1956, holds that all the possibilities described by quantum theory simultaneously occur in a multiverse composed of mostly independent parallel universes. This is a consequence of removing the axiom of the collapse of the wave packet. All possible states of the measured system and the measuring apparatus, together with the observer, are present in a real physical quantum superposition. While the multiverse is deterministic, we perceive non-deterministic behavior governed by probabilities, because we don't observe the multiverse as a whole, but only one parallel universe at a time. Exactly how this is supposed to work has been the subject of much debate. Several attempts have been made to make sense of this and derive the Born rule, with no consensus on whether they have been successful. Relational quantum mechanics appeared in the late 1990s as a modern derivative of Copenhagen-type ideas, and QBism was developed some years later. History Quantum mechanics was developed in the early decades of the 20th century, driven by the need to explain phenomena that, in some cases, had been observed in earlier times. Scientific inquiry into the wave nature of light began in the 17th and 18th centuries, when scientists such as Robert Hooke, Christiaan Huygens and Leonhard Euler proposed a wave theory of light based on experimental observations. In 1803 English polymath Thomas Young described the famous double-slit experiment. This experiment played a major role in the general acceptance of the wave theory of light. During the early 19th century, chemical research by John Dalton and Amedeo Avogadro lent weight to the atomic theory of matter, an idea that James Clerk Maxwell, Ludwig Boltzmann and others built upon to establish the kinetic theory of gases. The successes of kinetic theory gave further credence to the idea that matter is composed of atoms, yet the theory also had shortcomings that would only be resolved by the development of quantum mechanics. While the early conception of atoms from Greek philosophy had been that they were indivisible units the word "atom" deriving from the Greek for "uncuttable" the 19th century saw the formulation of hypotheses about subatomic structure. One important discovery in that regard was Michael Faraday's 1838 observation of a glow caused by an electrical discharge inside a glass tube containing gas at low pressure. Julius Plücker, Johann Wilhelm Hittorf and Eugen Goldstein carried on and improved upon Faraday's work, leading to the identification of cathode rays, which J. J. Thomson found to consist of subatomic particles that would be called electrons. The black-body radiation problem was discovered by Gustav Kirchhoff in 1859. In 1900, Max Planck proposed the hypothesis that energy is radiated and absorbed in discrete "quanta" (or energy packets), yielding a calculation that precisely matched the observed patterns of black-body radiation. The word quantum derives from the Latin, meaning "how great" or "how much". According to Planck, quantities of energy could be thought of as divided	mechanics (invented by Werner Heisenberg) and wave mechanics (invented by Erwin Schrödinger). An alternative formulation of quantum mechanics is Feynman's path integral formulation, in which a quantum-mechanical amplitude is considered as a sum over all possible classical and non-classical paths between the initial and final states. This is the quantum-mechanical counterpart of the action principle in classical mechanics. Symmetries and conservation laws The Hamiltonian is known as the generator of time evolution, since it defines a unitary time-evolution operator for each value of . From this relation between and , it follows that any observable that commutes with will be conserved: its expectation value will not change over time. This statement generalizes, as mathematically, any Hermitian operator can generate a family of unitary operators parameterized by a variable . Under the evolution generated by , any observable that commutes with will be conserved. Moreover, if is conserved by evolution under , then is conserved under the evolution generated by . This implies a quantum version of the result proven by Emmy Noether in classical (Lagrangian) mechanics: for every differentiable symmetry of a Hamiltonian, there exists a corresponding conservation law. Examples Free particle The simplest example of quantum system with a position degree of freedom is a free particle in a single spatial dimension. A free particle is one which is not subject to external influences, so that its Hamiltonian consists only of its kinetic energy: The general solution of the Schrödinger equation is given by which is a superposition of all possible plane waves , which are eigenstates of the momentum operator with momentum . The coefficients of the superposition are , which is the Fourier transform of the initial quantum state . It is not possible for the solution to be a single momentum eigenstate, or a single position eigenstate, as these are not normalizable quantum states. Instead, we can consider a Gaussian wave packet: which has Fourier transform, and therefore momentum distribution We see that as we make smaller the spread in position gets smaller, but the spread in momentum gets larger. Conversely, by making larger we make the spread in momentum smaller, but the spread in position gets larger. This illustrates the uncertainty principle. As we let the Gaussian wave packet evolve in time, we see that its center moves through space at a constant velocity (like a classical particle with no forces acting on it). However, the wave packet will also spread out as time progresses, which means that the position becomes more and more uncertain. The uncertainty in momentum, however, stays constant. Particle in a box The particle in a one-dimensional potential energy box is the most mathematically simple example where restraints lead to the quantization of energy levels. The box is defined as having zero potential energy everywhere inside a certain region, and therefore infinite potential energy everywhere outside that region. For the one-dimensional case in the direction, the time-independent Schrödinger equation may be written With the differential operator defined by the previous equation is evocative of the classic kinetic energy analogue, with state in this case having energy coincident with the kinetic energy of the particle. The general solutions of the Schrödinger equation for the particle in a box are or, from Euler's formula, The infinite potential walls of the box determine the values of and at and where must be zero. Thus, at , and . At , in which cannot be zero as this would conflict with the postulate that has norm 1. Therefore, since , must be an integer multiple of , This constraint on implies a constraint on the energy levels, yielding A finite potential well is the generalization of the infinite potential well problem to potential wells having finite depth. The finite potential well problem is mathematically more complicated than the infinite particle-in-a-box problem as the wave function is not pinned to zero at the walls of the well. Instead, the wave function must satisfy more complicated mathematical boundary conditions as it is nonzero in regions outside the well. Another related problem is that of the rectangular potential barrier, which furnishes a model for the quantum tunneling effect that plays an important role in the performance of modern technologies such as flash memory and scanning tunneling microscopy. Harmonic oscillator As in the classical case, the potential for the quantum harmonic oscillator is given by This problem can either be treated by directly solving the Schrödinger equation, which is not trivial, or by using the more elegant "ladder method" first proposed by Paul Dirac. The eigenstates are given by where Hn are the Hermite polynomials and the corresponding energy levels are This is another example illustrating the discretization of energy for bound states. Mach–Zehnder interferometer The Mach–Zehnder interferometer (MZI) illustrates the concepts of superposition and interference with linear algebra in dimension 2, rather than differential equations. It can be seen as a simplified version of the double-slit experiment, but it is of interest in its own right, for example in the delayed choice quantum eraser, the Elitzur–Vaidman bomb tester, and in studies of quantum entanglement. We can model a photon going through the interferometer by considering that at each point it can be in a superposition of only two paths: the "lower" path which starts from the left, goes straight through both beam splitters, and ends at the top, and the "upper" path which starts from the bottom, goes straight through both beam splitters, and ends at the right. The quantum state of the photon is therefore a vector that is a superposition of the "lower" path and the "upper" path , that is, for complex . In order to respect the postulate that we require that . Both beam splitters are modelled as the unitary matrix , which means that when a photon meets the beam splitter it will either stay on the same path with a probability amplitude of , or be reflected to the other path with a probability amplitude of . The phase shifter on the upper arm is modelled as the unitary matrix , which means that if the photon is on the "upper" path it will gain a relative phase of , and it will stay unchanged if it is in the lower path. A photon that enters the interferometer from the left will then be acted upon with a beam splitter , a phase shifter , and another beam splitter , and so end up in the state and the probabilities that it will be detected at the right or at the top are given respectively by One can therefore use the Mach–Zehnder interferometer to estimate the phase shift by estimating these probabilities. It is interesting to consider what would happen if the photon were definitely in either the "lower" or "upper" paths between the beam splitters. This can be accomplished by blocking one of the paths, or equivalently by removing the first beam splitter (and feeding the photon from the left or the bottom, as desired). In both cases there will be no interference between the paths anymore, and the probabilities are given by , independently of the phase . From this we can conclude that the photon does not take one path or another after the first beam splitter, but rather that it is in a genuine quantum superposition of the two paths. Applications Quantum mechanics has had enormous success in explaining many of the features of our universe, with regards to small-scale and discrete quantities and interactions which cannot be explained by classical methods. Quantum mechanics is often the only theory that can reveal the individual behaviors of the subatomic particles that make up all forms of matter (electrons, protons, neutrons, photons, and others). Solid-state physics and materials science are dependent upon quantum mechanics. In many aspects modern technology operates at a scale where quantum effects are significant. Important applications of quantum theory include quantum chemistry, quantum optics, quantum computing, superconducting magnets, light-emitting diodes, the optical amplifier and the laser, the transistor and semiconductors such as the microprocessor, medical and research imaging such as magnetic resonance imaging and electron microscopy. Explanations for many biological and physical phenomena are rooted in the nature of the chemical bond, most notably the macro-molecule DNA. Relation to other scientific theories Classical mechanics The rules of quantum mechanics assert that the state space of a system is a Hilbert space and that observables of the system are Hermitian operators acting on vectors in that space – although they do not tell us which Hilbert space or which operators. These can be chosen appropriately in order to obtain a quantitative description of a quantum system, a necessary step in making physical predictions. An important guide for making these choices is the correspondence principle, a heuristic which states that the predictions of quantum mechanics reduce to those of classical mechanics in the regime of large quantum numbers. One can also start from an established classical model of a particular system, and then try to guess the underlying quantum model that would give rise to the classical model in the correspondence limit. This approach is known as quantization. When quantum mechanics was originally formulated, it was applied to models whose correspondence limit was non-relativistic classical mechanics. For instance, the well-known model of the quantum harmonic oscillator uses an explicitly non-relativistic expression for the kinetic energy of the oscillator, and is thus a quantum version of the classical harmonic oscillator. Complications arise with chaotic systems, which do not have good quantum numbers, and quantum chaos studies the relationship between classical and quantum descriptions in these systems. Quantum decoherence is a mechanism through which quantum systems lose coherence, and thus become incapable of displaying many typically quantum effects: quantum superpositions become simply probabilistic mixtures, and quantum entanglement becomes simply classical correlations. Quantum coherence is not typically evident at macroscopic scales, except maybe at temperatures approaching absolute zero at which quantum behavior may manifest macroscopically. Many macroscopic properties of a classical system are a direct consequence of the quantum behavior of its parts. For example, the stability of bulk matter (consisting of atoms and molecules which would quickly collapse under electric forces alone), the rigidity of solids, and the mechanical, thermal, chemical, optical and magnetic properties of matter are all results of the interaction of electric charges under the rules of quantum mechanics. Special relativity and electrodynamics Early attempts to merge quantum mechanics with special relativity involved the replacement of the Schrödinger equation with a covariant equation such as the Klein–Gordon equation or the Dirac equation. While these theories were successful in explaining many experimental results, they had certain unsatisfactory qualities stemming from their neglect of the relativistic creation and annihilation of particles. A fully relativistic quantum theory required the development of quantum field theory, which applies quantization to a field (rather than a fixed set of particles). The first complete quantum field theory, quantum electrodynamics, provides a fully quantum description of the electromagnetic interaction. Quantum electrodynamics is, along with general relativity, one of the most accurate physical theories ever devised. The full apparatus of quantum field theory is often unnecessary for describing electrodynamic systems. A simpler approach, one that has been used since the inception of quantum mechanics, is to treat charged particles as quantum mechanical objects being acted on by a classical electromagnetic field. For example, the elementary quantum model of the hydrogen atom describes the electric field of the hydrogen atom using a classical Coulomb potential. This "semi-classical" approach fails if quantum fluctuations in the electromagnetic field play an important role, such as in the emission of photons by charged particles. Quantum field theories for the strong nuclear force and the weak nuclear force have also been developed. The quantum field theory of the strong nuclear force is called quantum chromodynamics, and describes the interactions of subnuclear particles such as quarks and gluons. The weak nuclear force and the electromagnetic force were unified, in their quantized forms, into a single quantum field theory (known as electroweak theory), by the physicists Abdus Salam, Sheldon Glashow and Steven Weinberg. Relation to general relativity Even though the predictions of both quantum theory and general relativity have been supported by rigorous and repeated empirical evidence, their abstract formalisms contradict each other and they have proven extremely difficult to incorporate into one consistent, cohesive model. Gravity is negligible in many areas of particle physics, so that unification between general relativity and quantum mechanics is not an urgent issue in those particular applications. However, the lack of a correct theory of quantum gravity is an important issue in physical cosmology and the search by physicists for an elegant "Theory of Everything" (TOE). Consequently, resolving the inconsistencies between both theories has been a major goal of 20th- and 21st-century physics. This TOE would combine not only the models of subatomic physics but also derive the four fundamental forces of nature from a single force or phenomenon. One proposal for doing so is string theory, which posits that the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string. In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries gravitational force. Another popular theory is loop quantum gravity (LQG), which describes quantum properties of gravity and is thus a theory of quantum spacetime. LQG is an attempt to merge and adapt standard quantum mechanics and standard general relativity. This theory describes space as an extremely fine fabric "woven" of finite loops called spin networks. The evolution of a spin network over time is called a spin foam. The characteristic length scale of a spin foam is the Planck length, approximately 1.616×10−35 m, and so lengths shorter than the Planck length are not physically meaningful in LQG. Philosophical implications Since its inception, the many counter-intuitive aspects and results of quantum mechanics have provoked strong philosophical debates and many interpretations. The arguments centre on the probabilistic nature of quantum mechanics, the difficulties with wavefunction collapse and the related measurement problem, and quantum nonlocality. Perhaps the only consensus that exists about these issues is that there is no consensus. Richard Feynman once said, "I think I can safely say that nobody understands quantum mechanics." According to Steven Weinberg, "There is now in my opinion no entirely satisfactory interpretation of quantum mechanics." The views of Niels Bohr, Werner Heisenberg and other physicists are often grouped together as the "Copenhagen interpretation". According to these views, the probabilistic nature of quantum mechanics is not a temporary feature which will eventually be replaced by a deterministic theory, but is instead a final renunciation of the classical idea of "causality". Bohr in particular emphasized that any well-defined application of the quantum mechanical formalism must always make reference to the experimental arrangement, due to the complementary nature of evidence obtained under different experimental situations. Copenhagen-type interpretations remain popular in the 21st century. Albert Einstein, himself one of the founders of quantum theory, was troubled by its apparent failure to respect some cherished metaphysical principles, such as determinism and locality. Einstein's long-running exchanges with Bohr about the meaning and status of quantum mechanics are now known as the Bohr–Einstein debates. Einstein believed that underlying quantum mechanics must be a theory that explicitly forbids action at a distance. He argued that quantum mechanics was incomplete, a theory that was valid but not fundamental, analogous to how thermodynamics is valid, but the fundamental theory behind it is statistical mechanics. In 1935, Einstein and his collaborators Boris Podolsky and Nathan Rosen published an argument that the principle of locality implies the incompleteness of quantum mechanics, a thought experiment later termed the Einstein–Podolsky–Rosen paradox. In 1964, John Bell showed that EPR's principle of locality, together with determinism, was actually incompatible with quantum mechanics: they implied constraints on the correlations produced by distance systems, now known as Bell inequalities, that can be violated by entangled particles. Since then several experiments have been performed to obtain these correlations, with the result that they do in fact violate Bell inequalities, and thus falsify the conjunction of locality with determinism. Bohmian mechanics shows that it is possible to reformulate quantum mechanics to make it deterministic, at the price of making it explicitly nonlocal. It attributes not only a wave function to a physical system, but in addition a real position, that evolves deterministically under a nonlocal guiding equation. The evolution of a physical system is given at all times by the Schrödinger equation together with the guiding equation; there is never a collapse of the wave function. This solves the measurement problem. Everett's many-worlds interpretation, formulated in 1956, holds that all the possibilities described by quantum theory simultaneously occur in a multiverse composed of mostly independent parallel universes. This is a consequence of removing the axiom of the collapse of the wave packet. All possible states of the measured system and the measuring apparatus, together with the observer, are present in a real physical quantum superposition. While the multiverse is deterministic, we perceive non-deterministic behavior governed by probabilities, because we don't observe the multiverse as a whole, but only one parallel universe at a time. Exactly how this is supposed to work has been the subject of much debate. Several attempts have been made to make sense of this and derive the Born rule, with no consensus on whether they have been successful. Relational quantum mechanics appeared in the late 1990s as a modern derivative of Copenhagen-type ideas, and QBism was developed some years later. History Quantum mechanics was developed in the early decades of the 20th century, driven by the need to explain phenomena that, in some cases, had been observed in earlier times. Scientific inquiry into the wave nature of light began in the 17th and 18th centuries, when scientists such as Robert Hooke, Christiaan Huygens and Leonhard Euler proposed a wave theory of light based on experimental observations. In 1803 English polymath Thomas Young described the famous double-slit experiment. This experiment played a major role in the general acceptance of the wave theory of light. During the early 19th century, chemical research by John Dalton and Amedeo Avogadro lent weight to the atomic theory of matter, an idea that James Clerk Maxwell, Ludwig Boltzmann and others built upon to establish the kinetic theory of gases. The successes of kinetic theory gave further credence to the idea that matter is composed of atoms, yet the theory also had shortcomings that would only be resolved by the development of quantum mechanics. While the early conception of atoms from Greek philosophy had been that they were indivisible units the word "atom" deriving from the Greek for "uncuttable" the 19th century saw the formulation of hypotheses about subatomic structure. One important discovery in that regard was Michael Faraday's 1838 observation of a glow caused by an electrical discharge inside a glass tube containing gas at low pressure. Julius Plücker, Johann Wilhelm Hittorf and Eugen Goldstein carried on and improved upon Faraday's work, leading to the identification of cathode rays, which J. J. Thomson found to consist of subatomic particles that would be called electrons. The black-body radiation problem was discovered by Gustav Kirchhoff in 1859. In 1900, Max Planck proposed the hypothesis that energy is radiated and absorbed in discrete "quanta" (or energy packets), yielding a calculation that precisely matched the observed patterns of black-body radiation. The word quantum derives from the Latin, meaning "how great" or "how much". According to Planck, quantities of energy could be thought of as divided into "elements" whose size (E) would be proportional to their frequency (ν): , where h is Planck's constant. Planck
large-scale (often chintz) and small-scale (often calico) patterns. Some antique quilts made in North America have worn-out blankets or older quilts as the internal batting layer, quilted between new layers of fabric and thereby extending the usefulness of old material. During American pioneer days, foundation piecing became popular. Paper was cut into shapes and used as a pattern; each individual piece of cut fabric was basted around the paper pattern. Paper was a scarce commodity in the early American west so women would save letters from home, postcards, newspaper clippings, and catalogs to use as patterns. The paper not only served as a pattern but as an insulator. The paper found between the old quilts has become a primary source of information about pioneer life. Quilts made without any insulation or batting were referred to as summer quilts. They were not made for warmth, only to keep the chill off during cooler summer evenings. African-American quilts There is a long tradition of African-American quilting beginning with quilts made by slaves, both for themselves and for the people who enslaved them. The style of these quilts was determined largely by time period and region, rather than race, and the documented slave-made quilts generally resemble those made by white women in their region. After 1865 and the end of slavery in the United States, African-Americans began to develop their own distinctive style of quilting. Harriet Powers, an African American woman born into slavery, made two famous "story quilts" and was one of the many African-American quilters who contributed to the development of quilting in the United States. The first nationwide recognition of African-American quilt-making came when the Gee's Bend quilting community was celebrated in an exhibition that opened in 2002 and traveled to many museums, including the Smithsonian. Gee's Bend is a small, isolated community of African-Americans in southern Alabama with a quilt-making tradition that goes back several generations and is characterized by pattern improvisation, multiple patterning, bright and contrasting colors, visual motion, and a lack of rules. The contributions made by Harriet Powers and other quilters of Gee's Bend, Alabama have been recognized by the US Postal Service with a series of stamps. The communal nature of the quilting process (and how it can bring together women of varied races and backgrounds) was honored in the series of stamps. Beginning with the children's story Sweet Clara and the Freedom Quilt (1989), a legend has developed that enslaved people used quilts as a means to share and transmit secret messages to escape slavery and travel the Underground Railroad. Consensus among historians is that there is no sound basis for this belief, and no documented mention among the thousands of slave narratives or other contemporary records. Amish quilts Another American group to develop a distinct style of quilting were the Amish. Typically, these quilts use only solid fabrics, are pieced from geometric shapes, do not contain appliqué, and construction is simple (corners are butted, rather than mitered, for instance) and done entirely by hand. Amish quilters also tend to use simple patterns: Lancaster County Amish are known for their Diamond-in-a-Square and Bars patterns, while other communities use patterns such as Brick, Streak of Lightning, Chinese Coins, and Log Cabins, and midwestern communities are known for their repeating block patterns. Borders and color choice also vary by community. For example, Lancaster quilts feature wide borders with lavish quilting, while Midwestern quilts feature narrower borders to balance the fancier piecing. Native American quilts Some Native Americans are thought to have learned quilting through observation of white settlers; others learned it from missionaries who taught quilting to Native American women along with other homemaking skills. Native American women quickly developed their own unique style, the Lone Star design (also called the Star of Bethlehem), a variation on Morning Star designs that had been featured on Native American clothing and other items for centuries. These quilts often featured floral appliqué framing the star design. Star quilts have become an important part of many Plains Indian ceremonies, replacing buffalo robes traditionally given away at births, marriages, tribal elections, and other ceremonies. Pictorial quilts, created with appliqué, were also common. Another distinctive style of Native American quilting is Seminole piecing, created by Seminoles living in the Florida Everglades. The style evolved out of a need for cloth (the closest town was often a week's journey away). Women would make strips of sewing the remnants of fabric rolls together, then sew these into larger pieces to make clothing. Eventually the style began to be used not just for clothing but for quilts as well. In 1900, with the introduction of sewing machines and readily available fabric in Seminole communities, the patterns became much more elaborate and the style continues to be in use today, both by Seminole women and by others who have copied and adapted their designs and techniques. Hawaiian quilting "Hawaiian quilting was well established by the beginning of the twentieth century. Hawaiian women learned to quilt from the wives of missionaries from New England in the 1820s. Though they learned both pieced work and applique, by the 1870s they had adapted applique techniques to create a uniquely Hawaiian mode of expression. The classic Hawaiian quilt design is a large, bold, curvilinear appliqué pattern that covers much of the surface of the quilt, with the symmetrical design cut from only one piece of fabric." South Asian quilting There are two primary forms of quilting that originate in South Asia: Nakshi Kantha and Ralli. Nakshi Kantha quilts originated in India and are typically made of scraps and worn-out fabric stitched together with old sari threads using kantha embroidery stitches. "The layers of cloth were spread on the ground, held in place with weights at the edges, and sewn together with rows of large basting stitches. The cloth was then folded and worked on whenever there was time." The first recorded kantha are more than 500 years old. Ralli quilts are traditionally made in Pakistan, western India, and the surrounding area. They are made by every sector of society including Hindu and Muslim women, women of different castes, and women from different towns or villages or tribes with the colors and designs varying among these groups. The name comes from ralanna, a word meaning to mix or connect. Quilts tops were designed and pieced by one woman using scraps of hand-dyed cotton. This cotton often comes from old dresses or shawls. Once pieced, the quilt top is placed on a reed mat with the other layers and sewn together using thick, colored thread in straight parallel lines by members of the designer's family and community. East Asian quilting Quilting in Japan, until the 20th century, generally covered local bast fibers with more valuable cotton cloth. The rectangular nature of Japanese cloth articles encouraged rectangle-based patterns. Sashiko stitching has now also developed purely decorative forms. Swedish quilting Quilting originated in Sweden in the fifteenth century with heavily stitched and appliquéd quilts made for the very wealthy. These quilts, created from silk, wool, and felt, were intended to be both decorative and functional and were found in churches and in the homes of nobility. Imported cotton first appeared in Sweden in 1870, and began to appear in Swedish quilts soon after along with scraps of wool, silk, and linen. As the availability of cotton increased and its price went down, quilting became widespread among all classes of Swedish society. Wealthier quilters used wool batting while others used linen scraps, rags, or paper mixed with animal hair. In general, these quilts were simple and narrow, made by both men and women. The biggest influence on Swedish quilting in this time period is thought to have come from America as Swedish immigrants to the United States returned to their home country when conditions there improved. Art quilting During the late 20th century, art quilts became popular for their aesthetic and artistic qualities rather than for functionality as they are displayed on a wall or table rather than being used on a bed.. "It is believed that decorative quilting came to Europe and Asia during the Crusades (A.D. 1100–1300), a likely idea because textile arts were more developed in China and India than in the West." American artist Judy Chicago stated in a 1981 interview that if not for sexism in the visual arts, the art world, and broader society, quilting would be regarded as a form of high art: Modern quilting In the early 21st century, modern quilting became a more prominent area of quilting. Modern quilting follows a distinct aesthetic style which draws on inspiration from modern style in architecture, art, and design using traditional quilt making techniques. Modern quilts are different from art quilts in that they are made to be used. Modern quilts are also influenced by the Quilters of Gee's Bend, Amish quilts, Nancy Crow, Denyse Schmidt, Gwen Marston, Yoshiko Jinzenji, Bill Kerr and Weeks Ringle. The Modern Quilt Guild has attempted to define modern quilting. The characteristics of a modern quilt may include: the use of bold colors and prints, high contrast and graphic areas of solid color, improvisational piecing, minimalism, expansive negative space, and alternate grid work. The Modern Quilt Guild, a non-profit corporation, with 14,000 members in more than 200 members guilds in 39 countries, fosters modern quilting via local guilds, workshops, webinars, and Quiltcon—an annual modern quilting conference and convention. The founding Modern Quilt Guild formed in October 2009 in Los Angeles. QuiltCon features a quilt show with 400+ quilts, quilt vendors, lectures, and quilting workshops and classes. The first	worked on whenever there was time." The first recorded kantha are more than 500 years old. Ralli quilts are traditionally made in Pakistan, western India, and the surrounding area. They are made by every sector of society including Hindu and Muslim women, women of different castes, and women from different towns or villages or tribes with the colors and designs varying among these groups. The name comes from ralanna, a word meaning to mix or connect. Quilts tops were designed and pieced by one woman using scraps of hand-dyed cotton. This cotton often comes from old dresses or shawls. Once pieced, the quilt top is placed on a reed mat with the other layers and sewn together using thick, colored thread in straight parallel lines by members of the designer's family and community. East Asian quilting Quilting in Japan, until the 20th century, generally covered local bast fibers with more valuable cotton cloth. The rectangular nature of Japanese cloth articles encouraged rectangle-based patterns. Sashiko stitching has now also developed purely decorative forms. Swedish quilting Quilting originated in Sweden in the fifteenth century with heavily stitched and appliquéd quilts made for the very wealthy. These quilts, created from silk, wool, and felt, were intended to be both decorative and functional and were found in churches and in the homes of nobility. Imported cotton first appeared in Sweden in 1870, and began to appear in Swedish quilts soon after along with scraps of wool, silk, and linen. As the availability of cotton increased and its price went down, quilting became widespread among all classes of Swedish society. Wealthier quilters used wool batting while others used linen scraps, rags, or paper mixed with animal hair. In general, these quilts were simple and narrow, made by both men and women. The biggest influence on Swedish quilting in this time period is thought to have come from America as Swedish immigrants to the United States returned to their home country when conditions there improved. Art quilting During the late 20th century, art quilts became popular for their aesthetic and artistic qualities rather than for functionality as they are displayed on a wall or table rather than being used on a bed.. "It is believed that decorative quilting came to Europe and Asia during the Crusades (A.D. 1100–1300), a likely idea because textile arts were more developed in China and India than in the West." American artist Judy Chicago stated in a 1981 interview that if not for sexism in the visual arts, the art world, and broader society, quilting would be regarded as a form of high art: Modern quilting In the early 21st century, modern quilting became a more prominent area of quilting. Modern quilting follows a distinct aesthetic style which draws on inspiration from modern style in architecture, art, and design using traditional quilt making techniques. Modern quilts are different from art quilts in that they are made to be used. Modern quilts are also influenced by the Quilters of Gee's Bend, Amish quilts, Nancy Crow, Denyse Schmidt, Gwen Marston, Yoshiko Jinzenji, Bill Kerr and Weeks Ringle. The Modern Quilt Guild has attempted to define modern quilting. The characteristics of a modern quilt may include: the use of bold colors and prints, high contrast and graphic areas of solid color, improvisational piecing, minimalism, expansive negative space, and alternate grid work. The Modern Quilt Guild, a non-profit corporation, with 14,000 members in more than 200 members guilds in 39 countries, fosters modern quilting via local guilds, workshops, webinars, and Quiltcon—an annual modern quilting conference and convention. The founding Modern Quilt Guild formed in October 2009 in Los Angeles. QuiltCon features a quilt show with 400+ quilts, quilt vendors, lectures, and quilting workshops and classes. The first QuiltCon was February 21–24, 2013 in Austin, TX. QuiltCon 2020 will be held in Austin, Texas, February 20–23, 2020 and will feature 400 juried modern quilts from quilters around the world. Quilting in fashion and design Unusual quilting designs have increasingly become popular as decorative textiles. As industrial sewing technology has become more precise and flexible, quilting using exotic fabrics and embroidery began to appear in home furnishings in the early 21st century. Quilt blocks The quilt block is traditionally a sub-unit composed of several pieces of fabric sewn together. The quilt blocks are repeated, or sometimes alternated with plain blocks, to form the overall design of a quilt. Barbara Brackman has documented over 4000 different quilt block patterns from the early 1830s to the 1970s in the Encyclopedia Of Pieced Quilt Patterns. Some of the simpler designs for quilt blocks include the Nine-Patch, Shoo Fly, Churn Dash, and the Prairie Queen. Most geometric quilt block designs fit into a "grid", which is the number of squares a pattern block is divided into. The five categories into which most square patterns fall are Four Patch, Nine Patch, Five-Patch, Seven-Patch, and Eight-Pointed Star. Each block can be subdivided into multiples: a Four-Patch can be constructed of 16 or 64 squares, for example. A simple Nine Patch is made by sewing five patterned or dark pieces (patches) to four light square pieces in alternating order. These nine sewn squares make one block. The Shoo Fly varies from this Nine Patch by dividing each of the four corner pieces into a light and dark triangle. Another variation develops when one square piece is divided into two equal rectangles in the basic Nine Patch design. The Churn Dash block combines the triangles and rectangle to expand the Nine Patch. The Prairie Queen block combines two large scale triangles in the corner section with the middle section using four squares. The center piece is one full size square. Each of the nine sections does have the same overall measurement and fits together. The number of patterns possible by subdividing Four-, Five-, Seven-, Nine-Patches and Eight-Pointed Stars and using triangles instead of squares in the small subdivisions is almost endless. Quilting techniques Many types of quilting exist today. The two most widely used are hand-quilting and machine quilting. Hand quilting is the process of using a needle and thread to sew a running stitch by hand across the entire area to be quilted. This binds the layers together. A quilting frame or hoop is often used to assist in holding the piece being quilted off the quilter's lap. A quilter can make one stitch at a time by first driving the needle through the fabric from the right side, then pushing it back up through the material from the wrong side to complete the stitch; this is called a stab stitch. Another option is called a rocking stitch, where the quilter has one hand, usually with a finger wearing a thimble, on top of the quilt, while the other hand is located beneath the piece to push the needle back up. A third option is called "loading the needle" and involves doing four or more stitches before pulling the needle through the cloth. Hand quilting is still practiced by the Amish and Mennonites within the United States and Canada, and is enjoying a resurgence worldwide. Machine quilting is the process of using a home sewing machine or a longarm machine to sew the layers together. With the home sewing machine, the layers are tacked together before quilting. This involves laying the top, batting, and backing out on a flat surface and either pinning (using large safety pins) or tacking the layers together. Longarm quilting involves placing the layers to be quilted on a special frame. The frame has bars on which the layers are rolled, keeping these together without the need for tacking or pinning. These frames are used with a professional sewing machine mounted on a platform. The platform rides along tracks so that the machine can be moved across the layers on the frame. A longarm machine is moved across the fabric. In contrast, the fabric is moved through a home sewing machine. Tying is another technique of fastening the three layers together. This is done primarily on quilts that are made to be used and are needed quickly. The process of tying the quilt is done with yarns or multiple strands of thread. Square knots are used to finish off the ties so that the quilt may be washed and used without fear of the knots coming undone. This technique is commonly called "tacking." In the Midwest, tacked bed covers are
e.g. Enterprise Controls are commercially sold by The Qt Company. Supported platforms Qt works on many different platforms; the following are officially supported: After Nokia opened the Qt source code to the community on Gitorious, various ports appeared. There are also some ports of Qt that may be available, but are not supported anymore. These platforms are listed in List of platforms supported by Qt. See also there for current community support for other lesser known platforms, such as SailfishOS. Licensing Qt is available under the following free software licenses: GPL 2.0, GPL 3.0, LGPL 3.0 and LGPL 2.1 (with Qt special exception). Note that some modules are available only under a GPL license, which means that applications which link to these modules need to comply with that license. In addition, Qt has always been available under a commercial license, like the Qt Commercial License, that allows developing proprietary applications with no restrictions on licensing. Qt tools Qt comes with its own set of tools to ease cross-platform development, which can otherwise be cumbersome due to different set of development tools. Qt Creator is a cross-platform IDE for C++ and QML. Qt Designer's GUI layout/design functionality is integrated into the IDE, although Qt Designer can still be started as a standalone tool. In addition to Qt Creator, Qt provides qmake, a cross-platform build script generation tool that automates the generation of Makefiles for development projects across different platforms. There are other tools available in Qt, including the Qt Designer interface builder and the Qt Assistant help browser (which are both embedded in Qt Creator), the Qt Linguist translation tool, uic (user interface compiler), and moc (Meta-Object Compiler). History of Qt Early developments In the summer of 1990, Haavard Nord and Eirik Chambe-Eng (the original developers of Qt and the CEO and President, respectively, of Trolltech) were working together on a database application for ultrasound images written in C++ and running on Mac OS, Unix, and Microsoft Windows. They began development of "Qt" in 1991, three years before the company was incorporated as Quasar Technologies, then changed the name to Troll Tech and then to Trolltech. The toolkit was called Qt because the letter Q looked appealing in Haavard's Emacs typeface, and "t" was inspired by Xt, the X toolkit. The first two versions of Qt had only two flavors: Qt/X11 for Unix and Qt/Windows for Windows. On 20 May 1995 Troll Tech publicly released Qt 0.90 for X11/Linux with the source code under the Qt Free Edition License. This license was viewed as not compliant with the free software definition by Free Software Foundation because, while the source was available, it did not allow the redistribution of modified versions. Trolltech used this license until version 1.45. Controversy erupted around 1998 when it became clear that the K Desktop Environment was going to become one of the leading desktop environments for Linux. As it was based on Qt, many people in the free software movement worried that an essential piece of one of their major operating systems would be proprietary. The Windows platform was available only under a proprietary license, which meant free/open source applications written in Qt for X11 could not be ported to Windows without purchasing the proprietary edition. Becoming free software–friendly With the release of version 2.0 of the toolkit in mid-1999, the license was changed to the Q Public License (QPL), a free software license, but one regarded by the Free Software Foundation as incompatible with the GPL. Compromises were sought between KDE and Trolltech whereby Qt would not be able to fall under a more restrictive license than the QPL, even if Trolltech was bought out or went bankrupt. This led to the creation of the KDE Free Qt foundation, which guarantees that Qt would fall under a BSD-style license should no free/open source version of Qt be released during 12 months. In 2000, Qt/X11 2.2 was released under the GPL v2, ending all controversy regarding GPL compatibility. At the end of 2001, Trolltech released Qt 3.0, which added support for Mac OS X (now known as macOS). The Mac OS X support was available only in the proprietary license until June 2003, when Trolltech released Qt 3.2 with Mac OS X support available under the GPL. In 2002, members of the KDE on Cygwin project began porting the GPL licensed Qt/X11 code base to Windows. This was in response to Trolltech's refusal to license Qt/Windows under the GPL on the grounds that Windows was not a free/open source software platform. The project achieved reasonable success although it never reached production quality. This was resolved when Trolltech released Qt 4.0 also for Windows under the GPL in June 2005. Qt 4 supported the same set of platforms in the free software/open source editions as in the proprietary edition, so it is possible, with Qt 4.0 and later releases, to create GPL-licensed free/open source applications using Qt on all supported platforms. The GPL v3 with special exception was later added as an added licensing option. The GPL exception allows the final application to be licensed under various GPL-incompatible free software/open source licenses such as the Mozilla Public License 1.1. Acquisition by Nokia Nokia acquired Trolltech ASA on 17 June 2008 and changed the name first to Qt Software, then to Qt Development Frameworks. Nokia focused on turning Qt into the main development platform for its devices, including a port to the Symbian S60 platform. Version 1.0 of the Nokia Qt SDK was released on 23 June 2010. The source code was made available over Gitorious, a community oriented git source code repository, with a goal of creating a broader community using and improving Qt. On 14 January 2009, Qt version 4.5 added another option, the LGPL, to make Qt more attractive for both non-GPL open source projects and closed applications. In February 2011, Nokia announced its decision to drop Symbian technologies and base their future smartphones on the Windows Phone platform instead (and since then support for that platform has also been dropped). One month later, Nokia announced the sale of Qt's commercial licensing and professional services to Digia, with the immediate goal of taking Qt support to Android, iOS and Windows 8 platforms, and to continue focusing on desktop and embedded development, although Nokia was to remain the main development force behind the framework at that time. Merging and demerging with Digia In March 2011, Nokia sold the commercial licensing part of Qt to Digia, creating Qt Commercial. In August 2012, Digia announced that it would acquire Qt from Nokia. The Qt team at Digia started their work in September 2012. They released Qt 5.0 within a month and newer versions every six months with new features and additional supported platforms. In September 2014, Digia transferred the Qt business and copyrights to their wholly owned subsidiary, The Qt Company, which owns 25 brands related to Qt. In May 2016, Digia and Qt demerged completely into two independent companies. The Qt Project and open governance Qt 5 was officially released on 19 December 2012. This new version marked a major change in the platform, with hardware-accelerated graphics, QML and JavaScript playing a major role. The traditional C++-only QWidgets continued to be supported, but did not benefit from the performance improvements available through the new architecture. Qt 5 brings significant improvements to the speed and ease of developing user interfaces. Framework development of Qt 5 moved to open governance at qt-project.org, which made it possible for developers outside Digia to submit patches for review. Qt contributors Aside from The Qt Company, many organizations and individuals using Qt as their development platform participate in the open development of Qt via the Qt Project. One such Qt contributor is Klarälvdalens Datakonsult AB, a Swedish Qt consulting company. KDAB is involved in many areas, including maintenance of several components. Together with RIM/BlackBerry, KDAB is maintaining the QNX and BlackBerry 10 ports of Qt. Another participator is Intel, contributing for example Wayland support. AudioCodes maintains IBM ClearCase support in Qt Creator. As a heavy user of Qt, the KDE project submits many patches and features from its developer library KDE Frameworks back to Qt. See also List of widget toolkits Android software development iOS SDK Wt (web toolkit) Bibliography Qt Wiki provides a comprehensive list of English books about Qt. This is a list of notable books: References External links Qt Marketplace 1992 software Application programming interfaces Articles with example C++ code C++ libraries Cross-platform software Cross-platform desktop-apps development Formerly proprietary software Free computer libraries	scientific, engineering, mathematical, and computing fields. Moonlight Stream, an open-source implementation of Nvidia Shield Musescore, an open-source, multiplatform notation software OBS, a libre cross-platform screencast software Orange data mining suite ParaView open-source cross-platform application for interactive, scientific visualization qBittorrent cross-platform free and open-source BitTorrent client QGIS geographic information system Qtractor Audio multitrack recorder and editing software QuiteRSS Feed Reader Retroshare F2F communication platform Roblox Studio a game creation tool used on the Roblox platform Scribus desktop publishing software Sibelius music composition and notation software Source 2 engine tools a 3D video game engine developed by Valve Stellarium, a planetarium program Subsurface, a software for logging and planning scuba dives initially designed and developed by Linus Torvalds SuperCollider, an environment and programming language for real-time audio synthesis and algorithmic composition Teamviewer, a computer software package for remote control, desktop sharing, online meetings, web conferencing and file transfer between computers Telegram, a messaging client available for Windows, Mac and Linux VirtualBox OS virtualization software VLC media player Wireshark, a packet analyzer WPS Office XaoS, a real-time fractal zoomer XnView MP Organizations using Qt Qt is utilized by a wide range of companies and organizations such as AMD Blizzard Entertainment BMW Crytek Daimler AG Electronic Arts European Space Agency DreamWorks LG Lucasfilm Microsoft Panasonic Philips Robert Bosch GmbH Samsung Siemens Tesla Tomtom Volvo German Air Traffic Control HP Walt Disney Animation Studios Valve Qt software architecture Qt concepts Qt is built on these key concepts: Complete abstraction of the GUI When first released, Qt used its own paint engine and controls, emulating the look of the different platforms it runs on when it drew its widgets. This made the porting work easier because very few classes in Qt really depended on the target platform; however, this occasionally led to slight discrepancies where that emulation was imperfect. Recent versions of Qt use the native style APIs of the different platforms, on platforms that have a native widget set, to query metrics and draw most controls, and do not suffer from such issues as often. On some platforms (such as MeeGo and KDE) Qt is the native API. Some other portable graphical toolkits have made different design decisions; for example, wxWidgets uses the toolkits of the target platform for its implementations. Signals and slots A language construct introduced in Qt for communication between objects which makes it easy to implement the observer pattern while avoiding boilerplate code. The concept is that GUI widgets can send signals containing event information which can be received by other controls using special functions known as slots. Metaobject compiler The metaobject compiler, termed moc, is a tool that is run on the sources of a Qt program. It interprets certain macros from the C++ code as annotations, and uses them to generate added C++ code with meta information about the classes used in the program. This meta information is used by Qt to provide programming features not available natively in C++: signals and slots, introspection and asynchronous function calls. Language bindingsQt can be used in several programming languages other than C++, such as Python, Javascript, C# and Rust via language bindings; many languages have bindings for Qt 5 and bindings for Qt 4. The Ring programming language includes Qt in the standard library. Qt modules Starting with Qt 4.0 the framework was split into individual modules. With Qt 5.0 the architecture was modularized even further. Qt is now split into essential and add-on modules. Qt essentials Qt add-ons Editions There are four editions of Qt available: Community, Indie Mobile, Professional and Enterprise. The Community version is under the open source licenses, while the Indie Mobile, Professional and Enterprise versions, which contain additional functionality and libraries, e.g. Enterprise Controls are commercially sold by The Qt Company. Supported platforms Qt works on many different platforms; the following are officially supported: After Nokia opened the Qt source code to the community on Gitorious, various ports appeared. There are also some ports of Qt that may be available, but are not supported anymore. These platforms are listed in List of platforms supported by Qt. See also there for current community support for other lesser known platforms, such as SailfishOS. Licensing Qt is available under the following free software licenses: GPL 2.0, GPL 3.0, LGPL 3.0 and LGPL 2.1 (with Qt special exception). Note that some modules are available only under a GPL license, which means that applications which link to these modules need to comply with that license. In addition, Qt has always been available under a commercial license, like the Qt Commercial License, that allows developing proprietary applications with no restrictions on licensing. Qt tools Qt comes with its own set of tools to ease cross-platform development, which can otherwise be cumbersome due to different set of development tools. Qt Creator is a cross-platform IDE for C++ and QML. Qt Designer's GUI layout/design functionality is integrated into the IDE, although Qt Designer can still be started as a standalone tool. In addition to Qt Creator, Qt provides qmake, a cross-platform build script generation tool that automates the generation of Makefiles for development projects across different platforms. There are other tools available in Qt, including the Qt Designer interface builder and the Qt Assistant help browser (which are both embedded in Qt Creator), the Qt Linguist translation tool, uic (user interface compiler), and moc (Meta-Object Compiler). History of Qt Early developments In the summer of 1990, Haavard Nord and Eirik Chambe-Eng (the original developers of Qt and the CEO and President, respectively, of Trolltech) were working together on a database application for ultrasound images written in C++ and running on Mac OS, Unix, and Microsoft Windows. They began development of "Qt" in 1991, three years before the company was incorporated as Quasar Technologies, then changed the name to Troll Tech and then to Trolltech. The toolkit was called Qt because the letter Q looked appealing in Haavard's Emacs typeface, and "t" was inspired by Xt, the X toolkit. The first two versions of Qt had only two flavors: Qt/X11 for Unix and Qt/Windows for Windows. On 20 May 1995 Troll Tech publicly released Qt 0.90 for X11/Linux with the source code under the Qt Free Edition License. This license was viewed as not compliant with the free software definition by Free Software Foundation because, while the source was available, it did not allow the redistribution of modified versions. Trolltech used this license until version 1.45. Controversy erupted around 1998 when it became clear that the K Desktop Environment was going to become one of the leading desktop environments for Linux. As it was based on Qt, many
logic using a custom scripting language and interpreter was dropped from the next generation Quake II engine in favor of compiled C code due to the overall inflexibility of QuakeC, the increasingly complex game logic, the performance to be gained by packaging game logic into a native dynamic link library, and the advantage of leveraging an already established programming language's community, tools, educational materials, and documentation. Distributing native code created new security and portability concerns. QuakeC bytecode afforded little opportunity for mischief, while native code has access to the whole machine. QuakeC bytecode also worked on any machine that could run Quake. Compiling to native code added an additional barrier to entry for novice mod developers, because they were being asked to set up a more complicated programming environment. The eventual solution, implemented by the Quake III engine, was to combine the advantages of original QuakeC with the advantages of compiling C to native code. The lcc C compiler was extended to compile standard C into bytecode, which could be interpreted by a virtual machine in a manner similar to QuakeC. This addressed the security, portability, and tool chain problems, but lost the performance advantage of native code. That was solved by further compiling the bytecode into native code at run time on supported machines. Modified compilers and language extensions A decompiler and a recompiler were released by Armin Rigo (called DEACC and REACC respectively). These programs were made through the process of reverse engineering, and were most likely published before the release of qcc. id Software released the source of qcc, their QuakeC compiler, along with the original QuakeC code in 1996. Modified versions soon sprung up, including Jonathan Roy's fastqcc and Ryan "FrikaC" Smith's FrikQCC. These added functionality, optimizations, and compiling speed boosts. In 1999, when id Software released the code from Quake's engine under the GNU General Public License (GPL), the workings of the bytecode interpreter were examined and new QuakeC compilers were released, such as J.P. Grossman's qccx and a new version of FrikQCC. These compilers took advantage of newly discovered features in a backwards-compatible way so that the bytecode could still be properly interpreted by unmodified Quake engines. New features include arrays, pointers, integers, for loops and string manipulation. With the Quake engine source code now able to be changed, further features were added to QuakeC in the form of new built-in functions. Features long yearned for by QuakeC coders finally reached realization as QuakeC now had file and string handling	simply not needed by the original game. Most video games at the time had their game logic written in plain C/C++ and compiled into the executable, which is faster. However, this makes it harder for the community to create mods and it makes the process of porting the game to another platform (such as Linux) more costly. Despite its advantages, the choice of implementing game logic using a custom scripting language and interpreter was dropped from the next generation Quake II engine in favor of compiled C code due to the overall inflexibility of QuakeC, the increasingly complex game logic, the performance to be gained by packaging game logic into a native dynamic link library, and the advantage of leveraging an already established programming language's community, tools, educational materials, and documentation. Distributing native code created new security and portability concerns. QuakeC bytecode afforded little opportunity for mischief, while native code has access to the whole machine. QuakeC bytecode also worked on any machine that could run Quake. Compiling to native code added an additional barrier to entry for novice mod developers, because they were being asked to set up a more complicated programming environment. The eventual solution, implemented by the Quake III engine, was to combine the advantages of original QuakeC with the advantages of compiling C to native code. The lcc C compiler was extended to compile standard C into bytecode, which could be interpreted by a virtual machine in a manner similar to QuakeC. This addressed the security, portability, and tool chain problems, but lost the performance advantage of native code. That was solved by further compiling the bytecode into native code at run time on supported machines. Modified compilers and language extensions A decompiler and a recompiler were released by Armin Rigo (called DEACC and REACC respectively). These programs were made through the process of reverse engineering, and were most likely published before the release of qcc. id Software released the source of qcc, their QuakeC compiler, along with the original QuakeC code in 1996. Modified versions soon sprung up, including Jonathan Roy's fastqcc and Ryan "FrikaC" Smith's FrikQCC. These added functionality, optimizations, and compiling speed boosts. In 1999, when id Software released the code from Quake's engine under the GNU General Public License (GPL), the workings of the bytecode interpreter were examined and new QuakeC compilers were released, such as J.P. Grossman's qccx and a new version of FrikQCC. These compilers took advantage of newly discovered features in a backwards-compatible way so that the bytecode could still be properly interpreted by unmodified Quake engines. New features include arrays, pointers, integers, for loops and string manipulation. With the Quake engine source code now able to be changed, further features were added to QuakeC in the form of new built-in functions. Features long yearned for by
