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65664 | Hall conductivity from Kubo: Bulk or edge? | Using the Kubo formula, Thouless, Kohmoto, Nightingale, and den Nijs (TKNN, PRL 49 405-408 (1982)), proved that upon summing all the contributions of the filled states of an insulator, the Hall conductivity must be an integer (the Chern number) times e^2/h. Their theorem uses periodic boundary conditions along x and y ... | How can we relate the Chern number obtained from the TKNN theorem, which describes the Hall conductivity in the bulk of an insulator, to the number of edge channels observed in the Quantum Hall Effect under open boundary conditions? | 20,315 | cqadupstack-physics |
15858 | Relation between unitarity and conservation of probability | In a seminar, I heard that the unitary aspect of representations was important physically, because in quantum mechanics unitarity is closely tied to the conservation of probability. Could someone explain why this is so? After a bit of thought, one vague connection I can think of is that a matrix generated by a Hermitia... | Can you explain why the representation of quantum mechanical operators as unitary matrices, specifically in the form \( U = e^{iH} \) where \( H \) is a Hermitian operator, is essential for the conservation of probability in quantum mechanics? Additionally, could you provide a quantitative example to illustrate how uni... | 2,539 | cqadupstack-physics |
23408 | shouldn't we add the oscillating terms into Bohr-Sommerfeld quantization formula | shouldn't be the quantization formula (in one dimension) equal to $ N_{smooth}(E)+N_{osc}(E) = \oint_{C}p.dq $ ?? where the Oscillating term is just the correction from Gutzwiller trace formula or a sum over Orbits why is just the oscillating term ignored .. | In one-dimensional quantum systems, the total number of states can be expressed as \( N(E) = N_{smooth}(E) + N_{osc}(E) \). If \( N_{smooth}(E) \) represents the smooth part of the density of states and \( N_{osc}(E) \) is the oscillating correction derived from the Gutzwiller trace formula, how can we quantitatively d... | 27,579 | cqadupstack-physics |
33181 | Relation among anomaly, unitarity bound and renormalizability | There is something I'm not sure about that has come up in a comment to other question: Why do we not have spin greater than 2? > It's a good question--- the violation of renormalizability is linked > directly to violation of unitarity, which was exploited by Weinberg > (surprise, surprise) to give an upper bound of som... | What is the maximum mass of the Higgs boson as derived from unitarity constraints in the context of electroweak interactions, and how is this related to the concept of renormalizability in quantum field theory? | 16,066 | cqadupstack-physics |
134818 | The triangle inequality in CHSH derivation, where is the triangle? | http://en.wikipedia.org/wiki/CHSH_inequality#Bell.27s_1971_derivation  ... |X + Y| <= |X| + |Y| ??? CHSH inequality is combined from four relative angles between four polarization axis which do not have any defined length. So where is the triangle, what... | In the context of the CHSH inequality and Bell's theorem, what is the expected value \( E(0, 22.5^\circ) \) when measuring the correlation of polarization between two entangled particles at angles 0 degrees and 22.5 degrees? What is the significance of this expectation value in relation to the CHSH inequality? | 18,500 | cqadupstack-physics |
91753 | Is speed of sound really constant? | Does not speed of sound actually depend on the frequency and/or amplitude of the waves? If so, why it is constant? | How does the speed of sound in a medium depend on physical properties such as temperature and density, and does it vary with frequency or amplitude of the sound waves? Provide a detailed explanation. | 10,439 | cqadupstack-physics |
56900 | What is the initial velocity of a projectile so that it passes through a target point in its trajectory? | Let's say I have a projectile being thrown by a player in my 2-D game. I want to work backwards and find the initial velocity to apply to the projectile such that it passes through a target point in space given that the launch point might not be at $y=0$. Some applications of this would be a basketball shot simulator o... | Given a projectile that is launched from an initial height \(y_0\) at an angle \(\theta_o\) with respect to the horizontal, and is required to hit a target point \((x_f, y_f)\), derive the expression to calculate the initial launch velocity \(v_o\) necessary to ensure the projectile reaches the target, assuming constan... | 5,559 | cqadupstack-physics |
103904 | Size of a photon | When detecting radio waves in space, we use very large telescopes or arrays of telescopes. But according to QM, aren't photons point particles when measured? Does a photon with a large wavelength have a wider probability distribution with regard to where it can be expected to be detected? Is that why photons with long ... | How does the wavelength of a photon affect its probability distribution in space, and how does this relationship justify the need for larger telescopes to detect longer wavelength photons compared to shorter ones? Provide a quantitative analysis of the relationship between wavelength, probability distribution width, an... | 37,104 | cqadupstack-physics |