Eric Christian Olsen, actor, Bettendorf Daniel David Palmer, chiropractor, Davenport Oran Pape, state patrol, Davenport Laurdine Patrick, musician, East Moline Mary Beth Peil, actress and singer, Davenport Nat Pendleton, wrestler and actor, Davenport Roger Perry, actor, Davenport James Philbrook, actor, Davenport Scott Pose, MLB baseball player, Davenport Hiram Price, politician, Davenport Margo Price, country singer, Aledo Linnea Quigley, actress and producer, Davenport Ed Reimers, announcer, Moline Otto Frederick Rohwedder, engineer, inventor of sliced bread, Davenport Seth Rollins, WWE wrestler, Davenport Randy Shilts, journalist, Davenport Jim Skinner, CEO of McDonald's, Davenport Dean Stone, MLB pitcher, Silvis Tim Sylvia, MMA fighter, Bettendorf Jason Tanamor, author, writer, Rock Island Julian Vandervelde, football player, Davenport Hynden Walch, actress, Davenport Henry Cantwell Wallace, U.S. Secretary of Agriculture, Rock Island Friedrich Weyerhäuser, lumber baron, Rock Island Dwight Deere Wiman, Broadway producer, Moline Bryan Woods, filmmaker, Bettendorf Education Colleges and universities Augustana College – A private, four-year liberal arts college in Rock Island. Bible Missionary Institute – A Bible college in Rock Island affiliated with the Bible Missionary Church. Black Hawk College – Community college in Moline, with a satellite campus in Kewanee, Illinois. Eastern Iowa Community College District – Consisting of campuses in Bettendorf, Clinton, and Muscatine. Bettendorf's campus is known as Scott Community College. Palmer Chiropractic College – Davenport, first chiropractic school in the world. Saint Ambrose University - A university in Davenport. Upper Iowa University – A satellite campus in Bettendorf. Western Illinois University-Quad Cities – The only public, four-year university in the Quad Cities region. The campus is located in Moline along the Mississippi Riverfront at the former site of the John Deere Technical Site. Culture Since 1916, the region has supported the Quad City Symphony Orchestra, which presents a year-round schedule of concerts at the Adler Theatre in Davenport and Centennial Hall in Rock Island. The Handel Oratorio Society, dating to 1880, is the second-oldest organization of its kind in the nation and presents annual performances of "Messiah" along with another major work for choir and orchestra. The Augustana Choir, founded at Rock Island's Augustana College in 1934, is one of the nation's leading collegiate choruses. Major outdoor summer music festivals include the Bix Beiderbecke Memorial Jazz Festival, Mississippi Valley Blues Festival, and River Roots Live. The Quad Cities' three traditional community theaters – Playcrafters Barn Theatre (founded in 1920, comedies and dramas) and Quad City Music Guild (1948, musicals) in Moline, and Genesius guild (1957, outdoor Shakespeare and Greek comedies and tragedies) in Rock Island – were joined in 1976 by Circa '21 Dinner Playhouse, a professional dinner theater in downtown Rock Island's historic Fort Theatre. Ballet is performed at Ballet Quad Cities. ComedySportz provides improv comedy. Bluebox Limited is a Bettendorf-based film production company, and many outside productions companies have filmed movies in the Quad Cities in recent years. Historic buildings and sites listed on state and the National Register of Historic Places interpret the history of people's settlement and lives in the area. Media The Quad Cities is the 151st largest radio market in the United States. It is ranked 97th by Nielsen Media Research for the 2008–09 television season with 309,600 television households. The area is served by over 13 commercial radio stations, 8 non-commercial radio stations, 3 low power FM radio stations, 8 TV stations and 3 daily newspapers. In 2012, the Mississippi Valley Fair that is held in Davenport served as the film location for Rodney Atkins' music video "Just Wanna Rock N' Roll." Also in 2012, the PBS Frontline documentary Poor Kids was filmed in and around the Quad Cities showing poverty from a child's perspective. Transportation Four interstate highways serve the Quad Cities: Interstate 80, Interstate 280, Interstate 74 serve both states while Interstate 88 serves just Illinois. United States highways include U.S. Route 6 and U.S. Route 67 which run through both Iowa and Illinois, while U.S. Route 61 serves just Iowa and U.S. Route 150 serves just Illinois. A total of five bridges accessible by automobiles connect Iowa with Illinois in the Quad Cities across the Mississippi River. The Fred Schwengel Memorial Bridge carries Interstate 80 and connects Le Claire, Iowa, with Rapids City, Illinois. Continuing downstream, the I-74 Bridge connects Bettendorf, Iowa, with Moline, Illinois, and is the busiest bridge with an average of 70,400 cars a day. The Government Bridge connects Downtown Davenport with the Rock Island Arsenal. Three bridges connect Davenport with Rock Island, Illinois; The Rock Island Centennial Bridge, The Crescent Rail Bridge, and the furthest downstream bridge, the Sergeant John F. Baker, Jr. Bridge which carries I-280. Several state highways also serve the area. Iowa Highway 22 is on Davenport's southwest side and runs west through the county, while Iowa Highway 130 runs along Northwest Boulevard on Davenport's north edge. Illinois Route 5 (John Deere Road) runs from Rock Island east till it runs into Interstate 88. Illinois Route 92 runs along the Mississippi River, while Illinois Route 84 runs along the east side of Rock Island County. Illinois Route 192 connects Highway 92 with Illinois Route 94 near Taylor Ridge. The Chicago – Kansas City Expressway also serves the area along Interstates 74, 80, and 88. There are three transit operators in the Quad Cities with limited interconnection between them. Rock Island County Metropolitan Mass Transit District (Quad Cities MetroLINK) serves the Illinois cities of Rock Island, Moline, East Moline, Milan, Silvis, Carbon Cliff, Hampton and Colona. It has 12 routes and a fleet of about 52 buses. It operates a river craft during summer months. In Iowa, Davenport Citibus has 10 fixed routes and operates 20 buses, seven days a week and Bettendorf Transit operates three routes, Monday–Saturday, and has eight buses. Amtrak currently does not serve the Quad Cities. The closest station is about away in Galesburg, Illinois. In 2008, United States Senators Tom Harkin, Chuck Grassley, Dick Durbin, and Barack Obama sent a letter to Amtrak asking them to begin plans to bring rail service to the Quad Cities. In October 2010, a $230 million federal fund was announced that will bring Amtrak service to the Quad Cities, with a new line running from Moline to Chicago. They hoped to have the line completed in 2015, and offer two round trips daily to Chicago. In December 2011, the federal government awarded $177 million in funding for the Amtrak connection. Budgetary and logistical issues have delayed the completion of all necessary track improvements, but the project is still in development. The multi-modal Moline Q Station building was completed in early 2018, with the attached Westin Element hotel opening in February. When the full project is completed, it will establish passenger rail through the Quad Cities, for the first time since the 1970s. The Quad Cities is served by the Quad Cities International Airport, Illinois' third-busiest airport, located in Moline. The airport is marketed as a regional alternative to the larger airports in Chicago, nearly away. The smaller Davenport Municipal Airport is the home of the Quad City Air Show. Sports From 1907 to 1926, Rock Island was home to the NFL's Rock Island Independents. The franchise was a charter member on the National Football League (NFL) in 1920. The first NFL Game ever was played by the Independents at Douglas Park in September 1920. Football legend Jim Thorpe was a member of the team in 1924. The Tri-Cities Blackhawks, named in honor of the Sauk war chief Black Hawk, was the next top-level professional sports franchise. The club played in the National Basketball League (NBL) from 1946 until its merger in 1949 with the Basketball Association of America to become the National Basketball Association (NBA). Hall of famer Red Auerbach coached the Blackhawks during their first NBA season. After the 1950–51 basketball season, the team moved to Milwaukee, where they were named the Hawks. After a second move to St. Louis, the team is now the Atlanta Hawks. Professional basketball returned to the Quad Cities during the 1980s and 1990s with the Quad City Thunder of the Continental Basketball Association. The CBA served as the NBA's premier developmental league and produced many highly regarded NBA stars. From 1987 through the 1992–93 season, the Thunder played at Wharton Field House in Moline. Starting with the 1993–94 season, the team played at The MARK of the Quad Cities (now the TaxSlayer Center.) After the CBA folded in 2001, the Thunder franchise ceased operations permanently. The TaxSlayer Center occasionally hosts NCAA Division I college basketball conference tournaments as well as NBA and NHL exhibitions. The Quad Cities has hosted minor league baseball teams since the Davenport Brown Stockings first played in 1878. The Rock Island Islanders and Moline Plowboys each fielded teams for many seasons. The Islanders began play in 1901 and played primarily at Douglas Park. The Plowboys were founded in 1914. Their home was Browning Field. The Davenport franchise has been a member of the Midwest League since 1960. They have played at Modern Woodman Park since 1931. Today, the Quad Cities River Bandits are High Class A affiliate of the Kansas City Royals The PGA Tour makes an annual stop in the Quad Cities. The golf tournament is currently known as the John Deere Classic. It has drawn dozens of top PGA players over the years, including Tiger Woods, Vijay Singh, and Payne Stewart. The Quad Cities Marathon has run annually in late September since 1998. Roughly 400-500 participants race through the four cities, beginning and ending in Moline. The race weekend also offers a half marathon and a 5K as well as races for children. Kenyan Kiplangat Terer holds the men's record with a 2:14:04, run in 2013. Ethiopian Hirut Guangul holds the woman's record at 2:35:07, from her 2012 win. Sports teams Quad City River Bandits is a Class A Midwest League minor league baseball team in Davenport. Their home games are played at Modern Woodmen Park, formerly John O'Donnell Stadium. The Davenport team has existed under a variety of names and Major League Baseball team affiliations since 1901. The River Bandits are currently affiliated with the Kansas City Royals. Quad City Mallards were an ice hockey team that played from 2009 to 2018 with home games held at the TaxSlayer Center in Moline. The new Mallards replaced the former Quad City Flames AHL team which played from 2007 to 2009. The original Mallards played in the United Hockey League from 1995 to 2007. The Quad City Storm was launched for the 2018–19 season in the Southern Professional Hockey League. The Quad City Steamwheelers were an AF2 arena football franchise that also played at the TaxSlayer Center. The Steamwheelers won the league's title game, the ArenaCup, in 2000 and 2001. After the AF2 league folded following its 2009 season, the Steamwheelers also ceased operations. A new Quad City Steamwheelers organization launched for the 2018 season in Champions Indoor Football and then moved to the Indoor Football League for 2019. Quad City Silverbacks were a professional mixed martial arts team competing in the now-defunct International Fight League. Home matches took place at the iWireless Center. Pat Miletich formed and based a mixed martial arts gym and fight team, Miletich Fighting Systems, in the Quad Cities. Miletich Fighting Systems is among MMA's first 'super-camps', and housed many of the consensus greatest fighters of the early 2000s, such as Jens Pulver, Matt Hughes, Robbie Lawler, Tim Sylvia, and Jeremy Horn, among others. The Quad City Riverhawks was a PBL (Premier Basketball League) team. They played home games at Wharton Field House in Moline during the 2008 season. They ended with that season. Previously, the Quad City Thunder were a CBA team playing in the late 1980s thru 2000, first at Wharton and then at The Mark. The Quad City Raiders are a semi-professional minor league football team that was formed in 2011 to serve the Quad City area. The Raiders play in the MidStates Football League and have reached the semi-finals in the league playoffs each season. See also Mississippi Athletic Conference for Iowa high	As it grew, Davenport annexed the communities of Rockingham, Nahant, Probstei, East Davenport, Oakdale, Cawiezeel, Blackhawk, Mt. Joy, Green Tree, and others. Bettendorf annexed portions of Pleasant Valley in the 1970s. In 1987, Rock Island, Moline, East Moline, Milan, Carbon Cliff, Hampton, Coal Valley and Silvis considered a super-city merger which would have seen the Illinois cities become the second-largest city in the state, but the proposal ultimately failed. Moline and East Moline considered a merger in 1997. That same year, Green Rock and Colona did merge. Geography The Quad Cities is located at the confluence of the Rock and Mississippi rivers, approximately west of Chicago, and form the largest metropolitan area along the Mississippi River between Minneapolis–Saint Paul and the St. Louis metropolitan area. Interstate 80 crosses the Mississippi River here. The Quad Cities area is distinctive because the Mississippi River flows from east to west as it passes through the heart of the area; the Iowa cities of Davenport and Bettendorf are located due north of Rock Island and Moline, respectively. The Quad Cities area is one where the telephone companies cooperate with regional phone calls. Iowa and Illinois have different area codes (563 and 309 respectively), yet most calls originating and terminating within the core urban area are placed without long-distance charges by dialing just a 7-digit number. This helps the bi-state area promote itself as a single community, "joined by a river." The Quad Cities Metropolitan Area consists of three counties: Scott County in Iowa, and Rock Island County and Henry County in Illinois. The Quad City metro population is 382,268. The Quad Cities Metropolitan Area is also considered part of the Great Lakes Megalopolis. Demographics According to the 2010 United States Census Count, the metropolitan area grew to 471,551. As of the 2000 census, a total of 96,495 households and 60,535 families resided in the area. Race and ethnicity The racial makeup of the area is 90.6% White (410,861), 3.7% Black or African American (27,757), 0.6% American Indian and Alaskan Native (1,255), 1.0% Asian (6,624), 0.03% Pacific Islander (156), and 2.0% from two or more races (11,929). 7.1% of the population is Hispanic or Latino of any race (37,070). The predominant ethnicities in the Quad Cities are of northern European descent, including German, Irish, and English, as well Scandinavian (Mostly Swedish and Norwegian) and Dutch. The primary minority groups in the area are African-Americans, which in Davenport make up the third largest black population in the state of Iowa, a community dating back to the 1830s when Iowa was a free territory. Many of the city's African-American residents have roots in the Southern/Border states of the U.S., including Mississippi, Arkansas, Alabama, and Missouri. The most significant Asian-American populations are South Asian and Vietnamese American. Religion According to resources, Christianity is the largest religion to be practiced in the area. However, the two states have a different population of Christian groups. In Davenport and Bettendorf, Catholics make up an 18.5% plurality, but Protestants with 15.1% Mainline and 11.6% Evangelical make up large minorities as well. The Black Protestants on the Iowa side comes in at 1.2%. On the Illinois side, between Rock Island, Moline, and East Moline, Catholicism is less prevalent at 12.4%, and at 12.5% Evangelical and 11.0% Mainline have smaller declines. The Jewish population is about 500–600, which is down from about 1,800–2,000 in the 1950s and 1960s. Landmarks The business Antique Archeology, featured on the History Channel show American Pickers, is located in LeClaire Brady Street Stadium, a major high-school sports venue along Davenport's Brady Street (U.S. 61) The Col Ballroom, a small arena for music concerts, in Davenport Davenport Skybridge Figge Art Museum, Davenport, formerly the Davenport Museum of Art, designed by British architect David Chipperfield and opened in 2005. Its holdings include extensive collections of Haitian, colonial Mexican and Midwestern art, particularly pieces by Thomas Hart Benton, Marvin Cone and Grant Wood, and personal effects from Wood's estate. Fred Schwengel Memorial Bridge, a four-lane steel-girder bridge on Interstate 80, crossing the Mississippi River to connect LeClaire and Rapids City. Opened in 1966. Government Bridge, a double-decked bridge adjacent to Lock and Dam 15, carrying motor and rail traffic between Arsenal Island and Davenport. The 1896 truss bridge, about 1,950 feet long, includes a 360-degree swing span over the twin locks. It connects to the Illinois side of the river via the Rock Island Viaduct. Iowa 80 Truck Stop – the world's largest truck stop is along Interstate 80 near Walcott, Iowa, west of Davenport. Interstate 74 Bridge, formerly known as the "Iowa-Illinois Memorial Bridge", connecting Bettendorf and Moline. The twin suspension spans across the Mississippi River were built in 1935 and 1959 and adapted to carry Interstate 74 in the early 1970s. The twinned towers are a symbol of the two-state Quad Cities community. The bridge is set to be replaced with eight lanes. John Deere Pavilion, a small museum and showcase for John Deere equipment, built adjacent to the John Deere Commons in the 1990s in downtown Moline. John Deere World Headquarters, designed by Eero Saarinen and completed in 1963 in Moline. The John Looney Mansion, designed and built in 1897 for the attorney, publisher and gangster John Looney in Rock Island which still stands off 20th Street and 17th Avenue. Lock and Dam No. 15, a 1,200-foot roller dam with twin locks across the Mississippi River between Arsenal Island and Davenport. The roller dam, billed as the longest of its type, maintains a pool upstream that allows river traffic to pass through the once notorious Rock Island Rapids. Mississippi Valley Fairgrounds, a fair and exposition venue in Davenport Modern Woodmen Park, formerly John O'Donnell Stadium, home of the Kansas City Royals' class high A affiliate, the Quad Cities River Bandits, on the Davenport riverfront. With the lights of Rock Island across the Mississippi and the Centennial Bridge looming just beyond the right-field fence, the park was named by USA Today as one of 10 great places for a baseball pilgrimage. The ball park added a 110 ft. ferris wheel before the start of the 2014 season. Old Main, completed in 1888, the oldest building on the campus of Augustana College. Located on a bluff overlooking the Mississippi River, its iconic and newly renovated dome was lighted as of October 2011. Putnam Museum in Davenport Quad City Botanical Center in Rock Island Quad Cities Waterfront Convention Center, located in Bettendorf RiverCenter/Adler Theatre, a convention and performing-arts complex in Davenport. The 2,400-seat Adler is the former RKO Orpheum Theater, which opened in 1931, designed by A.S. Graven of Chicago, whose projects included the Drake Hotel in Chicago and the Paramount Theater in New York City. The theater was extensively renovated and expanded in 1984–86 and 2005. River Music Experience, a performance, education and music-history venue in the Redstone Building, the former Petersen Harned Von Maur department store Rock Island Arsenal, manufacturer of military equipment and ordnance since the 1880s, now the largest government-owned weapons manufacturing arsenal in the United States. The arsenal is located on Arsenal Island (formerly known as Rock Island) in the Mississippi River between Davenport, Iowa, and Rock Island, Illinois. Fort Armstrong was built there in 1816. During the civil war, the island held a Union prison camp for Confederate soldiers. The Federal-style home of Colonel George Davenport, built in 1833–34, the oldest extant building in the Quad Cities, is on the north bank of the island. Rock Island Centennial Bridge over the Mississippi River between downtown Davenport and Rock Island, completed in 1940 to commemorate Rock Island's 100th anniversary. The five arches of the 3,853-foot through-arch bridge often are used as a symbol of the Quad Cities. Rock Island County Fairgrounds in East Moline, also the site of the Quad City Speedway Rock Island Auction Company from the Discovery Channel show Ready, Aim, Sold! TaxSlayer Center – 11,000-seat arena in Moline (formerly The Mark of the Quad Cities and the iWireless Center). Vander Veer Botanical Park is a 33-acre (130,000 m2) botanical garden in the Vander Veer Park Historic District of Davenport, Iowa. It is believed to be one of the first botanical parks west of the Mississippi River. The Quarter – a site in East Moline, alongside the Mississippi River, featuring shops, restaurants, condominiums, boat docks, sports and interpretive centers, and a working lighthouse, currently under development. (Geographical coordinates: ) Chicago, Milwaukee, St. Paul and Pacific Freight House, referred to locally as the "Freight House", is an entertainment venue TBK Bank Sports Complex, also known as the BettPlex, is a state-of-the-art sport and entertainment complex. Containing eight full-size volleyball and basketball courts. Four indoor and five outdoor sand volleyball courts, 10 lighted outdoor baseball and softball fields, the BettPlex is a 45 million dollar sporting facility that was created to host weekend sporting tournaments in the Quad Cities. Noteworthy companies Arconic Cobham plc Deere & Company (also known as/branded: John Deere) Genesis Health System Group O Guardian Industries Happy Joe's KONE, Inc (formerly Montgomery Elevator) Lee Enterprises Lewis Machine and Tool Company Modern Woodmen of America Nestlé Purina PetCare QCR Holdings Sears Seating (also known as Sears Manufacturing) Von Maur Whitey's Ice Cream Top employers According to Quad Cities website, the top employers in the Quad Cities area are: Notable people Eddie Albert, actor, Rock Island Ken Anderson, football player and coach, Rock Island Pat Angerer, football player, Bettendorf Matthew Ashford, actor, Davenport Tavian Banks, football player, Bettendorf Bonnie Bartlett, actress, Moline Scott Beck, filmmaker, Bettendorf Bix Beiderbecke, jazz musician, Davenport Louis Bellson, drummer, Moline Vincent Hugo Bendix, inventor and industrialist, Moline Ken Berry, actor, Moline Joseph W. Bettendorf, industrialist, Bettendorf (Gilbert) William P. Bettendorf, industrialist, Bettendorf (Gilbert) Chief Black Hawk, band leader and warrior of the Sauk Native American tribe Isabel Bloom, artist, Davenport Lisa Bluder, basketball coach, Marion Suzy Bogguss, country singer, Aledo Ken Bowman, football player, Milan Lara Flynn Boyle, actress, Davenport Ambrose Burke, priest and college president, Davenport Mike Butcher, pitcher and coach, Davenport Branden Campbell, bassist for the Neon Trees, Davenport Louise Carver, actress, Davenport Samuel Franklin Cody, aviator, Davenport William F. "Buffalo Bill" Cody, pioneer, LeClaire Danielle Colby, reality star American Pickers, Davenport/LeClaire Jude Cole, musician, Carbon Cliff Martin Cone, priest and college president, Davenport Ed Conroy, basketball coach, Davenport George Cram Cook, author, Davenport Roger Craig, football player, Davenport Doris Davenport, actress, Moline Colonel George Davenport, pioneer, US Army officer Dana Davis, actress, Davenport Ricky Davis, basketball player, Davenport John Deere, inventor, Moline Frederick Denkmann, lumber baron, Rock Island Justin Diercks, racecar driver, Davenport Acie Earl, basketball player, Moline Eugene Burton Ely, aviation pioneer, Davenport Embassy, Music Producer, Moline Bill Fitch, NBA basketball player and coach, Davenport John Flannagan, priest and college president, Davenport Jack Fleck, golfer, 1955 U.S. Open champion, Bettendorf Joe Frisco, vaudeville performer, Davenport John Getz, actor, Davenport Susan Glaspell, writer, Davenport Ethan Happ, Big Ten basketball player, Milan Warren Hearnes, governor of Missouri, Moline Anne Marie Howard, actress, Davenport Austin Howard, football player, Davenport Jim Jensen, NFL running back, Davenport Jesse Johnson (musician), The Time, Rock Island Mark Johnson, Olympic wrestler, Rock Island James Jones, football player, Davenport Gail Karp, cantor of the Reform Jewish synagogue, Davenport Hazel Keener, actress, Bettendor and Davenport Madison Keys, tennis player, Rock Island Josh Kroeger, athlete, Davenport Steve Kuberski, basketball player, Moline Perry Lafferty, producer, Davenport Elmer Layden, athlete and coach, Davenport Jim Leach, politician, Davenport Johnny Lujack, quarterback, 1947 Heisman Trophy winner, Bettendorf Sue Lyon, actress, Davenport Helen Mack, actress, Rock Island Cletus Madsen, priest and college president, Davenport Stuart Margolin, actor and director, Davenport Elisabeth Maurus, musician, Rock Island Carl Meinberg, priest and college president, Davenport Sebastian Menke, priest and college president, Davenport Julia Michaels, musician, Davenport Pat Miletich, MMA fighter, Bettendorf Marvin Mottet, priest, Davenport Don Nelson, NBA basketball player and coach, Rock Island Michael Nunn, boxer, Davenport Spike O'Dell, radio personality, East Moline Gerald Francis O'Keefe, priest, Davenport Gene Oliver, MLB player, Rock Island Eric Christian Olsen, actor, Bettendorf Daniel David Palmer, chiropractor, Davenport Oran Pape, state patrol, Davenport Laurdine Patrick, musician, East Moline Mary Beth Peil, actress and singer, Davenport Nat Pendleton, wrestler and actor, Davenport Roger Perry, actor, Davenport James Philbrook, actor, Davenport Scott Pose, MLB baseball player, Davenport Hiram Price, politician, Davenport Margo Price, country singer, Aledo Linnea Quigley, actress and producer, Davenport Ed Reimers, announcer, Moline Otto Frederick Rohwedder, engineer, inventor of sliced bread, Davenport Seth Rollins, WWE wrestler, Davenport Randy Shilts, journalist, Davenport Jim Skinner, CEO of McDonald's, Davenport Dean Stone, MLB pitcher, Silvis Tim Sylvia, MMA fighter, Bettendorf Jason Tanamor, author, writer, Rock Island Julian Vandervelde, football player, Davenport Hynden Walch, actress, Davenport Henry Cantwell Wallace, U.S. Secretary of Agriculture, Rock Island Friedrich Weyerhäuser, lumber baron, Rock Island Dwight Deere Wiman, Broadway producer, Moline Bryan Woods, filmmaker, Bettendorf Education Colleges and universities Augustana College – A private, four-year liberal arts college in Rock Island. Bible Missionary Institute – A Bible college in Rock Island affiliated with the Bible Missionary Church. Black Hawk College – Community college in Moline, with a satellite campus in Kewanee, Illinois. Eastern Iowa Community College District – Consisting of campuses in Bettendorf, Clinton, and Muscatine. Bettendorf's campus is known as Scott Community College. Palmer Chiropractic College – Davenport, first chiropractic school in the world. Saint Ambrose University - A university in Davenport. Upper Iowa University – A satellite campus in Bettendorf. Western Illinois University-Quad Cities – The only public, four-year university in the Quad Cities region. The campus is located in Moline along the Mississippi Riverfront at the former site of the John Deere Technical Site. Culture Since
scanning probe microscopy. Quantum chemistry studies the ground state of individual atoms and molecules, and the excited states, and transition states that occur during chemical reactions. On the calculations, quantum chemical studies use also semi-empirical and other methods based on quantum mechanical principles, and deal with time dependent problems. Many quantum chemical studies assume the nuclei are at rest (Born–Oppenheimer approximation). Many calculations involve iterative methods that include self-consistent field methods. Major goals of quantum chemistry include increasing the accuracy of the results for small molecular systems, and increasing the size of large molecules that can be processed, which is limited by scaling considerations—the computation time increases as a power of the number of atoms. History Some view the birth of quantum chemistry as starting with the discovery of the Schrödinger equation and its application to the hydrogen atom in 1926. However, the 1927 article of Walter Heitler (1904–1981) and Fritz London, is often recognized as the first milestone in the history of quantum chemistry. This is the first application of quantum mechanics to the diatomic hydrogen molecule, and thus to the phenomenon of the chemical bond. In the following years much progress was accomplished by Robert S. Mulliken, Max Born, J. Robert Oppenheimer, Linus Pauling, Erich Hückel, Douglas Hartree, Vladimir Fock, to cite a few. The history of quantum chemistry also goes through the 1838 discovery of cathode rays by Michael Faraday, the 1859 statement of the black-body radiation problem by Gustav Kirchhoff, the 1877 suggestion by Ludwig Boltzmann that the energy states of a physical system could be discrete, and the 1900 quantum hypothesis by Max Planck that any energy radiating atomic system can theoretically be divided into a number of discrete energy elements ε such that each of these energy elements is proportional to the frequency ν with which they each individually radiate energy and a numerical value called Planck's constant. Then, in 1905, to explain the photoelectric effect (1839), i.e., that shining light on certain materials can function to eject electrons	hydrogen molecular ion have been identified in terms of the generalized Lambert W function). Since all other atomic, or molecular systems, involve the motions of three or more "particles", their Schrödinger equations cannot be solved exactly and so approximate solutions must be sought. Valence bond Although the mathematical basis of quantum chemistry had been laid by Schrödinger in 1926, it is generally accepted that the first true calculation in quantum chemistry was that of the German physicists Walter Heitler and Fritz London on the hydrogen (H2) molecule in 1927. Heitler and London's method was extended by the American theoretical physicist John C. Slater and the American theoretical chemist Linus Pauling to become the valence-bond (VB) [or Heitler–London–Slater–Pauling (HLSP)] method. In this method, attention is primarily devoted to the pairwise interactions between atoms, and this method therefore correlates closely with classical chemists' drawings of bonds. It focuses on how the atomic orbitals of an atom combine to give individual chemical bonds when a molecule is formed, incorporating the two key concepts of orbital hybridization and resonance. Molecular orbital An alternative approach was developed in 1929 by Friedrich Hund and Robert S. Mulliken, in which electrons are described by mathematical functions delocalized over an entire molecule. The Hund–Mulliken approach or molecular orbital (MO) method is less intuitive to chemists, but has turned out capable of predicting spectroscopic properties better than the VB method. This approach is the conceptional basis of the Hartree–Fock method and further post Hartree–Fock methods. Density functional theory The Thomas–Fermi model was developed independently by Thomas and Fermi in 1927. This was the first attempt to describe many-electron systems on the basis of electronic density instead of wave functions, although it was not very successful in the treatment of entire molecules. The method did provide the basis for what is now known as density functional theory (DFT). Modern day DFT uses the Kohn–Sham method, where the density functional is split into four terms; the Kohn–Sham kinetic energy, an external potential, exchange and correlation energies.
Uppercase). is . is . Greek The stress accents, indicated in red, are produced by pressing that key (or shifted key) followed by an appropriate vowel. Use of the "AltGr" key may produce the characters shown in blue. German Germany, Austria, Switzerland, Liechtenstein, and Luxembourg use QWERTZ layouts, where the letter Z is to the right of T. Icelandic The Icelandic keyboard layout is different from the standard QWERTY keyboard because the Icelandic alphabet has some special letters, most of which it shares with the other Nordic countries: Þ/þ, Ð/ð, Æ/æ, and Ö/ö. (Æ/æ also occurs in Norwegian, Danish and Faroese, Ð/ð in Faroese, and Ö/ö in Swedish, Finnish and Estonian. In Norwegian Ö/ö could be substituted for Ø/Ø which is the same sound/letter and is widely understood). The letters Á/á, Ý/ý, Ú/ú, Í/í, and É/é are produced by first pressing the dead key and then the corresponding letter. The Nordic letters Å/å and Ä/ä can be produced by first pressing , located below the key, and (for ¨) which also works for the non-Nordic ÿ, Ü/ü, Ï/ï, and Ë/ë. These letters are not used natively in Icelandic, but may have been implemented for ease of communication in other Nordic languages. Additional diacritics may be found behind the key: for ˋ (grave accent) and for ˆ (circumflex). Irish Microsoft Windows includes an Irish layout which supports acute accents with for the Irish language and grave accents with the dead key for Scottish Gaelic. The other Insular Celtic languages have their own layout. The UK or UK-Extended layout is also frequently used. Italian Braces (right above square brackets and shown in purple) are given with both AltGr and Shift pressed. The tilde (~) and backquote (`) characters are not present on the Italian keyboard layout (with Linux, they are available by pressing ++, and ++; Windows might not recognise these keybindings). When using Microsoft Windows, the standard Italian keyboard layout does not allow one to write 100% correct Italian language, since it lacks capital accented vowels, and in particular the È key. The common workaround is writing E' (E followed by an apostrophe) instead, or relying on the auto-correction feature of several word processors when available. It is possible to obtain the È symbol in MS Windows by typing + . Mac users, however, can write the correct accented character by pressing + + or, in the usual Mac way, by pressing the correct key for the accent (in this case + ) and subsequently pressing the wanted letter (in this case + ). Linux users can also write it by pressing the key with enabled. There is an alternate layout, which differs only in disposition of characters accessible through , and includes the tilde and the curly brackets. It is commonly used in IBM keyboards. Italian typewriters often have the QZERTY layout instead. The Italian-speaking part of Switzerland uses the QWERTZ keyboard. Latvian Although rarely used, a keyboard layout specifically designed for the Latvian language called ŪGJRMV exists. The Latvian QWERTY keyboard layout is most commonly used; its layout is the same as Latin ones, but with a dead key, which allows entering special characters (āčēģīķļņõŗšūž). The most common dead key is the apostrophe ('), which is followed by Alt+Gr (Windows default for Latvian layout). Some prefer using the tick (`). Lithuanian Where in standard QWERTY the number row is located, you find in Lithuanian QWERTY: Ą, Č, Ę, Ė, Į, Š, Ų, Ū, Ž, instead of their counterparts 1, 2, 3, 4, 5, 6, 7, 8, =. If you still want to use the numbers of the mentioned 'number row', you can create them in combination with the -key. Aside from these changes the keyboard is standard QWERTY. Besides QWERTY, the ĄŽERTY layout without the adjustment of the number row is used. Maltese The Maltese language uses Unicode (UTF-8) to display the Maltese diacritics: ċ Ċ; ġ Ġ; ħ Ħ; ż Ż (together with à À; è È; ì Ì; ò Ò; ù Ù). There are two standard keyboard layouts for Maltese, according to "MSA 100:2002 Maltese Keyboard Standard"; one of 47 keys and one of 48 keys. The 48-key layout is the most popular. Norwegian The Norwegian languages use the same letters as Danish, but the Norwegian keyboard differs from the Danish layout regarding the placement of the , and (backslash) keys. On the Danish keyboard, the and are swapped. The Swedish keyboard is also similar to the Norwegian layout, but and are replaced with and . On some systems, the Norwegian keyboard may allow typing Ö/ö and Ä/ä by holding the or key while striking and , respectively. There is also an alternative keyboard layout called Norwegian with Sámi, which allows for easier input of the characters required to write various Sámi languages. All the Sámi characters are accessed through the key. On Macintosh computers, the Norwegian and Norwegian extended keyboard layouts have a slightly different placement for some of the symbols obtained with the help of the or keys. Notably, the $ sign is accessed with and ¢ with . Furthermore, the frequently used @ is placed between and . Polish Most typewriters use a QWERTZ keyboard with Polish letters (with diacritical marks) accessed directly (officially approved as "Typist's keyboard", , Polish Standard PN-87), which is mainly ignored in Poland as impractical (custom-made keyboards, e.g., those in the public sector as well as some Apple computers, present an exception to this paradigm); the "Polish programmer's" () layout has become the de facto standard, used on virtually all computers sold on the Polish market. Most computer keyboards in Poland are laid out according to the standard US visual and functional layout. Polish diacritics are accessed by using the AltGr key with a corresponding similar letter from the base Latin alphabet. Normal capitalization rules apply with respect to Shift and Caps Lock keys. For example, to enter "Ź", one can type Shift+AltGr+X with Caps Lock off, or turn on Caps Lock and type AltGr+X. Both ANSI and ISO mechanical layouts are common sights, and even some non-standard mechanical layouts are in use. ANSI is often preferred, as the additional key provides no additional function, at least in Microsoft Windows where it duplicates the backslash key, while taking space from the Shift key. Many keyboards do not label AltGr as such, leaving the Alt marking as in the US layout - the right Alt key nevertheless functions as AltGr in this layout, causing possible confusion when keyboard shortcuts with the Alt key are required (these usually work only with the left Alt) and causing the key to be commonly referred to as right Alt (). However, keyboards with AltGr marking are available and it is also officially used by Microsoft when depicting the layout. Also, on MS Windows, the tilde character "~" (Shift+`) acts as a dead key to type Polish letters (with diacritical marks) thus, to obtain an "Ł", one may press Shift+` followed by L. The tilde character is obtained with (Shift+`) then space. In Linux-based systems, the euro symbol is typically mapped to Alt+5 instead of Alt+U, the tilde acts as a normal key, and several accented letters from other European languages are accessible through combinations with left Alt. Polish letters are also accessible by using the compose key. Software keyboards on touchscreen devices usually make the Polish diacritics available as one of the alternatives which show up after long-pressing the corresponding Latin letter. However, modern predictive text and autocorrection algorithms largely mitigate the need to type them directly on such devices. There is also unofficial, expanded Polish keyboard layout since 2021, based on the layout from Polish 80s computers Mazovia and wide expanded into all Latin diacritical sings, Greek signs, mathematical signs, IPA signs, typographical signs, symbols and sign "zł" meaning Polish currency, like actual German expanded layout E1, available in two versions, QWERTZ and QWERTY. Portuguese Brazil The Brazilian computer keyboard layout is specified in the ABNT NBR 10346 variant 2 (alphanumeric portion) and 10347 (numeric portion) standards. Essentially, the Brazilian keyboard contains dead keys for five variants of diacritics in use in the language; the letter Ç, the only application of the cedilla in Portuguese, has its own key. In some keyboard layouts the + combination produces the ₢ character (Unicode 0x20A2), symbol for the old currency cruzeiro, a symbol that is not used in practice (the common abbreviation in the eighties and nineties used to be Cr$). The cent sign ¢, is accessible via +, but is not commonly used for the centavo, subunit of previous currencies as well as the current real, which itself is represented by R$. The Euro sign € is not standardized in this layout. The masculine and feminine ordinals ª and º are accessible via combinations. The section sign § (Unicode U+00A7), in Portuguese called parágrafo, is nowadays practically only used to denote sections of laws. Variant 2 of the Brazilian keyboard, the only which gained general acceptance (MS Windows treats both variants as the same layout), has a unique mechanical layout, combining some features of the ISO 9995-3 and the JIS keyboards in order to fit 12 keys between the left and right Shift (compared to the American standard of 10 and the international of 11). Its modern, IBM PS/2-based variations, are thus known as 107-keys keyboards, and the original PS/2 variation was 104-key. Variant 1, never widely adopted, was based on the ISO 9995-2 keyboards. To make this layout usable with keyboards with only 11 keys in the last row, the rightmost key (/?°) has its functions replicated across the +, +, and + combinations. Portugal Essentially, the Portuguese keyboard contains dead keys for five variants of diacritics; the letter Ç, the only application of the cedilla in Portuguese, has its own key, but there are also a dedicated key for the ordinal indicators and a dedicated key for quotation marks. The + combination for producing the euro sign € (Unicode 0x20AC) has become standard. On some QWERTY keyboards the key labels are translated, but the majority are labelled in English. During the 20th century, a different keyboard layout, HCESAR, was in widespread use in Portugal. Romanian (in Romania and Moldova) The current Romanian National Standard SR 13392:2004 establishes two layouts for Romanian keyboards: a "primary" one and a "secondary" one. The "primary" layout is intended for traditional users who have learned how to type with older, Microsoft-style implementations of the Romanian keyboard. The "secondary" layout is mainly used by programmers as it does not contradict the physical arrangement of keys on a US-style keyboard. The "secondary" arrangement is used as the default Romanian layout by Linux distributions, as defined in the "X Keyboard Configuration Database". There are four Romanian-specific characters that are incorrectly implemented in versions of Microsoft Windows until Vista came out: Ș (U+0218, S with comma), incorrectly implemented as Ş (U+015E, S with cedilla) ș (U+0219, s with comma), incorrectly implemented as ş (U+015F, s with cedilla) Ț (U+021A, T with comma), incorrectly implemented as Ţ (U+0162, T with cedilla) ț (U+021B, t with comma), incorrectly implemented as ţ (U+0163, t with cedilla) The cedilla-versions of the characters do not exist in the Romanian language (they came to be used due to a historic bug). The UCS now says that encoding this was a mistake because it messed up Romanian data and the letters with cedilla and the letters with comma are the same letter with a different style. Since Romanian hardware keyboards are not widely available, Cristian Secară has created a driver that allows Romanian characters to be generated with a US-style keyboard in all versions of Windows prior to Vista through the use of the AltGr key modifier. Windows Vista and newer versions include the correct diacritical signs in the default Romanian Keyboard layout. This layout has the Z and Y keys mapped like in English layouts and also includes characters like the 'at' (@) and dollar ($) signs, among others. The older cedilla-version layout is still included albeit as the 'Legacy' layout. Slovak In Slovakia, similarly to the Czech Republic, both QWERTZ and QWERTY keyboard layouts are used. QWERTZ is the default keyboard layout for Slovak in Microsoft Windows. Spanish Spain The Spanish keyboard layout is used to write in Spanish and in other languages of Spain such as Catalan, Basque, Galician, Aragonese, Asturian and Occitan. It includes Ñ for Spanish, Asturian and Galician, the acute accent, the diaeresis, the inverted question and exclamation marks (¿, ¡), the superscripted o and a (º, ª) for writing abbreviated ordinal numbers in masculine and feminine in Spanish and Galician, and finally, some characters required only for typing Catalan and Occitan, namely Ç, the grave accent and the interpunct ( / , used in l·l, n·h, s·h; located at Shift-3). It can also be used to write other international characters, such as those using a circumflex accent (used in French and Portuguese among others) or a tilde (used in both Spanish and Portuguese), which are available as dead keys. However, it lacks two characters used in Asturian: Ḥ and Ḷ (historically, general support for these two has been poor – they aren't present in the ISO 8859-1 character encoding standard, or any other ISO/IEC 8859 standard). Several alternative distributions, based on this one or created from scratch, have been created to address this issue (see the Other original layouts and layout design software section for more information). On most keyboards, € is marked as Alt Gr + E and not Alt Gr + 5 as shown in the image. However, in some keyboards, € is found marked twice. An alternative version exists, supporting all of ISO 8859-1. Spanish keyboards are usually labelled in Spanish instead of English, its abbreviations being: On some keyboards, the c-cedilla key (Ç) is located one or two lines above, rather than on the right of, the acute accent key (´). In some cases it is placed on the right of the plus sign key (+), while in other keyboards it is situated on the right of the inverted exclamation mark key (¡). Latin America, officially known as Spanish Latinamerican sort The Latin American Spanish keyboard layout is used throughout Mexico, Central and South America. Before its design, Latin American vendors had been selling the Spanish (Spain) layout as default. Its most obvious difference from the Spanish (Spain) layout is the lack of a Ç key; on Microsoft Windows it lacks a tilde (~) dead key, whereas on Linux systems the dead tilde can be optionally enabled. This is not a problem when typing in Spanish, but it is rather problematic when typing in Portuguese, which can be an issue in countries with large commercial ties to Brazil (Argentina, Uruguay and Paraguay). Normally "Bloq Mayús" is used instead of "Caps Lock", and "Intro" instead of "Enter". Swedish The central characteristics of the Swedish keyboard are the three additional letters Å/å, Ä/ä, and Ö/ö. The same visual layout is also in use in Finland and Estonia, as the letters Ä/ä and Ö/ö are shared with the Swedish language, and even Å/å is needed by Swedish-speaking Finns. However, the Finnish multilingual keyboard adds new letters and punctuation to the functional layout. The Norwegian keyboard largely resembles the Swedish layout, but the and are replaced with and . The Danish keyboard is also similar, but it has the and swapped. On some systems, the Swedish or Finnish keyboard may allow typing Ø/ø and Æ/æ by holding the or key while striking and , respectively. The Swedish with Sámi keyboard allows typing not only Ø/ø and Æ/æ, but even the letters required to write various Sámi languages. This keyboard has the same function for all the keys engraved on the regular Swedish keyboard, and the additional letters are available through the key. On Macintosh computers, the Swedish and Swedish Pro keyboards differ somewhat from the image shown above, especially as regards the characters available using the or keys. (on the upper row) produces the ° sign, and produces the € sign. The digit keys produce ©@£$∞§\|[]≈ with and ¡"¥¢‰¶\{}≠ with . On Linux systems, the Swedish keyboard may also give access to additional characters as follows: first row: ¶¡@£$€¥{[]}\± and ¾¹²³¼¢⅝÷«»°¿¬ second row: @ł€®þ←↓→œþ"~ and ΩŁ¢®Þ¥↑ıŒÞ°ˇ third row: ªßðđŋħjĸłøæ´ and º§ÐªŊĦJ&ŁØÆ× fourth row: \|«»©""nµ¸·̣ and ¦<>©‘’Nº˛˙˙ Several of these characters function as dead keys. Turkish Today the majority of Turkish keyboards are based on QWERTY (the so-called Q-keyboard layout), although there is also the older F-keyboard layout specifically designed for the language. Vietnamese The Vietnamese keyboard layout is an extended Latin QWERTY layout. The letters Ă, Â, Ê, and Ô are found on what would be the number keys – on the US English keyboard, with – producing the tonal marks (grave accent, hook, tilde, acute accent and dot below, in that order), producing Đ, producing the đồng sign (₫) when not shifted, and brackets () producing Ư and Ơ. Multilingual variants Multilingual keyboard layouts, unlike the default layouts supplied for one language and market, try to make it possible for the user to type in any of several languages using the same number of keys. Mostly this is done by adding a further virtual layer in addition to the -key by means of (or 'right ' reused as such), which contains a further repertoire of symbols and diacritics used by the desired languages. This section also tries to arrange the layouts in ascending order by the number of possible languages and not chronologically according to the Latin alphabet as usual. United Kingdom (Extended) Layout Windows From Windows XP SP2 onwards, Microsoft has included a variant of the British QWERTY keyboard (the "United Kingdom Extended" keyboard layout) that can additionally generate several diacritical marks. This supports input on a standard physical UK keyboard for many languages without changing positions of frequently used keys, which is useful when working with text in Welsh, Scottish Gaelic and Irish — languages native to parts of the UK (Wales, parts of Scotland and Northern Ireland respectively). In this layout, the grave accent key () becomes, as it also does in the US International layout, a dead key modifying the character generated by the next key pressed. The apostrophe, double-quote, tilde and circumflex (caret) keys are not changed, becoming dead keys only when 'shifted' with . Additional precomposed characters are also obtained by shifting the 'normal' key using the key. The extended keyboard is software installed from the Windows control panel, and the extended characters are not normally engraved on keyboards. The UK Extended keyboard uses mostly the AltGr key to add diacritics to the letters a, e, i, n, o, u, w and y (the last two being used in Welsh) as appropriate for each character, as well as to their capitals. Pressing the key and then a character that does not take the specific diacritic produces the behaviour of a standard keyboard. The key presses followed by spacebar generate a stand-alone mark.: grave accents (e.g. à, è, etc.) needed for Scots Gaelic are generated by pressing the grave accent (or 'backtick') key , which is a dead key, then the letter. Thus produces à. acute accents (e.g. á) needed for Irish are generated by pressing the key together with the letter (or acting as a dead key combination followed by the letter). Thus produces á; produces Á. (Some programs use the combination of and a letter for other functions, in which case the method must be used to generate acute accents). the circumflex diacritic needed for Welsh may be added by , acting as a dead key combination, followed by the letter. Thus then produces â, then produces the letter ŵ. Some other languages commonly studied in the UK and Ireland are also supported to some extent: diaeresis or umlaut (e.g. ä, ë, ö, etc.) is generated by a dead key combination , then the letter. Thus produces ä. tilde (e.g. ã, ñ, õ, etc., as used in Spanish and Portuguese) is generated by dead key combination , then the letter. Thus produces ã. cedilla (e.g. ç) under c is generated by , and the capital letter (Ç) is produced by The and letter method used for acutes and cedillas does not work for applications which assign shortcut menu functions to these key combinations. These combinations are intended to be mnemonic and designed to be easy to remember: the circumflex accent (e.g. â) is similar to the free-standing circumflex (caret) (^), printed above	in most electronic keyboards. Some keyboards, such as the Kinesis or TypeMatrix, retain the QWERTY layout but arrange the keys in vertical columns, to reduce unnecessary lateral finger motion. Computer keyboards The first computer terminals such as the Teletype were typewriters that could produce and be controlled by various computer codes. These used the QWERTY layouts and added keys such as escape (ESC) which had special meanings to computers. Later keyboards added function keys and arrow keys. Since the standardization of PC-compatible computers and Windows after the 1980s, most full-sized computer keyboards have followed this standard (see drawing at right). This layout has a separate numeric keypad for data entry at the right, 12 function keys across the top, and a cursor section to the right and center with keys for Insert, Delete, Home, End, Page Up, and Page Down with cursor arrows in an inverted-T shape. Diacritical marks QWERTY was designed for English, a language with accents ('diacritics') appearing only in a few words of foreign origin. The standard US keyboard has no provision for these at all; the need was later met by the so called "US-International" keyboard mapping, which uses "dead keys" to type accents without having to add more physical keys. (The same principle is used in the standard US keyboard layout for MacOS, but in a different way.) Most European (including UK) keyboards for PCs have an AltGr key ('Alternative Graphics' key, replaces the right Alt key) that enables easy access to the most common diacritics used in the territory where sold. For example, default keyboard mapping for the UK/Ireland keyboard has the diacritics used in Irish but these are rarely printed on the keys; but to type the accents used in Welsh and Scots Gaelic requires the use of a "UK Extended" keyboard mapping and the dead key or compose key method. This arrangement applies to Windows, ChromeOS and Linux; MacOS computers have different techniques. The US International and UK Extended mappings provide many of the diacritics needed for students of other European languages. Other keys and characters Specific language variants Minor changes to the arrangement are made for other languages. There are a large number of different keyboard layouts used for different languages written in Latin script. They can be divided into three main families according to where the , , , , and keys are placed on the keyboard. These are usually named after the first six letters, for example this QWERTY layout and the AZERTY layout. In this section you will also find keyboard layouts that include some additional symbols of other languages. But they are different from layouts that were designed with the goal to be usable for multiple languages (see Multilingual variants). The following sections give general descriptions of QWERTY keyboard variants along with details specific to certain operating systems. The emphasis is on Microsoft Windows. English Canada English-speaking Canadians have traditionally used the same keyboard layout as in the United States, unless they are in a position where they have to write French on a regular basis. French-speaking Canadians respectively have favoured the Canadian French keyboard layout (see French (Canada), below). The CSA keyboard is the official multilingual keyboard layout of Canada. United Kingdom The United Kingdom and Ireland use a keyboard layout based on the 48-key version defined in the (now withdrawn) British Standard BS 4822. It is very similar to that of the United States, but has an AltGr key and a larger Enter key, includes £ and € signs and some rarely used EBCDIC symbols (¬, ¦), and uses different positions for the characters @, ", #, ~, \, and \|. The BS 4822:1994 standard did not make any use of the AltGr key and lacked support for any non-ASCII characters other than ¬ and £. It also assigned a key for the non-ASCII character broken bar (¦), but lacked one for the far more commonly used ASCII character vertical bar (\|). It also lacked support for various diacritics used in the Welsh alphabet, and the Scottish Gaelic alphabet; and also is missing the letter yogh, ȝ, used very rarely in the Scots language. Therefore, various manufacturers have modified or extended the BS 4822 standard: The B00 key (left of Z), shifted, results in vertical bar (\|) on some systems (e.g. Windows UK/Ireland keyboard layout and Linux/X11 UK/Ireland keyboard layout), rather than the broken bar (¦) assigned by BS 4822 and provided in some systems (e.g. IBM OS/2 UK166 keyboard layout) The E00 key (left of 1) with AltGr provides either vertical bar (\|) (OS/2's UK166 keyboard layout, Linux/X11 UK keyboard layout) or broken bar (¦) (Microsoft Windows UK/Ireland keyboard layout) Support for the diacritics needed for Scots Gaelic and Welsh was added to Windows and Chrome OS using a "UK-extended" setting (see below); Linux and X-Windows systems have an explicit or redesignated compose key for this purpose. UK Apple keyboard The British version of the Apple Keyboard does not use the standard UK layout. Instead, some older versions have the US layout (see below) with a few differences: the sign is reached by and the sign by , the opposite to the US layout. The is also present and is typed with . Umlauts are reached by typing and then the vowel, and ß is reached by typing . Newer Apple "British" keyboards use a layout that is relatively unlike either the US or traditional UK keyboard. It uses an elongated return key, a shortened left with and in the newly created position, and in the upper left of the keyboard are and instead of the traditional EBCDIC codes. The middle-row key that fits inside the key has and . United States The arrangement of the character input keys and the Shift keys contained in this layout is specified in the US national standard ANSI-INCITS 154-1988 (R1999) (formerly ANSI X3.154-1988 (R1999)), where this layout is called "ASCII keyboard". The complete US keyboard layout, as it is usually found, also contains the usual function keys in accordance with the international standard ISO/IEC 9995-2, although this is not explicitly required by the US American national standard. US keyboards are used not only in the United States, but also in many other English-speaking places, (except UK and Ireland), including India, Australia, Anglophone Canada, Hong Kong, New Zealand, South Africa, Malaysia, Singapore, Philippines, and Indonesia that uses the same 26-letter alphabets as English. In many other English-speaking jurisdictions (e.g., Canada, Australia, the Caribbean nations, Hong Kong, Malaysia, India, Pakistan, Bangladesh, Singapore, New Zealand, and South Africa), local spelling sometimes conforms more closely to British English usage, although these nations decided to use a US English keyboard layout. Until Windows 8 and later versions, when Microsoft separated the settings, this had the undesirable side effect of also setting the language to US English, rather than the local orthography. The US keyboard layout has a second Alt key instead of the AltGr key and does not use any dead keys; this makes it inefficient for all but a handful of languages. On the other hand, the US keyboard layout (or the similar UK layout) is occasionally used by programmers in countries where the keys for []{} are located in less convenient positions on the locally customary layout. On some keyboards the enter key is bigger than traditionally and takes up also a part of the line above, more or less the area of the traditional location of the backslash key (\). In these cases the backslash is located in alternative places. It can be situated one line above the default location, on the right of the equals sign key (=). Sometimes it is placed one line below its traditional situation, on the right of the apostrophe key (') (in these cases the enter key is narrower than usual on the line of its default location). It may also be two lines below its default situation on the right of a narrower than traditionally right shift key. A variant of this layout is used in Arabic-speaking countries. This variant has the \| \ key to the left of Z, ~ ` key where the \| \ key is in the usual layout, and the > < key where the ~ ` key is in the usual layout. Czech The typewriter came to the Czech-speaking area in the late 19th century, when it was part of Austria-Hungary where German was the dominant language of administration. Therefore, Czech typewriters have the QWERTZ layout. However, with the introduction of imported computers, especially since the 1990s, the QWERTY keyboard layout is frequently used for computer keyboards. The Czech QWERTY layout differs from QWERTZ in that the characters (e.g. @$& and others) missing from the Czech keyboard are accessible with AltGr on the same keys where they are located on an American keyboard. In Czech QWERTZ keyboards the positions of these characters accessed through AltGr differs. Danish Both the Danish and Norwegian keyboards include dedicated keys for the letters Å/å, Æ/æ and Ø/ø, but the placement is a little different, as the and keys are swapped on the Norwegian layout. (The Finnish–Swedish keyboard is also largely similar to the Norwegian layout, but the and are replaced with and . On some systems, the Danish keyboard may allow typing Ö/ö and Ä/ä by holding the or key while striking and , respectively.) Computers with Windows are commonly sold with ÖØÆ and ÄÆØ printed on the two keys, allowing same computer hardware to be sold in Denmark, Finland, Norway and Sweden, with different operating system settings. Dutch (Netherlands) Though it is seldom used (most Dutch keyboards use US International layout), the Dutch layout uses QWERTY but has additions for the € sign, the diaresis (¨), and the braces ({ }) as well as different locations for other symbols. An older version contained a single-stroke key for the Dutch character IJ/ij, which is usually typed by the combination of and . In the 1990s, there was a version with the now-obsolete florin sign (Dutch: guldenteken) for IBM PCs. In Flanders (the Dutch-speaking part of Belgium), "AZERTY" keyboards are used instead, due to influence from the French-speaking part of Belgium. See also #US-International in the Netherlands below. Estonian The keyboard layout used in Estonia is virtually the same as the Swedish layout. The main difference is that the and keys (to the right of ) are replaced with and respectively (the latter letter being the most distinguishing feature of the Estonian alphabet). Some special symbols and dead keys are also moved around. Faroese The same as the Danish layout with added (Eth), since the Faroe Islands are a self-governed part of the Kingdom of Denmark. French (Canada) This keyboard layout is commonly used in Canada by French-speaking Canadians. It is the most common layout for laptops and stand-alone keyboards aimed at the Francophone market. Unlike the AZERTY layout used in France and Belgium, it is a QWERTY layout and as such is also relatively commonly used by English speakers in the US and Canada (accustomed to using US standard QWERTY keyboards) for easy access to the accented letters found in some French loanwords. It can be used to type all accented French characters, as well as some from other languages, and serves all English functions as well. It is popular mainly because of its close similarity to the basic US keyboard commonly used by English-speaking Canadians and Americans, historical use of US-made typewriters by French-Canadians, and is the standard for keyboards in Quebec. It can also easily 'map' to or from a standard US QWERTY keyboard with the sole loss the guillemet/degree sign key. Its significant difference from the US standard is that the right Alt key is reconfigured as an AltGr key that gives easy access to a further range of characters (marked in blue and red on the keyboard image. Blue indicates an alternative character that will display as typed. Red indicates a dead key: the diacritic will be applied to the next vowel typed.) In some variants, the key names are translated to French: is or (short for Fixer/Verrouiller Majuscule, meaning Lock Uppercase). is . is . Greek The stress accents, indicated in red, are produced by pressing that key (or shifted key) followed by an appropriate vowel. Use of the "AltGr" key may produce the characters shown in blue. German Germany, Austria, Switzerland, Liechtenstein, and Luxembourg use QWERTZ layouts, where the letter Z is to the right of T. Icelandic The Icelandic keyboard layout is different from the standard QWERTY keyboard because the Icelandic alphabet has some special letters, most of which it shares with the other Nordic countries: Þ/þ, Ð/ð, Æ/æ, and Ö/ö. (Æ/æ also occurs in Norwegian, Danish and Faroese, Ð/ð in Faroese, and Ö/ö in Swedish, Finnish and Estonian. In Norwegian Ö/ö could be substituted for Ø/Ø which is the same sound/letter and is widely understood). The letters Á/á, Ý/ý, Ú/ú, Í/í, and É/é are produced by first pressing the dead key and then the corresponding letter. The Nordic letters Å/å and Ä/ä can be produced by first pressing , located below the key, and (for ¨) which also works for the non-Nordic ÿ, Ü/ü, Ï/ï, and Ë/ë. These letters are not used natively in Icelandic, but may have been implemented for ease of communication in other Nordic languages. Additional diacritics may be found behind the key: for ˋ (grave accent) and for ˆ (circumflex). Irish Microsoft Windows includes an Irish layout which supports acute accents with for the Irish language and grave accents with the dead key for Scottish Gaelic. The other Insular Celtic languages have their own layout. The UK or UK-Extended layout is also frequently used. Italian Braces (right above square brackets and shown in purple) are given with both AltGr and Shift pressed. The tilde (~) and backquote (`) characters are not present on the Italian keyboard layout (with Linux, they are available by pressing ++, and ++; Windows might not recognise these keybindings). When using Microsoft Windows, the standard Italian keyboard layout does not allow one to write 100% correct Italian language, since it lacks capital accented vowels, and in particular the È key. The common workaround is writing E' (E followed by an apostrophe) instead, or relying on the auto-correction feature of several word processors when available. It is possible to obtain the È symbol in MS Windows by typing + . Mac users, however, can write the correct accented character by pressing + + or, in the usual Mac way, by pressing the correct key for the accent (in this case + ) and subsequently pressing the wanted letter (in this case + ). Linux users can also write it by pressing the key with enabled. There is an alternate layout, which differs only in disposition of characters accessible through , and includes the tilde and the curly brackets. It is commonly used in IBM keyboards. Italian typewriters often have the QZERTY layout instead. The Italian-speaking part of Switzerland uses the QWERTZ keyboard. Latvian Although rarely used, a keyboard layout specifically designed for the Latvian language called ŪGJRMV exists. The Latvian QWERTY keyboard layout is most commonly used; its layout is the same as Latin ones, but with a dead key, which allows entering special characters (āčēģīķļņõŗšūž). The most common dead key is the apostrophe ('), which is followed by Alt+Gr (Windows default for Latvian layout). Some prefer using the tick (`). Lithuanian Where in standard QWERTY the number row is located, you find in Lithuanian QWERTY: Ą, Č, Ę, Ė, Į, Š, Ų, Ū, Ž, instead of their counterparts 1, 2, 3, 4, 5, 6, 7, 8, =. If you still want to use the numbers of the mentioned 'number row', you can create them in combination with the -key. Aside from these changes the keyboard is standard QWERTY. Besides QWERTY, the ĄŽERTY layout without the adjustment of the number row is used. Maltese The Maltese language uses Unicode (UTF-8) to display the Maltese diacritics: ċ Ċ; ġ Ġ; ħ Ħ; ż Ż (together with à À; è È; ì Ì; ò Ò; ù Ù). There are two standard keyboard layouts for Maltese, according to "MSA 100:2002 Maltese Keyboard Standard"; one of 47 keys and one of 48 keys. The 48-key layout is the most popular. Norwegian The Norwegian languages use the same letters as Danish, but the Norwegian keyboard differs from the Danish layout regarding the placement of the , and (backslash) keys. On the Danish keyboard, the and are swapped. The Swedish keyboard is also similar to the Norwegian layout, but and are replaced with and . On some systems, the Norwegian keyboard may allow typing Ö/ö and Ä/ä by holding the or key while striking and , respectively. There is also an alternative keyboard layout called Norwegian with Sámi, which allows for easier input of the characters required to write various Sámi languages. All the Sámi characters are accessed through the key. On Macintosh computers, the Norwegian and Norwegian extended keyboard layouts have a slightly different placement for some of the symbols obtained with the help of the or keys. Notably, the $ sign is accessed with and ¢ with . Furthermore, the frequently used @ is placed between and . Polish Most typewriters use a QWERTZ keyboard with Polish letters (with diacritical marks) accessed directly (officially approved as "Typist's keyboard", , Polish Standard PN-87), which is mainly ignored in Poland as impractical (custom-made keyboards, e.g., those in the public sector as well as some Apple computers, present an exception to this paradigm); the "Polish programmer's" () layout has become the de facto standard, used on virtually all computers sold on the Polish market. Most computer keyboards in Poland are laid out according to the standard US visual and functional layout. Polish diacritics are accessed by using the AltGr key with a corresponding similar letter from the base Latin alphabet. Normal capitalization rules apply with respect to Shift and Caps Lock keys. For example, to enter "Ź", one can type Shift+AltGr+X with Caps Lock off, or turn on Caps Lock and type AltGr+X. Both ANSI and ISO mechanical layouts are common sights, and even some non-standard mechanical layouts are in use. ANSI is often preferred, as the additional key provides no additional function, at least in Microsoft Windows where it duplicates the backslash key, while taking space from the Shift key. Many keyboards do not label AltGr as such, leaving the Alt marking as in the US layout - the right Alt key nevertheless functions as AltGr in this layout, causing possible confusion when keyboard shortcuts with the Alt key are required (these usually work only with the left Alt) and causing the key to be commonly referred to as right Alt (). However, keyboards with AltGr marking are available and it is also officially used by Microsoft when depicting the layout. Also, on MS Windows, the tilde character "~" (Shift+`) acts as a dead key to type Polish letters (with diacritical marks) thus, to obtain an "Ł", one may press Shift+` followed by L. The tilde character is obtained with (Shift+`) then space. In Linux-based systems, the euro symbol is typically mapped to Alt+5 instead of Alt+U, the tilde acts as a normal key, and several accented letters from other European languages are accessible through combinations with left Alt. Polish letters are also accessible by using the compose key. Software
The single-player mode is played against computer-controlled bots. It features music composed by Sonic Mayhem and Front Line Assembly founder Bill Leeb. Notable features of Quake III Arena include the minimalist design, lacking rarely used items and features; the extensive customizability of player settings such as field of view, texture detail and enemy model; and advanced movement features such as strafe-jumping and rocket-jumping. The game was praised by reviewers who, for the most part, described the gameplay as fun and engaging. Many liked the crisp graphics and focus on multiplayer. Quake III Arena has also been used extensively in professional electronic sports tournaments such as QuakeCon, Cyberathlete Professional League, DreamHack, and the Electronic Sports World Cup. Gameplay Unlike its predecessors, Quake III Arena does not have a plot-based single-player campaign. Instead, it simulates the multiplayer experience with computer-controlled players known as bots. The game's story is brief: "the greatest warriors of all time fight for the amusement of a race called the Vadrigar in the Arena Eternal." The introduction video shows the abduction of such a warrior, Sarge, while making a last stand. Continuity with prior games in the Quake series and even Doom is maintained by the inclusion of player models and biographical information. A familiar mixture of gothic and technological map architecture as well as specific equipment is included, such as the Quad Damage power-up, the rocket launcher, and the BFG. In Quake III Arena, the player progresses through tiers of maps, combating different bot characters that increase in difficulty, from Crash (at Tier 0) to Xaero (at Tier 7). As the game progresses, the fights take place in more complex arenas and against tougher opponents. While deathmatch maps are designed for up to 16 players, tournament maps are designed for duels between 2 players and in the single-player game could be considered 'boss battles'. The weapons are balanced by role, with each weapon having advantages in certain situations, such as the railgun at long-range and the lightning gun at close quarters. The BFG super-weapon is an exception to this; compared to other similarly named weapons in the Doom/Quake series, Quake III Arenas incarnation of this weapon is basically a fast-firing rocket launcher and it is found in hard-to-reach locations. Weapons appear as level items, spawning at regular intervals in set locations on the map. If a player dies, all of their weapons are lost and they receive the spawn weapons for the current map, usually the gauntlet and machine gun. Players also drop the weapon they were using when killed, which other players can then pick up. Quake III Arena comes with several gameplay modes: Free for All (FFA), a classic deathmatch, where each player competes against the rest for the highest score, Team Deathmatch (TDM), where usually two teams of four compete for the highest team frag (kill) total, Tournament (1v1), a deathmatch between two players, usually ending after a set time and Capture the Flag, which is played on symmetrical maps where teams have to recover the enemy flag from the opponents' base while retaining their own. Quake III Arena was specifically designed for multiplayer. The game allows players whose computers are connected by a network or to the internet to play against each other in real time, and incorporates a handicap system. It employs a client–server model, requiring all players' clients to connect to a server. Quake III Arena'''s focus on multiplayer gameplay spawned a lively community, similar to QuakeWorld, that is still active as of 2021. CharactersQuake III Arena features several characters from previous entries in the Quake series including "Bitterman" from Quake II, the "Ranger" character from Quake as well as Doomguy from id Software's sister franchise Doom. Development During early March 1999, ATI leaked the internal hardware vendor (IHV) copy of the game, which unveiled to the public in Macworld Conference & Expo at Moscone Center in January and Makuhari Messe in February by Steve Jobs (CEO of Apple Inc. at the time when it unveiled). This was a functional version of the engine with a textured level and working guns. The IHV contained most of the weapons (excepting the Gauntlet) that would make it into the final game although most were not fully modeled; a chainsaw and grappling hook were also in the IHV but did not make it into the final release. Many of the sounds that would make it into the final release were also included. After the IHV leak, id Software released a beta of the game called Quake III Arena Test on April 24, 1999, initially only for Mac OS before expanding to Windows at a later date. The Q3Test started with version 1.05 and included three levels that would be included in the final release: dm7, dm17, and q3tourney2. Id Software continued to update Q3Test up until version 1.09. id co-founder and former technical director John Carmack has stated that Quake III Arena is his favorite game he has worked on.Quake III Arena was shipped to retailers on December 2, 1999; the official street date for the game was December 5, although id Software chief executive officer Todd Hollenshead expected the game to be available as early as December 3 from retailers like Babbage's and EB Games. the game was support for the A3D 2.0 HRTF technology by Aureal Semiconductor out of the box. Game engine The id Tech 3 engine is the name given to the engine that was developed for Quake III Arena. Unlike most other games released at the time, Quake III Arena requires an OpenGL-compliant graphics accelerator to run. making The game does not include a software or Direct3D renderer. The graphic technology of the game is based tightly around a "shader" system where the appearance of many surfaces can be defined in text files referred to as "shader scripts". Quake 3 also introduced spline-based curved surfaces in addition to planar volumes, which are responsible for many of the surfaces present within the game. Quake 3 also provided support for models animated using vertex animation with attachment tags (known as the .md3 format), allowing models to maintain separate torso and leg animations and hold weapons. Quake 3 is one of the first games where the third-person model is able to look up and down and around as the head, torso and legs are separate. Other visual features include volumetric fog, mirrors, portals, decals, and wave-form vertex distortion. For networking, id Tech 3 uses a "snapshot" system to relay information about game "frames" to the client over UDP. The server attempts to omit as much information as possible about each frame, relaying only differences from the last frame the client confirmed as received (Delta encoding). id Tech 3 uses a virtual machine to control object behavior on the server, effects and prediction on the client and the user interface. This presents many advantages as mod authors do not need to worry about crashing the entire game with bad code, clients could show more advanced effects and game menus than was possible in Quake II and the user interface for mods was entirely customizable. Unless operations which require a specific endianness are used, a QVM file will run the same on any platform supported by Quake III Arena. The engine also contains bytecode compilers for the x86 and PowerPC architectures, executing QVM instructions via an interpreter.Quake III Arena features an advanced AI with five difficulty levels which can accommodate both a beginner and an advanced player, though they usually do not pose a challenge to high-tier or competitive players. Each bot has its own, often humorous, 'personality', expressed as scripted lines that are triggered to simulate real player chat. If the player types certain phrases, the bots may respond: for example, typing "You bore me" might cause a bot to reply "You should have been here 3 hours ago!". Each bot has a number of alternative lines to reduce the repetition of bot chatter. The Gladiator bots from Quake II were ported to Quake III Arena and incorporated into the game by their creator - Jan Paul van Waveren, aka Mr. Elusive. Bot chat lines were written by R. A. Salvatore, Seven Swords and Steve Winter. Xaero, the hardest opponent in the game, was based on the Gladiator bot Zero. The bot Hunter appears on magazine covers in the later id game Doom 3. On August 19, 2005, id Software released the complete source code for Quake III Arena under the GNU General Public License v2.0 or later, as they have for most of their prior engines. As before, the engine, but not the content such as textures and models, was released, so that anyone who wishes to build the game from source will still need an original copy of the game to play it as intended.	"Bitterman" from Quake II, the "Ranger" character from Quake as well as Doomguy from id Software's sister franchise Doom. Development During early March 1999, ATI leaked the internal hardware vendor (IHV) copy of the game, which unveiled to the public in Macworld Conference & Expo at Moscone Center in January and Makuhari Messe in February by Steve Jobs (CEO of Apple Inc. at the time when it unveiled). This was a functional version of the engine with a textured level and working guns. The IHV contained most of the weapons (excepting the Gauntlet) that would make it into the final game although most were not fully modeled; a chainsaw and grappling hook were also in the IHV but did not make it into the final release. Many of the sounds that would make it into the final release were also included. After the IHV leak, id Software released a beta of the game called Quake III Arena Test on April 24, 1999, initially only for Mac OS before expanding to Windows at a later date. The Q3Test started with version 1.05 and included three levels that would be included in the final release: dm7, dm17, and q3tourney2. Id Software continued to update Q3Test up until version 1.09. id co-founder and former technical director John Carmack has stated that Quake III Arena is his favorite game he has worked on.Quake III Arena was shipped to retailers on December 2, 1999; the official street date for the game was December 5, although id Software chief executive officer Todd Hollenshead expected the game to be available as early as December 3 from retailers like Babbage's and EB Games. the game was support for the A3D 2.0 HRTF technology by Aureal Semiconductor out of the box. Game engine The id Tech 3 engine is the name given to the engine that was developed for Quake III Arena. Unlike most other games released at the time, Quake III Arena requires an OpenGL-compliant graphics accelerator to run. making The game does not include a software or Direct3D renderer. The graphic technology of the game is based tightly around a "shader" system where the appearance of many surfaces can be defined in text files referred to as "shader scripts". Quake 3 also introduced spline-based curved surfaces in addition to planar volumes, which are responsible for many of the surfaces present within the game. Quake 3 also provided support for models animated using vertex animation with attachment tags (known as the .md3 format), allowing models to maintain separate torso and leg animations and hold weapons. Quake 3 is one of the first games where the third-person model is able to look up and down and around as the head, torso and legs are separate. Other visual features include volumetric fog, mirrors, portals, decals, and wave-form vertex distortion. For networking, id Tech 3 uses a "snapshot" system to relay information about game "frames" to the client over UDP. The server attempts to omit as much information as possible about each frame, relaying only differences from the last frame the client confirmed as received (Delta encoding). id Tech 3 uses a virtual machine to control object behavior on the server, effects and prediction on the client and the user interface. This presents many advantages as mod authors do not need to worry about crashing the entire game with bad code, clients could show more advanced effects and game menus than was possible in Quake II and the user interface for mods was entirely customizable. Unless operations which require a specific endianness are used, a QVM file will run the same on any platform supported by Quake III Arena. The engine also contains bytecode compilers for the x86 and PowerPC architectures, executing QVM instructions via an interpreter.Quake III Arena features an advanced AI with five difficulty levels which can accommodate both a beginner and an advanced player, though they usually do not pose a challenge to high-tier or competitive players. Each bot has its own, often humorous, 'personality', expressed as scripted lines that are triggered to simulate real player chat. If the player types certain phrases, the bots may respond: for example, typing "You bore me" might cause a bot to reply "You should have been here 3 hours ago!". Each bot has a number of alternative lines to reduce the repetition of bot chatter. The Gladiator bots from Quake II were ported to Quake III Arena and incorporated into the game by their creator - Jan Paul van Waveren, aka Mr. Elusive. Bot chat lines were written by R. A. Salvatore, Seven Swords and Steve Winter. Xaero, the hardest opponent in the game, was based on the Gladiator bot Zero. The bot Hunter appears on magazine covers in the later id game Doom 3. On August 19, 2005, id Software released the complete source code for Quake III Arena under the GNU General Public License v2.0 or later, as they have for most of their prior engines. As before, the engine, but not the content such as textures and models, was released, so that anyone who wishes to build the game from source will still need an original copy of the game to play it as intended. Mods Like its predecessors, Quake and Quake II, Quake III Arena can be heavily modified, allowing the engine to be used for many different games. Mods range from small gameplay adjustments like Rocket Arena 3 and Orange Smoothie Productions to total conversions such as Smokin' Guns, DeFRaG, and Loki's Revenge. The source code's release has allowed total conversion mods such as Tremulous, World of Padman, OpenArena, and Urban Terror to evolve into free standalone games. Other mods like Weapons Factory Arena have moved to more modern commercial engines. Challenge ProMode Arena became the primary competitive mod for Quake III Arena since the Cyberathlete Professional League announced CPMA as its
of the N64 port is used as a prologue. Some enemy types were removed and two new enemies was added: the Arachnid, a human-spider cyborg with twin railgun arms, and the Guardian, a bipedal boss enemy. Saving the game is only possible between levels and at mid-level checkpoints where the game loads, while in the PC version the game could be saved and loaded at any time. The game supports the PlayStation Mouse peripheral to provide a greater parity with the PC version's gameplay. The music used in this port is a combination of the Quake II original music score and tracks from the PC version's mission packs, while the opening and closing cut-scenes are taken from the Ground Zero expansion pack. The PlayStation version uses a new engine developed by HammerHead for their future PlayStation projects and runs at a 512x240 resolution at 30 frames per second. The developer was keen to retain a visual parity with the PC version and avoid tricks such as the use of environmental fog. Colored lights for levels and enemies, and yellow highlights for gunfire and explosions, are carried across from the PC version, with the addition of lens flare effects located around the light sources on the original lightmaps. There is no skybox; instead, a flat Gouraud-textured purple "sky" is drawn across the ceiling. The game uses particles to render blood, debris, and rail gun beams analogously to the PC version. There is also a split-screen multiplayer mode for two to four players (a four player game is possible using the PlayStation's Multi-tap). The only available player avatar is a modified version of the male player avatar from the PC version, the most noticeable difference being the addition of a helmet. Players can only customize the color of their avatar's armor and change their name. The twelve multiplayer levels featured are unique to the PlayStation version, with none of the PC multiplayer maps being carried over. The Nintendo 64 version has completely different single player levels and multiplayer maps, and features multiplayer support for up to four players. This version also has new lighting effects, mostly seen in gunfire, and also uses the Expansion Pak for extra graphical detail. This port also features an entirely new soundtrack, consisting mostly of dark ambient pieces, composed by Aubrey Hodges. A port of Quake II was included with Quake 4 for the Xbox 360 on a bonus disc. This is a direct port of the original game, with some graphical improvements. The port allows for System Link play for up to sixteen players, split-screen for four players, and cooperative play in single-player for up to sixteen players or four players with split-screen alone. Unofficial In December 2018, Polish programmer Krzysztof Kondrak released the original Quake 2 v3.21 source code with Vulkan support added. The port, called vkQuake2, is available under the GPLv2. Mods As with the original Quake, Quake II was designed to allow players to easily create custom content. A large number of mods, maps, graphics such as player models and skins, and sound effects were created and distributed to others free of charge via the Internet. Popular websites such as PlanetQuake and Telefragged allowed players to gain access to custom content. Another improvement over Quake was that it was easier to select custom player models, skins, and sound effects because they could be selected from an in-game menu. Mods for the game include Action Quake from 1999. PC Gaming Worlds Simon Quirk wrote of the game, "The Action Quake team fancied a multiplayer-only total conversion of Quake II where strategy, accuracy, and cool-looking fights would dominate." Release Quake II released on December 9, 1997, in the United States (one day short of the release of Doom four years prior) and on December 12 in Europe. Despite the title, Quake II is a sequel to the original Quake in name only. The scenario, enemies, and theme are entirely separate and do not fall into the same continuity as Quake. id initially wanted to set it separately from Quake, but due to legal reasons (most of their suggested names were already taken), they decided to use the working title. Quake II was also adopted as a name to leverage the popularity of Quake according to Jennell Jaquays. Quake II has been released on Steam, but this version does not include the soundtrack. The game was released on a bonus disc included with Quake 4 Special Edition for the PC, along with both expansion packs. This version also lacks the soundtrack. Quake II is also available on a bonus disc with the Xbox 360 version of Quake 4. This version is a direct port featuring the original soundtrack and multiplayer maps. In 2015, Quake II: Quad Damage, a bundle containing the original game with the mission packs has been released at GOG.com, but unlike the previous releases, this one contains a new customizeable launcher and the official soundtrack in OGG format which was made possible to play in-game, making it the only digital release to include music. The game has also been included in the following official compilations: Quake II: Quad Damage – contains Quake II and all three official expansion packs. Quake II: Colossus – a compilation for Linux that contains Quake II and both mission packs. Ultimate Quake – a compilation including the original Quake trilogy. Quake II RTX A remastered version of the game, titled Quake II RTX was announced by Nvidia in March 2019 and was released on June 6 for Windows and Linux on Steam. This remastered version requires either a Nvidia RTX or an AMD Radeon RX 6000 series GPU to utilize these cards' hardware ray-tracing functionality, but a software fallback is available for graphics cards that are fast enough. The game, provided free of charge, includes the three levels present in the original Quake II demo, but can be used to play the full game if its data files are available. Unlike in most games, ray tracing is used extensively here for lighting, reflections, etc. This is only possible because of the otherwise low hardware demands of Quake II. Expansions Quake II Mission Pack: The Reckoning Quake II Mission Pack: The Reckoning is the first official expansion pack, released on May 30, 1998. It was developed by Xatrix Entertainment. First announced in January 1998, it features eighteen new single player levels, six new deathmatch levels, three new weapons (the Ion Ripper, Phalanx Particle Cannon, and Trap), a new power-up, two new enemies, seven modified versions of existing enemies, and five new music tracks. The storyline follows Joker, a member of an elite squad of marines on a mission to infiltrate a Strogg base on one of Stroggos' moons and destroy the Strogg fleet, which is preparing to attack. Joker crash lands in the swamps outside of the compound where his squad is waiting. He travels through the swamps and bypasses the compounds outer defenses and enters through the main gate, finding his squad just in time to watch them get executed by Strogg forces. Next, Joker escapes on his own to the fuel refinery where he helps the Air Force destroy all fuel production, then infiltrates the Strogg spaceport, boards a cargo ship and reaches the Moon Base, destroying it and the Strogg fleet. Notably, the section of the game that takes place on the Moon Base has low gravity, something that was previously used on one secret level of the original Quake. The Reckoning received mixed reviews. It holds 69.50% from Gamerankings and Gamespot given a score of 7.4/10. Quake II Mission Pack: Ground Zero Quake II Mission Pack: Ground Zero is the second official expansion pack, released on September 11, 1998. It was developed by Rogue Entertainment. It comes with fourteen new single-player levels, ten new multiplayer maps, five additional music tracks, five new enemies, seven new power-ups, and five new weapons. In the expansion's story the Gravity Well has trapped the Earth Fleet in orbit above the planet Stroggos. One of the marines who managed to land, Stepchild, must now make his way to the Gravity Well to destroy it and free the fleet above and disable the entire defenses of the planet. Ground Zero received average to mixed reviews. It holds 65.40% from Gamerankings. Patrick Baggatta of IGN gave the expansion 7.5/10, describing it as similar to the original, but noting occasionally confusing map design. Elliott Chin of GameSpot gave the game 7.9/10, citing it as decent for an expansion and praising the monsters and enhanced AI. Johnny B. of Game Revolution rated the expansion D+, citing bad level design and few additions to the original game, and noted the multiplayer power-up gameplay as the only fun feature. Quake II Netpack I: Extremities Quake II Netpack I: Extremities contains, among other features, 11 game mods and 12 deathmatch maps. Reception Sales Quake II entered PC Data's monthly computer game sales rankings at #2 for December 1997, behind Riven. The game's sales in the United States alone reached 240,913 copies by the end of 1997, after its release on December 9. According to PC Data, it was the country's 22nd-best-selling computer game of 1997. The following year, Quake II secured fifth place on PC Data's charts for January and February 1998, then dropped to #8 in March and #9 in April. It remained in PC Data's top 20 for another two months, before exiting in July 1998. Quake II surpassed 850,000 units shipped to retailers by May 1998, and 900,000 by June. According to PC Data, Quake II was the United States' 14th-best-selling computer game during the January–November 1998 period. It ultimately secured 15th place for the full year, with sales of 279,536 copies and revenues of $12.6 million. GameDaily reported in January 1999 that Quake IIs sales in the United States had reached 550,000 units; this number rose to 610,000 units by December of that year. Worldwide, Quake II sold over 1 million copies by 2002. Critical reviews Quake II received generally positive reviews across all platforms. Next Generation reviewed the PC version of the game, rating it four stars out of five, and stated that "all in all, id should be commended for the advancement of its technology and improvement in its single-player level design, but it's going to be up to mod designers to provide the necessary additions to the	attempt to prevent an alien invasion of Earth by launching a pre-emptive attack against the home planet of the hostile Strogg civilization. Most of the other soldiers are captured or killed as soon as they approach the planned landing zone. Bitterman survives because another Marine's personal capsule collided with his upon launch, causing him to crash far short of the landing zone. Bitterman fights his way through the Strogg city, destroying strategic objectives along the way, and finally kills the Strogg leader, the Makron in his orbital asteroid base. Development Originally, Quake II was supposed to be an entirely new game and IP; titles like "Strogg", "Lock and Load", and even just "Load" were toyed with in the early days of development. But after numerous failed attempts, the team at id decided to stick with 'Quake II' and forego the gothic Lovecraftian horror theme from the original in favor of a more sci-fi aesthetic. The game was developed with 13 person team. Artist and co-owner Adrian Carmack had said that Quake II is his favorite game in the series because "it was different and a cohesive project". This is also the last id Software game to feature American McGee before he was fired shortly after its release. Unlike Quake, where hardware-accelerated graphics controllers were supported only with later patches, Quake II came with OpenGL support out of the box. Later downloads from id Software added support for AMD's 3DNow! instruction set for improved performance on their K6-2 processors, and Rendition released a native renderer for their V1000 graphics chip. The latest version is 3.21. This update includes numerous bug fixes and new levels designed for multiplayer deathmatch. Version 3.21, available as source code on id Software's FTP server, has no improved functionality over version 3.20 and is simply a slight modification to make compiling for Linux easier. Quake II uses an improved client–server model introduced in Quake. The game code of Quake II, which defines all the functionality for weapons, entities, and game mechanics, can be changed in any way because id Software published the source code of their own implementation that shipped with the game. Quake II uses the shared library functionality of the operating system to load the game library at run-time—this is how mod authors are able to alter the game and provide different gameplay mechanics, new weapons, and much more. The full source code to Quake II version 3.19 was released under the terms of the GNU GPL-2.0-or-later on December 22, 2001. Version 3.21 followed later. An LCC-friendly version was released on January 1, 2002, by a modder going by the name of Major Bitch. Since the release of the Quake II source code, several updates from third-party projects to the game engine have been created; the most prominent of these are projects focused on graphical enhancements to the game such as most notable "Yamagi Quake II", Quake2maX, EGL, Quake II Evolved, and KMQuake II. The source release also revealed numerous security flaws which can result in remote compromise of both the Quake II client and server. As id Software no longer maintains Quake II, most third-party engines include fixes for these bugs. The unofficial patch 3.24 that fixes bugs and adds only meager tweaks is recommended for Quake II purists, as it is not intended to add new features or be an engine mod in its own right. The most popular server-side engine modification for multiplayer, R1Q2, is generally recommended as a replacement for the 3.20 release for both clients and servers. In July 2003, Vertigo Software released a port of Quake II for the Microsoft .NET platform, using Managed C++, called Quake II .NET. It became a poster application for the language, showcasing the powerful interoperability between .NET and standard C++ code. It remains one of the top downloads on the Visual C++ website. In May 2004, Bytonic Software released a port of Quake II (called Jake2) written in Java using JOGL. In 2010 Google ported Jake2 to HTML5, running in Safari and Chrome. Quake IIs game engine was a popular license and formed the basis for several commercial and free games, such as CodeRED: Alien Arena, War§ow, SiN, Anachronox, Heretic II, Daikatana, Soldier of Fortune, Kingpin: Life of Crime, and UFO: Alien Invasion. Valve's 1998 video game Half-Life used the Quake II engine during early development stages. However, the final version runs on a heavily modified version of the Quake engine, GoldSrc, with a small amount of the Quake II code. Ports Ports of Quake II were released in 1999 on the Nintendo 64 (ported by Raster Productions) and PlayStation (ported by HammerHead) video game consoles. In both cases, the core gameplay was largely identical; however, changes were made to the game sequence and split-screen multiplayer replaced network or Internet play. A Macintosh port was developed by Logicware and released in July 1999. Quake II: Colossus (Quake II with both official add-ons) was ported to Linux by id Software and published by Macmillan Digital Publishing in 1999. Be Inc. officially ported Quake II: Colossus to the BeOS to test their OpenGL acceleration in 1999, and provided the game files for free download at a later date—a Windows, Macintosh, or Linux install CD was required to install the game, with the official add-ons being optional. The PlayStation version contains abridged versions of Units 1, 3, 6, 7, 8, and 10 of the PC version, redesigned to meet the console's technical limitations. For example, many short airlock-like corridors were added to maps to provide loading pauses inside what were contiguous areas in the PC version. In addition, part of the first mission of the N64 port is used as a prologue. Some enemy types were removed and two new enemies was added: the Arachnid, a human-spider cyborg with twin railgun arms, and the Guardian, a bipedal boss enemy. Saving the game is only possible between levels and at mid-level checkpoints where the game loads, while in the PC version the game could be saved and loaded at any time. The game supports the PlayStation Mouse peripheral to provide a greater parity with the PC version's gameplay. The music used in this port is a combination of the Quake II original music score and tracks from the PC version's mission packs, while the opening and closing cut-scenes are taken from the Ground Zero expansion pack. The PlayStation version uses a new engine developed by HammerHead for their future PlayStation projects and runs at a 512x240 resolution at 30 frames per second. The developer was keen to retain a visual parity with the PC version and avoid tricks such as the use of environmental fog. Colored lights for levels and enemies, and yellow highlights for gunfire and explosions, are carried across from the PC version, with the addition of lens flare effects located around the light sources on the original lightmaps. There is no skybox; instead, a flat Gouraud-textured purple "sky" is drawn across the ceiling. The game uses particles to render blood, debris, and rail gun beams analogously to the PC version. There is also a split-screen multiplayer mode for two to four players (a four player game is possible using the PlayStation's Multi-tap). The only available
the centuries the descriptions of qi have varied and have sometimes been in conflict. Until China came into contact with Western scientific and philosophical ideas, the Chinese had not categorized all things in terms of matter and energy. Qi and li (: "pattern") were 'fundamental' categories similar to matter and energy. Fairly early on, some Chinese thinkers began to believe that there were different fractions of qi—the coarsest and heaviest fractions formed solids, lighter fractions formed liquids, and the most ethereal fractions were the "lifebreath" that animated living beings. Yuanqi is a notion of innate or prenatal qi which is distinguished from acquired qi that a person may develop over their lifetime. Philosophical roots The earliest texts that speak of qi give some indications of how the concept developed. In the Analects of Confucius qi could mean "breath". Combining it with the Chinese word for blood (making 血氣, xue–qi, blood and breath), the concept could be used to account for motivational characteristics: The philosopher Mozi used the word qi to refer to noxious vapors that would eventually arise from a corpse were it not buried at a sufficient depth. He reported that early civilized humans learned how to live in houses to protect their qi from the moisture that troubled them when they lived in caves. He also associated maintaining one's qi with providing oneself with adequate nutrition. In regard to another kind of qi, he recorded how some people performed a kind of prognostication by observing qi (clouds) in the sky. Mencius described a kind of qi that might be characterized as an individual's vital energies. This qi was necessary to activity and it could be controlled by a well-integrated willpower. When properly nurtured, this qi was said to be capable of extending beyond the human body to reach throughout the universe. It could also be augmented by means of careful exercise of one's moral capacities. On the other hand, the qi of an individual could be degraded by adverse external forces that succeed in operating on that individual. Living things were not the only things believed to have qi. Zhuangzi indicated that wind is the qi of the Earth. Moreover, cosmic yin and yang "are the greatest of qi. He described qi as "issuing forth" and creating profound effects. He also said "Human beings are born [because of] the accumulation of qi. When it accumulates there is life. When it dissipates there is death... There is one qi that connects and pervades everything in the world." The Guanzi essay Neiye (Inward Training) is the oldest received writing on the subject of the cultivation of vapor [qi] and meditation techniques. The essay was probably composed at the Jixia Academy in Qi in the late fourth century B.C. Xun Zi, another Confucian scholar of the Jixia Academy, followed in later years. At 9:69/127, Xun Zi says, "Fire and water have qi but do not have life. Grasses and trees have life but do not have perceptivity. Fowl and beasts have perceptivity but do not have yi (sense of right and wrong, duty, justice). Men have qi, life, perceptivity, and yi." Chinese people at such an early time had no concept of radiant energy, but they were aware that one can be heated by a campfire from a distance away from the fire. They accounted for this phenomenon by claiming "qi" radiated from fire. At 18:62/122, he also uses "qi" to refer to the vital forces of the body that decline with advanced age. Among the animals, the gibbon and the crane were considered experts at inhaling the qi. The Confucian scholar Dong Zhongshu (ca. 150 BC) wrote in Luxuriant Dew of the Spring and Autumn Annals: "The gibbon resembles a macaque, but he is larger, and his color is black. His forearms being long, he lives eight hundred years, because he is expert in controlling his breathing." ("") Later, the syncretic text assembled under the direction of Liu An, the Huai Nan Zi, or "Masters of Huainan", has a passage that presages most of what is given greater detail by the Neo-Confucians: Role in traditional Chinese medicine The Huangdi Neijing ("The Yellow Emperor's Classic of Medicine", circa 2nd century BCE) is historically credited with first establishing the pathways, called meridians, through which qi allegedly circulates in the human body. In traditional Chinese medicine, symptoms of various illnesses are believed to be either the product of disrupted, blocked, and unbalanced qi movement through meridians or deficiencies and imbalances of qi in the Zang Fu organs. Traditional Chinese medicine often seeks to relieve these imbalances by adjusting the circulation of qi using a variety of techniques including herbology, food therapy, physical training regimens (qigong, t'ai chi ch'uan, and other martial arts training), moxibustion, tui na, or acupuncture.The cultivation of Heavenly and Earthly qi allow for the maintenance of psychological actions The nomenclature of Qi in the human body is different depending on its sources, roles, and locations. For sources there is a difference between so-called "Primordial Qi" (acquired at birth from one's parents) and Qi acquired throughout one's life. Or again Chinese medicine differentiates between Qi acquired from the air we breathe (so called "Clean Air") and Qi acquired from food and drinks (so-called "Grain Qi"). Looking at roles Qi is divided into "Defensive Qi" and "Nutritive Qi". Defensive Qi's role is to defend the body against invasions while Nutritive Qi's role is to provide sustenance for the body. To protect against said invasions, medicines have four types of qi; cold, hot, warm, and cool. Cold qi medicines are used to treat invasions hot in nature, while hot qi medicines are used to treat invasions cold in nature. looking at locations, Qi is also named after the Zang-Fu organ or the Meridian in which it resides: "Liver Qi", "Spleen Qi", etc. Lastly, prolonged exposure to the three evil qi (wind, cold, and wetness) can result in the penetration of evil qi through surface body parts, eventually reaching Zang-Fu organs. A qi field (chu-chong) refers to the cultivation of an energy field by a group, typically for healing or other benevolent purposes. A qi field is believed to be produced by visualization and affirmation. They are an important component of Wisdom Healing'Qigong (Zhineng Qigong), founded by Grandmaster Ming Pang. Scientific view The existence of Qi has not been proven scientifically. A 1997 consensus statement on acupuncture by the United States National Institutes of Health noted that concepts such as qi "are difficult to reconcile with contemporary biomedical information". Practices involving qi Feng shui The traditional Chinese art of geomancy, the placement and arrangement of space called feng shui, is based on calculating the balance of qi, interactions between the five elements, yin and yang, and other factors. The retention or dissipation of qi is believed to affect the health, wealth, energy level, luck, and many other aspects of the occupants. Attributes of each item in a space affect the flow of qi by slowing it down, redirecting it or accelerating it. This is said to influence the energy level of the occupants. Positive qi flows in curved lines, whereas negative qi travels in straight lines. In order for qi to be nourishing and positive, it must continue to flow	/kʰɯds/ (Zhengzhang Shangfang) and /C.qʰəp-s/ (William H. Baxter and Laurent Sagart). The etymology of qì interconnects with Kharia kʰis "anger", Sora kissa "move with great effort", Khmer kʰɛs "strive after; endeavor", and Gyalrongic kʰɐs "anger". Characters In the East Asian languages, qì has three logographs: is the traditional Chinese character, Korean hanja, and Japanese kyūjitai ("old character form") kanji is the Japanese shinjitai ("new character form") kanji is the simplified Chinese character. In addition, qì is an uncommon character especially used in writing Daoist talismans. Historically, the word qì was generally written as until the Han dynasty (206 BCE–220 CE), when it was replaced by the graph clarified with mǐ "rice" indicating "steam (rising from rice as it cooks.)" This primary logograph , the earliest written character for qì, consisted of three wavy horizontal lines seen in Shang dynasty (c. 1600–1046 BCE) oracle bone script, Zhou dynasty (1046–256 BCE) bronzeware script and large seal script, and Qin dynasty (221–206 BCE) small seal script. These oracle, bronze, and seal scripts logographs were used in ancient times as a phonetic loan character to write qǐ "plead for; beg; ask" which did not have an early character. The vast majority of Chinese characters are classified as radical-phonetic characters. Such characters combine a semantically suggestive "radical characters" with a phonetic element approximating ancient pronunciation. For example, the widely known word dào "the Dao; the way" graphically combines the "walk" radical with a shǒu "head" phonetic. Although the modern dào and shǒu pronunciations are dissimilar, the Old Chinese lˤuʔ-s and l̥uʔ-s were alike. The regular script character qì is unusual because qì is both the "air radical" and the phonetic, with mǐ "rice" semantically indicating "steam; vapor". This qì "air/gas radical" was only used in a few native Chinese characters like yīnyūn "thick mist/smoke", but was also used to create new scientific characters for gaseous chemical elements. Some examples are based on pronunciations in European languages: fú (with a fú phonetic) "fluorine" and nǎi (with a nǎi phonetic) "neon". Others are based on semantics: qīng (with a jīng phonetic, abbreviating qīng "light-weight") "hydrogen (the lightest element)" and lǜ (with a lù phonetic, abbreviating lǜ "green") "(greenish-yellow) chlorine". Qì is the phonetic element in a few characters such as kài "hate" with the "heart-mind radical" or , xì "set fire to weeds" with the "fire radical" , and xì "to present food" with the "food radical" . The first Chinese dictionary of characters, the Shuowen Jiezi(121 CE) notes that the primary qì is a pictographic character depicting "cloudy vapors", and that the full combines "rice" with the phonetic qi , meaning "present provisions to guests" (later disambiguated as xì ). Meanings Qi is a polysemous word. The unabridged Chinese-Chinese character dictionary Hanyu Da Cidian defines it as "present food or provisions" for the xì pronunciation but also lists 23 meanings for the qì pronunciation. The modern ABC Chinese-English Comprehensive Dictionary, which enters xì "grain; animal feed; make a present of food", and a qì entry with seven translation equivalents for the noun, two for bound morphemes, and three equivalents for the verb. n. ① air; gas ② smell ③ spirit; vigor; morale ④ vital/material energy (in Ch[inese] metaphysics) ⑤ tone; atmosphere; attitude ⑥ anger ⑦ breath; respiration b.f. ① weather tiānqì ② [linguistics] aspiration sòngqì v. ① anger ② get angry ③ bully; insult. English borrowing Qi was an early Chinese loanword in English. It was romanized as k'i in Church Romanization in the early-19th century, as ch'i in Wade–Giles in the mid-19th century (sometimes misspelled chi omitting the apostrophe), and as qi in Pinyin in the mid-20th century. The Oxford English Dictionary entry for qi gives the pronunciation as , the etymology from Chinese qì "air; breath", and a definition of "The physical life-force postulated by certain Chinese philosophers; the material principle." It also gives eight usage examples, with the first recorded example of k'í in 1850 (The Chinese Repository), of ch'i in 1917 (The Encyclopaedia Sinica), and qi in 1971 (Felix Mann's Acupuncture) Concept References to concepts analogous to qi are found in many Asian belief systems. Philosophical conceptions of qi from the earliest records of Chinese philosophy (5th century BCE) correspond to Western notions of humours and to the ancient Hindu yogic concept of prana. An early form of qi comes from the writings of the Chinese philosopher Mencius (4th century BCE). The ancient Chinese described qi as "life force". They believed it permeated everything and linked their surroundings together. Qi was also linked to the flow of energy around and through the body, forming a cohesive functioning unit. By understanding the rhythm and flow of qi, they believed they could guide exercises and treatments to provide stability and longevity. Although the concept has been important within many Chinese philosophies, over the centuries the descriptions of qi have varied and have sometimes been in conflict. Until China came into contact with Western scientific and philosophical ideas, the Chinese had not categorized all things in terms of matter and energy. Qi and li (: "pattern") were 'fundamental' categories similar to matter and energy. Fairly early on, some Chinese thinkers began to believe that there were different fractions of qi—the coarsest and heaviest fractions formed solids, lighter fractions formed liquids, and the most ethereal fractions were the "lifebreath" that animated living beings. Yuanqi is a notion of innate or prenatal qi which is distinguished from acquired qi that a person may develop over their lifetime. Philosophical roots The earliest texts that speak of qi give some indications of how the concept developed. In the Analects of Confucius qi could mean "breath". Combining it with the Chinese word for blood (making 血氣, xue–qi, blood and breath), the concept could be used to account for motivational characteristics: The philosopher Mozi used the word qi to refer to noxious vapors that would eventually arise from a corpse were it not buried at a sufficient depth. He reported that early civilized humans learned how to live in houses to protect their qi from the moisture that troubled them when they lived in caves. He also associated maintaining one's qi with providing oneself with adequate nutrition. In regard to another kind of qi, he recorded how some people performed a kind of prognostication by observing qi (clouds) in the sky. Mencius described a kind of qi that might be characterized as an individual's vital energies. This qi was necessary to activity and it could be controlled by a well-integrated willpower. When properly nurtured, this qi was said to be capable of extending beyond the human body to reach throughout the universe. It could also be augmented by means of careful exercise of one's moral capacities. On the other hand, the qi of an
by AU Optronics QUANTA, a user group for the Sinclair QL computer Quanta Services, a US-based speciality contractor for the electric, gas, and telecommunications industries Quanta Technology, a utility infrastructure consulting company Technology Quanta, an algorithm for random	US-based speciality contractor for the electric, gas, and telecommunications industries Quanta Technology, a utility infrastructure consulting company Technology Quanta, an algorithm for random number generation for smart contracts Quanta Plus, a web development tool Music Quanta, a 1997 album by Gilberto Gil Quanta Live, a Grammy Award-winning 1998 album by Gilberto Gil Science Quanta (journal), an open-access academic journal Quanta Magazine, a magazine covering
Web pages, encrypted email, and many other types of data. Breaking these would have significant ramifications for electronic privacy and security. Identifying cryptographic systems that may be secure against quantum algorithms is an actively researched topic under the field of post-quantum cryptography. Some public-key algorithms are based on problems other than the integer factorization and discrete logarithm problems to which Shor's algorithm applies, like the McEliece cryptosystem based on a problem in coding theory. Lattice-based cryptosystems are also not known to be broken by quantum computers, and finding a polynomial time algorithm for solving the dihedral hidden subgroup problem, which would break many lattice based cryptosystems, is a well-studied open problem. It has been proven that applying Grover's algorithm to break a symmetric (secret key) algorithm by brute force requires time equal to roughly 2n/2 invocations of the underlying cryptographic algorithm, compared with roughly 2n in the classical case, meaning that symmetric key lengths are effectively halved: AES-256 would have the same security against an attack using Grover's algorithm that AES-128 has against classical brute-force search (see Key size). Quantum cryptography could potentially fulfill some of the functions of public key cryptography. Quantum-based cryptographic systems could, therefore, be more secure than traditional systems against quantum hacking. Search problems The most well-known example of a problem admitting a polynomial quantum speedup is unstructured search, finding a marked item out of a list of items in a database. This can be solved by Grover's algorithm using queries to the database, quadratically fewer than the queries required for classical algorithms. In this case, the advantage is not only provable but also optimal: it has been shown that Grover's algorithm gives the maximal possible probability of finding the desired element for any number of oracle lookups. Problems that can be efficiently addressed with Grover's algorithm have the following properties: There is no searchable structure in the collection of possible answers, The number of possible answers to check is the same as the number of inputs to the algorithm, and There exists a boolean function that evaluates each input and determines whether it is the correct answer For problems with all these properties, the running time of Grover's algorithm on a quantum computer scales as the square root of the number of inputs (or elements in the database), as opposed to the linear scaling of classical algorithms. A general class of problems to which Grover's algorithm can be applied is Boolean satisfiability problem, where the database through which the algorithm iterates is that of all possible answers. An example and possible application of this is a password cracker that attempts to guess a password. Breaking symmetric ciphers with this algorithm is of interest of government agencies. Simulation of quantum systems Since chemistry and nanotechnology rely on understanding quantum systems, and such systems are impossible to simulate in an efficient manner classically, many believe quantum simulation will be one of the most important applications of quantum computing. Quantum simulation could also be used to simulate the behavior of atoms and particles at unusual conditions such as the reactions inside a collider. Quantum simulations might be used to predict future paths of particles and protons under superposition in the double-slit experiment. About 2% of the annual global energy output is used for nitrogen fixation to produce ammonia for the Haber process in the agricultural fertilizer industry while naturally occurring organisms also produce ammonia. Quantum simulations might be used to understand this process increasing production. Quantum annealing and adiabatic optimization Quantum annealing or Adiabatic quantum computation relies on the adiabatic theorem to undertake calculations. A system is placed in the ground state for a simple Hamiltonian, which is slowly evolved to a more complicated Hamiltonian whose ground state represents the solution to the problem in question. The adiabatic theorem states that if the evolution is slow enough the system will stay in its ground state at all times through the process. Machine learning Since quantum computers can produce outputs that classical computers cannot produce efficiently, and since quantum computation is fundamentally linear algebraic, some express hope in developing quantum algorithms that can speed up machine learning tasks. For example, the quantum algorithm for linear systems of equations, or "HHL Algorithm", named after its discoverers Harrow, Hassidim, and Lloyd, is believed to provide speedup over classical counterparts. Some research groups have recently explored the use of quantum annealing hardware for training Boltzmann machines and deep neural networks. Computational biology In the field of computational biology, quantum computing has played a big role in solving many biological problems. One of the well-known examples would be in computational genomics and how computing has drastically reduced the time to sequence a human genome. Given how computational biology is using generic data modeling and storage, its applications to computational biology are expected to arise as well. Computer-aided drug design and generative chemistry Deep generative chemistry models emerge as powerful tools to expedite drug discovery. However, the immense size and complexity of the structural space of all possible drug-like molecules pose significant obstacles, which could be overcome in the future by quantum computers. Quantum computers are naturally good for solving complex quantum many-body problems and thus may be instrumental in applications involving quantum chemistry. Therefore, one can expect that quantum-enhanced generative models including quantum GANs may eventually be developed into ultimate generative chemistry algorithms. Hybrid architectures combining quantum computers with deep classical networks, such as Quantum Variational Autoencoders, can already be trained on commercially available annealers and used to generate novel drug-like molecular structures. Developing physical quantum computers Challenges There are a number of technical challenges in building a large-scale quantum computer. Physicist David DiVincenzo has listed these requirements for a practical quantum computer: Physically scalable to increase the number of qubits Qubits that can be initialized to arbitrary values Quantum gates that are faster than decoherence time Universal gate set Qubits that can be read easily Sourcing parts for quantum computers is also very difficult. Many quantum computers, like those constructed by Google and IBM, need helium-3, a nuclear research byproduct, and special superconducting cables made only by the Japanese company Coax Co. The control of multi-qubit systems requires the generation and coordination of a large number of electrical signals with tight and deterministic timing resolution. This has led to the development of quantum controllers which enable interfacing with the qubits. Scaling these systems to support a growing number of qubits is an additional challenge. Quantum decoherence One of the greatest challenges involved with constructing quantum computers is controlling or removing quantum decoherence. This usually means isolating the system from its environment as interactions with the external world cause the system to decohere. However, other sources of decoherence also exist. Examples include the quantum gates, and the lattice vibrations and background thermonuclear spin of the physical system used to implement the qubits. Decoherence is irreversible, as it is effectively non-unitary, and is usually something that should be highly controlled, if not avoided. Decoherence times for candidate systems in particular, the transverse relaxation time T2 (for NMR and MRI technology, also called the dephasing time), typically range between nanoseconds and seconds at low temperature. Currently, some quantum computers require their qubits to be cooled to 20 millikelvin (usually using a dilution refrigerator) in order to prevent significant decoherence. A 2020 study argues that ionizing radiation such as cosmic rays can nevertheless cause certain systems to decohere within milliseconds. As a result, time-consuming tasks may render some quantum algorithms inoperable, as maintaining the state of qubits for a long enough duration will eventually corrupt the superpositions. These issues are more difficult for optical approaches as the timescales are orders of magnitude shorter and an often-cited approach to overcoming them is optical pulse shaping. Error rates are typically proportional to the ratio of operating time to decoherence time, hence any operation must be completed much more quickly than the decoherence time. As described in the Quantum threshold theorem, if the error rate is small enough, it is thought to be possible to use quantum error correction to suppress errors and decoherence. This allows the total calculation time to be longer than the decoherence time if the error correction scheme can correct errors faster than decoherence introduces them. An often cited figure for the required error rate in each gate for fault-tolerant computation is 10−3, assuming the noise is depolarizing. Meeting this scalability condition is possible for a wide range of systems. However, the use of error correction brings with it the cost of a greatly increased number of required qubits. The number required to factor integers using Shor's algorithm is still polynomial, and thought to be between L and L2, where L is the number of digits in the number to be factored; error correction algorithms would inflate this figure by an additional factor of L. For a 1000-bit number, this implies a need for about 104 bits without error correction. With error correction, the figure would rise to about 107 bits. Computation time is about L2 or about 107 steps and at 1 MHz, about 10 seconds. A very different approach to the stability-decoherence problem is to create a topological quantum computer with anyons, quasi-particles used as threads and relying on braid theory to form stable logic gates. Quantum supremacy Quantum supremacy is a term coined by John Preskill referring to the engineering feat of demonstrating that a programmable quantum device can solve a problem beyond the capabilities of state-of-the-art classical computers. The problem need not be useful, so some view the quantum supremacy test only as a potential future benchmark. In October 2019, Google AI Quantum, with the help of NASA, became the first to claim to have achieved quantum supremacy by performing calculations on the Sycamore quantum computer more than 3,000,000 times faster than they could be done on Summit, generally considered the world's fastest computer. This claim has been subsequently challenged: IBM has stated that Summit can perform samples much faster than claimed, and researchers have since developed better algorithms for the sampling problem used to claim quantum supremacy, giving substantial reductions to or the closing of the gap between Sycamore and classical supercomputers. In December 2020, a group at USTC implemented a type of Boson sampling on 76 photons with a photonic quantum computer Jiuzhang to demonstrate quantum supremacy. The authors claim that a classical contemporary supercomputer would require a computational time of 600 million years to generate the number of samples their quantum processor can generate in 20 seconds. On November 16, 2021 at the quantum computing summit IBM presented a 127-qubit microprocessor named IBM Eagle. Skepticism Some researchers have expressed skepticism that scalable quantum computers could ever be built, typically because of the issue of maintaining coherence at large scales. Bill Unruh doubted the practicality of quantum computers in a paper published back in 1994. Paul Davies argued that a 400-qubit computer would even come into conflict with the cosmological information bound implied by the holographic principle. Skeptics like Gil Kalai doubt that quantum supremacy will ever be achieved. Physicist Mikhail Dyakonov has expressed skepticism of quantum computing as follows: "So the number of continuous parameters describing the state of such a useful quantum computer at any given moment must be... about 10300... Could we ever learn to control the more than 10300 continuously variable parameters defining the quantum state of such a system? My answer is simple. No, never." Candidates for physical realizations For physically implementing a quantum computer, many different candidates are being pursued, among them (distinguished by the physical system used to realize the qubits): Superconducting quantum computing (qubit implemented by the state of small superconducting circuits [Josephson junctions]) Trapped ion quantum computer (qubit implemented by the internal state of trapped ions) Neutral atoms in optical lattices (qubit implemented by internal states of neutral atoms trapped in an optical lattice) Quantum dot computer, spin-based (e.g. the Loss-DiVincenzo quantum computer) (qubit given by the spin states of trapped electrons) Quantum dot computer, spatial-based (qubit given by electron position in double quantum dot) Quantum computing using engineered quantum wells, which could in principle enable the construction of quantum computers that operate at room temperature Coupled quantum wire (qubit implemented by a pair of quantum wires coupled by a quantum point contact) Nuclear magnetic resonance quantum computer (NMRQC) implemented with the nuclear magnetic resonance of molecules in solution, where qubits are provided by nuclear spins within the dissolved molecule and probed with radio waves Solid-state NMR Kane quantum computers (qubit realized by the nuclear spin state of phosphorus donors in silicon) Vibrational quantum computer (qubits realized by vibrational superpositions in cold molecules) Electrons-on-helium quantum computers (qubit is the electron spin) Cavity quantum electrodynamics (CQED) (qubit provided by the internal state of trapped atoms coupled to high-finesse cavities) Molecular magnet (qubit given by spin states) Fullerene-based ESR quantum computer (qubit based on the electronic spin of atoms or molecules encased in fullerenes) Nonlinear optical quantum computer (qubits realized by processing states of different modes of light through both linear and nonlinear elements) Linear optical quantum computer (qubits realized by processing states of different modes of light through linear elements e.g. mirrors, beam splitters and phase shifters) Diamond-based quantum computer (qubit realized by the electronic or nuclear spin of nitrogen-vacancy centers in diamond) Bose-Einstein condensate-based quantum computer Transistor-based quantum computer – string quantum computers with entrainment of positive holes using an electrostatic trap Rare-earth-metal-ion-doped inorganic crystal based quantum computers (qubit realized by the internal electronic state of dopants in optical fibers) Metallic-like carbon nanospheres-based quantum computers The large number of candidates demonstrates that quantum computing, despite rapid progress, is still in its infancy. Models of computation for quantum computing There are a number of models of computation for quantum computing, distinguished by the basic elements in which the computation is decomposed. For practical implementations, the four relevant models of computation are: Quantum gate array – Computation decomposed into a sequence	replaced with a finite gate set by appealing to the Solovay-Kitaev theorem. Quantum algorithms Progress in finding quantum algorithms typically focuses on this quantum circuit model, though exceptions like the quantum adiabatic algorithm exist. Quantum algorithms can be roughly categorized by the type of speedup achieved over corresponding classical algorithms. Quantum algorithms that offer more than a polynomial speedup over the best known classical algorithm include Shor's algorithm for factoring and the related quantum algorithms for computing discrete logarithms, solving Pell's equation, and more generally solving the hidden subgroup problem for abelian finite groups. These algorithms depend on the primitive of the quantum Fourier transform. No mathematical proof has been found that shows that an equally fast classical algorithm cannot be discovered, although this is considered unlikely. Certain oracle problems like Simon's problem and the Bernstein–Vazirani problem do give provable speedups, though this is in the quantum query model, which is a restricted model where lower bounds are much easier to prove and doesn't necessarily translate to speedups for practical problems. Other problems, including the simulation of quantum physical processes from chemistry and solid-state physics, the approximation of certain Jones polynomials, and the quantum algorithm for linear systems of equations have quantum algorithms appearing to give super-polynomial speedups and are BQP-complete. Because these problems are BQP-complete, an equally fast classical algorithm for them would imply that no quantum algorithm gives a super-polynomial speedup, which is believed to be unlikely. Some quantum algorithms, like Grover's algorithm and amplitude amplification, give polynomial speedups over corresponding classical algorithms. Though these algorithms give comparably modest quadratic speedup, they are widely applicable and thus give speedups for a wide range of problems. Many examples of provable quantum speedups for query problems are related to Grover's algorithm, including Brassard, Høyer, and Tapp's algorithm for finding collisions in two-to-one functions, which uses Grover's algorithm, and Farhi, Goldstone, and Gutmann's algorithm for evaluating NAND trees, which is a variant of the search problem. Potential applications Cryptography A notable application of quantum computation is for attacks on cryptographic systems that are currently in use. Integer factorization, which underpins the security of public key cryptographic systems, is believed to be computationally infeasible with an ordinary computer for large integers if they are the product of few prime numbers (e.g., products of two 300-digit primes). By comparison, a quantum computer could efficiently solve this problem using Shor's algorithm to find its factors. This ability would allow a quantum computer to break many of the cryptographic systems in use today, in the sense that there would be a polynomial time (in the number of digits of the integer) algorithm for solving the problem. In particular, most of the popular public key ciphers are based on the difficulty of factoring integers or the discrete logarithm problem, both of which can be solved by Shor's algorithm. In particular, the RSA, Diffie–Hellman, and elliptic curve Diffie–Hellman algorithms could be broken. These are used to protect secure Web pages, encrypted email, and many other types of data. Breaking these would have significant ramifications for electronic privacy and security. Identifying cryptographic systems that may be secure against quantum algorithms is an actively researched topic under the field of post-quantum cryptography. Some public-key algorithms are based on problems other than the integer factorization and discrete logarithm problems to which Shor's algorithm applies, like the McEliece cryptosystem based on a problem in coding theory. Lattice-based cryptosystems are also not known to be broken by quantum computers, and finding a polynomial time algorithm for solving the dihedral hidden subgroup problem, which would break many lattice based cryptosystems, is a well-studied open problem. It has been proven that applying Grover's algorithm to break a symmetric (secret key) algorithm by brute force requires time equal to roughly 2n/2 invocations of the underlying cryptographic algorithm, compared with roughly 2n in the classical case, meaning that symmetric key lengths are effectively halved: AES-256 would have the same security against an attack using Grover's algorithm that AES-128 has against classical brute-force search (see Key size). Quantum cryptography could potentially fulfill some of the functions of public key cryptography. Quantum-based cryptographic systems could, therefore, be more secure than traditional systems against quantum hacking. Search problems The most well-known example of a problem admitting a polynomial quantum speedup is unstructured search, finding a marked item out of a list of items in a database. This can be solved by Grover's algorithm using queries to the database, quadratically fewer than the queries required for classical algorithms. In this case, the advantage is not only provable but also optimal: it has been shown that Grover's algorithm gives the maximal possible probability of finding the desired element for any number of oracle lookups. Problems that can be efficiently addressed with Grover's algorithm have the following properties: There is no searchable structure in the collection of possible answers, The number of possible answers to check is the same as the number of inputs to the algorithm, and There exists a boolean function that evaluates each input and determines whether it is the correct answer For problems with all these properties, the running time of Grover's algorithm on a quantum computer scales as the square root of the number of inputs (or elements in the database), as opposed to the linear scaling of classical algorithms. A general class of problems to which Grover's algorithm can be applied is Boolean satisfiability problem, where the database through which the algorithm iterates is that of all possible answers. An example and possible application of this is a password cracker that attempts to guess a password. Breaking symmetric ciphers with this algorithm is of interest of government agencies. Simulation of quantum systems Since chemistry and nanotechnology rely on understanding quantum systems, and such systems are impossible to simulate in an efficient manner classically, many believe quantum simulation will be one of the most important applications of quantum computing. Quantum simulation could also be used to simulate the behavior of atoms and particles at unusual conditions such as the reactions inside a collider. Quantum simulations might be used to predict future paths of particles and protons under superposition in the double-slit experiment. About 2% of the annual global energy output is used for nitrogen fixation to produce ammonia for the Haber process in the agricultural fertilizer industry while naturally occurring organisms also produce ammonia. Quantum simulations might be used to understand this process increasing production. Quantum annealing and adiabatic optimization Quantum annealing or Adiabatic quantum computation relies on the adiabatic theorem to undertake calculations. A system is placed in the ground state for a simple Hamiltonian, which is slowly evolved to a more complicated Hamiltonian whose ground state represents the solution to the problem in question. The adiabatic theorem states that if the evolution is slow enough the system will stay in its ground state at all times through the process. Machine learning Since quantum computers can produce outputs that classical computers cannot produce efficiently, and since quantum computation is fundamentally linear algebraic, some express hope in developing quantum algorithms that can speed up machine learning tasks. For example, the quantum algorithm for linear systems of equations, or "HHL Algorithm", named after its discoverers Harrow, Hassidim, and Lloyd, is believed to provide speedup over classical counterparts. Some research groups have recently explored the use of quantum annealing hardware for training Boltzmann machines and deep neural networks. Computational biology In the field of computational biology, quantum computing has played a big role in solving many biological problems. One of the well-known examples would be in computational genomics and how computing has drastically reduced the time to sequence a human genome. Given how computational biology is using generic data modeling and storage, its applications to computational biology are expected to arise as well. Computer-aided drug design and generative chemistry Deep generative chemistry models emerge as powerful tools to expedite drug discovery. However, the immense size and complexity of the structural space of all possible drug-like molecules pose significant obstacles, which could be overcome in the future by quantum computers. Quantum computers are naturally good for solving complex quantum many-body problems and thus may be instrumental in applications involving quantum chemistry. Therefore, one can expect that quantum-enhanced generative models including quantum GANs may eventually be developed into ultimate generative chemistry algorithms. Hybrid architectures combining quantum computers with deep classical networks, such as Quantum Variational Autoencoders, can already be trained on commercially available annealers and used to generate novel drug-like molecular structures. Developing physical quantum computers Challenges There are a number of technical challenges in building a large-scale quantum computer. Physicist David DiVincenzo has listed these requirements for a practical quantum computer: Physically scalable to increase the number of qubits Qubits that can be initialized to arbitrary values Quantum gates that are faster than decoherence time Universal gate set Qubits that can be read easily Sourcing parts for quantum computers is also very difficult. Many quantum computers, like those constructed by Google and IBM, need helium-3, a nuclear research byproduct, and special superconducting cables made only by the Japanese company Coax Co. The control of multi-qubit systems requires the generation and coordination of a large number of electrical signals with tight and deterministic timing resolution. This has led to the development of quantum controllers which enable interfacing with the qubits. Scaling these systems to support a growing number of qubits is an additional challenge. Quantum decoherence One of the greatest challenges involved with constructing quantum computers is controlling or removing quantum decoherence. This usually means isolating the system from its environment as interactions with the external world cause the system to decohere. However, other sources of decoherence also exist. Examples include the quantum gates, and the lattice vibrations and background thermonuclear spin of the physical system used to implement the qubits. Decoherence is irreversible, as it is effectively non-unitary, and is usually something that should be highly controlled, if not avoided. Decoherence times for candidate systems in particular, the transverse relaxation time T2 (for NMR and MRI technology, also called the dephasing time), typically range between nanoseconds and seconds at low temperature. Currently, some quantum computers require their qubits to be cooled to 20 millikelvin (usually using a dilution refrigerator) in order to prevent significant decoherence. A 2020 study argues that ionizing radiation such as cosmic rays can nevertheless cause certain systems to decohere within milliseconds. As a result, time-consuming tasks may render some quantum algorithms inoperable, as maintaining the state of qubits for a long enough duration will eventually corrupt the superpositions. These issues are more difficult for optical approaches as the timescales are orders of magnitude shorter and an often-cited approach to overcoming them is optical pulse shaping. Error rates are typically proportional to the ratio of operating time to decoherence time, hence any operation must be completed much more quickly than