60915 | Comparing interaction potential in standard $ϕ^4 $theory | I am posting this question again because, Willie Wong asked me to do it. So it is a continuing post of the Interaction potential in standard ϕ4 theory. I have been studying about solitions so I had to deal with scalar field theory. The problem I faced in Lagrangian of Scalar field is interacting potential. According to... | Can you show the steps to derive the potential in equation (4), $$V(\phi)= \frac{1}{8} \phi^2 (\phi -2)^2$$ from the potential in equation (2), $$V(\phi)= \frac{m^2}{2}\phi^2 +\frac{\lambda}{24}\phi^4$$, and explain why the coupling constant $\lambda$ does not appear in equation (4)? | 16,821 | cqadupstack-physics |
100740 | What is the difference between the process in which energy converts to matter and that in which it converts to antimatter? | What is the difference between the process in which energy converts to matter and the process in which it converts to antimatter? In colliders, for instance, is the product (either being the matter or the antimatter counterpart of a specific particle) solely a result of angular momentum conservation (given that this ce... | In high-energy particle colliders, how does the conservation of angular momentum influence the production ratio of matter versus antimatter in particle-antiparticle interactions, assuming no CP violation? Quantify the ratio of produced particles under these conditions using a specific example. | 1,344 | cqadupstack-physics |
109771 | Force constant of metals - Kohn anomaly | In _Introduction to Solid State Physics_ (Kittel), it assumed the force constant between plane $s$ and $s+p$ $C_p=A\frac{\sin pk_0a}{pa}$ in metals to represent a Kohn anomaly. It says such a form is expected in metals. But I have no idea why. Thinking of typical potential energy-distance curve with one inflection poin... | Why is the force constant between adjacent planes in metals expressed as \( C_p = A \frac{\sin pk_0a}{pa} \), and what physical principles underlying the Kohn anomaly restrict this behavior to metals, as opposed to other materials? | 35,019 | cqadupstack-physics |
61462 | What happens to pipe outlet temperature here? | I have a fluid flowing through a pipe in the ocean and there is heat transfer from the ocean to the fluid in the pipe. I prepared a simulation and the results show that if I increase the mass flow rate of the fluid through the pipe then the heat transfer rate to the fluid increases and the outlet temperature increases.... | If the mass flow rate of the fluid through a pipe in the ocean is increased, how does this affect the outlet temperature of the fluid, assuming the heat transfer rate to the fluid also increases? Provide a qualitative explanation supported by principles of thermodynamics and fluid dynamics. | 24,210 | cqadupstack-physics |
91266 | Using water to amplify sound | It seems that water generally dampens sound waves. Is there any way one could attach a speaker to a body of water in such a way that the water would actually amplify some frequencies (for nearby listeners in the air, not under water)? Imagine a speaker on a boat on a small creek. Listeners are on the bank. | What frequency range of sound waves would a submerged speaker in a small creek need to generate in order to maximize amplification for listeners on the bank, considering the principles of acoustic impedance and the properties of water? | 10,797 | cqadupstack-physics |
79648 | Conservation of angular momentum | We were learning about angular momentum in class today, and although it sort of makes sense, it's much harder for me to think about than linear momentum. So from what I can tell: * Angular momentum and linear momentum are conserved separately: i.e. they can't be converted to one another to 'compensate' for an apparen... | In the scenario where a disc with a rocket attached applies a tangential thrust, causing it to rotate and eject gas molecules, how can we determine the direction and magnitude of the torque that balances the torque applied by the rocket's thrust? Additionally, how does this affect the angular momentum of the system? | 1,373 | cqadupstack-physics |
33956 | At what rate does radiation exposure occur at high-c speeds? | If a future astronaut travelled to Alpha Centauri at a significant percentage of light-speed? Apart from increased blue shifted radiation from their direction of travel - how would they experience other cosmic radiation? If the trip took a subject several times faster than an observer on earth. Would the astronaut get ... | If an astronaut travels to Alpha Centauri at 75% of the speed of light, how would their exposure to cosmic radiation compare to that of an observer on Earth, and what factors would affect this difference in exposure? | 24,226 | cqadupstack-physics |
56517 | State space of QFT, CCR and quantization, and the spectrum of a field operator? | In the canonical quantization of fields, CCR is postulated as (for scalar boson field ): $$[\phi(x),\pi(y)]=i\delta(x-y)\qquad\qquad(1)$$ in analogy with the ordinary QM commutation relation: $$[x_i,p_j]=i\delta_{ij}\qquad\qquad(2)$$ However, using (2) we could demo the continuum feature of the spectrum of $x_i$, while... | What is the cardinality of the set of functions \( \{ g(x) \} \) that can be used in the configuration space of Quantum Field Theory (QFT), and is this state space a separable Hilbert space? | 30,928 | cqadupstack-physics |