science and technology Qt (software), a cross-platform application framework QuickTime, a multimedia technology from Apple Inc. Quiet Trader, cargo versions of the BAe 146 jet Quart (qt), a unit of volume equal to a quarter of a gallon Other uses Quality time, time spent with loved ones which is in some way special QT (New York City Subway service), a former New York City Subway	pop singer QT: QueerTelevision, an LGBT newsmagazine which aired on Canada's CityTV in the 1990s Quentin Tarantino (born 1963), American filmmaker Question Time (TV programme), a topical debate BBC television programme in the UK Organizations QuikTrip, a US convenience store chain QT Inc., manufacturer of the Q-Ray ionized bracelet QT Hotels & Resorts The Qt Company Science and technology Medicine Long QT syndrome, a rare hereditary and medication induced cardiac condition Short QT syndrome, a genetic disease of the electrical system of the heart QT interval, a measurement
elements. See small Latin squares and quasigroups. Infinite quasigroups For a countably infinite quasigroup Q, it is possible to imagine an infinite array in which every row and every column corresponds to some element q of Q, and where the element a*b is in the row corresponding to a and the column responding to b. In this situation too, the Latin Square property says that each row and each column of the infinite array will contain every possible value precisely once. For an uncountably infinite quasigroup, such as the group of non-zero real numbers under multiplication, the Latin square property still holds, although the name is somewhat unsatisfactory, as it is not possible to produce the array of combinations to which the above idea of an infinite array extends since the real numbers cannot all be written in a sequence. (This is somewhat misleading however, as the reals can be written in a sequence of length , assuming the Well-Ordering Theorem.) Inverse properties The binary operation of a quasigroup is invertible in the sense that both and , the left and right multiplication operators, are bijective, and hence invertible. Every loop element has a unique left and right inverse given by A loop is said to have (two-sided) inverses if for all x. In this case the inverse element is usually denoted by . There are some stronger notions of inverses in loops which are often useful: A loop has the left inverse property if for all and . Equivalently, or . A loop has the right inverse property if for all and . Equivalently, or . A loop has the antiautomorphic inverse property if or, equivalently, if . A loop has the weak inverse property when if and only if . This may be stated in terms of inverses via or equivalently . A loop has the inverse property if it has both the left and right inverse properties. Inverse property loops also have the antiautomorphic and weak inverse properties. In fact, any loop which satisfies any two of the above four identities has the inverse property and therefore satisfies all four. Any loop which satisfies the left, right, or antiautomorphic inverse properties automatically has two-sided inverses. Morphisms A quasigroup or loop homomorphism is a map between two quasigroups such that . Quasigroup homomorphisms necessarily preserve left and right division, as well as identity elements (if they exist). Homotopy and isotopy Let Q and P be quasigroups. A quasigroup homotopy from Q to P is a triple of maps from Q to P such that for all x, y in Q. A quasigroup homomorphism is just a homotopy for which the three maps are equal. An isotopy is a homotopy for which each of the three maps is a bijection. Two quasigroups are isotopic if there is an isotopy between them. In terms of Latin squares, an isotopy is given by a permutation of rows α, a permutation of columns β, and a permutation on the underlying element set γ. An autotopy is an isotopy from a quasigroup to itself. The set of all autotopies of a quasigroup form a group with the automorphism group as a subgroup. Every quasigroup is isotopic to a loop. If a loop is isotopic to a group, then it is isomorphic to that group and thus is itself a group. However, a quasigroup which is isotopic to a group need not be a group. For example, the quasigroup on R with multiplication given by is isotopic to the additive group , but is not itself a group. Every medial quasigroup is isotopic to an abelian group by the Bruck–Toyoda theorem. Conjugation (parastrophe) Left and right division are examples of forming a quasigroup by permuting the variables in the defining equation. From the original operation ∗ (i.e., ) we can form five new operations: (the opposite operation), / and \, and their opposites. That makes a total of six quasigroup operations, which are called the conjugates or parastrophes of ∗. Any two of these operations are said to be "conjugate" or "parastrophic" to each other (and to themselves). Isostrophe (paratopy) If the set Q has two quasigroup operations, ∗ and ·, and one of them is isotopic to a conjugate of the other, the operations are said to be isostrophic to each other. There are also many other names for this relation of "isostrophe", e.g., paratopy. Generalizations Polyadic or multiary quasigroups An n-ary quasigroup is a set with an n-ary operation, with , such that the equation has a unique solution for any one variable if all the other n variables are specified arbitrarily. Polyadic or multiary means n-ary for some nonnegative integer n. A 0-ary, or nullary, quasigroup is just a constant element of Q. A 1-ary, or unary, quasigroup is a bijection of Q to	One defines a quasigroup as a set with one binary operation, and the other, from universal algebra, defines a quasigroup as having three primitive operations. The homomorphic image of a quasigroup defined with a single binary operation, however, need not be a quasigroup. We begin with the first definition. Algebra A quasigroup is a non-empty set Q with a binary operation ∗ (that is, a magma, indicating that a quasigroup has to satisfy closure property), obeying the Latin square property. This states that, for each a and b in Q, there exist unique elements x and y in Q such that both a ∗ x = b, y ∗ a = b hold. (In other words: Each element of the set occurs exactly once in each row and exactly once in each column of the quasigroup's multiplication table, or Cayley table. This property ensures that the Cayley table of a finite quasigroup, and, in particular, finite group, is a Latin square.) The uniqueness requirement can be replaced by the requirement that the magma be cancellative. The unique solutions to these equations are written and . The operations '\' and '/' are called, respectively, left division and right division. The empty set equipped with the empty binary operation satisfies this definition of a quasigroup. Some authors accept the empty quasigroup but others explicitly exclude it. Universal algebra Given some algebraic structure, an identity is an equation in which all variables are tacitly universally quantified, and in which all operations are among the primitive operations proper to the structure. Algebraic structures axiomatized solely by identities are called varieties. Many standard results in universal algebra hold only for varieties. Quasigroups are varieties if left and right division are taken as primitive. A quasigroup is a type (2,2,2) algebra (i.e., equipped with three binary operations) satisfying the identities: y = x ∗ (x \ y), y = x \ (x ∗ y), y = (y / x) ∗ x, y = (y ∗ x) / x. In other words: Multiplication and division in either order, one after the other, on the same side by the same element, have no net effect. Hence if is a quasigroup according to the first definition, then is the same quasigroup in the sense of universal algebra. And vice versa: if is a quasigroup according to the sense of universal algebra, then is a quasigroup according to the first definition. Loops A loop is a quasigroup with an identity element; that is, an element, e, such that x ∗ e = x and e ∗ x = x for all x in Q. It follows that the identity element, e, is unique, and that every element of Q has unique left and right inverses (which need not be the same). A quasigroup with an idempotent element is called a pique ("pointed idempotent quasigroup"); this is a weaker notion than a loop but common nonetheless because, for example, given an abelian group, , taking its subtraction operation as quasigroup multiplication yields a pique with the group identity (zero) turned into a "pointed idempotent". (That is, there is a principal isotopy .) A loop that is associative is a group. A group can have a non-associative pique isotope, but it cannot have a nonassociative loop isotope. There are weaker associativity properties that have been given special names. For instance, a Bol loop is a loop that satisfies either: x ∗ (y ∗ (x ∗ z)) = (x ∗ (y ∗ x)) ∗ z for each x, y and z in Q (a left Bol loop), or else ((z ∗ x) ∗ y) ∗ x = z ∗ ((x ∗ y) ∗ x) for each x, y and z in Q (a right Bol loop). A loop that is both a left and right Bol loop is a Moufang loop. This is equivalent to any one of the following single Moufang identities holding for all x, y, z: x ∗ (y ∗ (x ∗ z)) = ((x ∗ y) ∗ x) ∗ z, z ∗ (x ∗ (y ∗ x)) = ((z ∗ x) ∗ y) ∗ x, (x ∗ y) ∗ (z ∗ x) = x ∗ ((y ∗ z) ∗ x), or (x ∗ y) ∗ (z ∗ x) = (x ∗ (y ∗ z)) ∗ x. Symmetries Smith (2007) names the following important properties and subclasses: Semisymmetry A quasigroup is semisymmetric if the following equivalent identities hold: x ∗ y = y / x, y ∗ x = x \ y, x = (y ∗ x) ∗ y, x = y ∗ (x ∗ y). Although this class may seem special, every quasigroup Q induces a semisymmetric quasigroup QΔ on the direct product cube Q3 via the following operation: where "//" and "\\" are the conjugate division operations given by and . Triality Total symmetry A narrower class is a totally symmetric quasigroup (sometimes abbreviated TS-quasigroup) in which all conjugates coincide as one operation: . Another way to define (the same notion of) totally symmetric quasigroup is as a semisymmetric quasigroup which also is commutative, i.e. . Idempotent total symmetric quasigroups are precisely (i.e. in a bijection with) Steiner triples, so such a quasigroup is also called a Steiner quasigroup, and sometimes the latter is even abbreviated as squag. The term sloop refers to an analogue for loops, namely, totally symmetric loops that satisfy instead of . Without idempotency, total symmetric quasigroups correspond to the geometric notion of extended
the early republic, there were two quaestors, and their duties were maintaining the public treasury, both taking in funds and deciding whom to pay them to. This continued until 421 BCE when the number of quaestors was doubled to 4. While two continued with the same duties of those that had come before, the other two had additional responsibilities, each being in service to the one of the consuls. When consuls went to war, each was assigned a quaestor. The quaestor's main responsibilities involved the distribution of war spoils between the aerarium, or public treasury, and the army. The key responsibility of the quaestor was the administration of public funds to higher-ranking officials in order to pursue their goals, whether those involve military conquests which require funding for armies or public works projects. The office of quaestor was a position bound to their superior, whether that be a consul, governor, or other magistrate, and the duties would often reflect their superiors. For example, Gaius Gracchus was quaestor under the consul Orestes in Sardinia, and many of his responsibilities involved leading military forces. While not in direct command of the army, the quaestor would be in charge of organizational and lesser duties that were a necessary part of the war machine. Roman Empire During the reign of the Emperor Constantine I, the office of quaestor was reorganized into a judicial position known as the quaestor sacri palatii. The office functioned as the primary legal adviser to the emperor, and was charged with the creation of laws as well as answers petitions to the emperor. From 440 onward, the office of the quaestor worked in conjunction with the praetorian prefect of the East to oversee the supreme tribunal, or supreme court, at Constantinople. There they heard appeals from the various subordinate courts and governors. Byzantine Empire Under the Emperor Justinian I, an additional office named quaestor was created to control police and judicial matters in Constantinople. In this new position, a quaestor was responsible for wills, as well as supervision of complaints by tenants regarding their landlords, and finally over the homeless. Notable quaestors See also Category: Roman Quaestors. Gaius Gracchus Following the death of his brother Tiberius Gracchus, Gaius Gracchus stayed out of the political spotlight for a period until he was forced to defend a good friend of his named Vettius in court. Hearing his vocal abilities, the Senate began to fear that Gaius would arouse the people in the same manner as his brother and appointed him quaestor to Gnaeus Aufidius Orestes in Sardinia to prevent him from becoming a tribune. Gaius used his position as quaestor to successfully defeat his enemies as well as gain a large amount of loyalty among his troops. Following an incident where Gaius won the support of a local village to provide for his troops, the Senate attempted to keep Gaius in Sardinia indefinitely by reappointing Orestes to stay in Sardinia. Gaius was not pleased by this and returned to Rome demanding an explanation, actions which eventually led to his election as a tribune of the people. Marcus Tullius Cicero Marcus Tullius Cicero was the Quaestor to the Propraetor/Proconsul of Sicily. He fixed major agricultural problems in the region and improved on the purchase and selling of grain. The farmers after this	would often reflect their superiors. For example, Gaius Gracchus was quaestor under the consul Orestes in Sardinia, and many of his responsibilities involved leading military forces. While not in direct command of the army, the quaestor would be in charge of organizational and lesser duties that were a necessary part of the war machine. Roman Empire During the reign of the Emperor Constantine I, the office of quaestor was reorganized into a judicial position known as the quaestor sacri palatii. The office functioned as the primary legal adviser to the emperor, and was charged with the creation of laws as well as answers petitions to the emperor. From 440 onward, the office of the quaestor worked in conjunction with the praetorian prefect of the East to oversee the supreme tribunal, or supreme court, at Constantinople. There they heard appeals from the various subordinate courts and governors. Byzantine Empire Under the Emperor Justinian I, an additional office named quaestor was created to control police and judicial matters in Constantinople. In this new position, a quaestor was responsible for wills, as well as supervision of complaints by tenants regarding their landlords, and finally over the homeless. Notable quaestors See also Category: Roman Quaestors. Gaius Gracchus Following the death of his brother Tiberius Gracchus, Gaius Gracchus stayed out of the political spotlight for a period until he was forced to defend a good friend of his named Vettius in court. Hearing his vocal abilities, the Senate began to fear that Gaius would arouse the people in the same manner as his brother and appointed him quaestor to Gnaeus Aufidius Orestes in Sardinia to prevent him from becoming a tribune. Gaius used his position as quaestor to successfully defeat his enemies as well as gain a large amount of loyalty among his troops. Following an incident where Gaius won the support of a local village to provide for his troops, the Senate attempted to keep Gaius in Sardinia indefinitely by reappointing Orestes to stay in Sardinia. Gaius was not pleased by this and returned to Rome demanding an explanation, actions which eventually led to his election as a tribune of the people. Marcus Tullius Cicero Marcus Tullius Cicero was the Quaestor to the Propraetor/Proconsul of Sicily. He fixed major agricultural problems in the region and improved on the purchase and selling of grain. The farmers after this loved Cicero and began
a simple statement such as "this completes the proof", "as required", "as desired", "as expected", "hence proved", "ergo", "so correct", or other similar locutions. Typographical forms used symbolically Due to the paramount importance of proofs in mathematics, mathematicians since the time of Euclid have developed conventions to demarcate the beginning and end of proofs. In printed English language texts, the formal statements of theorems, lemmas, and propositions are set in italics by tradition. The beginning of a proof usually follows immediately thereafter, and is indicated by the word "proof" in boldface or italics. On the other hand, several symbolic conventions exist to indicate the end of a proof. While some authors still use the classical abbreviation, Q.E.D., it is relatively uncommon in modern mathematical texts. Paul Halmos pioneered the use of a solid black square at the end of a proof as a Q.E.D symbol, a practice which has become standard, although not universal. Halmos adopted this use of a symbol from magazine typography customs in which simple geometric shapes had been used to indicate the end of an article. This symbol was later called the tombstone, the Halmos symbol, or even a halmos by mathematicians. Often the Halmos symbol is drawn on chalkboard to signal the end of a proof during a lecture, although this practice is not so common as its use in printed text. The tombstone symbol appears in TeX as the character (filled square, \blacksquare) and sometimes, as a (hollow square, \square or \Box). In the AMS Theorem Environment for LaTeX, the hollow square is the default end-of-proof symbol. Unicode explicitly provides the "end of proof" character, U+220E (∎). Some authors use other Unicode symbols to note the end of a proof, including, ▮ (U+25AE, a black vertical rectangle), and ‣ (U+2023, a triangular bullet). Other authors have adopted two forward slashes (//) or four forward slashes (////). In other cases, authors have elected to segregate proofs typographically—by displaying them as indented blocks. Modern humorous use In Joseph Heller's book Catch-22, the Chaplain, having been told to examine a forged letter allegedly signed by him (which he knew he didn't sign), verified that his name was in fact there. His investigator replied, "Then you wrote it. Q.E.D." The chaplain said he didn't write it and that it wasn't his handwriting, to which the investigator replied, "Then you signed your name in somebody else's handwriting again." In the 1978 science-fiction radio comedy, and later in the television, novel, and film adaptations of The Hitchhiker's Guide to the Galaxy, "Q.E.D." is referred to in the Guide's entry for the babel fish, when it is claimed that the babel fish – which serves the "mind-bogglingly" useful purpose of being able to translate any spoken language when inserted into a person's ear – is used as evidence for existence and non-existence of God. The exchange from the novel is as follows: "'I refuse to	Latin, and phrases such as Q.E.D. were often used to conclude proofs. Perhaps the most famous use of Q.E.D. in a philosophical argument is found in the Ethics of Baruch Spinoza, published posthumously in 1677. Written in Latin, it is considered by many to be Spinoza's magnum opus. The style and system of the book are, as Spinoza says, "demonstrated in geometrical order", with axioms and definitions followed by propositions. For Spinoza, this is a considerable improvement over René Descartes's writing style in the Meditations, which follows the form of a diary. Difference from Q.E.F. There is another Latin phrase with a slightly different meaning, usually shortened similarly, but being less common in use. , originating from the Greek geometers' closing (), meaning "which had to be done". Because of the difference in meaning, the two phrases should not be confused. Euclid used the Greek original of Quod Erat Faciendum (Q.E.F.) to close propositions that were not proofs of theorems, but constructions of geometric objects. For example, Euclid's first proposition showing how to construct an equilateral triangle, given one side, is concluded this way. English equivalent There is no common formal English equivalent, although the end of a proof may be announced with a simple statement such as "this completes the proof", "as required", "as desired", "as expected", "hence proved", "ergo", "so correct", or other similar locutions. Typographical forms used symbolically Due to the paramount importance of proofs in mathematics, mathematicians since the time of Euclid have developed conventions to demarcate the beginning and end of proofs. In printed English language texts, the formal statements of theorems, lemmas, and propositions are set in italics by tradition. The beginning of a proof usually follows immediately thereafter, and is indicated by the word "proof" in boldface or italics. On the other hand, several symbolic conventions exist to indicate the end of a proof. While some authors still use the classical abbreviation, Q.E.D., it is relatively uncommon in modern mathematical texts. Paul Halmos pioneered the use of a solid black square at the end of a proof as a Q.E.D symbol, a practice which has become standard, although not universal. Halmos adopted this use of a symbol from magazine typography customs in which simple geometric shapes had been used to indicate the end of
they live, and the quagga was the most southern-living of them all. Other large African ungulates diverged into separate species and subspecies during this period, as well, probably because of the same climate shift. The simplified cladogram below is based on the 2005 analysis (some taxa shared haplotypes and could, therefore, not be differentiated): A 2018 genetic study of plains zebras populations confirmed the quagga as a member of that species. They found no evidence for subspecific differentiation based on morphological differences between southern populations of zebras, including the quagga. Modern plains zebra populations may have originated from southern Africa, and the quagga appears to be less divergent from neighbouring populations than the northernmost living population in northeastern Uganda. Instead, the study supported a north–south genetic continuum for plains zebras, with the Ugandan population being the most distinct. Zebras from Namibia appear to be the closest genetically to the quagga. Description The quagga is believed to have been long and tall at the shoulder. Based on measurements of skins, mares were significantly longer and slightly taller than stallions, whereas the stallions of extant zebras are the largest. Its coat pattern was unique among equids: zebra-like in the front but more like a horse in the rear. It had brown and white stripes on the head and neck, brown upper parts and a white belly, tail and legs. The stripes were boldest on the head and neck and became gradually fainter further down the body, blending with the reddish brown of the back and flanks, until disappearing along the back. It appears to have had a high degree of polymorphism, with some having almost no stripes and others having patterns similar to the extinct southern population of Burchell's zebra, where the stripes covered most of the body except for the hind parts, legs and belly. It also had a broad dark dorsal stripe on its back. It had a standing mane with brown and white stripes. The only quagga to have been photographed alive was a mare at the Zoological Society of London's Zoo. Five photographs of this specimen are known, taken between 1863 and 1870. On the basis of photographs and written descriptions, many observers suggest that the stripes on the quagga were light on a dark background, unlike other zebras. The German naturalist Reinhold Rau, pioneer of the Quagga Project, claimed that this is an optical illusion: that the base colour is a creamy white and that the stripes are thick and dark. Living in the very southern end of the plains zebra's range, the quagga had a thick winter coat that moulted each year. Its skull was described as having a straight profile and a concave diastema, and as being relatively broad with a narrow occiput. Like other plains zebras, the quagga did not have a dewlap on its neck as the mountain zebra does. The 2004 morphological study found that the skeletal features of the southern Burchell's zebra population and the quagga overlapped, and that they were impossible to distinguish. Some specimens also appeared to be intermediate between the two in striping, and the extant Burchell's zebra population still exhibits limited striping. It can therefore be concluded that the two subspecies graded morphologically into each other. Today, some stuffed specimens of quaggas and southern Burchell's zebra are so similar that they are impossible to definitely identify as either, since no location data was recorded. Behaviour and ecology The quagga was the southernmost distributed plains zebra, mainly living south of the Orange River. It was a grazer, and its habitat range was restricted to the grasslands and arid interior scrubland of the Karoo region of South Africa, today forming parts of the provinces of Northern Cape, Eastern Cape, Western Cape and the Free State. These areas were known for distinctive flora and fauna and high amounts of endemism. Quaggas have been reported gathering into herds of 30–50, and sometimes travelled in a linear fashion. They may have been sympatric with Burchell's zebra between the Vaal and Orange rivers. This is disputed, and there is no evidence that they interbred. It could also have shared a small portion of its range with Hartmann's mountain zebra (Equus zebra hartmannae). Little is known about the behaviour of quaggas in the wild, and it is sometimes unclear what exact species of zebra is referred to in old reports. The only source that unequivocally describes the quagga in the Free State is that of the British military engineer and hunter William Cornwallis Harris. His 1840 account reads as follows: The geographical range of the quagga does not appear to extend to the northward of the river Vaal. The animal was formerly extremely common within the colony; but, vanishing before the strides of civilisation, is now to be found in very limited numbers and on the borders only. Beyond, on those sultry plains which are completely taken possession of by wild beasts, and may with strict propriety be termed the domains of savage nature, it occurs in interminable herds; and, although never intermixing with its more elegant congeners, it is almost invariably to be found ranging with the white-tailed gnu and with the ostrich, for the society of which bird especially it evinces the most singular predilection. Moving slowly across the profile of the ocean-like horizon, uttering a shrill, barking neigh, of which its name forms a correct imitation, long files of quaggas continually remind the early traveller of a rival caravan on its march. Bands of many hundreds are thus frequently seen doing their migration from the dreary and desolate plains of some portion of the interior, which has formed their secluded abode, seeking for those more luxuriant pastures where, during the summer months, various herbs thrust forth their leaves and flowers to form a green carpet, spangled with hues the most brilliant and diversified. The practical function of striping in zebras has been debated and it is unclear why the quagga lacked stripes on its hind parts. A cryptic function for protection from predators (stripes obscure the individual zebra in a herd) and biting flies (which are less attracted to striped objects), as well as various social functions, have been proposed for zebras in general. Differences in hind quarter stripes may have aided species recognition during stampedes of mixed herds, so that members of one subspecies or species would follow its own kind. It has also been evidence that the zebras developed striping patterns as thermoregulation to cool themselves down, and that the quagga lost them due to living in a cooler climate, although one problem with this is that the mountain zebra lives in similar environments and has a bold striping pattern. A 2014 study strongly supported the biting-fly hypothesis, and the quagga appears to have lived in areas with lesser amounts of fly activity than other zebras. A 2020 study suggested that the sexual dimorphism in size, with quagga mares being larger than stallions, could be due to the cold and droughts that affects the Karoo plateau, conditions that were even more severe in prehistoric times, such as during ice ages (other plains zebras live in warmer areas). Isolation, cold, and aridity could thereby have affected quagga evolution, including coat colour and size dimorphism. Since plains zebra mares are pregnant or lactate for much of their lives, larger size could have been a selective advantage for quagga mares, as they would therefore have more food reserves when food was scarce. Dimorphism and coat colour could also have evolved through genetic drift due to isolation, but these influences are not mutually exclusive, and could have worked	Rau, pioneer of the Quagga Project, claimed that this is an optical illusion: that the base colour is a creamy white and that the stripes are thick and dark. Living in the very southern end of the plains zebra's range, the quagga had a thick winter coat that moulted each year. Its skull was described as having a straight profile and a concave diastema, and as being relatively broad with a narrow occiput. Like other plains zebras, the quagga did not have a dewlap on its neck as the mountain zebra does. The 2004 morphological study found that the skeletal features of the southern Burchell's zebra population and the quagga overlapped, and that they were impossible to distinguish. Some specimens also appeared to be intermediate between the two in striping, and the extant Burchell's zebra population still exhibits limited striping. It can therefore be concluded that the two subspecies graded morphologically into each other. Today, some stuffed specimens of quaggas and southern Burchell's zebra are so similar that they are impossible to definitely identify as either, since no location data was recorded. Behaviour and ecology The quagga was the southernmost distributed plains zebra, mainly living south of the Orange River. It was a grazer, and its habitat range was restricted to the grasslands and arid interior scrubland of the Karoo region of South Africa, today forming parts of the provinces of Northern Cape, Eastern Cape, Western Cape and the Free State. These areas were known for distinctive flora and fauna and high amounts of endemism. Quaggas have been reported gathering into herds of 30–50, and sometimes travelled in a linear fashion. They may have been sympatric with Burchell's zebra between the Vaal and Orange rivers. This is disputed, and there is no evidence that they interbred. It could also have shared a small portion of its range with Hartmann's mountain zebra (Equus zebra hartmannae). Little is known about the behaviour of quaggas in the wild, and it is sometimes unclear what exact species of zebra is referred to in old reports. The only source that unequivocally describes the quagga in the Free State is that of the British military engineer and hunter William Cornwallis Harris. His 1840 account reads as follows: The geographical range of the quagga does not appear to extend to the northward of the river Vaal. The animal was formerly extremely common within the colony; but, vanishing before the strides of civilisation, is now to be found in very limited numbers and on the borders only. Beyond, on those sultry plains which are completely taken possession of by wild beasts, and may with strict propriety be termed the domains of savage nature, it occurs in interminable herds; and, although never intermixing with its more elegant congeners, it is almost invariably to be found ranging with the white-tailed gnu and with the ostrich, for the society of which bird especially it evinces the most singular predilection. Moving slowly across the profile of the ocean-like horizon, uttering a shrill, barking neigh, of which its name forms a correct imitation, long files of quaggas continually remind the early traveller of a rival caravan on its march. Bands of many hundreds are thus frequently seen doing their migration from the dreary and desolate plains of some portion of the interior, which has formed their secluded abode, seeking for those more luxuriant pastures where, during the summer months, various herbs thrust forth their leaves and flowers to form a green carpet, spangled with hues the most brilliant and diversified. The practical function of striping in zebras has been debated and it is unclear why the quagga lacked stripes on its hind parts. A cryptic function for protection from predators (stripes obscure the individual zebra in a herd) and biting flies (which are less attracted to striped objects), as well as various social functions, have been proposed for zebras in general. Differences in hind quarter stripes may have aided species recognition during stampedes of mixed herds, so that members of one subspecies or species would follow its own kind. It has also been evidence that the zebras developed striping patterns as thermoregulation to cool themselves down, and that the quagga lost them due to living in a cooler climate, although one problem with this is that the mountain zebra lives in similar environments and has a bold striping pattern. A 2014 study strongly supported the biting-fly hypothesis, and the quagga appears to have lived in areas with lesser amounts of fly activity than other zebras. A 2020 study suggested that the sexual dimorphism in size, with quagga mares being larger than stallions, could be due to the cold and droughts that affects the Karoo plateau, conditions that were even more severe in prehistoric times, such as during ice ages (other plains zebras live in warmer areas). Isolation, cold, and aridity could thereby have affected quagga evolution, including coat colour and size dimorphism. Since plains zebra mares are pregnant or lactate for much of their lives, larger size could have been a selective advantage for quagga mares, as they would therefore have more food reserves when food was scarce. Dimorphism and coat colour could also have evolved through genetic drift due to isolation, but these influences are not mutually exclusive, and could have worked together. Relationship with humans Quaggas have been identified in cave art attributed to the indigenous San people of Southern Africa. As it was easy to find and kill, the quagga was hunted by early Dutch settlers and later by Afrikaners to provide meat or for their skins. The skins were traded or used locally. The quagga was probably vulnerable to extinction due to its limited distribution, and it may have competed with domestic livestock for forage. Local farmers used them as guards for their livestock, as they were likely to attack intruders. Quaggas were said to be lively and highly strung, especially the stallions. Quaggas were brought to European zoos, and an attempt at captive breeding at London Zoo, but was halted when a lone stallion killed itself by bashing itself against a wall after losing its temper. On the other hand, captive quaggas in European zoos were said to be tamer and more docile than Burchell's zebra. One specimen was reported to have lived in captivity for 21 years and 4 months, dying in 1872. The quagga was long regarded a suitable candidate for domestication, as it counted as the most docile of the zebras. The Dutch colonists in South Africa had considered this possibility, because their imported work horses did not perform very well in the extreme climate and regularly fell prey to the feared African horse sickness. In 1843, the English naturalist Charles Hamilton Smith wrote that the quagga was 'unquestionably best calculated for domestication, both as regards strength and docility'. Some mentions have been given of tame or domesticated quaggas in South Africa. In Europe, two stallions were used to drive a phaeton by the sheriff of London in the early 19th century. In an attempt at domesticating the quagga, the British lord George Douglas, 16th Earl of Morton obtained a single male which he bred with a female horse of partial Arabian ancestry. This produced a female hybrid with stripes on its back and legs. Lord Morton's mare was sold and was subsequently bred with a black stallion, resulting in offspring that again had zebra stripes. An account of this was published in 1820 by the Royal Society. It is unknown what happened to the hybrid mare itself. This led to new ideas on telegony, referred to as pangenesis by the British naturalist Charles Darwin. At the close of the 19th century, the Scottish zoologist James Cossar Ewart argued against these ideas and proved, with several cross-breeding experiments, that zebra stripes could appear as an atavistic trait at any time. There are 23 known stuffed and mounted quagga specimens throughout the world, including a juvenile, two foals, and a foetus. In addition, a mounted head and neck, a foot, seven complete skeletons, and samples of various tissues remain. A 24th mounted specimen was destroyed in Königsberg, Germany, during World War II, and various skeletons and bones have also been lost. Extinction The quagga had disappeared from much of its range by the 1850s. The last population in the wild, in the Orange Free State, was extirpated in the late 1870s. The last known wild quagga died in 1878. The specimen in London died in 1872 and the one in Berlin in 1875. The last captive quagga, a female in Amsterdam's Natura Artis Magistra zoo, lived there from 9 May 1867 until it died on 12 August 1883, but its origin and cause of death are unclear. Its death was not recognised as signifying the extinction of its kind at the time, and the zoo requested another specimen; hunters believed it could still be found "closer to the interior" in the Cape Colony. Since locals used the term quagga to refer to all zebras,
operating systems. It is used to view picture files from the still image formats that QuickTime supports. In macOS, it is replaced by Preview. As of version 7.7.9, the Windows version requires one to go to their "Windows Uninstall Or Change A Program" screen to "modify" their installation of QuickTime 7 to include the "Legacy QuickTime Feature" of "QuickTime PictureViewer." File formats The native file format for QuickTime video, QuickTime File Format, specifies a multimedia container file that contains one or more tracks, each of which stores a particular type of data: audio, video, effects, or text (e.g. for subtitles). Each track either contains a digitally encoded media stream (using a specific format) or a data reference to the media stream located in another file. The ability to contain abstract data references for the media data, and the separation of the media data from the media offsets and the track edit lists means that QuickTime is particularly suited for editing, as it is capable of importing and editing in place (without data copying). Other file formats that QuickTime supports natively (to varying degrees) include AIFF, WAV, DV-DIF, MP3, and MPEG program stream. With additional QuickTime Components, it can also support ASF, DivX Media Format, Flash Video, Matroska, Ogg, and many others. QuickTime and MPEG-4 On February 11, 1998, the ISO approved the QuickTime file format as the basis of the MPEG‑4 file format. The MPEG-4 file format specification was created on the basis of the QuickTime format specification published in 2001. The MP4 (.mp4) file format was published in 2001 as the revision of the MPEG-4 Part 1: Systems specification published in 1999 (ISO/IEC 14496-1:2001). In 2003, the first version of MP4 format was revised and replaced by MPEG-4 Part 14: MP4 file format (ISO/IEC 14496-14:2003). The MP4 file format was generalized into the ISO Base Media File Format ISO/IEC 14496-12:2004, which defines a general structure for time-based media files. It in turn is used as the basis for other multimedia file formats (for example 3GP, Motion JPEG 2000). A list of all registered extensions for ISO Base Media File Format is published on the official registration authority website www.mp4ra.org. This registration authority for code-points in "MP4 Family" files is Apple Computer Inc. and it is named in Annex D (informative) in MPEG-4 Part 12. By 2000, MPEG-4 formats became industry standards, first appearing with support in QuickTime 6 in 2002. Accordingly, the MPEG-4 container is designed to capture, edit, archive, and distribute media, unlike the simple file-as-stream approach of MPEG-1 and MPEG-2. Profile support QuickTime 6 added limited support for MPEG-4, specifically encoding and decoding using Simple Profile (SP). Advanced Simple Profile (ASP) features, like B-frames, were unsupported (in contrast with, for example, encoders such as XviD or 3ivx). QuickTime 7 supports the H.264 encoder and decoder. Container benefits Because both MOV and MP4 containers can use the same MPEG-4 codecs, they are mostly interchangeable in a QuickTime-only environment. MP4, being an international standard, has more support. This is especially true on hardware devices, such as the Sony PSP and various DVD players, on the software side, most DirectShow / Video for Windows codec packs include a MP4 parser, but not one for MOV. In QuickTime Pro's MPEG-4 Export dialog, an option called "Passthrough" allows a clean export to MP4 without affecting the audio or video streams. QuickTime 7 now supports multi-channel AAC-LC and HE-AAC audio (used, for example, in the high-definition trailers on Apple's site), for both .MOV and .MP4 containers. History Apple released the first version of QuickTime on December 2, 1991 as a multimedia add-on for System 6 and later. The lead developer of QuickTime, Bruce Leak, ran the first public demonstration at the May 1991 Worldwide Developers Conference, where he played Apple's famous 1984 advertisement in a window at 320×240 pixels resolution. QuickTime 1.x The original video codecs included: the Animation codec, which used run-length encoding and was better suited to cartoon-type images with large areas of flat color the Apple Video codec (also known as "Road Pizza"), suited to normal live-action video. the Graphics codec, for 8-bit images, including ones that had undergone dithering The first commercial project produced using QuickTime 1.0 was the CD-ROM From Alice to Ocean. The first publicly visible use of QuickTime was Ben & Jerry's interactive factory tour (dubbed The Rik & Joe Show after its in-house developers). The Rik and Joe Show was demonstrated onstage at MacWorld in San Francisco when John Sculley announced QuickTime. Apple released QuickTime 1.5 for Mac OS in the latter part of 1992. This added the SuperMac-developed Cinepak vector-quantization video codec (initially known as Compact Video). It could play video at 320×240 resolution at 30 frames per second on a 25 MHz Motorola 68040 CPU. It also added text tracks, which allowed for captioning, lyrics and other potential uses. Apple contracted San Francisco Canyon Company to port QuickTime to the Windows platform. Version 1.0 of QuickTime for Windows provided only a subset of the full QuickTime API, including only movie playback functions driven through the standard movie controller. QuickTime 1.6 came out the following year. Version 1.6.2 first incorporated the "QuickTime PowerPlug" which replaced some components with PowerPC-native code when running on PowerPC Macs. QuickTime 2.x Apple released QuickTime 2.0 for System Software 7 in June 1994—the only version never released for free. It added support for music tracks, which contained the equivalent of MIDI data and which could drive a sound-synthesis engine built into QuickTime itself (using a limited set of instrument sounds licensed from Roland), or any external MIDI-compatible hardware, thereby producing sounds using only small amounts of movie data. Following Bruce Leak's departure to Web TV, the leadership of the QuickTime team was taken over by Peter Hoddie. QuickTime 2.0 for Windows appeared in November 1994 under the leadership of Paul Charlton. As part of the development effort for cross-platform QuickTime, Charlton (as architect and technical lead), along with ace individual contributor Michael Kellner and a small highly effective team including Keith Gurganus, ported a subset of the Macintosh Toolbox to Intel and other platforms (notably, MIPS and SGI Unix variants) as the enabling infrastructure for the QuickTime Media Layer (QTML) which was first demonstrated at the Apple Worldwide Developers Conference (WWDC) in May 1996. The QTML later became the foundation for the Carbon API which allowed legacy Macintosh applications to run on the Darwin kernel in Mac OS X. The next versions, 2.1 and 2.5, reverted to the previous model of giving QuickTime away for free. They improved the music support and added sprite tracks which allowed the creation of complex animations with the addition of little more than the static sprite images to the size of the movie. QuickTime 2.5 also fully integrated QuickTime VR 2.0.1 into QuickTime as a QuickTime extension. On January 16, 1997, Apple released the QuickTime MPEG Extension (PPC only) as an add-on to QuickTime 2.5, which added software MPEG-1 playback capabilities to QuickTime. Lawsuit against San Francisco Canyon In 1994, Apple filed suit against software developer San Francisco Canyon for intellectual property infringement and breach of contract. Apple alleged that San Francisco Canyon had helped develop Video for Windows using several hundred lines of unlicensed QuickTime source code. They were contracted by Intel to help make Video for Windows better use system resources on Intel processors, which was subsequently unilaterally removed. Microsoft and Intel were added to the lawsuit in 1995. The suit ended in a settlement in 1997. QuickTime 3.x The release of QuickTime 3.0 for Mac OS on March 30, 1998 introduced the now-standard revenue model of releasing the software for free, but with additional features of the Apple-provided MoviePlayer application that end-users could only unlock by buying a QuickTime Pro license code. Since the "Pro" features were the same as the existing features in QuickTime 2.5, any previous user of QuickTime could continue to use an older version of the central MoviePlayer application for the remaining lifespan of Mac OS to 2002; indeed, since these additional features were limited to MoviePlayer, any other QuickTime-compatible application remained unaffected. QuickTime 3.0 added support for graphics importer components that could read images from GIF, JPEG, TIFF and other file formats, and video output components which served primarily to export movie data via FireWire. Apple also licensed several third-party technologies for inclusion in QuickTime 3.0, including the Sorenson Video codec for advanced video compression, the QDesign Music codec for substantial audio compression, and the complete Roland Sound Canvas instrument set and GS Format extensions for improved playback of MIDI music files. It also added video effects which programmers could apply in real-time to video tracks. Some of these effects would even respond to mouse clicks by the user, as part of the new movie interaction support (known as wired movies). QuickTime interactive During the development cycle for QuickTime 3.0, part of the engineering team was working on a more advanced version of QuickTime to be known as QuickTime interactive or QTi. Although similar in concept to the wired movies feature released as part of QuickTime 3.0, QuickTime interactive was much more ambitious. It allowed any QuickTime movie to be a fully interactive and programmable container for media. A special track type was added that contained an interpreter for a custom programming language based on 68000 assembly language. This supported a comprehensive user interaction model for mouse and keyboard event handling based in part on the AML language from the Apple Media Tool. The QuickTime interactive movie was to have been the playback format for the next generation of HyperCard authoring tool. Both the QuickTime interactive and the HyperCard 3.0 projects were canceled in order to concentrate engineering resources on streaming support for QuickTime 4.0, and the projects were never released to the public. QuickTime 4.x Apple released QuickTime 4.0 on June 8, 1999 for Mac OS 7.5.5 through 8.6 (later Mac OS 9) and Windows 95, Windows 98, and Windows NT. Three minor updates (versions 4.0.1, 4.0.2, and 4.0.3) followed. It introduced features that most users now consider basic: Graphics exporter components, which could write some of the same formats that the previously introduced importers could read. (GIF support was omitted, possibly because of the LZW patent.) Support for the QDesign Music 2 and MPEG-1 Layer 3 audio (MP3). QuickTime 4 was the first version to support streaming. It was accompanied by the release of the free QuickTime Streaming Server version 1.0. QuickTime 4 Player introduced brushed metal to the Macintosh user interface. On December 17, 1999, Apple provided QuickTime 4.1, this version's first major update. Two minor versions (4.1.1 and 4.1.2) followed. The most notable improvements in the 4.1.x family were: Support for files larger than 2.0 GB in Mac OS 9. (This is a consequence of Mac OS 9 requiring the HFS Plus filesystem.) Variable bit rate (VBR) support for MPEG-1 Layer 3 (MP3) audio. Support for Synchronized Multimedia Integration Language (SMIL). Introduction of AppleScript support in Mac OS. The requirement of a PowerPC processor for Mac OS systems. QuickTime 4.1 dropped support for Motorola 68k Macintosh systems. QuickTime 5.x QuickTime 5 was one of the shortest-lived versions of QuickTime, released in April 2001 and superseded by QuickTime 6 a little over a year later. This version was the last to have greater capabilities under Mac OS 9 than under Mac OS X, and the last version of QuickTime to support Mac OS versions 7.5.5 through 8.5.1 on a PowerPC Mac and Windows 95. Version 5.0 was initially only released for Mac OS and Mac OS X on April 14, 2001, and version 5.0.1 followed shortly thereafter on April 23, 2001, supporting the classic Mac OS, Mac OS X, and Windows. Three more updates to QuickTime 5 (versions 5.0.2, 5.0.4, and 5.0.5) were released over its short lifespan. QuickTime 5 delivered the following enhancements: MPEG-1 playback for Windows, and updated MPEG-1 Layer 3 audio support for all systems. Sorenson Video 3 playback and export (added with the 5.0.2 update). Realtime rendering of effects & transitions in DV files, including enhancements to DV rendering, multiprocessor support, and Altivec enhancements for PowerPC G4 systems. Flash 4 playback and export. A new QuickTime VR engine, adding support for cubic VR panoramas. QuickTime 6.x On July 15, 2002, Apple released QuickTime 6.0, providing the following features: MPEG-4 playback, import, and export, including MPEG-4 Part 2 video and AAC Audio. Support for Flash 5, JPEG 2000, and improved Exif handling. Instant-on streaming playback. MPEG-2 playback (via the purchase of Apple's MPEG-2 Playback Component). Scriptable ActiveX control. QuickTime 6 was initially available for Mac OS 8.6 – 9.x, Mac OS X (10.1.5 minimum), and Windows 98, Me, 2000, and XP. Development of QuickTime 6 for Mac OS slowed considerably in early 2003, after the release of Mac OS X v10.2 in August 2002. QuickTime 6 for Mac OS continued on the 6.0.x path, eventually stopping with version 6.0.3. QuickTime 6.1 & 6.1.1 for Mac OS X v10.1 and Mac OS X v10.2 (released October 22, 2002) and QuickTime 6.1 for Windows (released March 31, 2003) offered ISO-Compliant MPEG-4 file creation and fixed the CAN-2003-0168 vulnerability. Apple released QuickTime 6.2 exclusively for Mac OS X on April 29, 2003 to provide support for iTunes 4, which allowed AAC encoding for songs in the iTunes library. (iTunes was not available for Windows until October 2003.) On June 3, 2003, Apple released QuickTime 6.3, delivering the following: Support for 3GPP, including 3G Text, video, and audio (AAC and AMR codecs). Support for the .3gp, .amr, and .sdv file formats via separate component. QuickTime 6.4, released on October 16, 2003 for Mac OS X v10.2, Mac OS X v10.3, and Windows, added the following: Addition of the Apple Pixlet codec (only for Mac OS X v10.3 and later). ColorSync support. Integrated 3GPP. On December 18, 2003, Apple released QuickTime 6.5, supporting the same systems as version 6.4. Versions 6.5.1 and 6.5.2 followed on April 28, 2004 and October 27, 2004. These versions would be the last to support Windows 98 and Me. The 6.5 family added the following features: 3GPP2 and AMC mobile multimedia formats. QCELP voice code. Apple Lossless (in version 6.5.1). QuickTime 6.5.3 was released on October 12, 2005 for Mac OS X v10.2.8 after the release of QuickTime 7.0, fixing a number of security issues. QuickTime 7.x Initially released on April 29, 2005 in conjunction with Mac OS X v10.4 (for version 10.3.9 and 10.4.x), QuickTime 7.0 featured the following: Improved MPEG-4 compliance. A H.264/MPEG-4 AVC codec (does not support the AVCHD H.264 AVC format from Sony HD camcorders). Support for Core Audio, a set of Application programming interfaces that supports high resolution sound and replaces Sound Manager. Support for using Core Image filters in Mac OS X v10.4 on live video (Not to be confused with Core Video). Support for Quartz Composer (.qtz) animations. Support for distinct decode order and display order. QuickTime Kit Framework (QTKit), a Cocoa framework for QuickTime. After a couple of preview Windows releases, Apple released 7.0.2 as the first stable release on September 7, 2005 for Windows 2000 and Windows XP. Version 7.0.4, released on January 10, 2006 was the first universal binary version. But it suffered numerous bugs, including	2.0 for System Software 7 in June 1994—the only version never released for free. It added support for music tracks, which contained the equivalent of MIDI data and which could drive a sound-synthesis engine built into QuickTime itself (using a limited set of instrument sounds licensed from Roland), or any external MIDI-compatible hardware, thereby producing sounds using only small amounts of movie data. Following Bruce Leak's departure to Web TV, the leadership of the QuickTime team was taken over by Peter Hoddie. QuickTime 2.0 for Windows appeared in November 1994 under the leadership of Paul Charlton. As part of the development effort for cross-platform QuickTime, Charlton (as architect and technical lead), along with ace individual contributor Michael Kellner and a small highly effective team including Keith Gurganus, ported a subset of the Macintosh Toolbox to Intel and other platforms (notably, MIPS and SGI Unix variants) as the enabling infrastructure for the QuickTime Media Layer (QTML) which was first demonstrated at the Apple Worldwide Developers Conference (WWDC) in May 1996. The QTML later became the foundation for the Carbon API which allowed legacy Macintosh applications to run on the Darwin kernel in Mac OS X. The next versions, 2.1 and 2.5, reverted to the previous model of giving QuickTime away for free. They improved the music support and added sprite tracks which allowed the creation of complex animations with the addition of little more than the static sprite images to the size of the movie. QuickTime 2.5 also fully integrated QuickTime VR 2.0.1 into QuickTime as a QuickTime extension. On January 16, 1997, Apple released the QuickTime MPEG Extension (PPC only) as an add-on to QuickTime 2.5, which added software MPEG-1 playback capabilities to QuickTime. Lawsuit against San Francisco Canyon In 1994, Apple filed suit against software developer San Francisco Canyon for intellectual property infringement and breach of contract. Apple alleged that San Francisco Canyon had helped develop Video for Windows using several hundred lines of unlicensed QuickTime source code. They were contracted by Intel to help make Video for Windows better use system resources on Intel processors, which was subsequently unilaterally removed. Microsoft and Intel were added to the lawsuit in 1995. The suit ended in a settlement in 1997. QuickTime 3.x The release of QuickTime 3.0 for Mac OS on March 30, 1998 introduced the now-standard revenue model of releasing the software for free, but with additional features of the Apple-provided MoviePlayer application that end-users could only unlock by buying a QuickTime Pro license code. Since the "Pro" features were the same as the existing features in QuickTime 2.5, any previous user of QuickTime could continue to use an older version of the central MoviePlayer application for the remaining lifespan of Mac OS to 2002; indeed, since these additional features were limited to MoviePlayer, any other QuickTime-compatible application remained unaffected. QuickTime 3.0 added support for graphics importer components that could read images from GIF, JPEG, TIFF and other file formats, and video output components which served primarily to export movie data via FireWire. Apple also licensed several third-party technologies for inclusion in QuickTime 3.0, including the Sorenson Video codec for advanced video compression, the QDesign Music codec for substantial audio compression, and the complete Roland Sound Canvas instrument set and GS Format extensions for improved playback of MIDI music files. It also added video effects which programmers could apply in real-time to video tracks. Some of these effects would even respond to mouse clicks by the user, as part of the new movie interaction support (known as wired movies). QuickTime interactive During the development cycle for QuickTime 3.0, part of the engineering team was working on a more advanced version of QuickTime to be known as QuickTime interactive or QTi. Although similar in concept to the wired movies feature released as part of QuickTime 3.0, QuickTime interactive was much more ambitious. It allowed any QuickTime movie to be a fully interactive and programmable container for media. A special track type was added that contained an interpreter for a custom programming language based on 68000 assembly language. This supported a comprehensive user interaction model for mouse and keyboard event handling based in part on the AML language from the Apple Media Tool. The QuickTime interactive movie was to have been the playback format for the next generation of HyperCard authoring tool. Both the QuickTime interactive and the HyperCard 3.0 projects were canceled in order to concentrate engineering resources on streaming support for QuickTime 4.0, and the projects were never released to the public. QuickTime 4.x Apple released QuickTime 4.0 on June 8, 1999 for Mac OS 7.5.5 through 8.6 (later Mac OS 9) and Windows 95, Windows 98, and Windows NT. Three minor updates (versions 4.0.1, 4.0.2, and 4.0.3) followed. It introduced features that most users now consider basic: Graphics exporter components, which could write some of the same formats that the previously introduced importers could read. (GIF support was omitted, possibly because of the LZW patent.) Support for the QDesign Music 2 and MPEG-1 Layer 3 audio (MP3). QuickTime 4 was the first version to support streaming. It was accompanied by the release of the free QuickTime Streaming Server version 1.0. QuickTime 4 Player introduced brushed metal to the Macintosh user interface. On December 17, 1999, Apple provided QuickTime 4.1, this version's first major update. Two minor versions (4.1.1 and 4.1.2) followed. The most notable improvements in the 4.1.x family were: Support for files larger than 2.0 GB in Mac OS 9. (This is a consequence of Mac OS 9 requiring the HFS Plus filesystem.) Variable bit rate (VBR) support for MPEG-1 Layer 3 (MP3) audio. Support for Synchronized Multimedia Integration Language (SMIL). Introduction of AppleScript support in Mac OS. The requirement of a PowerPC processor for Mac OS systems. QuickTime 4.1 dropped support for Motorola 68k Macintosh systems. QuickTime 5.x QuickTime 5 was one of the shortest-lived versions of QuickTime, released in April 2001 and superseded by QuickTime 6 a little over a year later. This version was the last to have greater capabilities under Mac OS 9 than under Mac OS X, and the last version of QuickTime to support Mac OS versions 7.5.5 through 8.5.1 on a PowerPC Mac and Windows 95. Version 5.0 was initially only released for Mac OS and Mac OS X on April 14, 2001, and version 5.0.1 followed shortly thereafter on April 23, 2001, supporting the classic Mac OS, Mac OS X, and Windows. Three more updates to QuickTime 5 (versions 5.0.2, 5.0.4, and 5.0.5) were released over its short lifespan. QuickTime 5 delivered the following enhancements: MPEG-1 playback for Windows, and updated MPEG-1 Layer 3 audio support for all systems. Sorenson Video 3 playback and export (added with the 5.0.2 update). Realtime rendering of effects & transitions in DV files, including enhancements to DV rendering, multiprocessor support, and Altivec enhancements for PowerPC G4 systems. Flash 4 playback and export. A new QuickTime VR engine, adding support for cubic VR panoramas. QuickTime 6.x On July 15, 2002, Apple released QuickTime 6.0, providing the following features: MPEG-4 playback, import, and export, including MPEG-4 Part 2 video and AAC Audio. Support for Flash 5, JPEG 2000, and improved Exif handling. Instant-on streaming playback. MPEG-2 playback (via the purchase of Apple's MPEG-2 Playback Component). Scriptable ActiveX control. QuickTime 6 was initially available for Mac OS 8.6 – 9.x, Mac OS X (10.1.5 minimum), and Windows 98, Me, 2000, and XP. Development of QuickTime 6 for Mac OS slowed considerably in early 2003, after the release of Mac OS X v10.2 in August 2002. QuickTime 6 for Mac OS continued on the 6.0.x path, eventually stopping with version 6.0.3. QuickTime 6.1 & 6.1.1 for Mac OS X v10.1 and Mac OS X v10.2 (released October 22, 2002) and QuickTime 6.1 for Windows (released March 31, 2003) offered ISO-Compliant MPEG-4 file creation and fixed the CAN-2003-0168 vulnerability. Apple released QuickTime 6.2 exclusively for Mac OS X on April 29, 2003 to provide support for iTunes 4, which allowed AAC encoding for songs in the iTunes library. (iTunes was not available for Windows until October 2003.) On June 3, 2003, Apple released QuickTime 6.3, delivering the following: Support for 3GPP, including 3G Text, video, and audio (AAC and AMR codecs). Support for the .3gp, .amr, and .sdv file formats via separate component. QuickTime 6.4, released on October 16, 2003 for Mac OS X v10.2, Mac OS X v10.3, and Windows, added the following: Addition of the Apple Pixlet codec (only for Mac OS X v10.3 and later). ColorSync support. Integrated 3GPP. On December 18, 2003, Apple released QuickTime 6.5, supporting the same systems as version 6.4. Versions 6.5.1 and 6.5.2 followed on April 28, 2004 and October 27, 2004. These versions would be the last to support Windows 98 and Me. The 6.5 family added the following features: 3GPP2 and AMC mobile multimedia formats. QCELP voice code. Apple Lossless (in version 6.5.1). QuickTime 6.5.3 was released on October 12, 2005 for Mac OS X v10.2.8 after the release of QuickTime 7.0, fixing a number of security issues. QuickTime 7.x Initially released on April 29, 2005 in conjunction with Mac OS X v10.4 (for version 10.3.9 and 10.4.x), QuickTime 7.0 featured the following: Improved MPEG-4 compliance. A H.264/MPEG-4 AVC codec (does not support the AVCHD H.264 AVC format from Sony HD camcorders). Support for Core Audio, a set of Application programming interfaces that supports high resolution sound and replaces Sound Manager. Support for using Core Image filters in Mac OS X v10.4 on live video (Not to be confused with Core Video). Support for Quartz Composer (.qtz) animations. Support for distinct decode order and display order. QuickTime Kit Framework (QTKit), a Cocoa framework for QuickTime. After a couple of preview Windows releases, Apple released 7.0.2 as the first stable release on September 7, 2005 for Windows 2000 and Windows XP. Version 7.0.4, released on January 10, 2006 was the first universal binary version. But it suffered numerous bugs, including a buffer overrun, which is more problematic to most users. Apple dropped support for Windows 2000 with the release of QuickTime 7.2 on July 11, 2007. The last version available for Windows 2000, 7.1.6, contains numerous security vulnerabilities. References to this version have been removed from the QuickTime site, but it can be downloaded from Apple's support section. Apple has not indicated that they will be providing any further security updates for older versions. QuickTime 7.2 is the first version for Windows Vista. Apple dropped support for Flash content in QuickTime 7.3, breaking content that relied on Flash for interactivity, or animation tracks. Security concerns seem to be part of the decision. Flash flv files can still be played in QuickTime if the free Perian plugin is added. In QuickTime 7.3, a processor that supports SSE is required. QuickTime 7.4 does not require SSE. Unlike versions 7.2 and 7.3, QuickTime 7.4 cannot be installed on Windows XP without service packs or with Service Pack 1/1A installed (its setup program checks if Service Pack 2 is installed). QuickTime 7.5 was released on June 10, 2008. QuickTime 7.5.5 was released on September 9, 2008, which requires Mac OS X v10.4 or higher, dropping 10.3 support. QuickTime 7.6 was released on January 21, 2009. QuickTime 7.7 was released on August 3, 2011. QuickTime 7.6.6 is available for OS X, 10.6.3 Snow Leopard until 10.14 Mojave, as 10.15 Catalina will only support 64-bit applications. There is a 7.7 release of QuickTime 7 for OS X, but it is only for Leopard 10.5. QuickTime 7.7.6 is the last release for Windows XP. As it's since version 7.4, they can be installed here only when Service Pack 2 or 3 is installed. QuickTime 7.7.9 is the last Windows release of QuickTime. Apple stopped supporting QuickTime on Windows afterwards. Safari 12, released on September 17, 2018 for macOS Sierra and macOS High Sierra (and the default browser included on macOS Mojave released on September 24, 2018), which drops support for NPAPI plug-ins (except for Adobe Flash) dropped its support for QuickTime 7's web plugin. On September 24, 2018, Apple dropped support for the macOS version of QuickTime 7. This effectively marked the end of the technology in Apple's codec and web development. Starting with macOS Catalina, QuickTime 7 applications, image, audio and video codecs will no longer be compatible with macOS or supported by Apple. QuickTime X (QuickTime Player v10.x) QuickTime X (pronounced QuickTime Ten) was initially demonstrated at WWDC on June 8, 2009, and shipped with Mac OS X v10.6. It includes visual chapters, conversion, sharing to YouTube, video editing, capture of video and audio streams, screen recording, GPU acceleration, and live streaming. But it removed support for various widely used formats, in particular the omission of MIDI caused significant inconvenience and trouble to many musicians and their potential audiences. In addition, a screen recorder is featured which records whatever is on the screen. However it is not possible to capture certain Digital rights management protected content. This includes iTunes/Apple TV video purchases, or any content protected by Apple's FairPlay DRM technology. While Safari uses FairPlay, Google Chrome, and Firefox use Widevine for DRM, whose content is not protected from QuickTime screen capturing. The reason for the jump in numbering from 7 to 10 (X) was to indicate a similar break with the previous versions of the product that Mac OS X indicated. QuickTime X is fundamentally different from previous versions, in that it is provided as a Cocoa (Objective-C) framework and breaks compatibility with the previous QuickTime 7 C-based APIs that were previously used. QuickTime X was completely rewritten to implement modern audio video codecs in 64-bit. QuickTime X is a combination of two technologies: QuickTime Kit
Quoin or Du Quoin may also refer to: Places Quoin Bluff, Western Australia Quoin Hill Airfield, Vanuatu Du Quoin, Illinois, USA Du Quoin station Du Quoin State Fairgrounds DuQuoin	Quoin or Du Quoin may also refer to: Places Quoin Bluff, Western Australia Quoin Hill Airfield, Vanuatu Du Quoin,
is the most common variety of crystalline quartz. The white color is caused by minute fluid inclusions of gas, liquid, or both, trapped during crystal formation, making it of little value for optical and quality gemstone applications. Rose quartz Rose quartz is a type of quartz which exhibits a pale pink to rose red hue. The color is usually considered as due to trace amounts of titanium, iron, or manganese, in the material. Some rose quartz contains microscopic rutile needles which produces an asterism in transmitted light. Recent X-ray diffraction studies suggest that the color is due to thin microscopic fibers of possibly dumortierite within the quartz. Additionally, there is a rare type of pink quartz (also frequently called crystalline rose quartz) with color that is thought to be caused by trace amounts of phosphate or aluminium. The color in crystals is apparently photosensitive and subject to fading. The first crystals were found in a pegmatite found near Rumford, Maine, US and in Minas Gerais, Brazil. Smoky quartz Smoky quartz is a gray, translucent version of quartz. It ranges in clarity from almost complete transparency to a brownish-gray crystal that is almost opaque. Some can also be black. The translucency results from natural irradiation acting on minute traces of aluminum in the crystal structure. Prasiolite Prasiolite, also known as vermarine, is a variety of quartz that is green in color. Since 1950, almost all natural prasiolite has come from a small Brazilian mine, but it is also seen in Lower Silesia in Poland. Naturally occurring prasiolite is also found in the Thunder Bay area of Canada. It is a rare mineral in nature; most green quartz is heat-treated amethyst. Synthetic and artificial treatments Not all varieties of quartz are naturally occurring. Some clear quartz crystals can be treated using heat or gamma-irradiation to induce color where it would not otherwise have occurred naturally. Susceptibility to such treatments depends on the location from which the quartz was mined. Prasiolite, an olive colored material, is produced by heat treatment; natural prasiolite has also been observed in Lower Silesia in Poland. Although citrine occurs naturally, the majority is the result of heat-treating amethyst or smoky quartz. Carnelian has been heat-treated to deepen its color since prehistoric times. Because natural quartz is often twinned, synthetic quartz is produced for use in industry. Large, flawless, single crystals are synthesized in an autoclave via the hydrothermal process. Like other crystals, quartz may be coated with metal vapors to give it an attractive sheen. Occurrence Quartz is a defining constituent of granite and other felsic igneous rocks. It is very common in sedimentary rocks such as sandstone and shale. It is a common constituent of schist, gneiss, quartzite and other metamorphic rocks. Quartz has the lowest potential for weathering in the Goldich dissolution series and consequently it is very common as a residual mineral in stream sediments and residual soils. Generally a high presence of quartz suggests a "mature" rock, since it indicates the rock has been heavily reworked and quartz was the primary mineral that endured heavy weathering. While the majority of quartz crystallizes from molten magma, quartz also chemically precipitates from hot hydrothermal veins as gangue, sometimes with ore minerals like gold, silver and copper. Large crystals of quartz are found in magmatic pegmatites. Well-formed crystals may reach several meters in length and weigh hundreds of kilograms. Naturally occurring quartz crystals of extremely high purity, necessary for the crucibles and other equipment used for growing silicon wafers in the semiconductor industry, are expensive and rare. A major mining location for high purity quartz is the Spruce Pine Gem Mine in Spruce Pine, North Carolina, United States. Quartz may also be found in Caldoveiro Peak, in Asturias, Spain. The largest documented single crystal of quartz was found near Itapore, Goiaz, Brazil; it measured approximately 6.1×1.5×1.5 m and weighed 39,916 kilograms. Mining Quartz is extracted from open pit mines. Miners occasionally use explosives to expose deep pockets of quartz. More frequently, bulldozers and backhoes are used to remove soil and clay and expose quartz veins, which are then worked using hand tools. Care must be taken to avoid sudden temperature changes that may damage the crystals. Almost all the industrial demand for quartz crystal (used primarily in electronics) is met with synthetic quartz produced by the hydrothermal process. However, synthetic crystals are less prized for use as gemstones. The popularity of crystal healing has increased the demand for natural quartz crystals, which are now often mined in developing countries using primitive mining methods, sometimes involving child labor. Related silica minerals Tridymite and cristobalite are high-temperature polymorphs of SiO2 that occur in high-silica volcanic rocks. Coesite is a denser polymorph of SiO2 found in some meteorite impact sites and in metamorphic rocks formed at pressures greater than those typical of the Earth's crust. Stishovite is a yet denser and higher-pressure polymorph of SiO2 found in some meteorite impact sites. Lechatelierite is an amorphous silica glass SiO2 which is formed by lightning strikes in quartz sand. Safety As quartz is a form of silica, it is a possible cause for concern in various workplaces. Cutting, grinding, chipping, sanding, drilling, and polishing natural and manufactured stone products can release hazardous levels of very small, crystalline silica dust particles into the air that workers breathe. Crystalline silica of respirable size is a recognized human carcinogen and may lead to other diseases of the lungs such as silicosis and pulmonary fibrosis. History The word "quartz" comes from the German , which is of Slavic origin (Czech miners called it křemen). Other sources attribute the word's origin to the Saxon word Querkluftertz, meaning cross-vein ore. Quartz is the most common material identified as the mystical substance maban in Australian Aboriginal mythology. It is found regularly in passage tomb cemeteries in Europe in a burial context,	only one termination pyramid is present. However, doubly terminated crystals do occur where they develop freely without attachment, for instance, within gypsum. α-quartz crystallizes in the trigonal crystal system, space group P3121 or P3221 (space group 152 or 154 resp.) depending on the chirality. Above , α-quartz in P3121 becomes the more symmetric hexagonal P6422 (space group 181), and α-quartz in P3221 goes to space group P6222 (no. 180). These space groups are truly chiral (they each belong to the 11 enantiomorphous pairs). Both α-quartz and β-quartz are examples of chiral crystal structures composed of achiral building blocks (SiO4 tetrahedra in the present case). The transformation between α- and β-quartz only involves a comparatively minor rotation of the tetrahedra with respect to one another, without a change in the way they are linked. Varieties (according to microstructure) Although many of the varietal names historically arose from the color of the mineral, current scientific naming schemes refer primarily to the microstructure of the mineral. Color is a secondary identifier for the cryptocrystalline minerals, although it is a primary identifier for the macrocrystalline varieties. Varieties (according to color) Pure quartz, traditionally called rock crystal or clear quartz, is colorless and transparent or translucent, and has often been used for hardstone carvings, such as the Lothair Crystal. Common colored varieties include citrine, rose quartz, amethyst, smoky quartz, milky quartz, and others. These color differentiations arise from the presence of impurities which change the molecular orbitals, causing some electronic transitions to take place in the visible spectrum causing colors. The most important distinction between types of quartz is that of macrocrystalline (individual crystals visible to the unaided eye) and the microcrystalline or cryptocrystalline varieties (aggregates of crystals visible only under high magnification). The cryptocrystalline varieties are either translucent or mostly opaque, while the transparent varieties tend to be macrocrystalline. Chalcedony is a cryptocrystalline form of silica consisting of fine intergrowths of both quartz, and its monoclinic polymorph moganite. Other opaque gemstone varieties of quartz, or mixed rocks including quartz, often including contrasting bands or patterns of color, are agate, carnelian or sard, onyx, heliotrope, and jasper. Amethyst Amethyst is a form of quartz that ranges from a bright vivid violet to dark or dull lavender shade. The world's largest deposits of amethysts can be found in Brazil, Mexico, Uruguay, Russia, France, Namibia and Morocco. Sometimes amethyst and citrine are found growing in the same crystal. It is then referred to as ametrine. An amethyst derives its color from traces of iron in its structure. Blue quartz Blue quartz contains inclusions of fibrous magnesio-riebeckite or crocidolite. Dumortierite quartz Inclusions of the mineral dumortierite within quartz pieces often result in silky-appearing splotches with a blue hue. Shades of purple or grey sometimes also are present. "Dumortierite quartz" (sometimes called "blue quartz") will sometimes feature contrasting light and dark color zones across the material. "Blue quartz" is a minor gemstone. Citrine Citrine is a variety of quartz whose color ranges from a pale yellow to brown due to a submicroscopic distribution of colloidal ferric hydroxide impurities. Natural citrines are rare; most commercial citrines are heat-treated amethysts or smoky quartzes. However, a heat-treated amethyst will have small lines in the crystal, as opposed to a natural citrine's cloudy or smoky appearance. It is nearly impossible to differentiate between cut citrine and yellow topaz visually, but they differ in hardness. Brazil is the leading producer of citrine, with much of its production coming from the state of Rio Grande do Sul. The name is derived from the Latin word citrina which means "yellow" and is also the origin of the word "citron". Sometimes citrine and amethyst can be found together in the same crystal, which is then referred to as ametrine. Citrine has been referred to as the "merchant's stone" or "money stone", due to a superstition that it would bring prosperity. Citrine was first appreciated as a golden-yellow gemstone in Greece between 300 and 150 BC, during the Hellenistic Age. The yellow quartz was used prior to that to decorate jewelry and tools but it was not highly sought after. Milky quartz Milk quartz or milky quartz is the most common variety of crystalline quartz. The white color is caused by minute fluid inclusions of gas, liquid, or both, trapped during crystal formation, making it of little value for optical and quality gemstone applications. Rose quartz Rose quartz is a type of quartz which exhibits a pale pink to rose red hue. The color is usually considered as due to trace amounts of titanium, iron, or manganese, in the material. Some rose quartz contains microscopic rutile needles which produces an asterism in transmitted light. Recent X-ray diffraction studies suggest that the color is due to thin microscopic fibers of possibly dumortierite within the quartz. Additionally, there is a rare type of pink quartz (also frequently called crystalline rose quartz) with color that is thought to be caused by trace amounts of phosphate or aluminium. The color in crystals is apparently photosensitive and subject to fading. The first crystals were found in a pegmatite found near Rumford, Maine, US and in Minas Gerais, Brazil. Smoky quartz Smoky quartz is a gray, translucent version of quartz. It ranges in clarity from almost complete transparency to a brownish-gray crystal that is almost opaque. Some can also be black. The translucency results from natural irradiation acting on minute traces of aluminum in the crystal structure. Prasiolite Prasiolite, also known as vermarine, is a variety of quartz that is green in color. Since 1950, almost all natural prasiolite has come from a small Brazilian mine, but it is also seen in Lower Silesia in Poland. Naturally occurring prasiolite is also found in the Thunder Bay area of Canada. It is a rare mineral in nature; most green quartz is heat-treated amethyst. Synthetic and artificial treatments Not all varieties of quartz are naturally occurring. Some clear quartz crystals can be treated using heat or gamma-irradiation to induce color where it would not otherwise have occurred naturally. Susceptibility to such treatments depends on the location from which the quartz was mined. Prasiolite, an olive colored material, is produced by heat treatment; natural prasiolite has also been observed in Lower Silesia in Poland. Although citrine occurs naturally, the majority is the result of heat-treating amethyst or smoky quartz. Carnelian has been heat-treated to deepen its color since prehistoric times. Because natural quartz is often twinned, synthetic quartz is produced for use in industry. Large, flawless, single crystals are synthesized in an autoclave via the hydrothermal process. Like other crystals, quartz may be coated with metal vapors to give it an attractive sheen. Occurrence Quartz is a defining constituent of granite and other felsic igneous rocks. It is very common in sedimentary rocks such as sandstone and shale. It is a common constituent of schist, gneiss, quartzite and other metamorphic rocks. Quartz has the lowest potential for weathering in the Goldich dissolution series and consequently it is very common as a residual mineral in stream sediments and residual soils. Generally a high presence of quartz suggests a "mature" rock, since it indicates the rock has been heavily reworked and quartz was the primary mineral that endured heavy weathering. While the majority of quartz crystallizes from molten magma, quartz also chemically precipitates from hot hydrothermal veins as gangue, sometimes with ore minerals like gold, silver and copper. Large crystals of quartz are found in magmatic pegmatites. Well-formed crystals may reach several meters in length and weigh hundreds of kilograms. Naturally occurring quartz crystals of extremely high purity, necessary for the crucibles and other equipment used for growing silicon wafers in the semiconductor industry, are expensive and rare. A major mining location for high purity quartz is the Spruce Pine Gem Mine in Spruce Pine, North Carolina, United States. Quartz may also be found in Caldoveiro Peak, in Asturias, Spain. The largest documented single crystal of quartz was found near Itapore, Goiaz, Brazil; it measured approximately 6.1×1.5×1.5 m and weighed 39,916 kilograms. Mining Quartz is extracted from open pit mines. Miners occasionally use explosives to expose deep pockets of quartz. More frequently, bulldozers and backhoes are used to remove soil and clay and expose quartz veins, which are then worked using hand tools. Care must be taken to avoid sudden temperature changes that may damage the crystals. Almost all
another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantities as such, music the relations between quantities, geometry magnitude at rest, spherics [astronomy] magnitude inherently moving. Medieval usage At many medieval universities, this would have been the course leading to the degree of Master of Arts (after the BA). After the MA, the student could enter for bachelor's degrees of the higher faculties (Theology, Medicine or Law). To this day, some of the postgraduate degree courses lead to the degree of Bachelor (the B.Phil and B.Litt. degrees are examples in the field of philosophy). The study was eclectic, approaching the philosophical objectives sought by considering it from each aspect of the quadrivium within the general structure demonstrated by Proclus (AD 412–485), namely arithmetic and music on the one hand and geometry and cosmology on the other. The subject of music within the quadrivium was originally the classical subject of harmonics, in particular the study of the proportions between the musical intervals created by the division of a monochord. A relationship to music as actually practised was not part of this study, but the framework of classical harmonics would substantially influence the content and structure of music theory as practised in both European and Islamic cultures. Modern usage In modern applications of the liberal arts as curriculum in colleges or universities, the quadrivium may be considered to be the study of number and its relationship to space or time: arithmetic was pure number, geometry was number in space, music was number in time, and astronomy was number in space and time. Morris Kline classified the four elements of the quadrivium as pure (arithmetic), stationary (geometry), moving (astronomy), and applied (music) number. This schema is sometimes referred to as "classical education", but it is more accurately a development of the 12th- and 13th-century Renaissance with recovered classical elements, rather than an organic growth from the educational systems of antiquity. The term continues to be used by the Classical education	a subject (nor faculty) in its own right, but was rather present implicitly as an 'auxiliary tool' within the discourses of the High faculties (especially theology); the complete emancipation of philosophy from theology happened only after the Medieval era. Origins These four studies compose the secondary part of the curriculum outlined by Plato in The Republic and are described in the seventh book of that work (in the order Arithmetic, Geometry, Astronomy, Music). The quadrivium is implicit in early Pythagorean writings and in the De nuptiis of Martianus Capella, although the term quadrivium was not used until Boethius, early in the sixth century. As Proclus wrote: The Pythagoreans considered all mathematical science to be divided into four parts: one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in its relation to another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantities as such, music the relations between quantities, geometry magnitude at rest, spherics [astronomy] magnitude inherently moving. Medieval usage At many medieval universities, this would have been the course leading to the degree of Master of Arts (after the BA). After the MA, the student could enter for bachelor's degrees of the higher
other roles (e.g., hands in the case of humans, wings in the case of birds, and fins in the case of whales). All of these animals are tetrapods, but none is a quadruped. Even snakes, whose limbs have become vestigial or lost entirely, are, nevertheless, tetrapods. In humans In July 2005, in rural Turkey, scientists discovered five Turkish siblings who had learned to walk naturally on their hands and feet. Unlike chimpanzees, which ambulate on their knuckles, the Ulas Family walked on their palms, allowing them to preserve the dexterity of their fingers. Many people, especially practitioners of parkour and freerunning and Georges Hébert's natural method, find benefit in quadrupedal movements to build full body strength. Kenichi Ito is a Japanese man famous for speed running on four limbs. Quadrupedalism is sometimes referred to as being on all fours, and is observed in crawling, especially by infants. Quadrupedal robots BigDog is a dynamically stable quadruped robot created in 2005 by Boston Dynamics with Foster-Miller, the NASA Jet Propulsion Laboratory, and the Harvard University Concord Field Station. Also by NASA JPL, in collaboration with University of California, Santa Barbara Robotics Lab, is RoboSimian, with emphasis on stability and deliberation. It has been demonstrated at the DARPA Robotics Challenge. Pronograde posture A related concept to quadrupedalism	maintains a four-legged posture and moves using all four limbs is said to be a quadruped (from Latin quattuor for "four", and pes, pedis for "foot"). Most quadrupeds are terrestrial vertebrates, including mammals and reptiles, though some are largely aquatic such as turtles, amphibians, and pinnipeds. Bipedal tetrapods such as some birds (such as the shoebill) sometimes use their wings to right themselves after lunging at prey. Quadrupeds vs. tetrapods Although the words ‘quadruped’ and ‘tetrapod’ are both derived from terms meaning ‘four-footed’, they have distinct meanings. A tetrapod is any member of the taxonomic unit Tetrapoda (which is defined by descent from a specific four-limbed ancestor), whereas a quadruped actually uses four limbs for locomotion. Not all tetrapods are quadrupeds and not all entities that could be described as ‘quadrupedal’ are tetrapods. This last meaning includes certain artificial objects; almost all quadruped organisms are tetrapods (with the exception of some raptorial arthropods adapted for four-footed locomotion, such as the Mantodea). The distinction between quadrupeds and tetrapods is important in evolutionary biology, particularly in the context of tetrapods whose limbs have adapted to other roles (e.g., hands in the case of humans, wings in the case of birds, and fins in the case of whales). All of these animals are tetrapods, but none is a quadruped. Even snakes, whose limbs have become vestigial or lost entirely, are, nevertheless, tetrapods. In humans In July 2005,
quarantine to wider society can be favourable." Short-term quarantines, e.g. for decontamination Quarantine periods can be very short, such as in the case of a suspected anthrax attack, in which people are allowed to leave as soon as they shed their potentially contaminated garments and undergo a decontamination shower. For example, an article entitled "Daily News workers quarantined" describes a brief quarantine that lasted until people could be showered in a decontamination tent. The February–March 2003 issue of HazMat Magazine suggests that people be "locked in a room until proper decon could be performed", in the event of "suspect anthrax". Standard-Times senior correspondent Steve Urbon (14 February 2003) describes such temporary quarantine powers: The purpose of such quarantine-for-decontamination is to prevent the spread of contamination and to contain the contamination such that others are not put at risk from a person fleeing a scene where contamination is suspect. It can also be used to limit exposure, as well as eliminate a vector. New developments for quarantine include new concepts in quarantine vehicles such as the ambulance bus, mobile hospitals, and lockdown/invacuation (inverse evacuation) procedures, as well as docking stations for an ambulance bus to dock to a facility under lockdown. Standard quarantine practices in different countries Australia Biosecurity in Australia is governed by the Biosecurity Act 2015. The Australian Quarantine and Inspection Service (AQIS) is responsible for border inspection of products brought into Australia, and assesses the risks the products might harm Australian environment. No person, goods, and vessels are permitted into Australia without clearance from AQIS. Visitors are required to fill in the information card on arriving in Australia. Besides other risk factors, visitors are required to declare what food and products made of wood and other natural materials they have. Visitors who fail to do so may be subject to a fine of A$444, or may face criminal prosecution and be fined up to A$444,000 or imprisonment of up to 10 years. Australia has very strict quarantine standards. Quarantine in northern Australia is especially important because of its proximity to South-East Asia and the Pacific, which have many pests and diseases not present in Australia. For this reason, the region from Cairns to Broome—including the Torres Strait—is the focus for quarantine activities that protect all Australians. As Australia has been geographically isolated from other major continents for millions of years, there is an endemically unique ecosystem free of several severe pests and diseases that are present in many parts of the world. If other products are brought inside along with pests and diseases, it would damage the ecosystem seriously and add millions of costs in the local agricultural businesses. Canada There are three quarantine Acts of Parliament in Canada: Quarantine Act (humans) and Health of Animals Act (animals) and Plant Protection Act (vegetations). The first legislation is enforced by the Canada Border Services Agency after a complete rewrite in 2005. The second and third legislations are enforced by the Canadian Food Inspection Agency. If a health emergency exists, the Governor in Council can prohibit importation of anything that it deems necessary under the Quarantine Act. Under the Quarantine Act, all travellers must submit to screening and if they believe they might have come into contact with communicable diseases or vectors, they must disclose their whereabouts to a Border Services Officer. If the officer has reasonable grounds to believe that the traveller is or might have been infected with a communicable disease or refused to provide answers, a quarantine officer (QO) must be called and the person is to be isolated. If a person refuses to be isolated, any peace officer may arrest without warrant. A QO who has reasonable grounds to believe that the traveller has or might have a communicable disease or is infested with vectors, after the medical examination of a traveller, can order him/her into treatment or measures to prevent the person from spreading the disease. QO can detain any traveller who refuses to comply with his/her orders or undergo health assessments as required by law. Under the Health of Animals Act and Plant Protection Act, inspectors can prohibit access to an infected area, dispose or treat any infected or suspected to be infected animals or plants. The Minister can order for compensation to be given if animals/plants were destroyed pursuant to these acts. Each province also enacts its own quarantine/environmental health legislation. Hong Kong Under the Prevention and Control of Disease Ordinance (HK Laws. Chap 599), a health officer may seize articles they believe to be infectious or containing infectious agents. All travellers, if requested, must submit themselves to a health officer. Failure to do so is against the law and is subject to arrest and prosecution. The law allows for health officers who have reasonable grounds to detain, isolate, quarantine anyone or anything believed to be infected, and to restrict any articles from leaving a designated quarantine area. He/she may also order the Civil Aviation Department to prohibit the landing or leaving, embarking or disembarking of an aircraft. This power also extends to land, sea or air crossings. Under the same ordinance, any police officer, health officer, member of the Civil Aid Service, or member of the Auxiliary Medical Service can arrest a person who obstructs or escapes from detention. United Kingdom To reduce the risk of introducing rabies from continental Europe, the United Kingdom used to require that dogs, and most other animals introduced to the country, spend six months in quarantine at an HM Customs and Excise pound; this policy was abolished in 2000 in favour of a scheme generally known as Pet Passports, where animals can avoid quarantine if they have documentation showing they are up to date on their appropriate vaccinations. British maritime quarantine rules 1711–1896 The plague had disappeared from England for more than thirty years before the practice of quarantine against it was definitely established by the Quarantine Act 1710 (9 Ann.). The first act was called for due to fears that the plague might be imported from Poland and the Baltic states. The second act of 1721 was due to the prevalence of plague at Marseille and other places in Provence, France. It was renewed in 1733 after a new outbreak in continental Europe, and again in 1743, due to an epidemic in Messina. In 1752 a rigorous quarantine clause was introduced into an act regulating trade with the Levant, and various arbitrary orders were issued during the next twenty years to meet the supposed danger of infection from the Baltic states. Although no plague cases ever came to England during that period, the restrictions on traffic became more stringent, and in 1788 a very strict Quarantine Act was passed, with provisions affecting cargoes in particular. The act was revised in 1801 and 1805, and in 1823–24 an elaborate inquiry was followed by an act making quarantine only at discretion of the privy council, which recognised yellow fever or other highly infectious diseases as calling for quarantine, along with plague. The threat of cholera in 1831 was the last occasion in England of the use of quarantine restrictions. Cholera affected every country in Europe, despite all efforts to keep it out. When cholera returned to England in 1849, 1853 and 1865–66, no attempt was made to seal the ports. In 1847 the privy council ordered all arrivals with a clean bill of health from the Black Sea and the Levant to be admitted, provided there had been no case of plague during the voyage, and afterwards the practice of quarantine was discontinued. After the passing of the first Quarantine Act (1710) the protective practices in England were haphazard and arbitrary. In 1721 two vessels carrying cotton goods from Cyprus, then affected by the plague, were ordered to be burned with their cargoes, the owners receiving an indemnity. By the clause in the Levant Trade Act of 1752, ships arriving in the United Kingdom with a "foul bill" (i.e. coming from a country where plague existed) had to return to the lazarets of Malta, Venice, Messina, Livorno, Genoa, or Marseille, to complete a quarantine or to have their cargoes opened and aired. Since 1741 Stangate Creek (on the Medway) had been the quarantine station but it was available only for vessels with clean bills of health. In 1755 lazarets in the form of floating hulks were established in England for the first time, the cleansing of cargo (particularly by exposure to dews) having been done previously on the ship's deck. No medical inspections were conducted, but control was the responsibility of the Officers of Royal Customs and quarantine. In 1780, when plague was in Poland, even vessels with grain from the Baltic had to spend forty days in quarantine, and unpack and air their cargoes, but due to complaints mainly from Edinburgh and Leith, an exception was made for grain after that date. About 1788 an order of the council required every ship liable to quarantine to hoist a yellow flag in the daytime and show a light at the main topmast head at night, in case of meeting any vessel at sea, or upon arriving within four leagues of the coast of Great Britain or Ireland. After 1800, ships from plague-affected countries (or with foul bills) were permitted to complete their quarantine in the Medway instead of at a Mediterranean port on the way, and an extensive lazaret was built on Chetney Hill near Chatham (although it was later demolished). The use of floating hulks as lazarets continued as before. In 1800 two ships with hides from Mogador in Morocco were ordered to be sunk with their cargoes at the Nore, the owners receiving an indemnity. Animal hides were suspected of harbouring infections, along with a long list of other items, and these had to be exposed on the ship's deck for twenty-one days or less (six days for each instalment of the cargo), and then transported to the lazaret, where they were opened and aired for another forty days. The whole detention of the vessel was from sixty to sixty-five days, including the time for reshipment of her cargo. Pilots had to pass fifteen days on board a convalescent ship. From 1846 onwards the quarantine establishments in the United Kingdom were gradually reduced, while the last vestige of the British quarantine law was removed by the Public Health Act of 1896, which repealed the Quarantine Act of 1825 (with dependent clauses of other acts), and transferred from the privy council to the Local Government Board the powers to deal with ships arriving infected with yellow fever or plague. The powers to deal with cholera ships had been already transferred by the Public Health Act 1875. British regulations of 9 November 1896 applied to yellow fever, plague and cholera. Officers of the Customs, as well as of Royal Coast Guard and the Board of Trade (for signalling), were empowered to take the initial steps. They certified in writing the master of a supposedly infected ship, and detained the vessel provisionally for not more than twelve hours, giving notice meanwhile to the port sanitary authority. The medical officer of the port boarded the ship and examined every person in it. Every person found infected was taken to a hospital and quarantined under the orders of the medical officer, and the vessel remained under his orders. Every person suspected could be detained on board for 48 hours or removed to the hospital for a similar period. All others were free to land upon giving the addresses of their destinations to be sent to the respective local authorities, so that the dispersed passengers and crew could be kept individually under observation for a few days. The ship was then disinfected, dead bodies buried at sea, infected clothing, bedding, etc., destroyed or disinfected, and bilge-water and water-ballast pumped out at a suitable distance before the ship entered a dock or basin. Mail was subject to no detention. A stricken ship within 3 miles of the shore had to fly a yellow and black flag at the main mast from sunrise to sunset. United States In the United States, authority to quarantine people with infectious diseases is split between the state and federal governments. States (and tribal governments recognised by the federal government) have primary authority to quarantine people within their boundaries. Federal jurisdiction only applies to people moving across state or national borders, or people on federal property. Federal rules Communicable diseases for which apprehension, detention, or conditional release of people are authorised must be specified in Executive Orders of the President. As of 2014, these include Executive Orders 13295 13375, and 13674; the latest executive order specifies the following infectious diseases: cholera, diphtheria, infectious tuberculosis, plague, smallpox, yellow fever, viral haemorrhagic fevers (Lassa, Marburg, Ebola, Crimean-Congo, South American, and others not yet isolated or named), severe acute respiratory syndromes (SARS), and influenza from a novel or re-emergent source. The Department of Health and Human Services is responsible for quarantine decisions, specifically the Centers for Disease Control and Prevention's Division of Global Migration and Quarantine. As of 21 March 2017, Centers for Disease Control and Prevention (CDC) regulations specify: All commercial passenger flights must report deaths or illnesses to the CDC. Individuals must apply for a travel permit if they are under a Federal quarantine, isolation, or conditional release order. When an individual who is moving between U.S. states is "reasonably believed to be infected" with a quarantinable communicable disease in a "qualifying stage", the CDC may apprehend or examine that individual for potential infection. This includes new regulatory authority permitting the CDC Director to prohibit the importation of animals or products that pose a threat to public health. The rules: Do not authorise compulsory medical testing, vaccination, or medical treatment without prior informed consent. Require CDC to advise individuals subject to medical examinations that they will be conducted by an authorised health worker and with prior informed consent. Include strong due process protections for individuals subject to public health orders, including a right to counsel for indigent individuals. Limit to 72 hours the amount of time that an individual may be apprehended pending the issuance of a federal order for isolation, quarantine, or conditional release. US quarantine facilities The Division of Global Migration and Quarantine (DGMQ) of the US Centers for Disease Control (CDC) operates small quarantine facilities at a number of US ports of entry. As of 2014, these included one land crossing (in El Paso, Texas) and 19 international airports. Besides the port of entry where it is located, each station is also responsible for quarantining potentially infected travellers entering through any ports of entry in its assigned region. These facilities are fairly small; each one is operated by a few staff members and capable of accommodating 1–2 travellers for a short observation period. Cost estimates for setting up a temporary larger facility, capable of accommodating 100 to 200 travellers for several weeks, have been published by the Airport Cooperative Research Program (ACRP) in 2008 of the Transportation Research Board. US quarantine of imported goods The United States puts immediate quarantines on imported products if a contagious disease is identified and can be traced back to a certain shipment or product. All imports will also be quarantined if the disease appears in other countries. According to Title 42 U.S.C. §§264 and 266 , these statutes provide the Secretary of Health and Human Services peacetime and wartime authority to control the movement of people into and within the United States to prevent the spread of communicable disease. History of quarantine laws in the US Quarantine law began in Colonial America in 1663, when in an attempt to curb an outbreak of smallpox, the city of New York established a quarantine. In the 1730s, the city built a quarantine station on the Bedloe's Island. The Philadelphia Lazaretto was the first quarantine hospital in the United States, built in 1799, in Tinicum Township, Delaware County, Pennsylvania. There are similar national landmarks such as the Columbia River Quarantine Station, Swinburne Island and Angel Island. The Pest House in Concord, Massachusetts was used as early as 1752 to quarantine those suffering from cholera, tuberculosis and smallpox. In early June 1832, during the cholera epidemic in New York, Governor Enos Throop called a special session of the Legislature for 21 June, to pass a Public Health Act by both Houses of the State Legislature. It included to a strict quarantine along the Upper and Lower New York-Canadian frontier. In addition, New York City Mayor Walter Browne established a quarantine against all peoples and products of Europe and Asia, which prohibited ships from approaching closer than 300 yards to the city, and all vehicles were ordered to stop 1.5 miles away. The Immigrant Inspection Station on Ellis Island, built in 1892, is often mistakenly assumed to have been a quarantine station, however its marine hospital (Ellis Island Immigrant Hospital) only qualified as a contagious disease facility to handle less virulent diseases like measles, trachoma and less advanced stages of tuberculosis and diphtheria; those afflicted with smallpox, yellow fever, cholera, leprosy or typhoid fever, could neither be received nor treated there. Mary Mallon was quarantined in 1907 under the Greater New York Charter, Sections 1169–1170, which permitted the New York City Board of Health to "remove to a proper place…any person sick with any contagious, pestilential or infectious disease." During the 1918 flu pandemic, people were also quarantined. Most commonly suspect cases of infectious diseases are requested to voluntarily quarantine themselves, and Federal and local quarantine statutes only have been uncommonly invoked since then, including for a suspected smallpox case in 1963. The 1944 Public Health Service Act "to apprehend, detain, and examine certain infected persons who are peculiarly likely to cause the interstate spread of disease" clearly established the federal government's quarantine authority for the first time. It gave the United States Public Health Service responsibility for preventing the introduction, transmission and spread of communicable diseases from foreign countries into the United States, and expanded quarantine authority to include incoming aircraft. The act states that "...any individual reasonably believed to be infected with a communicable disease in a qualifying stage and...if found to be infected, may be detained for such time and in such manner as may be reasonably necessary." No federal quarantine orders were issued from 1963 until 2020, as American citizens were evacuated from China during the COVID-19 pandemic. List of quarantine services in the world Australian Quarantine and Inspection Service MAF Quarantine Service, in the New Zealand Quarantine, Western Australia Samoa Quarantine Service, in the West Samoa Racehorse & Equine Quarantine Services, A company built & developed by Frankie Thevarasa Kuala Lumpur Malaysia Federal Service for Supervision of Consumer Rights Protection and Human Welfare, a Federal Quarantine Service of the Government of Russia. Notable quarantines Eyam village, 1665 (plague) Eyam was a village in Britain that imposed a cordon sanitaire on itself to stop the spread of the bubonic plague to other communities in 1665. The plague ran its course over 14 months and one account states that it killed at least 260 villagers. The church in Eyam has a record of 273 individuals who were victims of the plague. Convict ship Surry, Sydney Harbour, 1814 (typhoid) On 28 July 1814, the convict ship Surry arrived in Sydney Harbour from England. Forty-six people had died of typhoid during the voyage, including 36 convicts, and the ship was placed in quarantine on the North Shore. Convicts were landed, and a camp was established in the immediate vicinity of what is now Jeffrey Street in Kirribilli. This was the first site in Australia to be used for quarantine purposes. 'Typhoid Mary' (US), 1907–1910 and 1915–1938 Mary Mallon was a cook who was found to be a carrier of Salmonella enterica subsp. enterica, the cause of typhoid fever, and was forcibly isolated from 1907 to 1910. At least 53 cases of the infection were traced to her, and three deaths. Subsequently she spent a further 23 years	1780, when plague was in Poland, even vessels with grain from the Baltic had to spend forty days in quarantine, and unpack and air their cargoes, but due to complaints mainly from Edinburgh and Leith, an exception was made for grain after that date. About 1788 an order of the council required every ship liable to quarantine to hoist a yellow flag in the daytime and show a light at the main topmast head at night, in case of meeting any vessel at sea, or upon arriving within four leagues of the coast of Great Britain or Ireland. After 1800, ships from plague-affected countries (or with foul bills) were permitted to complete their quarantine in the Medway instead of at a Mediterranean port on the way, and an extensive lazaret was built on Chetney Hill near Chatham (although it was later demolished). The use of floating hulks as lazarets continued as before. In 1800 two ships with hides from Mogador in Morocco were ordered to be sunk with their cargoes at the Nore, the owners receiving an indemnity. Animal hides were suspected of harbouring infections, along with a long list of other items, and these had to be exposed on the ship's deck for twenty-one days or less (six days for each instalment of the cargo), and then transported to the lazaret, where they were opened and aired for another forty days. The whole detention of the vessel was from sixty to sixty-five days, including the time for reshipment of her cargo. Pilots had to pass fifteen days on board a convalescent ship. From 1846 onwards the quarantine establishments in the United Kingdom were gradually reduced, while the last vestige of the British quarantine law was removed by the Public Health Act of 1896, which repealed the Quarantine Act of 1825 (with dependent clauses of other acts), and transferred from the privy council to the Local Government Board the powers to deal with ships arriving infected with yellow fever or plague. The powers to deal with cholera ships had been already transferred by the Public Health Act 1875. British regulations of 9 November 1896 applied to yellow fever, plague and cholera. Officers of the Customs, as well as of Royal Coast Guard and the Board of Trade (for signalling), were empowered to take the initial steps. They certified in writing the master of a supposedly infected ship, and detained the vessel provisionally for not more than twelve hours, giving notice meanwhile to the port sanitary authority. The medical officer of the port boarded the ship and examined every person in it. Every person found infected was taken to a hospital and quarantined under the orders of the medical officer, and the vessel remained under his orders. Every person suspected could be detained on board for 48 hours or removed to the hospital for a similar period. All others were free to land upon giving the addresses of their destinations to be sent to the respective local authorities, so that the dispersed passengers and crew could be kept individually under observation for a few days. The ship was then disinfected, dead bodies buried at sea, infected clothing, bedding, etc., destroyed or disinfected, and bilge-water and water-ballast pumped out at a suitable distance before the ship entered a dock or basin. Mail was subject to no detention. A stricken ship within 3 miles of the shore had to fly a yellow and black flag at the main mast from sunrise to sunset. United States In the United States, authority to quarantine people with infectious diseases is split between the state and federal governments. States (and tribal governments recognised by the federal government) have primary authority to quarantine people within their boundaries. Federal jurisdiction only applies to people moving across state or national borders, or people on federal property. Federal rules Communicable diseases for which apprehension, detention, or conditional release of people are authorised must be specified in Executive Orders of the President. As of 2014, these include Executive Orders 13295 13375, and 13674; the latest executive order specifies the following infectious diseases: cholera, diphtheria, infectious tuberculosis, plague, smallpox, yellow fever, viral haemorrhagic fevers (Lassa, Marburg, Ebola, Crimean-Congo, South American, and others not yet isolated or named), severe acute respiratory syndromes (SARS), and influenza from a novel or re-emergent source. The Department of Health and Human Services is responsible for quarantine decisions, specifically the Centers for Disease Control and Prevention's Division of Global Migration and Quarantine. As of 21 March 2017, Centers for Disease Control and Prevention (CDC) regulations specify: All commercial passenger flights must report deaths or illnesses to the CDC. Individuals must apply for a travel permit if they are under a Federal quarantine, isolation, or conditional release order. When an individual who is moving between U.S. states is "reasonably believed to be infected" with a quarantinable communicable disease in a "qualifying stage", the CDC may apprehend or examine that individual for potential infection. This includes new regulatory authority permitting the CDC Director to prohibit the importation of animals or products that pose a threat to public health. The rules: Do not authorise compulsory medical testing, vaccination, or medical treatment without prior informed consent. Require CDC to advise individuals subject to medical examinations that they will be conducted by an authorised health worker and with prior informed consent. Include strong due process protections for individuals subject to public health orders, including a right to counsel for indigent individuals. Limit to 72 hours the amount of time that an individual may be apprehended pending the issuance of a federal order for isolation, quarantine, or conditional release. US quarantine facilities The Division of Global Migration and Quarantine (DGMQ) of the US Centers for Disease Control (CDC) operates small quarantine facilities at a number of US ports of entry. As of 2014, these included one land crossing (in El Paso, Texas) and 19 international airports. Besides the port of entry where it is located, each station is also responsible for quarantining potentially infected travellers entering through any ports of entry in its assigned region. These facilities are fairly small; each one is operated by a few staff members and capable of accommodating 1–2 travellers for a short observation period. Cost estimates for setting up a temporary larger facility, capable of accommodating 100 to 200 travellers for several weeks, have been published by the Airport Cooperative Research Program (ACRP) in 2008 of the Transportation Research Board. US quarantine of imported goods The United States puts immediate quarantines on imported products if a contagious disease is identified and can be traced back to a certain shipment or product. All imports will also be quarantined if the disease appears in other countries. According to Title 42 U.S.C. §§264 and 266 , these statutes provide the Secretary of Health and Human Services peacetime and wartime authority to control the movement of people into and within the United States to prevent the spread of communicable disease. History of quarantine laws in the US Quarantine law began in Colonial America in 1663, when in an attempt to curb an outbreak of smallpox, the city of New York established a quarantine. In the 1730s, the city built a quarantine station on the Bedloe's Island. The Philadelphia Lazaretto was the first quarantine hospital in the United States, built in 1799, in Tinicum Township, Delaware County, Pennsylvania. There are similar national landmarks such as the Columbia River Quarantine Station, Swinburne Island and Angel Island. The Pest House in Concord, Massachusetts was used as early as 1752 to quarantine those suffering from cholera, tuberculosis and smallpox. In early June 1832, during the cholera epidemic in New York, Governor Enos Throop called a special session of the Legislature for 21 June, to pass a Public Health Act by both Houses of the State Legislature. It included to a strict quarantine along the Upper and Lower New York-Canadian frontier. In addition, New York City Mayor Walter Browne established a quarantine against all peoples and products of Europe and Asia, which prohibited ships from approaching closer than 300 yards to the city, and all vehicles were ordered to stop 1.5 miles away. The Immigrant Inspection Station on Ellis Island, built in 1892, is often mistakenly assumed to have been a quarantine station, however its marine hospital (Ellis Island Immigrant Hospital) only qualified as a contagious disease facility to handle less virulent diseases like measles, trachoma and less advanced stages of tuberculosis and diphtheria; those afflicted with smallpox, yellow fever, cholera, leprosy or typhoid fever, could neither be received nor treated there. Mary Mallon was quarantined in 1907 under the Greater New York Charter, Sections 1169–1170, which permitted the New York City Board of Health to "remove to a proper place…any person sick with any contagious, pestilential or infectious disease." During the 1918 flu pandemic, people were also quarantined. Most commonly suspect cases of infectious diseases are requested to voluntarily quarantine themselves, and Federal and local quarantine statutes only have been uncommonly invoked since then, including for a suspected smallpox case in 1963. The 1944 Public Health Service Act "to apprehend, detain, and examine certain infected persons who are peculiarly likely to cause the interstate spread of disease" clearly established the federal government's quarantine authority for the first time. It gave the United States Public Health Service responsibility for preventing the introduction, transmission and spread of communicable diseases from foreign countries into the United States, and expanded quarantine authority to include incoming aircraft. The act states that "...any individual reasonably believed to be infected with a communicable disease in a qualifying stage and...if found to be infected, may be detained for such time and in such manner as may be reasonably necessary." No federal quarantine orders were issued from 1963 until 2020, as American citizens were evacuated from China during the COVID-19 pandemic. List of quarantine services in the world Australian Quarantine and Inspection Service MAF Quarantine Service, in the New Zealand Quarantine, Western Australia Samoa Quarantine Service, in the West Samoa Racehorse & Equine Quarantine Services, A company built & developed by Frankie Thevarasa Kuala Lumpur Malaysia Federal Service for Supervision of Consumer Rights Protection and Human Welfare, a Federal Quarantine Service of the Government of Russia. Notable quarantines Eyam village, 1665 (plague) Eyam was a village in Britain that imposed a cordon sanitaire on itself to stop the spread of the bubonic plague to other communities in 1665. The plague ran its course over 14 months and one account states that it killed at least 260 villagers. The church in Eyam has a record of 273 individuals who were victims of the plague. Convict ship Surry, Sydney Harbour, 1814 (typhoid) On 28 July 1814, the convict ship Surry arrived in Sydney Harbour from England. Forty-six people had died of typhoid during the voyage, including 36 convicts, and the ship was placed in quarantine on the North Shore. Convicts were landed, and a camp was established in the immediate vicinity of what is now Jeffrey Street in Kirribilli. This was the first site in Australia to be used for quarantine purposes. 'Typhoid Mary' (US), 1907–1910 and 1915–1938 Mary Mallon was a cook who was found to be a carrier of Salmonella enterica subsp. enterica, the cause of typhoid fever, and was forcibly isolated from 1907 to 1910. At least 53 cases of the infection were traced to her, and three deaths. Subsequently she spent a further 23 years in isolation prior to her death in 1938. The presence of the bacteria in her gallbladder was confirmed on autopsy. East Samoa, 1918 (flu pandemic) During the 1918 flu pandemic, the then Governor of American Samoa, John Martin Poyer, imposed a full protective sequestration of the islands from all incoming ships, successfully preventing influenza from infecting the population and thus achieving zero deaths within the territory. In contrast, the neighbouring New Zealand-controlled Western Samoa was among the hardest hit, with a 90% infection rate and over 20% of its adults dying from the disease. This failure by the New Zealand government to prevent and contain the Spanish Flu subsequently rekindled Samoan anti-colonial sentiments that led to its eventual independence. Gruinard Island, 1942–1990 (anthrax) In 1942, during World War II, British forces tested out their biological weapons program on Gruinard Island and infected it with anthrax. Subsequently a quarantine order was placed on the island. The quarantine was lifted in 1990, when the
observationally for the first time with images of the double quasar 0957+561. A study published in February, 2021, showed that there are more quasars in one direction (towards Hydra) than in the opposite direction, seemingly indicating that we are moving in that direction. But the direction of this dipole is about 28° away from the direction of our motion relative to the cosmic microwave background radiation. In March, 2021, a collaboration of scientists, related to the Event Horizon Telescope, presented, for the first time, a polarized-based image of a black hole, particularly the black hole at the center of Messier 87, an elliptical galaxy approximately 55 million light-years away in the constellation Virgo, revealing the forces giving rise to quasars. Current understanding It is now known that quasars are distant but extremely luminous objects, so any light that reaches the Earth is redshifted due to the metric expansion of space. Quasars inhabit the centers of active galaxies and are among the most luminous, powerful, and energetic objects known in the universe, emitting up to a thousand times the energy output of the Milky Way, which contains 200–400 billion stars. This radiation is emitted across the electromagnetic spectrum, almost uniformly, from X-rays to the far infrared with a peak in the ultraviolet optical bands, with some quasars also being strong sources of radio emission and of gamma-rays. With high-resolution imaging from ground-based telescopes and the Hubble Space Telescope, the "host galaxies" surrounding the quasars have been detected in some cases. These galaxies are normally too dim to be seen against the glare of the quasar, except with special techniques. Most quasars, with the exception of 3C 273, whose average apparent magnitude is 12.9, cannot be seen with small telescopes. Quasars are believed—and in many cases confirmed—to be powered by accretion of material into supermassive black holes in the nuclei of distant galaxies, as suggested in 1964 by Edwin Salpeter and Yakov Zel'dovich. Light and other radiation cannot escape from within the event horizon of a black hole. The energy produced by a quasar is generated outside the black hole, by gravitational stresses and immense friction within the material nearest to the black hole, as it orbits and falls inward. The huge luminosity of quasars results from the accretion discs of central supermassive black holes, which can convert between 6% and 32% of the mass of an object into energy, compared to just 0.7% for the p–p chain nuclear fusion process that dominates the energy production in Sun-like stars. Central masses of 105 to 109 solar masses have been measured in quasars by using reverberation mapping. Several dozen nearby large galaxies, including our own Milky Way galaxy, that do not have an active center and do not show any activity similar to a quasar, are confirmed to contain a similar supermassive black hole in their nuclei (galactic center). Thus it is now thought that all large galaxies have a black hole of this kind, but only a small fraction have sufficient matter in the right kind of orbit at their center to become active and power radiation in such a way as to be seen as quasars. This also explains why quasars were more common in the early universe, as this energy production ends when the supermassive black hole consumes all of the gas and dust near it. This means that it is possible that most galaxies, including the Milky Way, have gone through an active stage, appearing as a quasar or some other class of active galaxy that depended on the black-hole mass and the accretion rate, and are now quiescent because they lack a supply of matter to feed into their central black holes to generate radiation. The matter accreting onto the black hole is unlikely to fall directly in, but will have some angular momentum around the black hole, which will cause the matter to collect into an accretion disc. Quasars may also be ignited or re-ignited when normal galaxies merge and the black hole is infused with a fresh source of matter. In fact, it has been suggested that a quasar could form when the Andromeda Galaxy collides with our own Milky Way galaxy in approximately 3–5 billion years. In the 1980s, unified models were developed in which quasars were classified as a particular kind of active galaxy, and a consensus emerged that in many cases it is simply the viewing angle that distinguishes them from other active galaxies, such as blazars and radio galaxies. The highest-redshift quasar known () was ULAS J1342+0928, with a redshift of 7.54, which corresponds to a comoving distance of approximately 29.36 billion light-years from Earth (these distances are much larger than the distance light could travel in the universe's 13.8-billion-year history because space itself has also been expanding). Properties More than quasars have been found (as of August 2020), most from the Sloan Digital Sky Survey. All observed quasar spectra have redshifts between 0.056 and 7.64 (as of 2021). Applying Hubble's law to these redshifts, it can be shown that they are between 600 million and 29.36 billion light-years away (in terms of comoving distance). Because of the great distances to the farthest quasars and the finite velocity of light, they and their surrounding space appear as they existed in the very early universe. The power of quasars originates from supermassive black holes that are believed to exist at the core of most galaxies. The Doppler shifts of stars near the cores of galaxies indicate that they are revolving around tremendous masses with very steep gravity gradients, suggesting black holes. Although quasars appear faint when viewed from Earth, they are visible from extreme distances, being the most luminous objects in the known universe. The brightest quasar in the sky is 3C 273 in the constellation of Virgo. It has an average apparent magnitude of 12.8 (bright enough to be seen through a medium-size amateur telescope), but it has an absolute magnitude of −26.7. From a distance of about 33 light-years, this object would shine in the sky about as brightly as our Sun. This quasar's luminosity is, therefore, about 4 trillion (4) times that of the Sun, or about 100 times that of the total light of giant galaxies like the Milky Way. This assumes that the quasar is radiating energy in all directions, but the active galactic nucleus is believed to be radiating preferentially in the direction of its jet. In a universe containing hundreds of billions of galaxies, most of which had active nuclei billions of years ago but only seen today, it is statistically certain that thousands of energy jets should be pointed toward the Earth, some more directly than others. In many cases it is likely that the brighter the quasar, the more directly its jet is aimed at the Earth. Such quasars are called blazars. The hyperluminous quasar APM 08279+5255 was, when discovered in 1998, given an absolute magnitude of −32.2. High-resolution imaging with the Hubble Space Telescope and the 10 m Keck Telescope revealed that this system is gravitationally lensed. A study of the gravitational lensing of this system suggests that the light emitted has been magnified by a factor of ~10. It is still substantially more luminous than nearby quasars such as 3C 273. Quasars were much more common in the early universe than they are today. This discovery by Maarten Schmidt in 1967 was early strong evidence against steady-state cosmology and in favor of the Big Bang cosmology. Quasars show the locations where supermassive black holes are growing rapidly (by accretion). Detailed simulations reported in 2021 showed that galaxy structures, such as spiral arms, use gravitational forces to 'put the brakes on' gas that would otherwise orbit galaxy centers forever; instead the braking mechanism enabled the gas to fall into the supermassive black holes, releasing enormous radiant energies. These black holes co-evolve with the mass of stars in their host galaxy in a way not fully understood at present. One idea is that jets, radiation and winds created by the quasars shut down the formation of new stars in the host galaxy, a process called "feedback". The jets that produce strong radio emission in some quasars at the centers of clusters of galaxies are known to have enough power to prevent the hot gas in those clusters from cooling and falling on to the central galaxy. Quasars' luminosities are variable, with time scales that range from months to hours. This means that quasars generate and emit their energy from a very small region, since each part of the quasar would have to be in contact with other parts on such a time scale as to allow the coordination of the luminosity variations. This would mean that a quasar varying on a time scale of a few weeks cannot be larger than a few light-weeks across. The emission of large amounts of power from a small region requires a power source far more efficient than the nuclear fusion that powers stars. The conversion of gravitational potential energy to radiation by infalling to a black hole converts between 6% and 32% of the mass to energy, compared to 0.7% for the conversion of mass to energy in a star like our Sun. It is the only process known that can produce such high power over a very long term. (Stellar	(QSOs), a name which reflected their unknown nature, and this became shortened to "quasar". Early observations (1960s and earlier) The first quasars (3C 48 and 3C 273) were discovered in the late 1950s, as radio sources in all-sky radio surveys. They were first noted as radio sources with no corresponding visible object. Using small telescopes and the Lovell Telescope as an interferometer, they were shown to have a very small angular size. By 1960, hundreds of these objects had been recorded and published in the Third Cambridge Catalogue while astronomers scanned the skies for their optical counterparts. In 1963, a definite identification of the radio source 3C 48 with an optical object was published by Allan Sandage and Thomas A. Matthews. Astronomers had detected what appeared to be a faint blue star at the location of the radio source and obtained its spectrum, which contained many unknown broad emission lines. The anomalous spectrum defied interpretation. British-Australian astronomer John Bolton made many early observations of quasars, including a breakthrough in 1962. Another radio source, 3C 273, was predicted to undergo five occultations by the Moon. Measurements taken by Cyril Hazard and John Bolton during one of the occultations using the Parkes Radio Telescope allowed Maarten Schmidt to find a visible counterpart to the radio source and obtain an optical spectrum using the Hale Telescope on Mount Palomar. This spectrum revealed the same strange emission lines. Schmidt was able to demonstrate that these were likely to be the ordinary spectral lines of hydrogen redshifted by 15.8%, at the time, a high redshift (with only a handful of much fainter galaxies known with higher redshift). If this was due to the physical motion of the "star", then 3C 273 was receding at an enormous velocity, around , far beyond the speed of any known star and defying any obvious explanation. Nor would an extreme velocity help to explain 3C 273's huge radio emissions. If the redshift was cosmological (now known to be correct), the large distance implied that 3C 273 was far more luminous than any galaxy, but much more compact. Also, 3C 273 was bright enough to detect on archival photographs dating back to the 1900s; it was found to be variable on yearly timescales, implying that a substantial fraction of the light was emitted from a region less than 1 light-year in size, tiny compared to a galaxy. Although it raised many questions, Schmidt's discovery quickly revolutionized quasar observation. The strange spectrum of 3C 48 was quickly identified by Schmidt, Greenstein and Oke as hydrogen and magnesium redshifted by 37%. Shortly afterwards, two more quasar spectra in 1964 and five more in 1965 were also confirmed as ordinary light that had been redshifted to an extreme degree. While the observations and redshifts themselves were not doubted, their correct interpretation was heavily debated, and Bolton's suggestion that the radiation detected from quasars were ordinary spectral lines from distant highly redshifted sources with extreme velocity was not widely accepted at the time. Development of physical understanding (1960s) An extreme redshift could imply great distance and velocity but could also be due to extreme mass or perhaps some other unknown laws of nature. Extreme velocity and distance would also imply immense power output, which lacked explanation. The small sizes were confirmed by interferometry and by observing the speed with which the quasar as a whole varied in output, and by their inability to be seen in even the most powerful visible-light telescopes as anything more than faint starlike points of light. But if they were small and far away in space, their power output would have to be immense and difficult to explain. Equally, if they were very small and much closer to our galaxy, it would be easy to explain their apparent power output, but less easy to explain their redshifts and lack of detectable movement against the background of the universe. Schmidt noted that redshift is also associated with the expansion of the universe, as codified in Hubble's law. If the measured redshift was due to expansion, then this would support an interpretation of very distant objects with extraordinarily high luminosity and power output, far beyond any object seen to date. This extreme luminosity would also explain the large radio signal. Schmidt concluded that 3C 273 could either be an individual star around 10 km wide within (or near to) our galaxy, or a distant active galactic nucleus. He stated that a distant and extremely powerful object seemed more likely to be correct. Schmidt's explanation for the high redshift was not widely accepted at the time. A major concern was the enormous amount of energy these objects would have to be radiating, if they were distant. In the 1960s no commonly accepted mechanism could account for this. The currently accepted explanation, that it is due to matter in an accretion disc falling into a supermassive black hole, was only suggested in 1964 by Edwin Salpeter and Yakov Zel'dovich, and even then it was rejected by many astronomers, because in the 1960s, the existence of black holes was still widely seen as theoretical and too exotic, and because it was not yet confirmed that many galaxies (including our own) have supermassive black holes at their center. The strange spectral lines in their radiation, and the speed of change seen in some quasars, also suggested to many astronomers and cosmologists that the objects were comparatively small and therefore perhaps bright, massive and not far away; accordingly that their redshifts were not due to distance or velocity, and must be due to some other reason or an unknown process, meaning that the quasars were not really powerful objects nor at extreme distances, as their redshifted light implied. A common alternative explanation was that the redshifts were caused by extreme mass (gravitational redshifting explained by general relativity) and not by extreme velocity (explained by special relativity). Various explanations were proposed during the 1960s and 1970s, each with their own problems. It was suggested that quasars were nearby objects, and that their redshift was not due to the expansion of space but rather to light escaping a deep gravitational well. This would require a massive object, which would also explain the high luminosities. However, a star of sufficient mass to produce the measured redshift would be unstable and in excess of the Hayashi limit. Quasars also show forbidden spectral emission lines, previously only seen in hot gaseous nebulae of low density, which would be too diffuse to both generate the observed power and fit within a deep gravitational well. There were also serious concerns regarding the idea of cosmologically distant quasars. One strong argument against them was that they implied energies that were far in excess of known energy conversion processes, including nuclear fusion. There were suggestions that quasars were made of some hitherto unknown stable form of antimatter in similarly unknown types of region of space, and that this might account for their brightness. Others speculated that quasars were a white hole end of a wormhole, or a chain reaction of numerous supernovae. Eventually, starting from about the 1970s, many lines of evidence (including the first X-ray space observatories, knowledge of black holes and modern models of cosmology) gradually demonstrated that the quasar redshifts are genuine and due to the expansion of space, that quasars are in fact as powerful and as distant as Schmidt and some other astronomers had suggested, and that their energy source is matter from an accretion disc falling onto a supermassive black hole. This included crucial evidence from optical and X-ray viewing of quasar host galaxies, finding of "intervening" absorption lines, which explained various spectral anomalies, observations from gravitational lensing, Peterson and Gunn's 1971 finding that galaxies containing quasars showed the same redshift as the quasars, and Kristian's 1973 finding that the "fuzzy" surrounding of many quasars was consistent with a less luminous host galaxy. This model also fits well with other observations suggesting that many or even most galaxies have a massive central black hole. It would also explain why quasars are more common in the early universe: as a quasar draws matter from its accretion disc, there comes a point when there is less matter nearby, and energy production falls off or ceases, as the quasar becomes a more ordinary type of galaxy. The accretion-disc energy-production mechanism was finally modeled in the 1970s, and black holes were also directly detected (including evidence showing that supermassive black holes could be found at the centers of our own and many other galaxies), which resolved the concern that quasars were too luminous to be a result of very distant objects or that a suitable mechanism could not be confirmed to exist in nature. By 1987 it was "well accepted" that this was the correct explanation for quasars, and the cosmological distance and energy output of quasars was accepted by almost all researchers. Modern observations (1970s onward) Later it was found that not all quasars have strong radio emission; in fact only about 10% are "radio-loud". Hence the name "QSO" (quasi-stellar object) is used (in addition to "quasar") to refer to these objects, further categorised into the "radio-loud" and the "radio-quiet" classes. The discovery of the quasar had large implications for the field of astronomy in the 1960s, including drawing physics and astronomy closer together. In 1979 the gravitational lens effect predicted by Albert Einstein's general theory of relativity was confirmed observationally for the first time with images of the double quasar 0957+561. A study published in February, 2021, showed that there are more quasars in one direction (towards Hydra) than in the opposite direction, seemingly indicating that we are moving in that direction. But the direction of this dipole is about 28° away from the direction of our motion relative to the cosmic microwave background radiation. In March, 2021, a collaboration of scientists, related to the Event Horizon Telescope, presented, for the first time, a polarized-based image of a black hole, particularly the black hole at the center of Messier 87, an elliptical galaxy approximately 55 million light-years away in the constellation Virgo, revealing the forces giving rise to quasars. Current understanding It is now known that quasars are distant but extremely luminous objects, so any light that reaches the Earth is redshifted due to the metric expansion of space. Quasars inhabit the centers of active galaxies and are among the most luminous, powerful, and energetic objects known in the universe, emitting up to a thousand times the energy output of the Milky Way, which contains 200–400 billion stars. This radiation is emitted across the electromagnetic spectrum, almost uniformly, from X-rays to the far infrared with a peak in the ultraviolet optical bands, with some quasars also being strong sources of radio emission and of gamma-rays. With high-resolution imaging from ground-based telescopes and the Hubble Space Telescope, the "host galaxies" surrounding the quasars have been detected in some cases. These galaxies are normally too dim to be seen against the glare of the quasar, except with special techniques. Most quasars, with the exception of 3C 273, whose average apparent magnitude is 12.9, cannot be seen with small telescopes. Quasars are believed—and in many cases confirmed—to be powered by accretion of material into supermassive black holes in the nuclei of distant galaxies, as suggested in 1964 by Edwin Salpeter and Yakov Zel'dovich. Light and other radiation cannot escape from within the event horizon of a black hole. The energy produced by a quasar is generated outside the black hole, by gravitational stresses and immense friction within the material nearest to the black hole, as it orbits and falls inward. The huge luminosity of quasars results from the accretion discs of central supermassive black holes, which can convert between 6% and 32% of the mass of an object into energy, compared to just 0.7% for the p–p chain nuclear fusion process that dominates the energy production in Sun-like stars. Central masses of 105 to 109 solar masses have been measured in quasars by using reverberation mapping. Several dozen nearby large galaxies, including our own Milky Way galaxy, that do not have an active center and do not show any activity similar to a quasar, are confirmed to contain a similar supermassive black hole in their nuclei (galactic center). Thus it is now thought that all large galaxies have a black hole of this kind, but only a small fraction have sufficient matter in the right kind of orbit at their center to become active and power radiation in such a way as to be seen as quasars. This also explains why quasars were more common in the early universe, as this energy production ends when the supermassive black hole consumes all of the gas and dust near it. This means that it is possible that most galaxies, including the Milky Way, have gone through an active stage, appearing as a quasar or some other class of active galaxy that depended on the black-hole mass and the accretion rate, and are now quiescent because they lack a supply of matter to feed into their central black holes to generate radiation. The matter accreting onto the black hole is unlikely to fall directly in, but will have some angular momentum around the black hole, which will cause the matter to collect into an accretion disc. Quasars may also be ignited or re-ignited when normal galaxies merge and the black hole is infused with a fresh source of matter. In fact, it has been suggested that a
Shrovetide rods (fastelavnsris), which "branches decorated with sweets, little presents, etc., that are used to decorate the home or give to children." In the Revised Common Lectionary the Sunday before Lent is designated "Transfiguration Sunday", and the gospel reading is the story of the Transfiguration of Jesus from Matthew, Mark, or Luke. Some churches whose lectionaries derive from the RCL, e.g. the Church of England, use these readings but do not designate the Sunday "Transfiguration Sunday". Etymology The name Quinquagesima originates from Latin quinquagesimus (fiftieth). This is in reference to the fifty days before Easter Day using inclusive counting which counts both Sundays (normal counting would count only one of these). Since the forty days of Lent do not include Sundays, the first day of Lent, Ash Wednesday, succeeds Quinquagesima Sunday by only three days. The name Estomihi is derived from the incipit or opening words of the Introit for the Sunday, Esto mihi in Deum protectorem, et in locum refugii, ut salvum me facias, ("Be Thou unto me a God, a Protector, and a place of refuge, to save me") . Dates and significance The earliest Quinquagesima Sunday can occur is February 1 and the latest is March 7. Recent and upcoming dates: Western Christianity Roman Catholic Church In the Roman Catholic Church, the terms for this Sunday (and the two immediately before it — Sexagesima and Septuagesima Sundays) were eliminated in the reforms following the Second Vatican Council, and these Sundays are part of Ordinary Time. According to the reformed Roman Rite Roman Catholic calendar, this Sunday is now known by its number within Ordinary Time — fourth through ninth, depending upon the date of Easter. The earlier form of the Roman Rite, with its references to Quinquagesima Sunday, and to the Sexagesima and Septuagesima Sundays, continues to be observed in some communities. In traditional lectionaries, the Sunday concentrates on , "Jesus took the twelve aside and said, 'Lo, we go to Jerusalem, and everything written by the prophets about the Son of Man shall be fulfilled' ... The disciples, however, understood none of this," which from verse 35 is followed by Luke's version of Healing the blind near Jericho. The passage presages the themes of Lent and Holy Week. In most churches, palms blessed on Palm Sunday of the previous year are burned on this day after the last Mass of the day, the ashes of these burned palms are used for the liturgy of Ash Wednesday. Lutheran Churches In Lutheranism is combined with (Paul's praise of love). Composers writing cantatas for Estomihi Sunday include: Johann Sebastian Bach: BWV 22, 23, 127 and 159 (see Church cantata (Bach)#Estomihi) Christoph Graupner: 25 cantatas (see List of cantatas	Roman Rite, with its references to Quinquagesima Sunday, and to the Sexagesima and Septuagesima Sundays, continues to be observed in some communities. In traditional lectionaries, the Sunday concentrates on , "Jesus took the twelve aside and said, 'Lo, we go to Jerusalem, and everything written by the prophets about the Son of Man shall be fulfilled' ... The disciples, however, understood none of this," which from verse 35 is followed by Luke's version of Healing the blind near Jericho. The passage presages the themes of Lent and Holy Week. In most churches, palms blessed on Palm Sunday of the previous year are burned on this day after the last Mass of the day, the ashes of these burned palms are used for the liturgy of Ash Wednesday. Lutheran Churches In Lutheranism is combined with (Paul's praise of love). Composers writing cantatas for Estomihi Sunday include: Johann Sebastian Bach: BWV 22, 23, 127 and 159 (see Church cantata (Bach)#Estomihi) Christoph Graupner: 25 cantatas (see List of cantatas by Christoph Graupner#GWV 1119) Georg Philipp Telemann: 21 extant cantatas, including TWV 1:1258 (Harmonischer Gottes-Dienst). Lutheran countries such as Denmark mark Quinquagesima Sunday as the peak of the Fastelavn. After attending the Mass on Shrove Sunday, congregants enjoy Shrovetide buns (fastelavnsboller), "round sweet buns that are covered with icing and filled with cream and/or jam." Children often dress up and collect money from people while singing. They also practice the tradition of hitting a barrel, which represents fighting Satan; after doing this, children enjoy the sweets inside the barrel. Lutheran Christians in these nations carry Shrovetide rods (fastelavnsris), which "branches decorated with sweets, little presents, etc., that are used to decorate the home or give to children." Anglican Communion This Sunday
the family Simaroubaceae. Its size is disputed; some botanists treat it as consisting of only one species, Quassia amara from tropical South America, while others treat it in a wide circumscription as a pantropical genus containing up to 40 species of trees and shrubs. The genus was named after a former slave from Suriname, Graman Quassi in the eighteenth century. He discovered the medicinal properties of the bark of Quassia amara. Distribution Members of the genus are found in the Tropics throughout the world. Countries and regions where species are native include: Andaman Islands, Angola, Bangladesh, Belize, Benin, Bismarck Archipelago, Borneo, North and Northeast Brazil, Burkina,	America, while others treat it in a wide circumscription as a pantropical genus containing up to 40 species of trees and shrubs. The genus was named after a former slave from Suriname, Graman Quassi in the eighteenth century. He discovered the medicinal properties of the bark of Quassia amara. Distribution Members of the genus are found in the Tropics throughout the world. Countries and regions where species are native include: Andaman Islands, Angola, Bangladesh, Belize, Benin, Bismarck Archipelago, Borneo, North and Northeast Brazil, Burkina, Cabinda, Cambodia, Cameroon, Central African Republic, Chad, Colombia, Comoros, Congo, Costa Rica, El Salvador, Equatorial Guinea, Gabon, Gambia, Ghana, Guatemala, Guinea, Guinea-Bissau, Gulf of Guinea Islands, Honduras, India, Ivory Coast, Kenya, Laos, Leeward Islands, Liberia, Madagascar, Malaya, Mali, Central, Southeast
surname as a term predates World War II. The first recorded use of the term was by Norwegian Labour Party politician Oscar Torp in a 2 January 1933 newspaper interview, where he used it as a general term for Quisling's followers. Quisling was at this point in the process of establishing the Nasjonal Samling (National Unity) party, a fascist party modelled on the German Nazi Party. Further uses of the term were made by Aksel Sandemose, in a newspaper article in Dagbladet in 1934, and by the newspaper Vestfold Arbeiderblad, in 1936. The term with the opposite meaning, a Norwegian patriot, is Jøssing. Popularization in World War II The use of the name as a term for collaborators or traitors in general probably came about upon Quisling's unsuccessful 1940 coup d'état, when he attempted to seize power and make Norway cease resisting the invading Germans. The term was widely introduced to an English-speaking audience by the British newspaper The Times. It published an editorial on 19 April 1940 titled "Quislings everywhere", in which it was asserted that "To writers, the word Quisling is a gift from the gods. If they had been ordered to invent a new word for traitor... they could hardly have hit upon a more brilliant combination of letters. Aurally it contrives to suggest something at once slippery and tortuous." The Daily Mail picked up the term four days after The Times editorial was published. The War Illustrated discussed "potential Quislings" among the Dutch during the German invasion of the Netherlands. Subsequently, the BBC brought the word into common use internationally. Chips Channon described how during the Norway Debate of 7–8 May 1940, he and other Conservative MPs who supported Prime Minister of the United Kingdom Neville Chamberlain called those who voted against a motion of no confidence "Quislings". Chamberlain's successor Winston Churchill used the term during an address to the Allied Delegates at St. James's Palace on 21 June 1941, when he said: "A vile race of Quislings—to use a new word which will carry the scorn of mankind down the centuries—is hired to fawn upon the conqueror, to collaborate in his designs and to enforce his rule upon their fellow countrymen while grovelling low themselves." He used the term again in an address to both houses of Congress in the United States of America on 26 December 1941. Commenting upon the effect of a number of Allied victories against Axis forces, and	to enforce his rule upon their fellow countrymen while grovelling low themselves." He used the term again in an address to both houses of Congress in the United States of America on 26 December 1941. Commenting upon the effect of a number of Allied victories against Axis forces, and moreover the United States’ decision to enter the war, Churchill opined: "Hope has returned to the hearts of scores of millions of men and women, and with that hope there burns the flame of anger against the brutal, corrupt invader. And still more fiercely burn the fires of hatred and contempt for the filthy Quislings whom he has suborned." The term subsequently entered the language and became a target for political cartoonists. In the United States, it was used often. In the Warner Bros. cartoon Tom Turk and Daffy (1944), it was uttered by a Thanksgiving turkey whose presence is betrayed to Porky Pig by Daffy Duck. In the American film Edge of Darkness (1943), about the Resistance in Norway, the heroine's brother is often described as a quisling. Verb form The back-formed verb, to quisle () exists, and gave rise to a much less common version of the noun: quisler. However, the verb form was rare even during World War II and has entirely disappeared from contemporary usage. Postwar use "Quisling" was applied to some who cooperated with communist takeovers. As an illustration, the renegade social democrat Zdeněk Fierlinger of Czechoslovakia was frequently derided as "Quislinger" for his collaboration with the Communist Party of Czechoslovakia. "The Patriot Game", one of the best known songs to emerge from the Irish nationalist struggle, includes the line "...those quislings who sold out the Patriot Game" in some versions (although the original uses "cowards" and other versions substitute "rebels" or "traitors"). In the Norwegian television series Occupied, Norwegians who are seen as collaborating with the Russian invaders and later with European Union peacekeepers are called Quislings. In the epilogue of Farnham's Freehold by Robert A. Heinlein, a sign is posted listing available goods and services. One of the items listed is "Jerked Quisling (by the neck)". 21st century In the early 21st century, the term demonstrated continued currency as it was used by some American writers to describe President Donald Trump and his associates. In a June 2018 New York Times column, Paul Krugman called US President Trump a "quisling", in reference to what Krugman described as Trump's "serv[ing] the interests of foreign masters at his own country’s expense" and "defend[ing] Russia while attacking our closest allies". Other publications also applied the term. For instance, Joe Scarborough in the Washington Post ("These are desperate times
North America Quadrangle (Springfield, Massachusetts), a cluster of museums and cultural institutions Quadrangle Dormitories (University of Pennsylvania) Francis Quadrangle, University of Missouri Memorial Quadrangle, Yale University Radcliffe Quadrangle (Harvard) Schenley Quadrangle, University of Pittsburgh University of Alabama Quad, University of Alabama Europe Mob Quad, Merton College, Oxford Radcliffe Quadrangle, University College, Oxford Tom Quad (Great Quadrangle), Christ Church, Oxford Main Quad at the Main Building of University College London Oceania University of Sydney Quadrangle, a sandstone building at the University of Sydney (Camperdown) Other Quadrangle (geography), a United States Geological Survey topographical map Quadrangle (horse), American thoroughbred,	College, Oxford Radcliffe Quadrangle, University College, Oxford Tom Quad (Great Quadrangle), Christ Church, Oxford Main Quad at the Main Building of University College London Oceania University of Sydney Quadrangle, a sandstone building at the University of Sydney (Camperdown) Other Quadrangle (geography), a United States Geological Survey topographical map Quadrangle (horse), American thoroughbred, winner of the 1964 Belmont Stakes Quadrangle Books, an imprint of Times Books Quadrangle Group investment fund in New York City BDP
images on manuscripts, although many illuminators and painters preferred fine brushes for their work. The variety of different strokes in formal hands was accomplished by good penmanship as the tip was square cut and rigid, exactly as it is today with modern steel pens. It was much later, in the 1600s, with the increased popularity of writing, especially in the copperplate script promoted by the many printed manuals available from the 'Writing Masters', that quills became more pointed and flexible. Quills are denominated from the order in which they are fixed in the wing; the first is favoured by the expert calligrapher, the second and third quills being very satisfactory also, plus the pinion feather. Flags the 5th and 6th feathers are also used. No other feather on the wing would be considered suitable by a professional scribe. Information can be obtained on the techniques of curing and cutting quills: In order to harden a quill that is soft, thrust the barrel into hot ashes, stirring it till it is soft; then taking it out, press it almost flat upon your knees with the back of a penknife, and afterwards reduce it to a roundness with your fingers. If you have a number to harden, set water and alum over the fire; and while it is boiling put in a handful of quills, the barrels only, for a minute, and then lay them by. An accurate account of the Victorian process by William Bishop, from researches with one of the last London quill dressers, is recorded in the Calligrapher's Handbook cited on this page. As a symbol From the 19th century in radical and socialist symbolism, quills have been used to symbolize clerks and intelligentsia. Some notable examples are the Radical Civic Union, the Czech National Social Party in combination with the hammer, symbol of the labour movement, or the Democratic Party of Socialists of Montenegro. Quills appear on the seals of the United States Census Bureau and the Administrative Office of the United States Courts. They also appear in the coats of arms of several US Army Adjutant general units which focus on administrative duties. Quills are on the coats of arms of a number of municipalities such as Bargfeld-Stegen in Germany and La Canonja in Spain. Three books and a quill pen are the symbols of Saint Hilary of Poitiers. Quill and pen knives A quill knife was the original primary tool used for cutting and sharpening quills, known as "dressing". Following the decline of the quill in the 1820s, after the introduction of the maintenance-free, mass-produced steel dip nib by John Mitchell, knives were still manufactured but became known as desk knives, stationery knives or latterly as the name stuck "pen" knives. There is a small but significant difference between a pen knife	clerks and intelligentsia. Some notable examples are the Radical Civic Union, the Czech National Social Party in combination with the hammer, symbol of the labour movement, or the Democratic Party of Socialists of Montenegro. Quills appear on the seals of the United States Census Bureau and the Administrative Office of the United States Courts. They also appear in the coats of arms of several US Army Adjutant general units which focus on administrative duties. Quills are on the coats of arms of a number of municipalities such as Bargfeld-Stegen in Germany and La Canonja in Spain. Three books and a quill pen are the symbols of Saint Hilary of Poitiers. Quill and pen knives A quill knife was the original primary tool used for cutting and sharpening quills, known as "dressing". Following the decline of the quill in the 1820s, after the introduction of the maintenance-free, mass-produced steel dip nib by John Mitchell, knives were still manufactured but became known as desk knives, stationery knives or latterly as the name stuck "pen" knives. There is a small but significant difference between a pen knife and a quill knife, in that the quill knife has a blade that is flat on one side and convex on the other which facilitates the round cuts required to shape a quill. A "pen" knife by contrast has two flat sides. This distinction is not recognised by modern traders, dealers or collectors, who define a quill knife as any small knife with a fixed or hinged blade, including such items as ornamental fruit knives. Today While quills are rarely used as writing instruments in the modern day, they are still being produced as specialty items, mostly for hobbyists. Such quills tend to have metal nibs or are sometimes even outfitted with a ballpoint pen inside to remove the need for a separate source of ink. According to the Supreme Court Historical Society, 20 goose-quill pens, neatly crossed, are placed at the four counsel tables each day the U.S. Supreme Court is in session; "most lawyers appear before the Court only once, and gladly take the quills home as souvenirs." This has been done since the earliest sessions of the Court. In the Jewish tradition quill pens, called kulmus (), are used by scribes to write Torah Scrolls, Mezuzot, and Tefillin. Music Plectra for psalteries and lutes can be cut similarly to writing pens. The rachis, the portion of the stem between the barbs, not the calamus, of the primary flight feathers of birds of the Corvidae was preferred for harpsichords. In modern instruments, plastic is more common, but they are
going to Rome to be crucified again"). Peter then gains the courage to continue his ministry and returns to the city, where he is martyred by being crucified upside-down. The Church of Domine Quo Vadis in Rome is built where the meeting between Peter and Jesus allegedly took place. The words "quo vadis" as a question also occur at least seven times in the Latin Vulgate. In culture The Polish writer Henryk Sienkiewicz wrote the novel Quo Vadis: A	risen Christ during their encounter along the Appian Way. According to the apocryphal Acts of Peter (Vercelli Acts XXXV; late 2nd century AD), as Peter flees from crucifixion in Rome at the hands of the government, and along the road outside the city, he meets the risen Jesus. In the Latin translation, Peter asks Jesus, "Quō vādis?" He replies, "Rōmam eō iterum crucifīgī" ("I am going to Rome to be crucified again"). Peter then gains the courage to continue his ministry and returns to the city, where he is martyred by being crucified upside-down. The Church of Domine Quo Vadis in Rome is built where the meeting between Peter and Jesus allegedly took place. The words "quo vadis" as a question also occur at least seven times in the Latin Vulgate. In
Pennsylvania Music QED (band), a 1980s Australian band Q.E.D. (Terje Rypdal album), 1993 Q.E.D. (Jim Allchin album) QED Records or Emanem Records Other uses Granville Gee Bee R-6, named "Q.E.D.", a 1930s racing monoplane QED: The Strange Theory of Light and Matter, a 1985 physics book by Richard Feynman Quod Erat Demonstrandum, a 1903 novel by Gertrude Stein ''Q.E.D. (novel), a 1930 mystery novel by Lynn Brock Quod Erat Demonstrandum (film), a 2013 Romanian drama film QED (play), a 2001 play by Peter Parnell about Richard Feynman Q.E.D. (manga), a 1997 manga by Motohiro Katou QED International, a film company QED: Question,	disk image format for machine emulation and virtualization Quantum Effect Devices, a microprocessor design company Television KQED (TV), public television station in San Francisco, California Q.E.D. (U.S. TV series) Q.E.D. (UK TV series) WQED (TV), public television station in Pittsburgh, Pennsylvania Music QED (band), a 1980s Australian band Q.E.D. (Terje Rypdal album), 1993 Q.E.D. (Jim Allchin album) QED Records or Emanem Records Other uses Granville Gee Bee R-6, named "Q.E.D.", a 1930s racing
served pride cookies to its passengers. It had a rainbow roo float in the Mardi Gras parade. There has been criticism of Qantas using its corporate power to prosecute the private interests on their staff and the community. Peter Dutton has said that chief executives such as Alan Joyce at Qantas should "stick to their knitting" rather than using the company's brand to advocate for political causes. A senior church leader has made similar comments. Despite the criticism, Qantas will continue to advocate for marriage equality which will include offering customers specially commissioned rings with the phrase, "until we all belong". This phrase will also appear on Qantas boarding passes and other paraphernalia. The cost of the campaign by Qantas and other participating companies is expected to be more than $5 million. Joyce has pledged Qantas will, "continue social-justice campaigning". In relation to a rugby player, sacked by Rugby Australia which is financially supported by Qantas, following his social media postings on homosexuality. Fundamental structural change In August 2011, the company announced that following financial losses of A$200 million ($209 million) for the year ending June 2011 and a decline in market share, major structural changes would be made. One planned change that did not come to fruition was the plan to create a new Asia-based premium airline that would operate under a different name. In addition to this plan, Qantas announced it planned to cut 1,000 jobs. The reforms included route changes, in particular the cessation of services to London via Hong Kong and Bangkok. While Qantas still operated in these cities, onward flights to London would be via its Oneworld partner British Airways under a code-share service. The following year Qantas reported an A$245 million full-year loss to the end of June 2012, citing high fuel prices, intense competition and industrial disputes. This was the first full year loss since Qantas was fully privatised 17 years previously, in 1995, and led to the airline cancelling its order of 35 new Boeing 787 aircraft, to reduce its spending. Qantas subsequently divested itself of its 50% holding of StarTrack, Australia's largest road freight company, in part for acquiring full interest in Australian airExpress. On 26 March 2012, Qantas set up Jetstar Hong Kong with China Eastern Airlines Corporation, which was intended to begin flights in 2013, but became embroiled in a protracted approval process. Qantas and Emirates began an alliance on 31 March 2013, in which their combined carriers offered 98 flights per week to Dubai, that saw bookings up six-fold. In September 2013, following the announcement the carrier expected another A$250 million ( million) net loss for the half-year period that ended on 31 December and the implementation of further cost-cutting measures that would see the cut of 1,000 jobs within a year, S&P downgraded Qantas credit from BBB- (the lowest investment grade) to BB+. Moody's applied a similar downgrading a month later. Losses continued into 2014 reporting year, with the Qantas Group reporting a half year loss of A$235 million ( million) and eventual full year loss of A$2.84 billion. In February 2014 additional cost-cutting measures to save A$2 billion, including the loss of 5,000 jobs that will see the workforce lowered from 32,000 to 27,000 by 2017 were announced. In May 2014 the company stated it expected to shed 2,200 jobs by June 2014, including those of 100 pilots. The carrier also reduced the size of its fleet by retiring aircraft and deferring deliveries; and planned to sell some of its assets. With 2,200 employees laid off by June 2014, another 1,800 job positions were planned to be cut by June 2015. Also during 2014 the Qantas Sale Act, under which the airline was privatised, was amended to repeal parts of section 7. That act limits foreign ownership of Qantas to 49 percent, with foreign airlines subject to further restrictions, including a 35-percent limit for all foreign airline shareholdings combined. In addition, a single foreign entity can hold no more than 25 percent of the airline's shares. The airline returned to profit in 2015, announcing a A$557 million after tax profit in August 2015, in contrast with a A$2.84 billion loss the year earlier. In 2015, Qantas sold its lease of Terminal 3 at Sydney Airport, which was due to continue until 2019, back to Sydney Airport Corporation for $535 million. This meant Sydney Airport resumed operational responsibility of the terminal, including the lucrative retail areas. Uniform Paris-based Australian designer Martin Grant is responsible for the new Qantas airline staff uniforms that were publicly unveiled on 16 April 2013. These were to replace the previous uniforms, dubbed colloquially as "Morrisey" by staff after the designer, Peter Morrissey. The new outfits combine the colours of navy blue, red and fuchsia pink. Qantas chief executive Alan Joyce stated that the new design "speaks of Australian style on the global stage" at the launch event that involved Qantas employees modelling the uniforms. Grant consulted with Qantas staff members over the course of one year to finalise the 35 styles that were eventually created. Not all employees were happy with the new uniform, however, with one flight attendant being quoted as saying "The uniforms are really tight and they are simply not practical for the very physical job we have to do." Destinations Qantas operates flightseeing charters to Antarctica on behalf of Croydon Travel. It first flew Antarctic flightseeing trips in 1977. They were suspended for a number of years due to the crash of Air New Zealand Flight 901 on Mount Erebus in 1979. Qantas restarted the flights in 1994. Although these flights do not touch down, they require specific polar operations and crew training due to factors like sector whiteout, which contributed to the 1979 Air New Zealand disaster. With Flights 7 and 8 – a non-stop service between Sydney and Dallas/Fort Worth operated by the Airbus A380 – commencing on 29 September 2014, Qantas operated the world's longest passenger flight on the world's largest passenger aircraft. This was overtaken on 1 March 2016 by Emirates' new Auckland-Dubai service. After it ordered Boeing 787 aircraft, Qantas announced an intention to launch non-stop flights between Australia and the United Kingdom during March 2018 from Perth to London. The inaugural flight left Perth on 24 March. On 19 March 2020, Qantas confirmed it would suspend all international flights and about 60% of domestic flights from the end of March until at least 31 May 2020 following expanded government travel restrictions due to the COVID-19 pandemic. Codeshare agreements , Qantas had codeshare agreements with the following airlines: Air France Air New Zealand Air Niugini Air Tahiti Nui Air Vanuatu Aircalin Airnorth Alaska Airlines American Airlines Asiana Airlines Bangkok Airways British Airways Cathay Pacific China Airlines China Eastern Airlines China Southern Airlines El Al Emirates Fiji Airways Finnair ITA Airways Japan Airlines Jetstar Jetstar Asia Jetstar Japan Jetstar Pacific KLM LATAM Chile Solomon Airlines SriLankan Airlines Vietnam Airlines WestJet Joint ventures In addition to the above codeshares, Qantas has entered into joint ventures with the following airlines: American Airlines China Eastern Airlines Emirates Fleet , Qantas and its subsidiaries operated 297 aircraft, including 71 aircraft by Jetstar Airways; 90 by the various QantasLink-branded airlines and six by Express Freighters Australia (on behalf of Qantas Freight, which also wet leases three Atlas Air Boeing 747-400Fs). Liveries Indigenous Art liveries Two Qantas aircraft are currently decorated with an Indigenous Australian art scheme. One aircraft, a Boeing 737–800, wears a livery called Mendoowoorrji, which was revealed in November 2013. The design was drawn from the late West Australian Aboriginal artist Paddy Bedford. A Boeing 787–9 Dreamliner is adorned in a paint scheme inspired by the late Emily Kame Kngwarreye's 1991 painting Yam Dreaming. The adaptation of Yam Dreaming to the aircraft, led by Balarinji, a Sydney-based and Aboriginal-owned design firm, incorporates the red Qantas tailfin into the design, which includes white dots with red and orange tones. The design depicts the yam plant, an important and culturally significant symbol in Kngwarreye's Dreaming stories, and a staple food source in her home region of Utopia. The design was applied to the aircraft during manufacture, prior to its delivery in March 2018 to Alice Springs Airport, situated 230 kilometers southeast of Utopia, where the aircraft was met by Kngwarreye's descendants, the local community, and Qantas executives. The aircraft would later operate Qantas' inaugural nonstop services between Perth and London Heathrow, and between Melbourne and San Francisco, scheduled with Boeing 787 aircraft. Australian Aboriginal art designs have previously adorned some Qantas aircraft; the first design was called Wunala Dreaming, which was unveiled in 1994 and had been painted on now-retired Boeing 747–400 and 747-400ER aircraft between 1994 and 2012. The motif was an overall-red design depicting ancestral spirits in the form of kangaroos travelling in the outback. The second design was called Nalanji Dreaming and was depicted on a Boeing 747–300 from 1995 until its retirement in 2005. Nalanji Dreaming was a bright blue design inspired by rainforest landscape and tropical seas. The third design was titled Yananyi Dreaming, and featured a depiction of Uluru. The scheme was designed by Uluru-based artist Rene Kulitja, in collaboration with Balarinji. It was painted on the 737 at the Boeing factory prior to its delivery in 2002. It was repainted into the standard livery in 2014. Retro Roo liveries In November 2014 the airline revealed that the 75th Boeing 737–800 jet to be delivered would carry a 'retro-livery' based on the airline's 1971 'ochre' colour scheme design featuring the iconic 'Flying Kangaroo' on its tail and other aspects drawn from its 1970s fleet. The aircraft was delivered on 17 November. Qantas announced a second 737–800 would receive a 'retro roo' livery in October 2015. On 16 November 2015 the airline unveiled the second 'retro roo' 737, bearing a replica livery from 1959 to celebrate the airline's 95th birthday. Other liveries Several Qantas aircraft have been decorated with promotional liveries, promoting telecommunications company Optus; the Disney motion picture Planes; the Australian national association football team, the Socceroos; and the Australian national rugby union team, the Wallabies. Two aircraft – an Airbus A330-200 and a Boeing 747-400ER – were decorated with special liveries promoting the Oneworld airline alliance (of which Qantas is a member) in 2009. On 29 September 2014, nonstop Airbus A380 service to Dallas/Fort Worth International Airport was inaugurated using an A380 decorated with a commemorative cowboy hat and bandana on the kangaroo tail logo. Prior to the 2017 Sydney Mardi Gras, Qantas decorated one of its Airbus A330-300 aircraft with rainbow lettering and depicted a rainbow flag on the tail of the aircraft. Cabin Domestic Qantas domestic flights are primarily operated by Boeing 737–800 and Airbus A330-200 aircraft; Airbus A330-300s sometimes operate domestically as well. A two-class configuration (Business and Economy) is offered. Business Domestic Business Class is offered on all Boeing 737 and Airbus A330 aircraft. On the Boeing 737, Business is exclusively available in the first three rows of the cabin, with a seat configuration of 2–2, seat recline, and a larger pitch between seats. As the A330s operate international flights, Business Suites are sometimes available on domestic routes. These seats feature all-aisle access in a 1-2-1 configuration and a fully flat bed. Economy Domestic Economy Class is offered on all Boeing 737 and Airbus A330 aircraft. Seat pitch is usually and seat width ranges from . Layouts are 3–3 on the 737 and 2-4-2 on the A330. International Qantas international flights are primarily operated on Airbus A380s, A330-300s, Boeing 787s, and sometimes on Airbus A330-200s and Boeing 737-800s. Passenger class configuration varies by aircraft, with the Airbus A330-300 offering a two-class configuration of Business and Economy on short to medium-haul flights. This compares to the Airbus A380, which offers a four-class configuration of First, Business, Premium Economy, and Economy on selected long haul flights. First First class is offered exclusively on the Airbus A380. It offers 14 individual suites in a 1-1-1 layout. The seats rotate, facing forward for takeoff, but rotating to the side for dining and sleeping, with 83.5 in seat pitch (extending to a 212 cm fully flat bed) and a width of . Each suite has a widescreen HD monitor with 1,000 AVOD programs. In addition to 110 V AC power outlets, USB ports are offered for connectivity. Passengers are also able to make use of the on-board business lounge on the upper deck. Complimentary access to both the first class and business class lounges (or affiliated lounges) is offered. Updated versions of this seat were fitted to the airline's refurbished Airbus A380 aircraft from late 2019. This seat featured refreshed cushioning and larger entertainment screens compared to the older version seat. Business International Business class is offered on all Qantas mainline passenger aircraft. On all International and selected Domestic flights, Qantas offers two different types of Business Class seats, as listed below. Business Suites Business Suites are offered on all Boeing 787, Airbus A330-300, and selected Airbus A330-200 and A380 aircraft. These seats include beds and are in a 1-2-1 configuration. The Business Suite was introduced on the A330 in October 2014, and also contains a bed. This seat includes a Panasonic eX3 system with a touchscreen. By the end of 2016, the business class seats of Qantas' entire Airbus A330 fleet were refitted. Airbus A330 Business Suites are available on Asian routes, transcontinental routes across Australia and smaller routes such as the East Coast triangle. Updated versions of this seat were fitted to the airline's new Boeing 787 fleet from late 2017. Business Skybeds Business Skybeds are offered exclusively on selected A380 aircraft. On the Airbus A380, 64 fully-flat Skybed seats are available with seat pitch (converting to a 200 cm long bed). These seats are located on the upper deck in a 2-2-2 configuration in two separate cabins. Features include a 30 cm touchscreen monitor with 1,000 AVOD programmes and an on-board lounge. Airbus A380 Business Skybeds are available on Qantas' flagship routes such as Australia to/from London via Singapore, Los Angeles, Dallas, and Hong Kong (seasonal). The Skybed 1 (Mark I) version of the lie-flat seats, featured between 2003 and 2019 had of seat pitch and width; however passengers slept at a distinct slope to the cabin floor. The Skybed 2 (Mark II) version, introduced in 2008 has a pitch, and allows passengers to lie fully horizontal. On the now-retired Boeing 747, seating was in a 2-3-2 configuration on the main deck and a 2–2 configuration on the upper deck. Skybed seats on Boeing 747s featured a touchscreen monitor with 400 AVOD programs. Before their retirement, Boeing 747 Business Skybeds were available on Asian, African, and South American routes. In 2019, Qantas began the process of retrofitting its Airbus A380 aircraft with new Business Suites as offered on Airbus A330 and Boeing 787 aircraft. The aircraft will gain six business class seats compared to the previous configuration. Complimentary access to the Qantas business class lounge (or affiliated lounges) is also offered. Premium Economy Premium economy class is offered on all Airbus A380 and Boeing 787–9 aircraft. On the Airbus A380, the seat pitch ranges from , with a width of . On the Boeing 787, it is configured in a 2-3-2 seating arrangement around the middle of the aircraft, whereas it is in a 2-3-2 seating arrangement at the rear of the upper deck on the A380. The total number of seats depends on the aircraft type, as A380s have 35–60 seats, (depending on the configuration) and 787s have 28 seats. Qantas premium economy is presented as a lighter business class product rather than most other airlines' premium economy, which is often presented as a higher economy class, however Qantas premium economy does not offer access to premium lounges, and meals are only a slightly uprated version of economy class meals. In 2019, Qantas began the process of retrofitting its Airbus A380 aircraft with new Premium Economy seats, as offered on Boeing 787 aircraft. The aircraft will gain 25 premium economy seats compared to the previous configuration. Economy International Economy class is available on all Qantas mainline passenger aircraft. Seat pitch is usually and seat width ranges from . Layouts are 3–3 on the 737, 2-4-2 on the A330, 3-3-3 on the B787-9 and 3-4-3 on the 747. On the A380, the layout is 3-4-3 and there are four self-service snack bars located in between cabins. In 2019, Qantas began the process of retrofitting its Airbus A380 aircraft which includes new Economy seats with new seat cushions and improved inflight entertainment, as offered on Boeing 787 aircraft. The aircraft will have fewer economy seats compared to the previous configuration due to an increase in the number of premium seats. In-flight entertainment Every Qantas mainline aircraft has some form of video audio entertainment. Qantas has several types of in-flight entertainment (IFE) systems installed on its aircraft and refers to the in-flight experience as "On:Q". Audio-video entertainment systems The "Total Entertainment System" by Rockwell Collins was featured on selected domestic and international aircraft between 2000 and 2019. This AVOD system included personal LCD screens in all classes, located in the seat back for economy and business class, and in the armrest for premium economy and first class. The Mainscreen System is featured on selected Boeing 737–800 aircraft. This entertainment system, introduced between 2002 and 2011, has overhead video screens as the main form of entertainment. Movies are shown on the screens for lengthier flights or TV programmes on shorter flights. A news telecast will usually feature at the start of the flight. Audio options are less varied than on Q, iQ or the Total Entertainment System. The "iQ" inflight entertainment system by Panasonic Avionics Corporation is featured on all Boeing 747, and selected Airbus A380 and Boeing 737–800 aircraft. This audio video on demand (AVOD) experience, introduced in 2008, is based on the Panasonic Avionics system and features expanded entertainment options; touch screens; and new communications-related features such as Wi-Fi and mobile phone functionality; as well as increased support for electronics (such as USB and iPod connectivity). The "Q" inflight entertainment system by Panasonic Avionics Corporation in collaboration with Massive Interactive is featured on all Airbus A330-300, A330-200, Boeing 787 and selected Airbus A380 aircraft. This audio video on demand (AVOD) experience, introduced in 2014 and updated in 2018 on selected aircraft, is based on the Panasonic eX3 system and features extensive entertainment options; enhanced touch screens; and communications-related features such as Wi-Fi and mobile phone functionality; as well as increased support for electronics (such as USB and iPod connectivity). A "my flight" feature offers access to maps, playlists, and a service timeline showing when drinks and meals will be served and the best time for resting on long-haul flights. Wireless entertainment systems and Wi-Fi Q Streaming is an in-flight entertainment system in which entertainment is streamed to iPads or personal devices available in all classes on selected aircraft. A selection of movies, TV, music, and a kids' choice are available. In 2007, Qantas conducted a trial for use of mobile telephones with AeroMobile, during domestic services for three months on a Boeing 767. During the trial, passengers were allowed to send and receive text messages and emails but were not able to make or receive calls. Since 2014, Sky News Australia has provided multiple news bulletins both in-flight and in Qantas branded lounges. Previously, the Australian Nine Network provided a news bulletin for Qantas entitled Nine's Qantas Inflight News, which was the same broadcast as Nine's Early Morning News, however Nine lost the contract to Sky News. In July 2015, Qantas signed a deal with American cable network HBO to provide over 120 hours of television programming in-flight from the network which will be updated monthly, as well as original lifestyle and entertainment programming from both Foxtel and the National Geographic Channel. In 2017 Qantas commenced rolling out complimentary high speed Wi-Fi on domestic aircraft. The services utilises NBN Co Sky Muster satellites to deliver higher speeds than generally offered by onboard Wi-Fi. Previously, in July 2007 Qantas had announced Wi-Fi on would be available on its long haul A380s and 747-400s although that system ultimately did not proceed following trials. Inflight magazine Qantas: The Australian Way is the airline's in-flight magazine. In mid-2015, the magazine ended a 14-year publishing deal with Bauer Media, switching its publisher to Medium Rare. Services The Qantas Club Facilities The Qantas Club is the airline lounge for Qantas with airport locations around Australia and the world. Additionally, Qantas operates dedicated international first-class lounges in Sydney, Melbourne, Auckland, Los Angeles and Singapore. Domestically, Qantas also offers dedicated Business Lounges at Sydney, Melbourne, Brisbane, Canberra and Perth for domestic Business Class, Qantas Platinum and Platinum One, and OneWorld Emerald frequent flyers. In April 2013, Qantas opened its new flagship lounge in Singapore, the Qantas Singapore Lounge. This replaced the former separate first- and business-class lounges as a result of the new Emirates alliance. Similar combined lounges were also opened in Hong Kong in April 2014 and in Brisbane in October 2016. These new lounges provide the same service currently offered by Sofitel in its flagship First lounges in Sydney and Melbourne and a dining experience featuring Neil Perry's Spice Temple inspired dishes and signature cocktails. Lounge access Qantas Club Members, Gold Frequent Flyers, and Oneworld Sapphire holders are permitted to enter domestic Qantas Clubs when flying on Qantas or Jetstar flights along with one guest who need not be travelling. Platinum and Oneworld Emerald Members are permitted to bring in two guests who do not need to be travelling. Internationally, members use Qantas International Business Class lounges (or the Oneworld equivalent). Guests of the member must be travelling to gain access to international lounges. When flying with American Airlines, members have access to Admirals Club lounges and when flying on British Airways, members have access to British Airways' Terraces and Galleries Lounges. Platinum Frequent Flyers had previously been able to access the Qantas Club in Australian domestic terminals at any time, regardless of whether they were flying that day. Travellers holding Oneworld Sapphire or Emerald status are also allowed in Qantas Club lounges worldwide. Access to Qantas First lounges is open to passengers travelling on internationally operated Qantas or	a rainbow flag on the tail of the aircraft. Cabin Domestic Qantas domestic flights are primarily operated by Boeing 737–800 and Airbus A330-200 aircraft; Airbus A330-300s sometimes operate domestically as well. A two-class configuration (Business and Economy) is offered. Business Domestic Business Class is offered on all Boeing 737 and Airbus A330 aircraft. On the Boeing 737, Business is exclusively available in the first three rows of the cabin, with a seat configuration of 2–2, seat recline, and a larger pitch between seats. As the A330s operate international flights, Business Suites are sometimes available on domestic routes. These seats feature all-aisle access in a 1-2-1 configuration and a fully flat bed. Economy Domestic Economy Class is offered on all Boeing 737 and Airbus A330 aircraft. Seat pitch is usually and seat width ranges from . Layouts are 3–3 on the 737 and 2-4-2 on the A330. International Qantas international flights are primarily operated on Airbus A380s, A330-300s, Boeing 787s, and sometimes on Airbus A330-200s and Boeing 737-800s. Passenger class configuration varies by aircraft, with the Airbus A330-300 offering a two-class configuration of Business and Economy on short to medium-haul flights. This compares to the Airbus A380, which offers a four-class configuration of First, Business, Premium Economy, and Economy on selected long haul flights. First First class is offered exclusively on the Airbus A380. It offers 14 individual suites in a 1-1-1 layout. The seats rotate, facing forward for takeoff, but rotating to the side for dining and sleeping, with 83.5 in seat pitch (extending to a 212 cm fully flat bed) and a width of . Each suite has a widescreen HD monitor with 1,000 AVOD programs. In addition to 110 V AC power outlets, USB ports are offered for connectivity. Passengers are also able to make use of the on-board business lounge on the upper deck. Complimentary access to both the first class and business class lounges (or affiliated lounges) is offered. Updated versions of this seat were fitted to the airline's refurbished Airbus A380 aircraft from late 2019. This seat featured refreshed cushioning and larger entertainment screens compared to the older version seat. Business International Business class is offered on all Qantas mainline passenger aircraft. On all International and selected Domestic flights, Qantas offers two different types of Business Class seats, as listed below. Business Suites Business Suites are offered on all Boeing 787, Airbus A330-300, and selected Airbus A330-200 and A380 aircraft. These seats include beds and are in a 1-2-1 configuration. The Business Suite was introduced on the A330 in October 2014, and also contains a bed. This seat includes a Panasonic eX3 system with a touchscreen. By the end of 2016, the business class seats of Qantas' entire Airbus A330 fleet were refitted. Airbus A330 Business Suites are available on Asian routes, transcontinental routes across Australia and smaller routes such as the East Coast triangle. Updated versions of this seat were fitted to the airline's new Boeing 787 fleet from late 2017. Business Skybeds Business Skybeds are offered exclusively on selected A380 aircraft. On the Airbus A380, 64 fully-flat Skybed seats are available with seat pitch (converting to a 200 cm long bed). These seats are located on the upper deck in a 2-2-2 configuration in two separate cabins. Features include a 30 cm touchscreen monitor with 1,000 AVOD programmes and an on-board lounge. Airbus A380 Business Skybeds are available on Qantas' flagship routes such as Australia to/from London via Singapore, Los Angeles, Dallas, and Hong Kong (seasonal). The Skybed 1 (Mark I) version of the lie-flat seats, featured between 2003 and 2019 had of seat pitch and width; however passengers slept at a distinct slope to the cabin floor. The Skybed 2 (Mark II) version, introduced in 2008 has a pitch, and allows passengers to lie fully horizontal. On the now-retired Boeing 747, seating was in a 2-3-2 configuration on the main deck and a 2–2 configuration on the upper deck. Skybed seats on Boeing 747s featured a touchscreen monitor with 400 AVOD programs. Before their retirement, Boeing 747 Business Skybeds were available on Asian, African, and South American routes. In 2019, Qantas began the process of retrofitting its Airbus A380 aircraft with new Business Suites as offered on Airbus A330 and Boeing 787 aircraft. The aircraft will gain six business class seats compared to the previous configuration. Complimentary access to the Qantas business class lounge (or affiliated lounges) is also offered. Premium Economy Premium economy class is offered on all Airbus A380 and Boeing 787–9 aircraft. On the Airbus A380, the seat pitch ranges from , with a width of . On the Boeing 787, it is configured in a 2-3-2 seating arrangement around the middle of the aircraft, whereas it is in a 2-3-2 seating arrangement at the rear of the upper deck on the A380. The total number of seats depends on the aircraft type, as A380s have 35–60 seats, (depending on the configuration) and 787s have 28 seats. Qantas premium economy is presented as a lighter business class product rather than most other airlines' premium economy, which is often presented as a higher economy class, however Qantas premium economy does not offer access to premium lounges, and meals are only a slightly uprated version of economy class meals. In 2019, Qantas began the process of retrofitting its Airbus A380 aircraft with new Premium Economy seats, as offered on Boeing 787 aircraft. The aircraft will gain 25 premium economy seats compared to the previous configuration. Economy International Economy class is available on all Qantas mainline passenger aircraft. Seat pitch is usually and seat width ranges from . Layouts are 3–3 on the 737, 2-4-2 on the A330, 3-3-3 on the B787-9 and 3-4-3 on the 747. On the A380, the layout is 3-4-3 and there are four self-service snack bars located in between cabins. In 2019, Qantas began the process of retrofitting its Airbus A380 aircraft which includes new Economy seats with new seat cushions and improved inflight entertainment, as offered on Boeing 787 aircraft. The aircraft will have fewer economy seats compared to the previous configuration due to an increase in the number of premium seats. In-flight entertainment Every Qantas mainline aircraft has some form of video audio entertainment. Qantas has several types of in-flight entertainment (IFE) systems installed on its aircraft and refers to the in-flight experience as "On:Q". Audio-video entertainment systems The "Total Entertainment System" by Rockwell Collins was featured on selected domestic and international aircraft between 2000 and 2019. This AVOD system included personal LCD screens in all classes, located in the seat back for economy and business class, and in the armrest for premium economy and first class. The Mainscreen System is featured on selected Boeing 737–800 aircraft. This entertainment system, introduced between 2002 and 2011, has overhead video screens as the main form of entertainment. Movies are shown on the screens for lengthier flights or TV programmes on shorter flights. A news telecast will usually feature at the start of the flight. Audio options are less varied than on Q, iQ or the Total Entertainment System. The "iQ" inflight entertainment system by Panasonic Avionics Corporation is featured on all Boeing 747, and selected Airbus A380 and Boeing 737–800 aircraft. This audio video on demand (AVOD) experience, introduced in 2008, is based on the Panasonic Avionics system and features expanded entertainment options; touch screens; and new communications-related features such as Wi-Fi and mobile phone functionality; as well as increased support for electronics (such as USB and iPod connectivity). The "Q" inflight entertainment system by Panasonic Avionics Corporation in collaboration with Massive Interactive is featured on all Airbus A330-300, A330-200, Boeing 787 and selected Airbus A380 aircraft. This audio video on demand (AVOD) experience, introduced in 2014 and updated in 2018 on selected aircraft, is based on the Panasonic eX3 system and features extensive entertainment options; enhanced touch screens; and communications-related features such as Wi-Fi and mobile phone functionality; as well as increased support for electronics (such as USB and iPod connectivity). A "my flight" feature offers access to maps, playlists, and a service timeline showing when drinks and meals will be served and the best time for resting on long-haul flights. Wireless entertainment systems and Wi-Fi Q Streaming is an in-flight entertainment system in which entertainment is streamed to iPads or personal devices available in all classes on selected aircraft. A selection of movies, TV, music, and a kids' choice are available. In 2007, Qantas conducted a trial for use of mobile telephones with AeroMobile, during domestic services for three months on a Boeing 767. During the trial, passengers were allowed to send and receive text messages and emails but were not able to make or receive calls. Since 2014, Sky News Australia has provided multiple news bulletins both in-flight and in Qantas branded lounges. Previously, the Australian Nine Network provided a news bulletin for Qantas entitled Nine's Qantas Inflight News, which was the same broadcast as Nine's Early Morning News, however Nine lost the contract to Sky News. In July 2015, Qantas signed a deal with American cable network HBO to provide over 120 hours of television programming in-flight from the network which will be updated monthly, as well as original lifestyle and entertainment programming from both Foxtel and the National Geographic Channel. In 2017 Qantas commenced rolling out complimentary high speed Wi-Fi on domestic aircraft. The services utilises NBN Co Sky Muster satellites to deliver higher speeds than generally offered by onboard Wi-Fi. Previously, in July 2007 Qantas had announced Wi-Fi on would be available on its long haul A380s and 747-400s although that system ultimately did not proceed following trials. Inflight magazine Qantas: The Australian Way is the airline's in-flight magazine. In mid-2015, the magazine ended a 14-year publishing deal with Bauer Media, switching its publisher to Medium Rare. Services The Qantas Club Facilities The Qantas Club is the airline lounge for Qantas with airport locations around Australia and the world. Additionally, Qantas operates dedicated international first-class lounges in Sydney, Melbourne, Auckland, Los Angeles and Singapore. Domestically, Qantas also offers dedicated Business Lounges at Sydney, Melbourne, Brisbane, Canberra and Perth for domestic Business Class, Qantas Platinum and Platinum One, and OneWorld Emerald frequent flyers. In April 2013, Qantas opened its new flagship lounge in Singapore, the Qantas Singapore Lounge. This replaced the former separate first- and business-class lounges as a result of the new Emirates alliance. Similar combined lounges were also opened in Hong Kong in April 2014 and in Brisbane in October 2016. These new lounges provide the same service currently offered by Sofitel in its flagship First lounges in Sydney and Melbourne and a dining experience featuring Neil Perry's Spice Temple inspired dishes and signature cocktails. Lounge access Qantas Club Members, Gold Frequent Flyers, and Oneworld Sapphire holders are permitted to enter domestic Qantas Clubs when flying on Qantas or Jetstar flights along with one guest who need not be travelling. Platinum and Oneworld Emerald Members are permitted to bring in two guests who do not need to be travelling. Internationally, members use Qantas International Business Class lounges (or the Oneworld equivalent). Guests of the member must be travelling to gain access to international lounges. When flying with American Airlines, members have access to Admirals Club lounges and when flying on British Airways, members have access to British Airways' Terraces and Galleries Lounges. Platinum Frequent Flyers had previously been able to access the Qantas Club in Australian domestic terminals at any time, regardless of whether they were flying that day. Travellers holding Oneworld Sapphire or Emerald status are also allowed in Qantas Club lounges worldwide. Access to Qantas First lounges is open to passengers travelling on internationally operated Qantas or Oneworld first-class flights, as well as Qantas platinum and Oneworld emerald frequent flyers. Emirates first-class passengers are also eligible for access to the Qantas first lounges in Sydney and Melbourne. The Qantas Club also offers membership by paid subscription (one, two, or four years) or by achievement of Gold or Platinum frequent flyer status. Benefits of membership include lounge access, priority check-in, priority luggage handling and increased luggage allowances. Qantas Frequent Flyer The Qantas frequent-flyer program is aimed at rewarding customer loyalty. The program is long-standing, although the date of the actual inception has been a matter that has generated some commentary. Qantas state the program launched in 1987 although other sources claim what is the current program was launched in the early 1990s, with a Captain's Club program existing before that. Points are accrued based on distance flown, with bonuses that vary by travel class. Points can also be earned on other Oneworld airlines as well as through other non-airline partners. Points can be redeemed for flights or upgrades on flights operated by Qantas, Oneworld airlines, and other partners. Other partners include credit cards, car rental companies, hotels and many others. Flights with Qantas and selected partner airlines earn Status Credits — and accumulation of these allows progression to Silver status (Oneworld Ruby), Gold status (Oneworld Sapphire), Platinum and Platinum One status (Oneworld Emerald). Membership of the program has grown significantly since 2000, when the program had 2.4 million members. By 2005 membership had grown to 4.3 million, then to 7.2 million by 2010 and 10.8 million in 2015. As at 2018, the program has 12.3 million members, or approaching the equivalent of half of the Australian population. Qantas has faced criticism regarding availability of seats for members redeeming points. In 2004, the Australian Competition and Consumer Commission directed Qantas to provide greater disclosure to members regarding the availability of frequent-flyer seats. In March 2008, an analyst at JPMorgan Chase suggested that the Qantas frequent-flyer program could be worth A$2 billion (US$1.9 billion), representing more than a quarter of the total market value of Qantas. On 1 July 2008 a major overhaul of the program was announced. The two key new features of the program were Any Seat rewards, in which members could now redeem any seat on an aircraft, rather than just selected seats — at a price. The second new feature was Points Plus Pay, which has enabled members to use a combination of cash and points to redeem an award. Additionally, the Frequent Flyer store was also expanded to include a greater range of products and services. Announcing the revamp, Qantas confirmed it would be seeking to raise about A$1 billion in 2008 by selling up to 40% of the frequent flyer program. However, in September 2008, it stated it would defer the float, citing volatile market conditions. Accidents and incidents It is often claimed that Qantas has never had an aircraft crash. While it is true that the company has neither lost a jet airliner nor had any jet fatalities, it had eight fatal accidents and an aircraft shot down between 1927 and 1945, with the loss of 63 people. Half of these accidents and the shoot-down occurred during World War II, when the Qantas aircraft were operating on behalf of Allied military forces. Post-war, it lost another four aircraft (one was owned by BOAC and operated by Qantas in a pooling arrangement) with a total of 21 people killed. The last fatal accidents suffered by Qantas were in 1951, with three fatal crashes in five months. Qantas' safety record allows the airline to be officially known as the world's safest airline for seven years in a row from 2012 until 2019 and again in 2021. Since the end of World War II, the following accidents and incidents have occurred: On 23 March 1946, an Avro Lancastrian registered G-AGLX disappeared while flying over the Indian Ocean. The BOAC-owned aircraft was being operated by Qantas on the Karachi—Sydney part of the two airlines' joint service from London to Sydney. It disappeared with seven passengers and crew on board between Colombo, Ceylon (now Sri Lanka), and the Cocos (Keeling) Islands, approximately three hours before it was due to arrive at the Cocos islands. On 7 April 1949, an Avro Lancastrian registered VH-EAS swung on landing at Dubbo, New South Wales during a training flight, causing the gear to collapse. The aircraft was destroyed by fire, but the crew evacuated safely. On 16 July 1951, a de Havilland Australia DHA-3 Drover registered VH-EBQ crashed off the coast of New Guinea (in the Huon Gulf near the mouth of the Markham River) after the centre engine's propeller failed. The pilot and the six passengers on board were killed. On 21 September 1951, a de Havilland DH.84 Dragon registered VH-AXL, crashed in mountainous country southeast of Arona in the central highlands of New Guinea, no passengers were on board, the pilot was killed. On 13 December 1951, a de Havilland DH.84 Dragon registered VH-URV crashed in mountainous country near Mount Hagen, central highlands of New Guinea. The pilot and the two passengers were killed. To date, this was the last fatal accident suffered by Qantas. On 24 August 1960, a Lockheed L-1049 Super Constellation registered VH-EAC crashed on take-off at Mauritius en route to the Cocos Islands, Australia. The take-off was aborted following an engine failure, the aircraft ran off the runway, and was destroyed by fire. There were no fatalities. On 23 September 1999, Qantas Flight 1, a Boeing 747–400 registered VH-OJH, overran the runway while landing at Bangkok, Thailand, during a heavy thunderstorm. The aircraft came to a stop on a golf course, but without fatalities. The Australian Transport Safety Bureau criticised numerous inadequacies in Qantas' operational and training processes. On 25 July 2008, Qantas Flight 30, a Boeing 747–400 registered VH-OJK, suffered a ruptured fuselage and decompression as a result of an oxygen tank explosion over the South China Sea. En route from Hong Kong International Airport to Melbourne Airport, the aircraft made an emergency landing in the Philippines with no injuries. On 7 October 2008, an Airbus A330-300 registered VH-QPA, travelling from Singapore Changi Airport to Perth, Western Australia as Qantas Flight 72, suffered a rapid loss of altitude in two sudden uncommanded pitch down manoeuvres causing serious injuries while from Learmonth. The aircraft safely landed in Learmonth, with 14 people requiring transportation by air ambulance to Perth. Another 30 people also required hospital treatment, while an additional 30 people had injuries not requiring hospital treatment. Initial investigations identified an inertial reference system fault in the Number-1 Air Data Inertial Reference Unit as the likely origin of the event. On receiving false indication of a very high angle of attack, the flight control systems commanded a pitch down movement, reaching a maximum of 8.5 degrees pitch down. (7news documentary) On 4 November 2010, Qantas Flight 32, an Airbus A380 registered VH-OQA, fitted with four Rolls-Royce Trent 972 engines, suffered an uncontained turbine disc failure of its left inboard engine shortly after taking off from Singapore Changi Airport en route to Sydney. The aircraft returned to Singapore and landed safely. None of the 440 passengers or 29 crew on board were injured. Extortion attempts On 26 May 1971 Qantas received a call from a "Mr. Brown" claiming that there was a bomb planted on a Hong Kong-bound jet and demanding $500,000 in unmarked $20 notes. The caller and threat were taken seriously when he directed police to an airport locker where a functional bomb was found. Arrangements were made to pick up the money in front of the head office of the airline in the heart of the Sydney business district. Qantas paid the money and
by A. W. Winklehoff. Dennis Ritchie, Ken Thompson and Brian Kernighan wrote the QED manuals used at Bell Labs. Given that the authors were the primary developers of the Unix operating system, it is natural that QED had a strong influence on the classic UNIX text editors ed, sed and their descendants such as ex and sam, and more distantly AWK and Perl. A version of QED named FRED (Friendly Editor) was written at the University of Waterloo for Honeywell systems by Peter Fraser. A University of Toronto team consisting of Tom Duff, Rob Pike, Hugh Redelmeier, and David Tilbrook implemented a version of QED that runs on UNIX; David Tilbrook later included QED as part of his QEF tool set. QED was also used as a character-oriented editor on the Norwegian-made Norsk Data systems, first Nord TSS, then Sintran III. It was implemented for the Nord-1 computer in 1971 by Bo Lewendal who after working with Deutsch and Lampson at Project Genie and at the Berkeley Computer Corporation, had taken a job with Norsk Data (and who developed the	a line-oriented computer text editor that was developed by Butler Lampson and L. Peter Deutsch for the Berkeley Timesharing System running on the SDS 940. It was implemented by L. Peter Deutsch and Dana Angluin between 1965 and 1966. QED (for "quick editor") addressed teleprinter usage, but systems "for CRT displays [were] not considered, since many of their design considerations [were] quite different." Later implementations Ken Thompson later wrote a version for CTSS; this version was notable for introducing regular expressions. Thompson rewrote QED in BCPL for Multics. The Multics version was ported to the GE-600 system used at Bell Labs in the late 1960s under GECOS and later GCOS after Honeywell took over GE's computer business. The GECOS-GCOS port used I/O routines written by A. W. Winklehoff. Dennis Ritchie, Ken Thompson and Brian Kernighan wrote the QED manuals used at Bell Labs. Given that the authors were the primary developers
found. Brigadier general Frank Helmick, the assistant commander of 101st Airborne, commented that all occupants of the house died during the gun battle before U.S. troops were able to enter. Soldiers, who tried to enter the house three times, encountered resistance with AK-47 and grenades in the first two attempts. Uday, Qusay and guard protected the street and the first floor from the bathroom at the front of the house; Qusay's son took cover from the bedroom in the back and defended themselves. The American forces then bombed the house many times and fired missiles. Three adults were thought to have died due to the TOW missile fired into the front of the house. In the third attempt, the soldiers killed Qusay's only remaining 14-year-old son after he fired. Brigade commander Col. Joe Anderson said an Arabic announcement was made at 10 A.M. on the day and called on people inside to come out peacefully. The answer he received was bullet bombardment. An experienced team of commandos tried to attack the building, but they had to retreat under fire. Four American soldiers were injured. Anderson then ordered his men to fire with 50-caliber heavy machine guns. Uday and Qusay Hussein refused to surrender even after a helicopter fired a rocket and the Strike Brigade fired 40mm grenades at them. The Colonel decided that more firepower was necessary to take down the brothers, leading to 12 TOW missiles being fired into the building. After his sons death, Saddam Hussein recorded a tape and said, "Beloved Iraqis, your brothers Uday and Qusay, and Mustafa, the son of Qusay, took a stand of faith, which pleases God, makes a friend happy, and makes an enemy angry. They stood in the arena of jihad in Mosul, after a valiant battle with the enemy that lasted six hours. The armies of aggression mobilised all types of weapons of the ground forces against them and succeeded to harm them only when they used planes against the house where they were. Thus, they adopted a stand with which God has honoured this Hussein family so that the present would be a continuation of the brilliant, genuine, faithful, and honourable past. We thank God for what he has ordained for us when he honoured us with their martyrdom for his sake. We ask Almighty God to satisfy them and all the righteous martyrs after they satisfied him with their faithful Jihadist stand. Had Saddam Hussein had 100 children, other than Uday and Qusay, Saddam Hussein would have sacrificed them on the same path. God honoured us by their martyrdom. If you had killed Uday, Qusay, Mustafa, and another mujahideen man with them, all the youths of our nation and the youths of Iraq are Uday, Qusay, and Mustafa in the fields of jihad." Later, the American command said that dental records had conclusively identified two of the dead men as Saddam Hussein's sons. They also announced that the informant (possibly the owner of the villa, Nawaf al-Zaidan, in Mosul in which the brothers were killed) would receive the combined $30 million reward previously offered for their apprehension. On 23 July 2003, the American command stated that it had conclusively identified two of the dead men as Saddam Hussein's sons from dental records.	Unlike Uday, who was known for extravagance and erratic, violent behavior, Qusay kept a low profile so details regarding his actions and roles are obscure. Iraqi dissidents claimed that Qusay was responsible for the killing of many political activists. The Sunday Times reported that Qusay Hussein ordered the killing of Khalis Mohsen al-Tikriti, an engineer at the military industrialization organization, because he believed Mohsen was planning to leave Iraq. In 1998, Iraqi opposition groups accused Qusay Hussein of ordering the execution of thousands of political prisoners after hundreds of inmates were similarly executed to make room for new prisoners in crowded jails. Hussein's service in the Iraqi Republican Guard began in 2000. It is believed that he became the supervisor of the Guard and the head of internal security forces (possibly the Special Security Organization (SSO)), and had authority over other Iraqi military units. Hours before the 2003 invasion of Iraq, Qusay withdrew approximately $1bn from the central bank in Baghdad, acting on personal orders from Saddam. He arrived at the bank in Baghdad at 4am on March 18, (hours before the first US strikes) seized around $900m in $100 bills and a further $100m in euros, loaded them into three tractor-trailers and left. Death On the afternoon of 22 July 2003, troops of the 101st Airborne 3/327th Infantry HQ and C-Company, aided by U.S. Special Forces, killed Qusay Hussein, his 14-year-old son Mustafa, his older brother Uday Hussein and a bodyguard during a raid on a house in the northern Iraqi city of Mosul. Acting on a tip provided the previous day from Nawaf al-Zaidan, an alleged cousin and friend of Saddam Hussein who had been sheltering the four in his home for numerous weeks, a special forces team attempted to apprehend everyone in the house at the time. After being fired on, the special forces moved back and called for backup. After Task Force 121 members were wounded, the 3/327th Infantry surrounded and fired on the house with a TOW missile, Mark 19 Automatic Grenade Launcher, M2 50 Caliber Machine guns and small arms. After about four hours of battle (the whole operation lasted 6 hours), the soldiers entered the house and found four dead, including the two brothers and their bodyguard. There were reports that Qusay Hussein's 14-year-old son Mustafa was the fourth body found. Brigadier general Frank Helmick, the assistant commander of 101st Airborne, commented that all occupants of the house
are fifteen possible rhyme schemes, but the most traditional and common are ABAA, AAAA, ABAB, and ABBA. Forms The heroic stanza or elegiac stanza consists of the iambic pentameter, with the rhyme scheme of ABAB or AABB. An example can be found in the following of Thomas Gray's "Elegy Written in a Country Churchyard". The curfew tolls the knell of parting day, The lowing herd wind slowly o'er the lea, The plowman homeward plods his weary way, And leaves the world to darkness and to me. The hymnal stanza consists of alternating rhymes with the iambic trimeter and the iambic tetrameter, with a rhyme scheme of ABCB. An example can be found in Robert Burns, "A Red, Red Rose". O, my luve’s like a red, red rose, That’s newly sprung in June; O, my luve’s like the melodie That’s sweetly played in tune. The memoriam stanza consists of the iambic tetrameter and a rhyme scheme of ABBA. An example can be found in Alfred Lord Tennyson's "In Memoriam A.H.H.". So word by word, and line by line, The dead man touch’d me from the past, And all at once it seem’d at last The living soul was flash’d on mine. An envelope stanza is when the same stanza starts and ends a poem with little change of wording, although this term is also used on stanzas that have a symmetrical rhyme scheme of ABBA. An example can be found in William Blake's "The Tyger". (these are the first and last stanzas of the	a particularly widespread verse form: the form rubaiyat reflects the plural. One of FitzGerald's verses may serve to illustrate: Come, fill the Cup, and in the fire of Spring Your Winter garment of Repentance fling: The Bird of Time has but a little way To flutter—and the Bird is on the Wing. The Midnight Songs poetry form is from Fourth Century China, consisting of regular five-character lines, with each quatrain formed from a pair of rhymed couplets. The person matter involves the personal thoughts and feelings of a courtesan during the four seasons, into which the quatrains are individually assigned. Shairi (also known as Rustavelian Quatrain) is an AAAA rhyming form used mainly in The Knight in the Panther's Skin. The Shichigon-zekku form used on Classical Chinese poetry and Japanese poetry. This type of quatrain uses a seven characters length of line. Both rhyme and rhythm are key elements, although the former is not restricted to falling at the end of the phrase. Ballad meter (The examples from "The Unquiet Grave" and "The Wife of Usher's Well" are both examples of ballad meter.) Decasyllabic quatrain used by John Dryden in Annus Mirabilis, William Davenant in Gondibert, and Thomas Gray Various hymns employ specific forms, such as the common meter, long meter, and short meter. In the Malay tradition, syair, pantun and pantoum are arranged
way, invented in 1961 by Gell-Mann and Yuval Ne'eman. Gell-Mann and George Zweig, correcting an earlier approach of Shoichi Sakata, went on to propose in 1963 that the structure of the groups could be explained by the existence of three flavors of smaller particles inside the hadrons: the quarks. Gell-Mann also briefly discussed a field theory model in which quarks interact with gluons. Perhaps the first remark that quarks should possess an additional quantum number was made as a short footnote in the preprint of Boris Struminsky in connection with the Ω− hyperon being composed of three strange quarks with parallel spins (this situation was peculiar, because since quarks are fermions, such a combination is forbidden by the Pauli exclusion principle): Boris Struminsky was a PhD student of Nikolay Bogolyubov. The problem considered in this preprint was suggested by Nikolay Bogolyubov, who advised Boris Struminsky in this research. In the beginning of 1965, Nikolay Bogolyubov, Boris Struminsky and Albert Tavkhelidze wrote a preprint with a more detailed discussion of the additional quark quantum degree of freedom. This work was also presented by Albert Tavkhelidze without obtaining consent of his collaborators for doing so at an international conference in Trieste (Italy), in May 1965. A similar mysterious situation was with the Δ++ baryon; in the quark model, it is composed of three up quarks with parallel spins. In 1964–65, Greenberg and Han–Nambu independently resolved the problem by proposing that quarks possess an additional SU(3) gauge degree of freedom, later called color charge. Han and Nambu noted that quarks might interact via an octet of vector gauge bosons: the gluons. Since free quark searches consistently failed to turn up any evidence for the new particles, and because an elementary particle back then was defined as a particle that could be separated and isolated, Gell-Mann often said that quarks were merely convenient mathematical constructs, not real particles. The meaning of this statement was usually clear in context: He meant quarks are confined, but he also was implying that the strong interactions could probably not be fully described by quantum field theory. Richard Feynman argued that high energy experiments showed quarks are real particles: he called them partons (since they were parts of hadrons). By particles, Feynman meant objects that travel along paths, elementary particles in a field theory. The difference between Feynman's and Gell-Mann's approaches reflected a deep split in the theoretical physics community. Feynman thought the quarks have a distribution of position or momentum, like any other particle, and he (correctly) believed that the diffusion of parton momentum explained diffractive scattering. Although Gell-Mann believed that certain quark charges could be localized, he was open to the possibility that the quarks themselves could not be localized because space and time break down. This was the more radical approach of S-matrix theory. James Bjorken proposed that pointlike partons would imply certain relations in deep inelastic scattering of electrons and protons, which were verified in experiments at SLAC in 1969. This led physicists to abandon the S-matrix approach for the strong interactions. In 1973 the concept of color as the source of a "strong field" was developed into the theory of QCD by physicists Harald Fritzsch and , together with physicist Murray Gell-Mann. In particular, they employed the general field theory developed in 1954 by Chen Ning Yang and Robert Mills (see Yang–Mills theory), in which the carrier particles of a force can themselves radiate further carrier particles. (This is different from QED, where the photons that carry the electromagnetic force do not radiate further photons.) The discovery of asymptotic freedom in the strong interactions by David Gross, David Politzer and Frank Wilczek allowed physicists to make precise predictions of the results of many high energy experiments using the quantum field theory technique of perturbation theory. Evidence of gluons was discovered in three-jet events at PETRA in 1979. These experiments became more and more precise, culminating in the verification of perturbative QCD at the level of a few percent at LEP, at CERN. The other side of asymptotic freedom is confinement. Since the force between color charges does not decrease with distance, it is believed that quarks and gluons can never be liberated from hadrons. This aspect of the theory is verified within lattice QCD computations, but is not mathematically proven. One of the Millennium Prize Problems announced by the Clay Mathematics Institute requires a claimant to produce such a proof. Other aspects of non-perturbative QCD are the exploration of phases of quark matter, including the quark–gluon plasma. The relation between the short-distance particle limit and the confining long-distance limit is one of the topics recently explored using string theory, the modern form of S-matrix theory. Theory Some definitions Every field theory of particle physics is based on certain symmetries of nature whose existence is deduced from observations. These can be local symmetries, which are the symmetries that act independently at each point in spacetime. Each such symmetry is the basis of a gauge theory and requires the introduction of its own gauge bosons. global symmetries, which are symmetries whose operations must be simultaneously applied to all points of spacetime. QCD is a non-abelian gauge theory (or Yang–Mills theory) of the SU(3) gauge group obtained by taking the color charge to define a local symmetry. Since the strong interaction does not discriminate between different flavors of quark, QCD has approximate flavor symmetry, which is broken by the differing masses of the quarks. There are additional global symmetries whose definitions require the notion of chirality, discrimination between left and right-handed. If the spin of a particle has a positive projection on its direction of motion then it is called right-handed; otherwise, it is left-handed. Chirality and handedness are not the same, but become approximately equivalent at high energies. Chiral symmetries involve independent transformations of these two types of particle. Vector symmetries (also called diagonal symmetries) mean the same transformation is applied on the two chiralities. Axial symmetries are those in which one transformation is applied on left-handed particles and the inverse on the right-handed particles. Additional remarks: duality As mentioned, asymptotic freedom means that at large energy – this corresponds also to short distances – there is practically no interaction between the particles. This is in contrast – more precisely one would say dual– to what one is used to, since usually one connects the absence of interactions with large distances. However, as already mentioned in the original paper of Franz Wegner, a solid state theorist who introduced 1971 simple gauge invariant lattice models, the high-temperature behaviour of the original model, e.g. the strong decay of correlations at large distances, corresponds to the low-temperature behaviour of the (usually ordered!) dual model, namely the asymptotic decay of non-trivial correlations, e.g. short-range deviations from almost perfect arrangements, for short distances. Here, in contrast to Wegner, we have only the dual model, which is that one described in this article. Symmetry groups The color group SU(3) corresponds to the local symmetry whose gauging gives rise to QCD. The electric charge labels a representation of the local symmetry group U(1), which is gauged to give QED: this is an abelian group. If one considers a version of QCD with Nf flavors of massless quarks, then there is a global (chiral) flavor symmetry group SUL(Nf) × SUR(Nf) × UB(1) × UA(1). The chiral symmetry is spontaneously broken by the QCD vacuum to the vector (L+R) SUV(Nf) with the formation of a chiral condensate. The vector symmetry, UB(1) corresponds to the baryon number of quarks and is an exact symmetry. The axial symmetry UA(1) is exact in the classical theory, but broken in the quantum theory, an occurrence called an anomaly. Gluon field configurations called instantons are closely related to this anomaly. There are two different types of SU(3) symmetry: there is the symmetry that acts on the different colors of quarks, and this is an exact gauge symmetry mediated by the gluons, and there is also a flavor symmetry that rotates different flavors of quarks to each other, or flavor SU(3). Flavor SU(3) is an approximate symmetry of the vacuum of QCD, and is not a fundamental symmetry at all. It is an accidental consequence of the small mass of the three lightest quarks. In the QCD vacuum there are vacuum condensates of all the quarks whose mass is less than the QCD scale. This includes the up and down quarks, and to a lesser extent the strange quark, but not any of the others. The vacuum is symmetric under SU(2) isospin rotations of up and down, and to a lesser extent under rotations of up, down, and strange, or full flavor group SU(3), and the observed particles make isospin and SU(3) multiplets. The approximate flavor symmetries do have associated gauge bosons, observed particles like the rho and the omega, but these particles are nothing like the gluons and they are not massless. They are emergent gauge bosons in an approximate string description of QCD. Lagrangian The dynamics of the quarks and gluons are controlled by the quantum chromodynamics Lagrangian. The gauge invariant QCD Lagrangian is where is the quark field, a dynamical function of spacetime, in the fundamental representation of the SU(3) gauge group, indexed by and running from to ; is the gauge covariant derivative; the γμ are Dirac matrices connecting the spinor representation to the vector representation of the Lorentz group. Herein, the gauge covariant derivative couples the quark field with a coupling strength to the gluon fields via the infinitesimal SU(3) generators in the fundamental representation. An explicit representation of these generators is given by , wherein the are the Gell-Mann matrices. The symbol represents the gauge invariant gluon field strength tensor, analogous to the electromagnetic field strength tensor, Fμν, in quantum electrodynamics. It is given by: where are the gluon fields, dynamical functions of spacetime, in the adjoint representation of the SU(3) gauge group, indexed by a, b and c running from to ; and fabc are the structure constants of SU(3). Note that the rules to move-up or pull-down the a, b, or c indices are trivial, (+, ..., +), so that fabc = fabc = fabc whereas for the μ or ν indices one has the non-trivial relativistic rules corresponding to the metric signature (+ − − −). The variables m and g correspond to the quark mass and coupling of the theory, respectively, which are subject to renormalization. An important theoretical concept is the Wilson loop (named after Kenneth G. Wilson). In lattice QCD, the final term of the above Lagrangian is discretized via Wilson loops, and more generally the behavior of Wilson loops can distinguish confined and deconfined phases. Fields Quarks are massive spin- fermions that carry a color charge whose gauging is the content of QCD. Quarks are represented by Dirac fields in the fundamental representation 3 of the gauge group SU(3). They also carry electric charge (either − or +) and participate in weak interactions as part of weak isospin doublets. They carry global quantum numbers including the baryon number, which is for each quark, hypercharge and one of the flavor quantum numbers. Gluons are spin-1 bosons that also carry color charges, since they lie in the adjoint representation 8 of SU(3). They have no electric charge, do not participate in the weak interactions, and have no flavor. They lie in the singlet representation 1 of all these symmetry groups. Each type of quark has a corresponding antiquark, of which the charge is exactly opposite. Dynamics According to the rules of quantum field theory, and the associated Feynman diagrams, the above theory gives rise to three basic interactions: a quark may emit (or absorb) a gluon, a gluon may emit (or absorb) a gluon, and two gluons may directly interact. This contrasts with QED, in which only the first kind of interaction occurs, since photons have no charge. Diagrams involving Faddeev–Popov ghosts must be considered too (except in the unitarity gauge). Area law and confinement Detailed computations with the	respectively, which are subject to renormalization. An important theoretical concept is the Wilson loop (named after Kenneth G. Wilson). In lattice QCD, the final term of the above Lagrangian is discretized via Wilson loops, and more generally the behavior of Wilson loops can distinguish confined and deconfined phases. Fields Quarks are massive spin- fermions that carry a color charge whose gauging is the content of QCD. Quarks are represented by Dirac fields in the fundamental representation 3 of the gauge group SU(3). They also carry electric charge (either − or +) and participate in weak interactions as part of weak isospin doublets. They carry global quantum numbers including the baryon number, which is for each quark, hypercharge and one of the flavor quantum numbers. Gluons are spin-1 bosons that also carry color charges, since they lie in the adjoint representation 8 of SU(3). They have no electric charge, do not participate in the weak interactions, and have no flavor. They lie in the singlet representation 1 of all these symmetry groups. Each type of quark has a corresponding antiquark, of which the charge is exactly opposite. Dynamics According to the rules of quantum field theory, and the associated Feynman diagrams, the above theory gives rise to three basic interactions: a quark may emit (or absorb) a gluon, a gluon may emit (or absorb) a gluon, and two gluons may directly interact. This contrasts with QED, in which only the first kind of interaction occurs, since photons have no charge. Diagrams involving Faddeev–Popov ghosts must be considered too (except in the unitarity gauge). Area law and confinement Detailed computations with the above-mentioned Lagrangian show that the effective potential between a quark and its anti-quark in a meson contains a term that increases in proportion to the distance between the quark and anti-quark (), which represents some kind of "stiffness" of the interaction between the particle and its anti-particle at large distances, similar to the entropic elasticity of a rubber band (see below). This leads to confinement of the quarks to the interior of hadrons, i.e. mesons and nucleons, with typical radii Rc, corresponding to former "Bag models" of the hadrons The order of magnitude of the "bag radius" is 1 fm (= 10−15 m). Moreover, the above-mentioned stiffness is quantitatively related to the so-called "area law" behavior of the expectation value of the Wilson loop product PW of the ordered coupling constants around a closed loop W; i.e. is proportional to the area enclosed by the loop. For this behavior the non-abelian behavior of the gauge group is essential. Methods Further analysis of the content of the theory is complicated. Various techniques have been developed to work with QCD. Some of them are discussed briefly below. Perturbative QCD This approach is based on asymptotic freedom, which allows perturbation theory to be used accurately in experiments performed at very high energies. Although limited in scope, this approach has resulted in the most precise tests of QCD to date. Lattice QCD Among non-perturbative approaches to QCD, the most well established is lattice QCD. This approach uses a discrete set of spacetime points (called the lattice) to reduce the analytically intractable path integrals of the continuum theory to a very difficult numerical computation that is then carried out on supercomputers like the QCDOC, which was constructed for precisely this purpose. While it is a slow and resource-intensive approach, it has wide applicability, giving insight into parts of the theory inaccessible by other means, in particular into the explicit forces acting between quarks and antiquarks in a meson. However, the numerical sign problem makes it difficult to use lattice methods to study QCD at high density and low temperature (e.g. nuclear matter or the interior of neutron stars). 1/N expansion A well-known approximation scheme, the expansion, starts from the idea that the number of colors is infinite, and makes a series of corrections to account for the fact that it is not. Until now, it has been the source of qualitative insight rather than a method for quantitative predictions. Modern variants include the AdS/CFT approach. Effective theories For specific problems, effective theories may be written down that give qualitatively correct results in certain limits. In the best of cases, these may then be obtained as systematic expansions in some parameters of the QCD Lagrangian. One such effective field theory is chiral perturbation theory or ChiPT, which is the QCD effective theory at low energies. More precisely, it is a low energy expansion based on the spontaneous chiral symmetry breaking of QCD, which is an exact symmetry when quark masses are equal to zero, but for the u, d and s quark, which have small mass, it is still a good approximate symmetry. Depending on the number of quarks that are treated as light, one uses either SU(2) ChiPT or SU(3) ChiPT. Other effective theories are heavy quark effective theory (which expands around heavy quark mass near infinity), and soft-collinear effective theory (which expands around large ratios of energy scales). In addition to effective theories, models like the Nambu–Jona-Lasinio model and the chiral model are often used when discussing general features. QCD sum rules Based on an Operator product expansion one can derive sets of relations that connect different observables with each other. Experimental tests The notion of quark flavors was prompted by the necessity of explaining the properties of hadrons during the development of the quark model. The notion of color was necessitated by the puzzle of the . This has been dealt with in the section on the history of QCD. The first evidence for quarks as real constituent elements of hadrons was obtained in deep inelastic scattering experiments at SLAC. The first evidence for gluons came in three-jet events at PETRA. Several good quantitative tests of perturbative QCD exist: The running of the QCD coupling as deduced from many observations Scaling violation in polarized and unpolarized deep inelastic scattering Vector boson production at colliders (this includes the Drell-Yan process) Direct photons produced in hadronic collisions Jet cross sections in colliders Event shape observables at the LEP Heavy-quark production in colliders Quantitative tests of non-perturbative QCD are fewer, because the predictions are harder to make. The best is probably the running of the QCD coupling as probed through lattice computations of heavy-quarkonium spectra. There is a recent claim about the mass of the heavy meson Bc . Other non-perturbative tests are currently at the level of 5% at best. Continuing work on masses and form factors of hadrons and their weak matrix elements are promising candidates for future quantitative tests. The whole subject of quark matter and the quark–gluon plasma is a non-perturbative test bed for QCD that still remains to be properly exploited. One qualitative prediction of QCD is that there exist composite particles made solely of gluons called glueballs that have not yet been definitively observed experimentally. A definitive observation of a glueball with the properties predicted by QCD would strongly confirm the theory. In principle, if glueballs could be definitively ruled out, this would be a serious experimental blow to QCD. But, as of 2013, scientists are unable to confirm or deny the existence of glueballs definitively, despite the fact that particle accelerators have sufficient energy to generate them. Cross-relations to condensed matter physics There are unexpected cross-relations to condensed matter physics. For example, the notion of gauge invariance forms the basis of the well-known Mattis spin glasses, which are systems with the usual spin degrees of freedom for i =1,...,N, with the special fixed "random" couplings Here the εi and εk quantities can independently and "randomly" take the values ±1, which corresponds to a most-simple gauge transformation This means that thermodynamic expectation values of measurable quantities, e.g. of the energy are invariant. However, here the coupling degrees of freedom , which in the QCD correspond to the gluons, are "frozen" to fixed values (quenching). In contrast, in the QCD they "fluctuate" (annealing), and through the large number of gauge degrees of freedom the entropy plays an important role (see below). For positive J0 the thermodynamics of the Mattis spin glass corresponds in fact simply to a "ferromagnet in disguise", just because these systems have no "frustration" at all. This term is a basic measure in spin glass theory. Quantitatively it is identical with the loop product along a closed loop W. However, for a Mattis spin glass – in contrast to "genuine" spin glasses – the quantity PW never becomes negative. The basic notion "frustration" of the spin-glass is actually similar to the Wilson loop quantity of the QCD. The only difference is again that in the QCD one is dealing with SU(3) matrices, and that one is dealing with a "fluctuating" quantity. Energetically, perfect absence of frustration should be non-favorable and atypical for a spin glass, which means that one should add the loop product to the Hamiltonian, by some kind of term representing a "punishment". In the QCD the Wilson loop is essential for the Lagrangian rightaway. The relation between the QCD and "disordered magnetic systems" (the spin glasses belong to them) were additionally stressed in a paper by Fradkin, Huberman and Shenker, which also stresses the notion of duality. A further analogy consists in the already mentioned similarity to polymer physics, where, analogously to Wilson Loops, so-called "entangled nets" appear, which are important for the formation of the entropy-elasticity (force proportional to the length) of a rubber band. The non-abelian character of the SU(3) corresponds thereby to the non-trivial "chemical links", which glue different loop segments together, and "asymptotic freedom" means in the polymer analogy simply the fact that in the short-wave limit, i.e. for (where Rc is a characteristic correlation length for the glued loops, corresponding to the above-mentioned "bag radius", while λw is the wavelength of an excitation) any non-trivial correlation vanishes totally, as if the system had crystallized. There is also a correspondence between confinement in QCD – the fact that the color field is only different from zero in the interior of hadrons – and the behaviour of the usual magnetic field in the theory of type-II superconductors: there the magnetism is confined to the interior of the Abrikosov flux-line lattice, i.e., the London penetration depth λ of that theory is analogous to the confinement radius Rc of quantum chromodynamics. Mathematically, this correspondendence is supported by the second term, on the r.h.s. of the Lagrangian. See also For overviews: Standard Model Standard model (basic details) – for its field theoretical formulation Strong interaction Quark Gluon Hadron Colour confinement QCD matter Quark–gluon plasma For details: Gauge theory Quantum gauge theory, BRST quantization and Faddeev–Popov ghost Quantum field theory – a more general category For techniques: Lattice QCD 1/N expansion Perturbative QCD Soft-collinear effective theory Heavy
head and tail drift around endlessly in that circle makes it unnecessary to ever move items stored in the array. If n is the size of the array, then computing indices modulo n will turn the array into a circle. This is still the conceptually simplest way to construct a queue in a high-level language, but it does admittedly slow things down a little, because the array indices must be compared to zero and the array size, which is comparable to the time taken to check whether an array index is out of bounds, which some languages do, but this will certainly be the method of choice for a quick and dirty implementation, or for any high-level language that does not have pointer syntax. The array size must be declared ahead of time, but some implementations simply double the declared array size when overflow occurs. Most modern languages with objects or pointers can implement or come with libraries for dynamic lists. Such data structures may have not specified a fixed capacity limit besides memory constraints. Queue overflow results from trying to add an element onto a full queue and queue underflow happens when trying to remove an element from an empty queue. A bounded queue is a queue limited to a fixed number of items. There are several efficient implementations of FIFO queues. An efficient implementation is one that can perform the operations—en-queuing and de-queuing—in O(1) time. Linked list A doubly linked list has O(1) insertion and deletion at both ends, so it is a natural choice for queues. A regular singly linked list only has efficient insertion and deletion at one end. However, a small modification—keeping a pointer to the last node in addition to the first one—will enable it to implement an efficient queue. A deque implemented using a modified dynamic array Queues and programming languages Queues may be implemented as a separate data type, or maybe considered a special case of a double-ended queue (deque) and not implemented separately. For example, Perl and Ruby allow pushing and popping an array from both ends, so one can use push and unshift functions to enqueue and dequeue a list (or, in reverse, one can use shift and pop), although in some cases these operations are not efficient. C++'s Standard Template Library provides a "queue" templated class which is restricted to only push/pop operations. Since J2SE5.0, Java's library contains a interface that specifies queue operations; implementing classes include and (since J2SE 1.6) . PHP has an SplQueue class and third party libraries like beanstalk'd and Gearman. Example A simple queue implemented in JavaScript: class Queue { constructor() { this.items = new Array(0); } enqueue(element) { this.items.push(element); } dequeue() { return this.items.shift(); } } Purely functional implementation Queues can also be implemented as a purely functional data structure. There are two implementations. The first one only achieves per operation on average. That is, the amortized time is , but individual operations can take where n is the number of elements in the queue. The second implementation is called a real-time queue and it allows the queue to be persistent with operations in O(1) worst-case time. It is a more complex implementation and requires lazy lists with memoization. Amortized queue This queue's data is stored in two singly-linked lists named and . The list holds the front part of the queue. The list holds the remaining elements (a.k.a., the rear of the queue) in reverse order. It is easy to insert into the front of the queue by adding a node at the head of . And, if is not empty, it is easy to remove from the end of the queue by removing the node at the head of . When is empty, the list is reversed and assigned to and then the head of is removed. The insert ("enqueue") always takes time. The removal ("dequeue") takes when the list is not empty. When is empty, the reverse takes where is the number of elements in . But, we can say it is amortized time, because every element in had to be inserted and we can assign a constant cost for each element in the reverse to when it was inserted. Real-time queue The real-time queue achieves time for all operations, without amortization. This discussion will be technical, so recall that, for a list, denotes its length, that NIL represents an empty list and represents the list whose head is h and whose tail is t. The data structure used to implement our queues consists of three singly-linked lists where f is the front of the queue, r is the rear of the queue in reverse order. The invariant of the structure is that s is the rear of f without its first elements, that is . The tail of the queue is then almost and inserting an element x to is almost .	removing an element from the front is known as dequeue. Other operations may also be allowed, often including a peek or front operation that returns the value of the next element to be dequeued without dequeuing it. The operations of a queue make it a first-in-first-out (FIFO) data structure. In a FIFO data structure, the first element added to the queue will be the first one to be removed. This is equivalent to the requirement that once a new element is added, all elements that were added before have to be removed before the new element can be removed. A queue is an example of a linear data structure, or more abstractly a sequential collection. Queues are common in computer programs, where they are implemented as data structures coupled with access routines, as an abstract data structure or in object-oriented languages as classes. Common implementations are circular buffers and linked lists. Queues provide services in computer science, transport, and operations research where various entities such as data, objects, persons, or events are stored and held to be processed later. In these contexts, the queue performs the function of a buffer. Another usage of queues is in the implementation of breadth-first search. Queue implementation Theoretically, one characteristic of a queue is that it does not have a specific capacity. Regardless of how many elements are already contained, a new element can always be added. It can also be empty, at which point removing an element will be impossible until a new element has been added again. Fixed-length arrays are limited in capacity, but it is not true that items need to be copied towards the head of the queue. The simple trick of turning the array into a closed circle and letting the head and tail drift around endlessly in that circle makes it unnecessary to ever move items stored in the array. If n is the size of the array, then computing indices modulo n will turn the array into a circle. This is still the conceptually simplest way to construct a queue in a high-level language, but it does admittedly slow things down a little, because the array indices must be compared to zero and the array size, which is comparable to the time taken to check whether an array index is out of bounds, which some languages do, but this will certainly be the method of choice for a quick and dirty implementation, or for any high-level language that does not have pointer syntax. The array size must be declared ahead
special abilities. For example, the bread-and-butter Soldier class has medium armor, medium speed, and a well-rounded selection of weapons and grenades, while the Scout class is lightly armored, very fast, has a scanner that detects nearby enemies, but has very weak offensive weapons. One of the other differences with CTF is the fact that the flag is not returned automatically when a player drops it: running over one's flag in Threewave CTF would return the flag to the base, and in TF the flag remains in the same spot for preconfigured time and it has to be defended on remote locations. This caused a shift in defensive tactics compared to Threewave CTF. Team Fortress maintained its standing as the most-played online Quake modification for many years. Team Fortress would go on to become Team Fortress Classic and get a sequel, Team Fortress 2. Another popular mod was Threewave Capture the Flag (CTF), primarily authored by Dave 'Zoid' Kirsch. Threewave CTF is a partial conversion consisting of new levels, a new weapon (a grappling hook), power-ups, new textures, and new gameplay rules. Typically, two teams (red and blue) would compete in a game of Capture the flag, though a few maps with up to four teams (red, blue, green, and yellow) were created. Capture the Flag soon became a standard game mode included in most popular multiplayer games released after Quake. Rocket Arena provides the ability for players to face each other in small, open arenas with changes in the gameplay rules so that item collection and detailed level knowledge are no longer factors. A series of short rounds, with the surviving player in each round gaining a point, instead tests the player's aiming and dodging skills and reflexes. Clan Arena is a further modification that provides team play using Rocket Arena rules. One mod category, "bots", was introduced to provide surrogate players in multiplayer mode. Arcane Dimensions is a singleplayer mod. It's a partial conversion with breakable objects and walls, enhanced particle system, numerous visual improvements and new enemies and weapons. The level design is much more complex in terms of geometry and gameplay than in the original game. There are a large number of custom levels that have been made by users and fans of Quake. , new maps are still being made, over twenty years since the game's release. Custom maps are new maps that are playable by loading them into the original game. Custom levels of various gameplay types have been made, but most are in the single-player and deathmatch genres. More than 1500 single-player and a similar number of deathmatch maps have been made for Quake. Reception Sales According to David Kushner in Masters of Doom, id Software released a retail shareware version of Quake before the game's full retail distribution by GT Interactive. These shareware copies could be converted into complete versions through passwords purchased via phone. However, Kushner wrote that "gamers wasted no time hacking the shareware to unlock the full version of the game for free." This problem, combined with the scale of the operation, led id Software to cancel the plan. As a result, the company was left with 150,000 unsold shareware copies in storage. The venture damaged Quakes initial sales and caused its retail push by GT Interactive to miss the holiday shopping season. Following the game's full release, Kushner remarked that its early "sales were good — with 250,000 units shipped — but not a phenomenon like Doom II." In the United States, Quake placed sixth on PC Data's monthly computer game sales charts for November and December 1996. Its shareware edition was the sixth-best-selling computer game of 1996 overall, while its retail SKU claimed 20th place. The shareware version sold 393,575 copies and grossed $3,005,519 in the United States during 1996. It remained in PC Data's monthly top 10 from January to April 1997, but was absent by May. During its first 12 months, Quake sold 373,000 retail copies and earned $18 million in the United States, according to PC Data. Its final retail sales for 1997 were 273,936 copies, which made it the country's 16th-highest computer game seller for the year. Sales of Quake reached 550,000 units in the United States alone by December 1999. In 1997, id estimated that there may be as many as 5 million copies of Quake circulating. The game sold over 1.4 million copies by December 1997. Critical reviews Quake was critically acclaimed on the PC. Aggregating review websites GameRankings and Metacritic gave the original PC version 93% and 94/100, and the Nintendo 64 port 76% and 74/100. A Next Generation critic lauded the game's realistic 3D physics and genuinely unnerving sound effects. GamePro said Quake had been over-hyped but is excellent nonetheless, particularly its usage of its advanced 3D engine. The review also praised the sound effects, atmospheric music, and graphics, though it criticized that the polygons used to construct the enemies are too obvious at close range. Less than a month after Quake was released (and a month before they actually reviewed the game), Next Generation listed it as number 9 on their "Top 100 Games of All Time", saying that it is similar to Doom but supports a maximum of eight players instead of four. In 1996, Computer Gaming World declared Quake the 36th-best computer game ever released, and listed "telefragged" as #1 on its list of "the 15 best ways to die in computer gaming". In 1997, the Game Developers Choice Awards gave Quake three spotlight awards for Best Sound Effects, Best Music or Soundtrack and Best On-Line/Internet Game. Entertainment Weekly gave the game a B+ and called it "an extended bit of subterranean mayhem that offers three major improvements over its immediate predecessor [Doom]." He identified these as the graphics, the audio design, and the amount of violent action. Next Generation reviewed the Macintosh version of the game, rating it four stars out of five, and stated that "Though replay value is limited by the lack of interactive environments or even the semblance of a plot, there's no doubt that Quake and its engine are something powerful and addictive." The Saturn version received mostly negative reviews, as critics generally agreed that it did not bring over the elements that make the game enjoyable. In particular, critics reviled the absence of the multiplayer mode, which they felt had eclipsed the single player campaign as the reason to play Quake. Kraig Kujawa wrote in Electronic Gaming Monthly, "Quake is not a great one-player game - it gained its notoriety on the Net as a multiplayer." and his co-reviewer Sushi-X concluded "Without multiplayer, I'd pass." Most reviews also said the controls are much worse than the PC original, in particular the difficulty of aiming at enemies without the benefit of either mouse-controlled camera or a second analog stick. GamePro noted that the graphics are very pixelated and blurry, to the point where people unfamiliar with Quake would not be able to discern what they're looking at. They concluded, "Quake may not be the worst Saturn game available, but it certainly doesn't live up to its PC heritage." Most critics did find the port technically impressive, particularly the added light sourcing. However, Next Generation pointed out that "Porting Quake to a console is nothing more than an excuse for bragging rights. It's simply a way to show that the limited architecture of a 32-bit system has the power to push the same game that those mighty Pentium PCs take for granted." Even Rich Leadbetter of Sega Saturn Magazine, which gave the port a 92%, acknowledged that it was a proverbial dancing bear, noting several conspicuous compromises the port made and stating as his concluding argument, "Look, it's Quake on the Saturn - the machine has no right to be doing this!" GameSpot opined that the game's lack of plot makes the single-player campaign feel too shallow and lacking in motivation to appeal to most gamers. Most critics compared the port unfavorably to the Saturn version of Duke Nukem 3D (which came out just a few months earlier), mainly in terms of gameplay. Next Generation reviewed the Nintendo 64 version of the game, rating it three stars out of five, and stated that "As a whole, Quake 64 doesn't live up to the experience offered by the high-end, 3D-accelerated PC version; it is, however, an entertaining gaming experience that is worthy of a close look and a nice addition to the blossoming number of first-person shooters for Nintendo 64." Next Generation reviewed the arcade version of the game, rating it three stars out of five, and stated that "For those who don't have LAN or internet capabilities, check out arcade Quake. It's a blast." In 1998, PC Gamer declared it the 28th-best computer game ever released, and the editors called it "one of the most addictive, adaptable, and pulse-pounding 3D shooters ever created". In 2003, Quake was inducted into GameSpot's list of the greatest games of all time. Speedruns As an example of the dedication that Quake has inspired in its fan community, a group of expert players recorded speedrun demos (replayable recordings of the player's movement) of Quake levels completed in record time on the "Nightmare" skill level. The footage was edited into a continuous 19 minutes, 49 seconds demo called Quake done Quick and released on June 10, 1997. Owners of Quake could replay this demo in the game engine, watching the run unfold as if they were playing it themselves. Most full-game speedruns are a collaborative effort by a number of runners (though some have been done by single runners on their own). Although each particular level is credited to one runner, the ideas and techniques used are iterative and collaborative in nature, with each runner picking up tips and ideas from the others, so that speeds keep improving beyond what was thought possible as the runs are further optimized and new tricks or routes are discovered. Further time improvements of the continuous whole game run were achieved into the 21st century. In addition, many thousands of individual level runs are kept at Speed Demos Archive's Quake section, including many on custom maps. Speedrunning is a counterpart to multiplayer modes in making Quake one of the first games promoted as a virtual sport. Legacy The source code of the Quake and QuakeWorld engines was licensed under the GNU GPL-2.0-or-later on December 21, 1999. The id Software maps, objects, textures, sounds, and other creative works remain under their original proprietary license. The shareware distribution of Quake is still freely redistributable and usable with the GPLed engine code. One must purchase a copy of Quake in order to receive the registered version of the game which includes more single-player episodes and the deathmatch maps. Based on the success of the first Quake game, and later published Quake II and Quake III Arena, Quake 4 was released in October 2005, developed by Raven Software using the Doom 3 engine. Quake was the game primarily responsible for the emergence of the machinima artform of films made in game engines, thanks to edited Quake demos such as Ranger Gone Bad and Blahbalicious, the in-game film The Devil's Covenant, and the in-game-rendered, four-hour epic film The Seal of Nehahra. On June 22, 2006, it had been ten years since the original uploading of the game to cdrom.com archives. Many Internet forums had topics about it, and it was a front-page story on Slashdot. On October 11, 2006, John Romero released the original map files for all of the levels in Quake under the GPL. Quake has four sequels: Quake II, Quake III Arena, Quake 4, and Enemy Territory: Quake Wars. In 2002, a version of Quake was produced for mobile phones. A copy of Quake was also released as a compilation in 2001, labeled Ultimate Quake, which included the original Quake, Quake II, and Quake III Arena which was published by Activision. In 2008, Quake was honored at the 59th Annual Technology & Engineering Emmy Awards for advancing the art form of user modifiable games. John Carmack accepted the award. Years after its original release, Quake is still regarded by many critics as one of the greatest and most influential games ever made. Expansions and ports There were two official expansion packs released for Quake. The expansion packs pick up where the first game left off, include all of the same weapons, power-ups, monsters, and gothic atmosphere/architecture, and continue/finish the story of the first game and its protagonist. An unofficial third expansion pack, Abyss of Pandemonium, was developed by the Impel Development Team, published by Perfect Publishing, and released on April 14, 1998; an updated version, version 2.0, titled Abyss of Pandemonium – The Final Mission was released as freeware. An authorized expansion pack, Q!ZONE was developed and published by WizardWorks, and released in 1996. An authorized level editor, Deathmatch Maker was developed by Virtus Corporation and published by Macmillan Digital Publishing in 1997. It contained an exclusive Virtus' Episode. In honor of Quake'''s 20th anniversary, MachineGames, an internal development studio of ZeniMax Media, who are the current owners of the Quake IP, released online a new expansion pack for free, called Episode 5: Dimension of the Past. Quake Mission Pack No. 1: Scourge of ArmagonQuake Mission Pack No. 1: Scourge of Armagon was the first official mission pack, released on March 5, 1997. Developed by Hipnotic Interactive, it features three episodes divided into seventeen new single-player levels (three of which are secret), a new multiplayer level, a new soundtrack composed by Jeehun Hwang, and gameplay features not originally present in Quake, including rotating structures and breakable walls. Unlike the main Quake game and Mission Pack No. 2, Scourge does away with the episode hub, requiring the three episodes to be played sequentially. The three new enemies include Centroids, large cybernetic scorpions with nailguns; Gremlins, small goblins that can steal weapons and multiply by feeding on enemy corpses; and Spike Mines, floating orbs that detonate when near the player. The three new weapons include the Mjolnir, a large lightning emitting hammer; the Laser Cannon, which shoots bouncing bolts of energy; and the Proximity Mine Launcher, which fires grenades that attach to surfaces and detonate when an opponent comes near. The three new power-ups include the Horn of Conjuring, which summons an enemy to protect the player; the Empathy Shield, which halves the damage taken by the player between the player and the attacking enemy; and the Wetsuit, which renders the player invulnerable to electricity and allows the player to stay underwater for a period of time. The storyline follows Armagon, a general of Quake's forces, planning to invade Earth via a portal known as the 'Rift'. Armagon resembles a giant gremlin with cybernetic legs and a combined rocket launcher/laser cannon for arms. Tim Soete of GameSpot gave it a score 8.6 out of 10. Quake Mission Pack No. 2: Dissolution of EternityQuake Mission Pack No. 2: Dissolution of Eternity was the second official mission pack, released on March 19, 1997. Developed by Rogue Entertainment, it features two episodes divided into fifteen new single-player levels, a new multiplayer level, a new soundtrack, and several new enemies and bosses. Notably, the pack lacks secret levels. The eight new enemies include Electric Eels, Phantom Swordsmen, Multi-Grenade Ogres (which fire cluster grenades), Hell Spawn, Wraths (floating, robed undead), Guardians (resurrected ancient Egyptian warriors), Mummies, and statues of various enemies that can come to life. The four new types of bosses include Lava Men, Overlords, large Wraths, and a dragon guarding the "temporal energy converter". The two new power-ups include the Anti Grav Belt, which allows the player to jump higher; and the Power Shield, which lowers the damage the player receives. Rather than offering new weapons, the mission pack gives the player four new types of ammo for existing weapons, such as "lava nails" for the Nailgun, cluster grenades for the Grenade Launcher,	a class system for the players. Players choose a class, which creates various restrictions on weapons and armor types available to that player, and also grants special abilities. For example, the bread-and-butter Soldier class has medium armor, medium speed, and a well-rounded selection of weapons and grenades, while the Scout class is lightly armored, very fast, has a scanner that detects nearby enemies, but has very weak offensive weapons. One of the other differences with CTF is the fact that the flag is not returned automatically when a player drops it: running over one's flag in Threewave CTF would return the flag to the base, and in TF the flag remains in the same spot for preconfigured time and it has to be defended on remote locations. This caused a shift in defensive tactics compared to Threewave CTF. Team Fortress maintained its standing as the most-played online Quake modification for many years. Team Fortress would go on to become Team Fortress Classic and get a sequel, Team Fortress 2. Another popular mod was Threewave Capture the Flag (CTF), primarily authored by Dave 'Zoid' Kirsch. Threewave CTF is a partial conversion consisting of new levels, a new weapon (a grappling hook), power-ups, new textures, and new gameplay rules. Typically, two teams (red and blue) would compete in a game of Capture the flag, though a few maps with up to four teams (red, blue, green, and yellow) were created. Capture the Flag soon became a standard game mode included in most popular multiplayer games released after Quake. Rocket Arena provides the ability for players to face each other in small, open arenas with changes in the gameplay rules so that item collection and detailed level knowledge are no longer factors. A series of short rounds, with the surviving player in each round gaining a point, instead tests the player's aiming and dodging skills and reflexes. Clan Arena is a further modification that provides team play using Rocket Arena rules. One mod category, "bots", was introduced to provide surrogate players in multiplayer mode. Arcane Dimensions is a singleplayer mod. It's a partial conversion with breakable objects and walls, enhanced particle system, numerous visual improvements and new enemies and weapons. The level design is much more complex in terms of geometry and gameplay than in the original game. There are a large number of custom levels that have been made by users and fans of Quake. , new maps are still being made, over twenty years since the game's release. Custom maps are new maps that are playable by loading them into the original game. Custom levels of various gameplay types have been made, but most are in the single-player and deathmatch genres. More than 1500 single-player and a similar number of deathmatch maps have been made for Quake. Reception Sales According to David Kushner in Masters of Doom, id Software released a retail shareware version of Quake before the game's full retail distribution by GT Interactive. These shareware copies could be converted into complete versions through passwords purchased via phone. However, Kushner wrote that "gamers wasted no time hacking the shareware to unlock the full version of the game for free." This problem, combined with the scale of the operation, led id Software to cancel the plan. As a result, the company was left with 150,000 unsold shareware copies in storage. The venture damaged Quakes initial sales and caused its retail push by GT Interactive to miss the holiday shopping season. Following the game's full release, Kushner remarked that its early "sales were good — with 250,000 units shipped — but not a phenomenon like Doom II." In the United States, Quake placed sixth on PC Data's monthly computer game sales charts for November and December 1996. Its shareware edition was the sixth-best-selling computer game of 1996 overall, while its retail SKU claimed 20th place. The shareware version sold 393,575 copies and grossed $3,005,519 in the United States during 1996. It remained in PC Data's monthly top 10 from January to April 1997, but was absent by May. During its first 12 months, Quake sold 373,000 retail copies and earned $18 million in the United States, according to PC Data. Its final retail sales for 1997 were 273,936 copies, which made it the country's 16th-highest computer game seller for the year. Sales of Quake reached 550,000 units in the United States alone by December 1999. In 1997, id estimated that there may be as many as 5 million copies of Quake circulating. The game sold over 1.4 million copies by December 1997. Critical reviews Quake was critically acclaimed on the PC. Aggregating review websites GameRankings and Metacritic gave the original PC version 93% and 94/100, and the Nintendo 64 port 76% and 74/100. A Next Generation critic lauded the game's realistic 3D physics and genuinely unnerving sound effects. GamePro said Quake had been over-hyped but is excellent nonetheless, particularly its usage of its advanced 3D engine. The review also praised the sound effects, atmospheric music, and graphics, though it criticized that the polygons used to construct the enemies are too obvious at close range. Less than a month after Quake was released (and a month before they actually reviewed the game), Next Generation listed it as number 9 on their "Top 100 Games of All Time", saying that it is similar to Doom but supports a maximum of eight players instead of four. In 1996, Computer Gaming World declared Quake the 36th-best computer game ever released, and listed "telefragged" as #1 on its list of "the 15 best ways to die in computer gaming". In 1997, the Game Developers Choice Awards gave Quake three spotlight awards for Best Sound Effects, Best Music or Soundtrack and Best On-Line/Internet Game. Entertainment Weekly gave the game a B+ and called it "an extended bit of subterranean mayhem that offers three major improvements over its immediate predecessor [Doom]." He identified these as the graphics, the audio design, and the amount of violent action. Next Generation reviewed the Macintosh version of the game, rating it four stars out of five, and stated that "Though replay value is limited by the lack of interactive environments or even the semblance of a plot, there's no doubt that Quake and its engine are something powerful and addictive." The Saturn version received mostly negative reviews, as critics generally agreed that it did not bring over the elements that make the game enjoyable. In particular, critics reviled the absence of the multiplayer mode, which they felt had eclipsed the single player campaign as the reason to play Quake. Kraig Kujawa wrote in Electronic Gaming Monthly, "Quake is not a great one-player game - it gained its notoriety on the Net as a multiplayer." and his co-reviewer Sushi-X concluded "Without multiplayer, I'd pass." Most reviews also said the controls are much worse than the PC original, in particular the difficulty of aiming at enemies without the benefit of either mouse-controlled camera or a second analog stick. GamePro noted that the graphics are very pixelated and blurry, to the point where people unfamiliar with Quake would not be able to discern what they're looking at. They concluded, "Quake may not be the worst Saturn game available, but it certainly doesn't live up to its PC heritage." Most critics did find the port technically impressive, particularly the added light sourcing. However, Next Generation pointed out that "Porting Quake to a console is nothing more than an excuse for bragging rights. It's simply a way to show that the limited architecture of a 32-bit system has the power to push the same game that those mighty Pentium PCs take for granted." Even Rich Leadbetter of Sega Saturn Magazine, which gave the port a 92%, acknowledged that it was a proverbial dancing bear, noting several conspicuous compromises the port made and stating as his concluding argument, "Look, it's Quake on the Saturn - the machine has no right to be doing this!" GameSpot opined that the game's lack of plot makes the single-player campaign feel too shallow and lacking in motivation to appeal to most gamers. Most critics compared the port unfavorably to the Saturn version of Duke Nukem 3D (which came out just a few months earlier), mainly in terms of gameplay. Next Generation reviewed the Nintendo 64 version of the game, rating it three stars out of five, and stated that "As a whole, Quake 64 doesn't live up to the experience offered by the high-end, 3D-accelerated PC version; it is, however, an entertaining gaming experience that is worthy of a close look and a nice addition to the blossoming number of first-person shooters for Nintendo 64." Next Generation reviewed the arcade version of the game, rating it three stars out of five, and stated that "For those who don't have LAN or internet capabilities, check out arcade Quake. It's a blast." In 1998, PC Gamer declared it the 28th-best computer game ever released, and the editors called it "one of the most addictive, adaptable, and pulse-pounding 3D shooters ever created". In 2003, Quake was inducted into GameSpot's list of the greatest games of all time. Speedruns As an example of the dedication that Quake has inspired in its fan community, a group of expert players recorded speedrun demos (replayable recordings of the player's movement) of Quake levels completed in record time on the "Nightmare" skill level. The footage was edited into a continuous 19 minutes, 49 seconds demo called Quake done Quick and released on June 10, 1997. Owners of Quake could replay this demo in the game engine, watching the run unfold as if they were playing it themselves. Most full-game speedruns are a collaborative effort by a number of runners (though some have been done by single runners on their own). Although each particular level is credited to one runner, the ideas and techniques used are iterative and collaborative in nature, with each runner picking up tips and ideas from the others, so that speeds keep improving beyond what was thought possible as the runs are further optimized and new tricks or routes are discovered. Further time improvements of the continuous whole game run were achieved into the 21st century. In addition, many thousands of individual level runs are kept at Speed Demos Archive's Quake section, including many on custom maps. Speedrunning is a counterpart to multiplayer modes in making Quake one of the first games promoted as a virtual sport. Legacy The source code of the Quake and QuakeWorld engines was licensed under the GNU GPL-2.0-or-later on December 21, 1999. The id Software maps, objects, textures, sounds, and other creative works remain under their original proprietary license. The shareware distribution of Quake is still freely redistributable and usable with the GPLed engine code. One must purchase a copy of Quake in order to receive the registered version of the game which includes more single-player episodes and the deathmatch maps. Based on the success of the first Quake game, and later published Quake II and Quake III Arena, Quake 4 was released in October 2005, developed by Raven Software using the Doom 3 engine. Quake was the game primarily responsible for the emergence of the machinima artform of films made in game engines, thanks to edited Quake demos such as Ranger Gone Bad and Blahbalicious, the in-game film The Devil's Covenant, and the in-game-rendered, four-hour epic film The Seal of Nehahra. On June 22, 2006, it had been ten years since the original uploading of the game to
but understandable.—J. Schwinger Standard Model In 1954, Yang Chen-Ning and Robert Mills generalised the local symmetry of QED, leading to non-Abelian gauge theories (also known as Yang–Mills theories), which are based on more complicated local symmetry groups. In QED, (electrically) charged particles interact via the exchange of photons, while in non-Abelian gauge theory, particles carrying a new type of "charge" interact via the exchange of massless gauge bosons. Unlike photons, these gauge bosons themselves carry charge. Sheldon Glashow developed a non-Abelian gauge theory that unified the electromagnetic and weak interactions in 1960. In 1964, Abdus Salam and John Clive Ward arrived at the same theory through a different path. This theory, nevertheless, was non-renormalizable. Peter Higgs, Robert Brout, François Englert, Gerald Guralnik, Carl Hagen, and Tom Kibble proposed in their famous Physical Review Letters papers that the gauge symmetry in Yang–Mills theories could be broken by a mechanism called spontaneous symmetry breaking, through which originally massless gauge bosons could acquire mass. By combining the earlier theory of Glashow, Salam, and Ward with the idea of spontaneous symmetry breaking, Steven Weinberg wrote down in 1967 a theory describing electroweak interactions between all leptons and the effects of the Higgs boson. His theory was at first mostly ignored, until it was brought back to light in 1971 by Gerard 't Hooft's proof that non-Abelian gauge theories are renormalizable. The electroweak theory of Weinberg and Salam was extended from leptons to quarks in 1970 by Glashow, John Iliopoulos, and Luciano Maiani, marking its completion. Harald Fritzsch, Murray Gell-Mann, and Heinrich Leutwyler discovered in 1971 that certain phenomena involving the strong interaction could also be explained by non-Abelian gauge theory. Quantum chromodynamics (QCD) was born. In 1973, David Gross, Frank Wilczek, and Hugh David Politzer showed that non-Abelian gauge theories are "asymptotically free", meaning that under renormalization, the coupling constant of the strong interaction decreases as the interaction energy increases. (Similar discoveries had been made numerous times previously, but they had been largely ignored.) Therefore, at least in high-energy interactions, the coupling constant in QCD becomes sufficiently small to warrant a perturbative series expansion, making quantitative predictions for the strong interaction possible. These theoretical breakthroughs brought about a renaissance in QFT. The full theory, which includes the electroweak theory and chromodynamics, is referred to today as the Standard Model of elementary particles. The Standard Model successfully describes all fundamental interactions except gravity, and its many predictions have been met with remarkable experimental confirmation in subsequent decades. The Higgs boson, central to the mechanism of spontaneous symmetry breaking, was finally detected in 2012 at CERN, marking the complete verification of the existence of all constituents of the Standard Model. Other developments The 1970s saw the development of non-perturbative methods in non-Abelian gauge theories. The 't Hooft–Polyakov monopole was discovered theoretically by 't Hooft and Alexander Polyakov, flux tubes by Holger Bech Nielsen and Poul Olesen, and instantons by Polyakov and coauthors. These objects are inaccessible through perturbation theory. Supersymmetry also appeared in the same period. The first supersymmetric QFT in four dimensions was built by Yuri Golfand and Evgeny Likhtman in 1970, but their result failed to garner widespread interest due to the Iron Curtain. Supersymmetry only took off in the theoretical community after the work of Julius Wess and Bruno Zumino in 1973. Among the four fundamental interactions, gravity remains the only one that lacks a consistent QFT description. Various attempts at a theory of quantum gravity led to the development of string theory, itself a type of two-dimensional QFT with conformal symmetry. Joël Scherk and John Schwarz first proposed in 1974 that string theory could be the quantum theory of gravity. Condensed matter physics Although quantum field theory arose from the study of interactions between elementary particles, it has been successfully applied to other physical systems, particularly to many-body systems in condensed matter physics. Historically, the Higgs mechanism of spontaneous symmetry breaking was a result of Yoichiro Nambu's application of superconductor theory to elementary particles, while the concept of renormalization came out of the study of second-order phase transitions in matter. Soon after the introduction of photons, Einstein performed the quantization procedure on vibrations in a crystal, leading to the first quasiparticle—phonons. Lev Landau claimed that low-energy excitations in many condensed matter systems could be described in terms of interactions between a set of quasiparticles. The Feynman diagram method of QFT was naturally well suited to the analysis of various phenomena in condensed matter systems. Gauge theory is used to describe the quantization of magnetic flux in superconductors, the resistivity in the quantum Hall effect, as well as the relation between frequency and voltage in the AC Josephson effect. Principles For simplicity, natural units are used in the following sections, in which the reduced Planck constant and the speed of light are both set to one. Classical fields A classical field is a function of spatial and time coordinates. Examples include the gravitational field in Newtonian gravity and the electric field and magnetic field in classical electromagnetism. A classical field can be thought of as a numerical quantity assigned to every point in space that changes in time. Hence, it has infinitely many degrees of freedom. Many phenomena exhibiting quantum mechanical properties cannot be explained by classical fields alone. Phenomena such as the photoelectric effect are best explained by discrete particles (photons), rather than a spatially continuous field. The goal of quantum field theory is to describe various quantum mechanical phenomena using a modified concept of fields. Canonical quantisation and path integrals are two common formulations of QFT. To motivate the fundamentals of QFT, an overview of classical field theory is in order. The simplest classical field is a real scalar field — a real number at every point in space that changes in time. It is denoted as , where is the position vector, and is the time. Suppose the Lagrangian of the field, , is where is the Lagrangian density, is the time-derivative of the field, is the gradient operator, and is a real parameter (the "mass" of the field). Applying the Euler–Lagrange equation on the Lagrangian: we obtain the equations of motion for the field, which describe the way it varies in time and space: This is known as the Klein–Gordon equation. The Klein–Gordon equation is a wave equation, so its solutions can be expressed as a sum of normal modes (obtained via Fourier transform) as follows: where is a complex number (normalised by convention), denotes complex conjugation, and is the frequency of the normal mode: Thus each normal mode corresponding to a single can be seen as a classical harmonic oscillator with frequency . Canonical quantisation The quantisation procedure for the above classical field to a quantum operator field is analogous to the promotion of a classical harmonic oscillator to a quantum harmonic oscillator. The displacement of a classical harmonic oscillator is described by where is a complex number (normalised by convention), and is the oscillator's frequency. Note that is the displacement of a particle in simple harmonic motion from the equilibrium position, not to be confused with the spatial label of a quantum field. For a quantum harmonic oscillator, is promoted to a linear operator : Complex numbers and are replaced by the annihilation operator and the creation operator , respectively, where denotes Hermitian conjugation. The commutation relation between the two is The vacuum state , which is the lowest energy state, is defined by Any quantum state of a single harmonic oscillator can be obtained from by successively applying the creation operator : By the same token, the aforementioned real scalar field , which corresponds to in the single harmonic oscillator, is also promoted to a quantum field operator , while the annihilation operator , the creation operator and the angular frequency are now for a particular : Their commutation relations are: where is the Dirac delta function. The vacuum state is defined by Any quantum state of the field can be obtained from by successively applying creation operators , e.g. Although the quantum field appearing in the Lagrangian is spatially continuous, the quantum states of the field are discrete. While the state space of a single quantum harmonic oscillator contains all the discrete energy states of one oscillating particle, the state space of a quantum field contains the discrete energy levels of an arbitrary number of particles. The latter space is known as a Fock space, which can account for the fact that particle numbers are not fixed in relativistic quantum systems. The process of quantising an arbitrary number of particles instead of a single particle is often also called second quantisation. The foregoing procedure is a direct application of non-relativistic quantum mechanics and can be used to quantise (complex) scalar fields, Dirac fields, vector fields (e.g. the electromagnetic field), and even strings. However, creation and annihilation operators are only well defined in the simplest theories that contain no interactions (so-called free theory). In the case of the real scalar field, the existence of these operators was a consequence of the decomposition of solutions of the classical equations of motion into a sum of normal modes. To perform calculations on any realistic interacting theory, perturbation theory would be necessary. The Lagrangian of any quantum field in nature would contain interaction terms in addition to the free theory terms. For example, a quartic interaction term could be introduced to the Lagrangian of the real scalar field: where is a spacetime index, , etc. The summation over the index has been omitted following the Einstein notation. If the parameter is sufficiently small, then the interacting theory described by the above Lagrangian can be considered as a small perturbation from the free theory. Path integrals The path integral formulation of QFT is concerned with the direct computation of the scattering amplitude of a certain interaction process, rather than the establishment of operators and state spaces. To calculate the probability amplitude for a system to evolve from some initial state at time to some final state at , the total time is divided into small intervals. The overall amplitude is the product of the amplitude of evolution within each interval, integrated over all intermediate states. Let be the Hamiltonian (i.e. generator of time evolution), then Taking the limit , the above product of integrals becomes the Feynman path integral: where is the Lagrangian involving and its derivatives with respect to spatial and time coordinates, obtained from the Hamiltonian via Legendre transformation. The initial and final conditions of the path integral are respectively In other words, the overall amplitude is the sum over the amplitude of every possible path between the initial and final states, where the amplitude of a path is given by the exponential in the integrand. Two-point correlation function In calculations, one often encounters expression likein the free or interacting theory, respectively. Here, and are position four-vectors, is the time ordering operator that shuffles its operands so the time-components and increase from right to left, and is the ground state (vacuum state) of the interacting theory, different from the free ground state . This expression represents the probability amplitude for the field to propagate from to , and goes by multiple names, like the two-point propagator, two-point correlation function, two-point Green's function or two-point function for short. The free two-point function, also known as the Feynman propagator, can be found for the real scalar field by either canonical quantisation or path integrals to be In an interacting theory, where the Lagrangian or Hamiltonian contains terms or that describe interactions, the two-point function is more difficult to define. However, through both the canonical quantisation formulation and the path integral formulation, it is possible to express it through an infinite perturbation series of the free two-point function. In canonical quantisation, the two-point correlation function can be written as: where is an infinitesimal number and is the field operator under the free theory. Here, the exponential should be understood as its power series expansion. For example, in -theory, the interacting term of the Hamiltonian is , and the expansion of the two-point correlator in terms of becomesThis perturbation expansion expresses the interacting two-point function in terms of quantities that are evaluated in the free theory. In the path integral formulation, the two-point correlation function can be written where is the Lagrangian density. As in the previous paragraph, the exponential can be expanded as a series in , reducing the interacting two-point function to quantities in the free theory. Wick's theorem further reduce any -point correlation function in the free theory to a sum of products of two-point correlation functions. For example, Since interacting correlation functions can be expressed in terms of free correlation functions, only the latter need to be evaluated in order to calculate all physical quantities in the (perturbative) interacting theory. This makes the Feynman propagator one of the most important quantities in quantum field theory. Feynman diagram Correlation functions in the interacting theory can be written as a perturbation series. Each term in the series is a product of Feynman propagators in the free theory and can be represented visually by a Feynman diagram. For example, the term in the two-point correlation function in the theory is After applying Wick's theorem, one of the terms is This term can instead be obtained from the Feynman diagram . The diagram consists of external vertices connected with one edge and represented by dots (here labelled and ). internal vertices connected with four edges and represented by dots (here labelled ). edges connecting the vertices and represented by lines. Every vertex corresponds to a single field factor at the corresponding point in spacetime, while the edges correspond to the propagators between the spacetime points. The term in the perturbation series corresponding to the diagram is obtained by writing down the expression that follows from the Feynman rules: For every internal vertex , write down a factor . For every edge that connects two vertices and , write down a factor . Divide by the symmetry factor of the diagram. With the symmetry factor , following these rules yields exactly the expression above. By Fourier transforming the propagator, the Feynman rules can be reformulated from position space into momentum space. In order to compute the -point correlation function to the -th order, list all valid Feynman diagrams with external points and or fewer vertices, and then use Feynman rules to obtain the expression for each term. To be precise, is equal to the sum of (expressions corresponding to) all connected diagrams with external points. (Connected diagrams are those in which every vertex is connected to an external point through lines. Components that are totally disconnected from external lines are sometimes called "vacuum bubbles".) In the interaction theory discussed above, every vertex must have four legs. In realistic applications, the scattering amplitude of a certain interaction or the decay rate of a particle can be computed from the S-matrix, which itself can be found using the Feynman diagram method. Feynman diagrams devoid of "loops" are called tree-level diagrams, which describe the lowest-order interaction processes; those containing loops are referred to as -loop diagrams, which describe higher-order contributions, or radiative corrections, to the interaction. Lines whose end points are vertices can be thought of as the propagation of virtual particles. Renormalization Feynman rules can be used to directly evaluate tree-level diagrams. However, naïve computation of loop diagrams such as the one shown above will result in divergent momentum integrals, which seems to imply that almost all terms in the perturbative expansion are infinite. The renormalisation procedure is a systematic process for removing such infinities. Parameters appearing in the Lagrangian, such as the mass and the coupling constant , have no physical meaning — , , and the field strength are not experimentally measurable quantities and are referred to here as the bare mass, bare coupling constant, and bare field, respectively. The physical mass and coupling constant are measured in some interaction process and are generally different from the bare quantities. While computing physical quantities from this interaction process, one may limit the domain of divergent momentum integrals to be below some momentum cut-off , obtain expressions for the physical quantities, and then take the limit . This is an example of regularisation, a class of methods to treat divergences in QFT, with being the regulator. The approach illustrated above is called bare perturbation theory, as calculations involve only the bare quantities such as mass and coupling constant. A different approach, called renormalised perturbation theory, is to use physically meaningful quantities from the very beginning. In the case of theory, the field strength is first redefined: where is the bare field, is the renormalised field, and is a constant to be determined. The Lagrangian density becomes: where and are the experimentally measurable, renormalised, mass and coupling constant, respectively, and are constants to be determined. The first three terms are the Lagrangian density written in terms of the renormalised quantities, while the latter three terms are referred to as "counterterms". As the Lagrangian now contains more terms, so the Feynman diagrams should include additional elements, each with their own Feynman rules. The procedure is outlined as follows. First select a regularisation scheme (such as the cut-off regularisation introduced above or dimensional regularization); call the regulator . Compute Feynman diagrams, in which divergent terms will depend on . Then, define , , and such that Feynman diagrams for the counterterms will exactly cancel the divergent terms in the normal Feynman diagrams when the limit is taken. In this way, meaningful finite quantities are obtained. It is only possible to eliminate all infinities to obtain a finite result in renormalisable theories, whereas in non-renormalisable theories infinities cannot be removed by the redefinition of a small number of parameters. The Standard Model of elementary particles is a renormalisable QFT, while quantum gravity is non-renormalisable. Renormalisation group The renormalisation group, developed by Kenneth Wilson, is a mathematical apparatus used to study the changes in physical parameters (coefficients in the Lagrangian) as the system is viewed at different scales. The way in which each parameter changes with scale is described by its β function. Correlation functions, which underlie quantitative physical predictions, change with scale according to the Callan–Symanzik equation. As an example, the coupling constant in QED, namely the elementary charge , has the following β function: where is the energy scale under which the measurement of is performed. This differential equation implies that the observed elementary charge increases as the scale increases. The renormalized coupling constant, which changes with the energy scale, is also called the running coupling constant. The coupling constant in quantum chromodynamics, a non-Abelian gauge theory based on the symmetry group , has the following β function: where is the number of quark flavours. In the case where (the Standard Model has ), the coupling constant decreases as the energy scale increases. Hence, while the strong interaction is strong at low energies, it becomes very weak in high-energy interactions, a phenomenon known as asymptotic freedom. Conformal field theories (CFTs) are special QFTs that admit conformal symmetry. They are insensitive to changes in the scale, as all their coupling constants have vanishing β function. (The converse is not true, however — the vanishing of all β functions does not imply conformal symmetry of the theory.) Examples include string theory and supersymmetric Yang–Mills theory. According to Wilson's picture, every QFT is fundamentally accompanied by its energy cut-off , i.e. that the theory is no longer valid at energies higher than , and all degrees of freedom above the scale are to be omitted. For example, the cut-off could be the inverse of the atomic spacing in a condensed matter system, and in elementary particle physics it could be associated with the fundamental "graininess" of spacetime caused by quantum fluctuations in gravity. The cut-off scale of theories of particle interactions lies far beyond current experiments. Even if the theory were very complicated at that scale, as long as its couplings are sufficiently weak, it must be described at low energies by a renormalisable effective field theory. The difference between renormalisable and non-renormalisable theories is that the former are	Murray Gell-Mann, and Heinrich Leutwyler discovered in 1971 that certain phenomena involving the strong interaction could also be explained by non-Abelian gauge theory. Quantum chromodynamics (QCD) was born. In 1973, David Gross, Frank Wilczek, and Hugh David Politzer showed that non-Abelian gauge theories are "asymptotically free", meaning that under renormalization, the coupling constant of the strong interaction decreases as the interaction energy increases. (Similar discoveries had been made numerous times previously, but they had been largely ignored.) Therefore, at least in high-energy interactions, the coupling constant in QCD becomes sufficiently small to warrant a perturbative series expansion, making quantitative predictions for the strong interaction possible. These theoretical breakthroughs brought about a renaissance in QFT. The full theory, which includes the electroweak theory and chromodynamics, is referred to today as the Standard Model of elementary particles. The Standard Model successfully describes all fundamental interactions except gravity, and its many predictions have been met with remarkable experimental confirmation in subsequent decades. The Higgs boson, central to the mechanism of spontaneous symmetry breaking, was finally detected in 2012 at CERN, marking the complete verification of the existence of all constituents of the Standard Model. Other developments The 1970s saw the development of non-perturbative methods in non-Abelian gauge theories. The 't Hooft–Polyakov monopole was discovered theoretically by 't Hooft and Alexander Polyakov, flux tubes by Holger Bech Nielsen and Poul Olesen, and instantons by Polyakov and coauthors. These objects are inaccessible through perturbation theory. Supersymmetry also appeared in the same period. The first supersymmetric QFT in four dimensions was built by Yuri Golfand and Evgeny Likhtman in 1970, but their result failed to garner widespread interest due to the Iron Curtain. Supersymmetry only took off in the theoretical community after the work of Julius Wess and Bruno Zumino in 1973. Among the four fundamental interactions, gravity remains the only one that lacks a consistent QFT description. Various attempts at a theory of quantum gravity led to the development of string theory, itself a type of two-dimensional QFT with conformal symmetry. Joël Scherk and John Schwarz first proposed in 1974 that string theory could be the quantum theory of gravity. Condensed matter physics Although quantum field theory arose from the study of interactions between elementary particles, it has been successfully applied to other physical systems, particularly to many-body systems in condensed matter physics. Historically, the Higgs mechanism of spontaneous symmetry breaking was a result of Yoichiro Nambu's application of superconductor theory to elementary particles, while the concept of renormalization came out of the study of second-order phase transitions in matter. Soon after the introduction of photons, Einstein performed the quantization procedure on vibrations in a crystal, leading to the first quasiparticle—phonons. Lev Landau claimed that low-energy excitations in many condensed matter systems could be described in terms of interactions between a set of quasiparticles. The Feynman diagram method of QFT was naturally well suited to the analysis of various phenomena in condensed matter systems. Gauge theory is used to describe the quantization of magnetic flux in superconductors, the resistivity in the quantum Hall effect, as well as the relation between frequency and voltage in the AC Josephson effect. Principles For simplicity, natural units are used in the following sections, in which the reduced Planck constant and the speed of light are both set to one. Classical fields A classical field is a function of spatial and time coordinates. Examples include the gravitational field in Newtonian gravity and the electric field and magnetic field in classical electromagnetism. A classical field can be thought of as a numerical quantity assigned to every point in space that changes in time. Hence, it has infinitely many degrees of freedom. Many phenomena exhibiting quantum mechanical properties cannot be explained by classical fields alone. Phenomena such as the photoelectric effect are best explained by discrete particles (photons), rather than a spatially continuous field. The goal of quantum field theory is to describe various quantum mechanical phenomena using a modified concept of fields. Canonical quantisation and path integrals are two common formulations of QFT. To motivate the fundamentals of QFT, an overview of classical field theory is in order. The simplest classical field is a real scalar field — a real number at every point in space that changes in time. It is denoted as , where is the position vector, and is the time. Suppose the Lagrangian of the field, , is where is the Lagrangian density, is the time-derivative of the field, is the gradient operator, and is a real parameter (the "mass" of the field). Applying the Euler–Lagrange equation on the Lagrangian: we obtain the equations of motion for the field, which describe the way it varies in time and space: This is known as the Klein–Gordon equation. The Klein–Gordon equation is a wave equation, so its solutions can be expressed as a sum of normal modes (obtained via Fourier transform) as follows: where is a complex number (normalised by convention), denotes complex conjugation, and is the frequency of the normal mode: Thus each normal mode corresponding to a single can be seen as a classical harmonic oscillator with frequency . Canonical quantisation The quantisation procedure for the above classical field to a quantum operator field is analogous to the promotion of a classical harmonic oscillator to a quantum harmonic oscillator. The displacement of a classical harmonic oscillator is described by where is a complex number (normalised by convention), and is the oscillator's frequency. Note that is the displacement of a particle in simple harmonic motion from the equilibrium position, not to be confused with the spatial label of a quantum field. For a quantum harmonic oscillator, is promoted to a linear operator : Complex numbers and are replaced by the annihilation operator and the creation operator , respectively, where denotes Hermitian conjugation. The commutation relation between the two is The vacuum state , which is the lowest energy state, is defined by Any quantum state of a single harmonic oscillator can be obtained from by successively applying the creation operator : By the same token, the aforementioned real scalar field , which corresponds to in the single harmonic oscillator, is also promoted to a quantum field operator , while the annihilation operator , the creation operator and the angular frequency are now for a particular : Their commutation relations are: where is the Dirac delta function. The vacuum state is defined by Any quantum state of the field can be obtained from by successively applying creation operators , e.g. Although the quantum field appearing in the Lagrangian is spatially continuous, the quantum states of the field are discrete. While the state space of a single quantum harmonic oscillator contains all the discrete energy states of one oscillating particle, the state space of a quantum field contains the discrete energy levels of an arbitrary number of particles. The latter space is known as a Fock space, which can account for the fact that particle numbers are not fixed in relativistic quantum systems. The process of quantising an arbitrary number of particles instead of a single particle is often also called second quantisation. The foregoing procedure is a direct application of non-relativistic quantum mechanics and can be used to quantise (complex) scalar fields, Dirac fields, vector fields (e.g. the electromagnetic field), and even strings. However, creation and annihilation operators are only well defined in the simplest theories that contain no interactions (so-called free theory). In the case of the real scalar field, the existence of these operators was a consequence of the decomposition of solutions of the classical equations of motion into a sum of normal modes. To perform calculations on any realistic interacting theory, perturbation theory would be necessary. The Lagrangian of any quantum field in nature would contain interaction terms in addition to the free theory terms. For example, a quartic interaction term could be introduced to the Lagrangian of the real scalar field: where is a spacetime index, , etc. The summation over the index has been omitted following the Einstein notation. If the parameter is sufficiently small, then the interacting theory described by the above Lagrangian can be considered as a small perturbation from the free theory. Path integrals The path integral formulation of QFT is concerned with the direct computation of the scattering amplitude of a certain interaction process, rather than the establishment of operators and state spaces. To calculate the probability amplitude for a system to evolve from some initial state at time to some final state at , the total time is divided into small intervals. The overall amplitude is the product of the amplitude of evolution within each interval, integrated over all intermediate states. Let be the Hamiltonian (i.e. generator of time evolution), then Taking the limit , the above product of integrals becomes the Feynman path integral: where is the Lagrangian involving and its derivatives with respect to spatial and time coordinates, obtained from the Hamiltonian via Legendre transformation. The initial and final conditions of the path integral are respectively In other words, the overall amplitude is the sum over the amplitude of every possible path between the initial and final states, where the amplitude of a path is given by the exponential in the integrand. Two-point correlation function In calculations, one often encounters expression likein the free or interacting theory, respectively. Here, and are position four-vectors, is the time ordering operator that shuffles its operands so the time-components and increase from right to left, and is the ground state (vacuum state) of the interacting theory, different from the free ground state . This expression represents the probability amplitude for the field to propagate from to , and goes by multiple names, like the two-point propagator, two-point correlation function, two-point Green's function or two-point function for short. The free two-point function, also known as the Feynman propagator, can be found for the real scalar field by either canonical quantisation or path integrals to be In an interacting theory, where the Lagrangian or Hamiltonian contains terms or that describe interactions, the two-point function is more difficult to define. However, through both the canonical quantisation formulation and the path integral formulation, it is possible to express it through an infinite perturbation series of the free two-point function. In canonical quantisation, the two-point correlation function can be written as: where is an infinitesimal number and is the field operator under the free theory. Here, the exponential should be understood as its power series expansion. For example, in -theory, the interacting term of the Hamiltonian is , and the expansion of the two-point correlator in terms of becomesThis perturbation expansion expresses the interacting two-point function in terms of quantities that are evaluated in the free theory. In the path integral formulation, the two-point correlation function can be written where is the Lagrangian density. As in the previous paragraph, the exponential can be expanded as a series in , reducing the interacting two-point function to quantities in the free theory. Wick's theorem further reduce any -point correlation function in the free theory to a sum of products of two-point correlation functions. For example, Since interacting correlation functions can be expressed in terms of free correlation functions, only the latter need to be evaluated in order to calculate all physical quantities in the (perturbative) interacting theory. This makes the Feynman propagator one of the most important quantities in quantum field theory. Feynman diagram Correlation functions in the interacting theory can be written as a perturbation series. Each term in the series is a product of Feynman propagators in the free theory and can be represented visually by a Feynman diagram. For example, the term in the two-point correlation function in the theory is After applying Wick's theorem, one of the terms is This term can instead be obtained from the Feynman diagram . The diagram consists of external vertices connected with one edge and represented by dots (here labelled and ). internal vertices connected with four edges and represented by dots (here labelled ). edges connecting the vertices and represented by lines. Every vertex corresponds to a single field factor at the corresponding point in spacetime, while the edges correspond to the propagators between the spacetime points. The term in the perturbation series corresponding to the diagram is obtained by writing down the expression that follows from the Feynman rules: For every internal vertex , write down a factor . For every edge that connects two vertices and , write down a factor . Divide by the symmetry factor of the diagram. With the symmetry factor , following these rules yields exactly the expression above. By Fourier transforming the propagator, the Feynman rules can be reformulated from position space into momentum space. In order to compute the -point correlation function to the -th order, list all valid Feynman diagrams with external points and or fewer vertices, and then use Feynman rules to obtain the expression for each term. To be precise, is equal to the sum of (expressions corresponding to) all connected diagrams with external points. (Connected diagrams are those in which every vertex is connected to an external point through lines. Components that are totally disconnected from external lines are sometimes called "vacuum bubbles".) In the interaction theory discussed above, every vertex must have four legs. In realistic applications, the scattering amplitude of a certain interaction or the decay rate of a particle can be computed from the S-matrix, which itself can be found using the Feynman diagram method. Feynman diagrams devoid of "loops" are called tree-level diagrams, which describe the lowest-order interaction processes; those containing loops are referred to as -loop diagrams, which describe higher-order contributions, or radiative corrections, to the interaction. Lines whose end points are vertices can be thought of as the propagation of virtual particles. Renormalization Feynman rules can be used to directly evaluate tree-level diagrams. However, naïve computation of loop diagrams such as the one shown above will result in divergent momentum integrals, which seems to imply that almost all terms in the perturbative expansion are infinite. The renormalisation procedure is a systematic process for removing such infinities. Parameters appearing in the Lagrangian, such as the mass and the coupling constant , have no physical meaning — , , and the field strength are not experimentally measurable quantities and are referred to here as the bare mass, bare coupling constant, and bare field, respectively. The physical mass and coupling constant are measured in some interaction process and are generally different from the bare quantities. While computing physical quantities from this interaction process, one may limit the domain of divergent momentum integrals to be below some momentum cut-off , obtain expressions for the physical quantities, and then take the limit . This is an example of regularisation, a class of methods to treat divergences in QFT, with being the regulator. The approach illustrated above is called bare perturbation theory, as calculations involve only the bare quantities such as mass and coupling constant. A different approach, called renormalised perturbation theory, is to use physically meaningful quantities from the very beginning. In the case of theory, the field strength is first redefined: where is the bare field, is the renormalised field, and is a constant to be determined. The Lagrangian density becomes: where and are the experimentally measurable, renormalised, mass and coupling constant, respectively, and are constants to be determined. The first three terms are the Lagrangian density written in terms of the renormalised quantities, while the latter three terms are referred to as "counterterms". As the Lagrangian now contains more terms, so the Feynman diagrams should include additional elements, each with their own Feynman rules. The procedure is outlined as follows. First select a regularisation scheme (such as the cut-off regularisation introduced above or dimensional regularization); call the regulator . Compute Feynman diagrams, in which divergent terms will depend on . Then, define , , and such that Feynman diagrams for the counterterms will exactly cancel the divergent terms in the normal Feynman diagrams when the limit is taken. In this way, meaningful finite quantities are obtained. It is only possible to eliminate all infinities to obtain a finite result in renormalisable theories, whereas in non-renormalisable theories infinities cannot be removed by the redefinition of a small number of parameters. The Standard Model of elementary particles is a renormalisable QFT, while quantum gravity is non-renormalisable. Renormalisation group The renormalisation group, developed by Kenneth Wilson, is a mathematical apparatus used to study the changes in physical parameters (coefficients in the Lagrangian) as the system is viewed at different scales. The way in which each parameter changes with scale is described by its β function. Correlation functions, which underlie quantitative physical predictions, change with scale according to the Callan–Symanzik equation. As an example, the coupling constant in QED, namely the elementary charge , has the following β function: where is the energy scale under which the measurement of is performed. This differential equation implies that the observed elementary charge increases as the scale increases. The renormalized coupling constant, which changes with the energy scale, is also called the running coupling constant. The coupling constant in quantum chromodynamics, a non-Abelian gauge theory based on the symmetry group , has the following β function: where is the number of quark flavours. In the case where (the Standard Model has ), the coupling constant decreases as the energy scale increases. Hence, while the strong interaction is strong at low energies, it becomes very weak in high-energy interactions, a phenomenon known as asymptotic freedom. Conformal field theories (CFTs) are special QFTs that admit conformal symmetry. They are insensitive to changes in the scale, as all their coupling constants have vanishing β function. (The converse is not true, however — the vanishing of all β functions does not imply conformal symmetry of the theory.) Examples include string theory and supersymmetric Yang–Mills theory. According to Wilson's picture, every QFT is fundamentally accompanied by its energy cut-off , i.e. that the theory is no longer valid at energies higher than , and all degrees of freedom above the scale are to be omitted. For example, the cut-off could be the inverse of the atomic spacing in a condensed matter system, and in elementary particle physics it could be associated with the fundamental "graininess" of spacetime caused by quantum fluctuations in gravity. The cut-off scale of theories of particle interactions lies far beyond current experiments. Even if the theory were very complicated at that scale, as long as its couplings are sufficiently weak, it must be described at low energies by a renormalisable effective field theory. The difference between renormalisable and non-renormalisable theories is that the former are insensitive to details at high energies, whereas the latter do depend on them. According to this view, non-renormalisable theories are to be seen as low-energy effective theories of a more fundamental theory. The failure to remove the cut-off from calculations in such a theory merely indicates that new physical phenomena appear at scales above , where a new theory is necessary. Other theories The quantisation and renormalisation procedures outlined in the preceding sections are performed for the free theory and theory of the real scalar field. A similar process can be done for other types of fields, including the complex scalar field, the vector field, and the Dirac field, as well as other types of interaction terms, including the electromagnetic interaction and the Yukawa interaction. As an example, quantum electrodynamics contains a Dirac field representing the electron field and a vector field representing the electromagnetic field (photon field). (Despite its name, the quantum electromagnetic "field" actually corresponds to the classical electromagnetic four-potential, rather than the classical electric and magnetic fields.) The full QED Lagrangian density is: where are Dirac matrices, , and is the electromagnetic field strength. The parameters in this theory are the (bare) electron mass and the (bare) elementary charge . The first and second terms in the Lagrangian density correspond to the free Dirac field and free vector fields, respectively. The last term describes the interaction between the electron and photon fields, which is treated as a perturbation from the free theories. Shown above is an example of a tree-level Feynman diagram in QED. It describes an electron and a positron annihilating, creating an off-shell photon, and then decaying into a new pair of electron and positron. Time runs from left to right. Arrows pointing forward in time represent the propagation of positrons, while those pointing backward in time represent the propagation of electrons. A wavy line represents the propagation of a photon. Each vertex in QED Feynman diagrams must have an incoming and an outgoing fermion (positron/electron) leg as well as a photon leg. Gauge symmetry If the following transformation to the fields is performed at every spacetime point (a local transformation), then the QED Lagrangian remains unchanged, or invariant: where is any function of spacetime coordinates. If a theory's Lagrangian (or more precisely the action) is invariant under a certain local transformation, then the transformation is referred to as a gauge symmetry of the theory. Gauge symmetries form a group at every spacetime point. In the case of QED, the successive application of two different local symmetry transformations and is yet another symmetry transformation . For any , is an element of the group, thus QED is said to have gauge symmetry. The photon field may be referred to as the gauge boson. is an Abelian group, meaning that the result is the same regardless of the order in which its elements are applied. QFTs can also be built on non-Abelian groups, giving rise to non-Abelian gauge theories (also known as Yang–Mills theories). Quantum chromodynamics, which describes the strong interaction, is a non-Abelian gauge theory with an gauge symmetry. It contains three Dirac fields representing quark fields as well as eight vector fields representing gluon fields, which are the gauge bosons. The QCD Lagrangian density is: where is the gauge covariant derivative: where is the coupling constant, are the eight generators of in the fundamental representation ( matrices), and are the structure constants of . Repeated indices are implicitly summed over following Einstein notation. This Lagrangian is invariant under the transformation: where is an element of at every spacetime point : The preceding discussion of symmetries is on the level of the Lagrangian. In other words, these are "classical" symmetries. After quantisation, some theories will no longer exhibit their classical symmetries, a phenomenon called anomaly. For instance, in the path integral formulation, despite the invariance of the Lagrangian density under a certain local transformation of the fields, the measure of the path integral may change. For a theory describing nature to be consistent, it must not contain any anomaly in its gauge symmetry. The Standard Model of elementary particles is a gauge theory based on the group , in which all anomalies exactly cancel. The theoretical foundation of general relativity, the equivalence principle, can also be understood as a form of gauge symmetry, making general relativity a gauge theory based on the Lorentz group. Noether's theorem states that every continuous symmetry, i.e. the parameter in the symmetry transformation being continuous rather than discrete, leads to a corresponding conservation law. For example, the symmetry of QED implies charge conservation. Gauge transformations do not relate distinct quantum states. Rather, it relates two equivalent mathematical descriptions of the same quantum state. As an example, the photon field , being a four-vector, has four apparent degrees of freedom, but the actual state of a photon is described by its two degrees of freedom corresponding to the polarisation. The remaining two degrees of freedom are said to be "redundant" — apparently different ways of writing can be related to each other by a gauge transformation and in fact describe the same state of the photon field. In this sense, gauge invariance is not a "real" symmetry, but a reflection of the "redundancy" of the chosen mathematical description. To account for the gauge redundancy in the path integral formulation, one must perform the so-called Faddeev–Popov gauge fixing procedure. In non-Abelian gauge theories, such a procedure introduces new fields called "ghosts". Particles corresponding to the ghost fields are called ghost particles, which cannot be detected externally. A more rigorous generalisation of the Faddeev–Popov procedure is given by BRST quantization. Spontaneous symmetry breaking Spontaneous symmetry breaking is a mechanism whereby the symmetry of the Lagrangian is violated by the system described by it. To illustrate the mechanism, consider a linear sigma model containing real scalar fields, described by the Lagrangian density: where and are real parameters. The theory admits an global symmetry: The lowest energy state (ground state or vacuum state) of the classical theory is any uniform field satisfying Without loss of generality, let the ground state be in the -th direction: The original fields can be rewritten as: and the original Lagrangian density as: where . The original global symmetry is no longer manifest, leaving only the subgroup . The larger symmetry before spontaneous symmetry breaking is said to be "hidden" or spontaneously broken. Goldstone's theorem states that under spontaneous symmetry breaking, every broken continuous global symmetry leads to a massless field called the Goldstone boson. In the above example, has continuous symmetries (the dimension of its Lie algebra), while has . The number of broken symmetries is their difference, , which corresponds to the massless fields . On the other hand, when a gauge (as opposed to global) symmetry is spontaneously broken, the resulting Goldstone boson is "eaten" by the corresponding gauge boson by becoming an additional degree of freedom for the gauge boson. The Goldstone boson equivalence theorem states that at high energy, the amplitude for emission or absorption of a longitudinally polarised massive gauge boson becomes equal to the amplitude for emission or absorption of the Goldstone boson that was eaten by the gauge boson. In the QFT of ferromagnetism, spontaneous symmetry breaking can explain the alignment of magnetic dipoles at low temperatures. In the Standard Model of elementary particles, the W and Z bosons, which would otherwise be massless as a result of gauge symmetry, acquire mass through spontaneous symmetry breaking of the Higgs boson, a process called the Higgs mechanism. Supersymmetry All experimentally known symmetries in nature relate bosons to bosons and fermions to fermions. Theorists have hypothesised the existence of a type of symmetry, called supersymmetry, that relates bosons and fermions. The Standard Model obeys Poincaré symmetry, whose generators are the spacetime translations and the Lorentz transformations . In addition to these generators, supersymmetry in (3+1)-dimensions includes additional generators , called supercharges, which themselves transform as Weyl fermions. The symmetry group generated by all these generators is known as the super-Poincaré group. In general there can be more than one set of supersymmetry generators, , which generate the corresponding supersymmetry, supersymmetry, and so on. Supersymmetry can also be constructed in other dimensions, most notably in (1+1) dimensions for its application in superstring theory. The Lagrangian of a supersymmetric theory must be invariant under the action of the super-Poincaré group. Examples of such theories include: Minimal Supersymmetric Standard Model (MSSM),
it fails to take into account the fact that both photons and electrons can be polarized, which is to say that their orientations in space and time have to be taken into account. Therefore, P(A to B) consists of 16 complex numbers, or probability amplitude arrows. There are also some minor changes to do with the quantity j, which may have to be rotated by a multiple of 90° for some polarizations, which is only of interest for the detailed bookkeeping. Associated with the fact that the electron can be polarized is another small necessary detail, which is connected with the fact that an electron is a fermion and obeys Fermi–Dirac statistics. The basic rule is that if we have the probability amplitude for a given complex process involving more than one electron, then when we include (as we always must) the complementary Feynman diagram in which we exchange two electron events, the resulting amplitude is the reverse – the negative – of the first. The simplest case would be two electrons starting at A and B ending at C and D. The amplitude would be calculated as the "difference", , where we would expect, from our everyday idea of probabilities, that it would be a sum. Propagators Finally, one has to compute P(A to B) and E(C to D) corresponding to the probability amplitudes for the photon and the electron respectively. These are essentially the solutions of the Dirac equation, which describe the behavior of the electron's probability amplitude and the Maxwell's equations, which describes the behavior of the photon's probability amplitude. These are called Feynman propagators. The translation to a notation commonly used in the standard literature is as follows: where a shorthand symbol such as stands for the four real numbers that give the time and position in three dimensions of the point labeled A. Mass renormalization A problem arose historically which held up progress for twenty years: although we start with the assumption of three basic "simple" actions, the rules of the game say that if we want to calculate the probability amplitude for an electron to get from A to B, we must take into account all the possible ways: all possible Feynman diagrams with those endpoints. Thus there will be a way in which the electron travels to C, emits a photon there and then absorbs it again at D before moving on to B. Or it could do this kind of thing twice, or more. In short, we have a fractal-like situation in which if we look closely at a line, it breaks up into a collection of "simple" lines, each of which, if looked at closely, are in turn composed of "simple" lines, and so on ad infinitum. This is a challenging situation to handle. If adding that detail only altered things slightly, then it would not have been too bad, but disaster struck when it was found that the simple correction mentioned above led to infinite probability amplitudes. In time this problem was "fixed" by the technique of renormalization. However, Feynman himself remained unhappy about it, calling it a "dippy process". Conclusions Within the above framework physicists were then able to calculate to a high degree of accuracy some of the properties of electrons, such as the anomalous magnetic dipole moment. However, as Feynman points out, it fails to explain why particles such as the electron have the masses they do. "There is no theory that adequately explains these numbers. We use the numbers in all our theories, but we don't understand them – what they are, or where they come from. I believe that from a fundamental point of view, this is a very interesting and serious problem." Mathematical formulation Mathematically, QED is an abelian gauge theory with the symmetry group U(1). The gauge field, which mediates the interaction between the charged spin-1/2 fields, is the electromagnetic field. The QED Lagrangian for a spin-1/2 field interacting with the electromagnetic field is given in natural units by the real part of where are Dirac matrices; a bispinor field of spin-1/2 particles (e.g. electron–positron field); , called "psi-bar", is sometimes referred to as the Dirac adjoint; is the gauge covariant derivative; e is the coupling constant, equal to the electric charge of the bispinor field; m is the mass of the electron or positron; is the covariant four-potential of the electromagnetic field generated by the electron itself; is the external field imposed by external source; is the electromagnetic field tensor. Equations of motion Substituting the definition of D into the Lagrangian gives From this Lagrangian, the equations of motion for the ψ and A fields can be obtained. Using the field-theoretic Euler–Lagrange equation for ψ, The derivatives of the Lagrangian concerning ψ are Inserting these into () results in with Hermitian conjugate Bringing the middle term to the right-hand side yields The left-hand side is like the original Dirac equation, and the right-hand side is the interaction with the electromagnetic field. Using the Euler–Lagrange equation for the A field, the derivatives this time are Substituting back into () leads to Now, if we impose the Lorenz gauge condition the equations reduce to which is a wave equation for the four-potential, the QED version of the classical Maxwell equations in the Lorenz gauge. (The square represents the D'Alembert operator, .) Interaction picture This theory can be straightforwardly quantized by treating bosonic and fermionic sectors as free. This permits us to build a set of asymptotic states that can be used to start computation of the probability amplitudes for different processes. In order to do so, we have to compute an evolution operator, which for a given initial state will give a final state in such a way to have This technique is also known as the S-matrix. The evolution operator is obtained in the interaction picture, where time evolution is given by the interaction Hamiltonian, which is the integral over space of the second term in the Lagrangian density given above: and so, one has where T is the time-ordering operator. This evolution operator only has meaning as a series, and what we get here is a perturbation series with the fine-structure constant as the development parameter. This series is called the Dyson series. Feynman diagrams Despite the conceptual clarity of this Feynman approach to QED, almost no early textbooks follow him in their presentation. When performing calculations, it is much easier to work with the Fourier transforms of the propagators. Experimental tests of quantum electrodynamics are typically scattering experiments. In scattering theory, particles' momenta rather than their positions are considered, and it is convenient to think of particles as being created or annihilated when they interact. Feynman diagrams then look the same, but the lines have different interpretations. The electron line represents an electron with a given energy and momentum, with a similar interpretation of the photon line. A vertex diagram represents the annihilation of one electron and the creation of another together with the absorption or creation of a photon, each having specified energies and momenta. Using Wick's theorem on the terms of the Dyson series, all the terms of the S-matrix for quantum electrodynamics can be computed through the technique of Feynman diagrams. In this case, rules for drawing are the following To these rules we must add a further one for closed loops that implies an integration on momenta , since these internal ("virtual") particles are not constrained to any specific energy–momentum, even that usually required by special relativity (see Propagator for details). From them, computations of probability amplitudes are straightforwardly given. An example is Compton scattering, with an electron and a photon undergoing elastic scattering. Feynman diagrams are in this case and so we are able to get the corresponding amplitude at the first order of a perturbation series for the S-matrix: from which we can compute the cross section for this scattering. Nonperturbative phenomena The predictive success of quantum electrodynamics largely rests on the use of perturbation theory, expressed in Feynman diagrams. However, quantum electrodynamics also leads to predictions beyond perturbation theory. In the presence of very strong electric fields, it predicts that electrons and positrons will be spontaneously produced, so causing the decay of the field. This process, called the Schwinger effect, cannot be understood in terms of any finite number of Feynman diagrams and hence is described as nonperturbative. Mathematically, it can be derived by a semiclassical approximation to the path integral of quantum electrodynamics. Renormalizability Higher-order terms can be straightforwardly computed for the evolution operator, but these terms display diagrams containing the following simpler ones that, being closed loops, imply the presence of diverging integrals having no mathematical meaning. To overcome this difficulty, a technique called renormalization has been devised, producing finite results in very close agreement with experiments. A criterion for the theory being meaningful after renormalization is that the number of diverging diagrams is finite. In this case, the theory is said to be "renormalizable". The reason for this is that to get observables renormalized, one needs a finite number of constants to maintain the predictive value of the theory untouched. This is exactly the case of quantum electrodynamics displaying just three diverging diagrams. This procedure gives observables in very close agreement with experiment as seen e.g. for electron gyromagnetic ratio. Renormalizability has become an essential criterion for a quantum field theory to be considered as a viable one. All the theories describing fundamental interactions, except gravitation, whose quantum counterpart is only conjectural and presently under very active research, are renormalizable theories. Nonconvergence of series An argument by Freeman Dyson shows that the radius of convergence of the perturbation series in QED is zero. The basic argument goes as follows: if the coupling constant were negative, this would be equivalent to the Coulomb force constant being negative. This would "reverse" the electromagnetic interaction so that like charges would attract and unlike charges would repel. This would render the vacuum unstable against decay into a cluster of electrons on one side of the universe and a cluster of positrons on the other side of the universe. Because the theory is "sick" for any negative value of the coupling constant, the series does not converge but are at best an asymptotic series. From a modern perspective, we say that QED is not well defined as a quantum field theory to arbitrarily high energy. The coupling constant runs to infinity at finite energy, signalling a Landau pole. The problem is essentially that QED appears to suffer from quantum triviality issues. This is one of the motivations for embedding QED within a Grand Unified Theory. See also Abraham–Lorentz force Anomalous magnetic moment Bhabha scattering Cavity quantum electrodynamics Circuit quantum electrodynamics Compton scattering Euler–Heisenberg	any such complex interaction. It turns out that the basic idea of QED can be communicated while assuming that the square of the total of the probability amplitudes mentioned above (P(A to B), E(C to D) and j) acts just like our everyday probability (a simplification made in Feynman's book). Later on, this will be corrected to include specifically quantum-style mathematics, following Feynman. The basic rules of probability amplitudes that will be used are: Basic constructions Suppose, we start with one electron at a certain place and time (this place and time being given the arbitrary label A) and a photon at another place and time (given the label B). A typical question from a physical standpoint is: "What is the probability of finding an electron at C (another place and a later time) and a photon at D (yet another place and time)?". The simplest process to achieve this end is for the electron to move from A to C (an elementary action) and for the photon to move from B to D (another elementary action). From a knowledge of the probability amplitudes of each of these sub-processes – E(A to C) and P(B to D) – we would expect to calculate the probability amplitude of both happening together by multiplying them, using rule b) above. This gives a simple estimated overall probability amplitude, which is squared to give an estimated probability. But there are other ways in which the end result could come about. The electron might move to a place and time E, where it absorbs the photon; then move on before emitting another photon at F; then move on to C, where it is detected, while the new photon moves on to D. The probability of this complex process can again be calculated by knowing the probability amplitudes of each of the individual actions: three electron actions, two photon actions and two vertexes – one emission and one absorption. We would expect to find the total probability amplitude by multiplying the probability amplitudes of each of the actions, for any chosen positions of E and F. We then, using rule a) above, have to add up all these probability amplitudes for all the alternatives for E and F. (This is not elementary in practice and involves integration.) But there is another possibility, which is that the electron first moves to G, where it emits a photon, which goes on to D, while the electron moves on to H, where it absorbs the first photon, before moving on to C. Again, we can calculate the probability amplitude of these possibilities (for all points G and H). We then have a better estimation for the total probability amplitude by adding the probability amplitudes of these two possibilities to our original simple estimate. Incidentally, the name given to this process of a photon interacting with an electron in this way is Compton scattering. There is an infinite number of other intermediate "virtual" processes in which more and more photons are absorbed and/or emitted. For each of these processes, a Feynman diagram could be drawn describing it. This implies a complex computation for the resulting probability amplitudes, but provided it is the case that the more complicated the diagram, the less it contributes to the result, it is only a matter of time and effort to find as accurate an answer as one wants to the original question. This is the basic approach of QED. To calculate the probability of any interactive process between electrons and photons, it is a matter of first noting, with Feynman diagrams, all the possible ways in which the process can be constructed from the three basic elements. Each diagram involves some calculation involving definite rules to find the associated probability amplitude. That basic scaffolding remains when one moves to a quantum description, but some conceptual changes are needed. One is that whereas we might expect in our everyday life that there would be some constraints on the points to which a particle can move, that is not true in full quantum electrodynamics. There is a nonzero probability amplitude of an electron at A, or a photon at B, moving as a basic action to any other place and time in the universe. That includes places that could only be reached at speeds greater than that of light and also earlier times. (An electron moving backwards in time can be viewed as a positron moving forward in time.) Probability amplitudes Quantum mechanics introduces an important change in the way probabilities are computed. Probabilities are still represented by the usual real numbers we use for probabilities in our everyday world, but probabilities are computed as the square modulus of probability amplitudes, which are complex numbers. Feynman avoids exposing the reader to the mathematics of complex numbers by using a simple but accurate representation of them as arrows on a piece of paper or screen. (These must not be confused with the arrows of Feynman diagrams, which are simplified representations in two dimensions of a relationship between points in three dimensions of space and one of time.) The amplitude arrows are fundamental to the description of the world given by quantum theory. They are related to our everyday ideas of probability by the simple rule that the probability of an event is the square of the length of the corresponding amplitude arrow. So, for a given process, if two probability amplitudes, v and w, are involved, the probability of the process will be given either by or The rules as regards adding or multiplying, however, are the same as above. But where you would expect to add or multiply probabilities, instead you add or multiply probability amplitudes that now are complex numbers. Addition and multiplication are common operations in the theory of complex numbers and are given in the figures. The sum is found as follows. Let the start of the second arrow be at the end of the first. The sum is then a third arrow that goes directly from the beginning of the first to the end of the second. The product of two arrows is an arrow whose length is the product of the two lengths. The direction of the product is found by adding the angles that each of the two have been turned through relative to a reference direction: that gives the angle that the product is turned relative to the reference direction. That change, from probabilities to probability amplitudes, complicates the mathematics without changing the basic approach. But that change is still not quite enough because it fails to take into account the fact that both photons and electrons can be polarized, which is to say that their orientations in space and time have to be taken into account. Therefore, P(A to B) consists of 16 complex numbers, or probability amplitude arrows. There are also some minor changes to do with the quantity j, which may have to be rotated by a multiple of 90° for some polarizations, which is only of interest for the detailed bookkeeping. Associated with the fact that the electron can be polarized is another small necessary detail, which is connected with the fact that an electron is a fermion and obeys Fermi–Dirac statistics. The basic rule is that if we have the probability amplitude