71949 | Quantum XOR: How do you generalize it? | Consider the classical XOR Gate: Given a 2 bit system: $G = [u_1, u_2]$ $$XOR(G) = (u_1 + u_2) \ mod \ 2$$ Is the following a good generalizaiton of a Quantum XOR Gate: Given a 2-qubit system: $Q = a_1|00] + a_2|01] + a_3|10] + a_4|11]$ We now write: $$XOR(Q) = a_1|0] + a_2|1] + a_3|1] + a_4|0] = (a_1 + a_4)|0] + (a_2 ... | If we consider a 2-qubit quantum state \( Q = a_1|00\rangle + a_2|01\rangle + a_3|10\rangle + a_4|11\rangle \) and apply the generalized quantum XOR operation defined by \( XOR(Q) = (a_1 + a_4)|0\rangle + (a_2 + a_3)|1\rangle \), what is the output of the operation for the specific case when \( a_1 = 1, a_2 = 0, a_3 = ... | 13,371 | cqadupstack-physics |
50026 | Pair production in complete vacuum | I want to prove that pair production (electron-positron) cannot happen in complete vacuum. This is why I obeyed conservation of energy and got equation: $$h \nu = m_e c^2 \Bigl[ \gamma(v_1) + \gamma(v_{2})\Bigl]$$ I did the same for conservation of momentum and got an equation which is different: $$h \nu = m_e c \Bigl[... | In pair production, conservation of energy requires the photon energy to equal the rest mass energy of the produced particles, while conservation of momentum must be conserved in the process. Given that $$h \nu = m_e c^2 \Bigl[ \gamma(v_1) + \gamma(v_{2})\Bigl]$$ represents energy conservation and $$h \nu = m_e c \Bigl... | 33,498 | cqadupstack-physics |
95595 | Diffusion coefficient of a crystal | I've been trying to work this out so I can give a hand waving argument for one of the effects I'm observing on the fly and I find myself going down a rabbit hole that seems way too complicated for what I need. Thanks for any help. I have a TiO2 rutile (so the unit cell is a body centered tetragonal cell) material. The ... | Given a TiO2 rutile material with unit cell parameters a=b=4.5 Å and c=3 Å, and knowing the diffusion coefficients for oxygen along the a direction (Da) and the c direction (Dc), how can I calculate the diffusion coefficient in the (111) direction? Additionally, how can I determine the percentage of oxygen that will mi... | 15,899 | cqadupstack-physics |
26148 | How are interplanetary trajectories found? | How are interplanetary trajectories that involve gravity assist maneuvers found? Examples: * the MESSENGER spacecraft made flybys of Earth, Venus, and Mercury before getting into orbit * the Juno spacecraft will flyby Earth (returning after launch) before continuing to Jupiter * many more... Are these found using... | Given that gravity assist maneuvers can significantly alter the trajectory of a spacecraft, calculate the optimal launch window for a trip to Neptune using gravity assists from Earth and Venus. Assume you want to minimize travel time and the spacecraft's initial velocity is 10 km/s. What alignment of the planets would ... | 22,894 | cqadupstack-physics |
64592 | Flavour diagonal SUSY breaking | Because there is a single Yukawa matrix for the SM leptons, the lepton mass and flavour states can be aligned, by diagonalization, even if the Yukawa matrix had off-diagonal elements. SUSY breaking, however, introduces soft-breaking masses for the sleptons, which could be off-diagonal and introduce flavour-changing cur... | What is the mathematical relationship between soft-breaking masses for sleptons and the Yukawa couplings in the context of the minimal supersymmetric standard model (mSUGRA), and how does this relate to the phenomenon of flavor-changing currents such as \(e \to \mu \gamma\)? | 23,550 | cqadupstack-physics |
87325 | Some question on the definition of flux in the projective construction? | Here I have some confusing points about the definition of **flux** in the projective construction. For example, consider the same mean-field Hamiltonian in my previous question, and assume the $2\times 2$ complex matrix $\chi_{ij}$ has the form $\begin{pmatrix} t_{ij}& \Delta_{ij}\\\ \Delta_{ij}^* & -t_{ij}^* \end{pmat... | In a 2D lattice with a loop consisting of \( n \) links, if the complex matrix for each link is given by \(\chi_i=\begin{pmatrix} t_i& \Delta_i\\ \Delta_i^* & -t_i^* \end{pmatrix}\), where \( t_i \) and \( \Delta_i \) are complex numbers, what is the flux phase through an even loop compared to an odd loop, and can you ... | 3,719 | cqadupstack-physics |
83086 | Will a moving neutron produce a magnetic field around it? | Will a moving neutron produce a magnetic field around it? I know that neutrons have no charge, so magnetic field should not be produced along it...but neutrons have a magnetic moment. So why can't this magnetic moment help it to generate a magnetic field around it? | If a neutron is moving with a velocity of \( v \) in a vacuum, what magnetic field strength \( B \) can be calculated at a distance \( r \) from the neutron's path due to its intrinsic magnetic moment, given that the neutron has a magnetic moment of approximately \( 0.966 \times 10^{-26} \, \text{J/T} \)? | 24,663 | cqadupstack-physics |
69521 | Negative Energy and Wormholes | Apparently to create wormholes you need negative energy/matter. Say you had negative matter/energy, how would it be applied towards making a wormhole? | If negative energy or matter is required to create wormholes, what is the minimum theoretical amount of negative energy necessary for a stable wormhole to connect two points in space, assuming a specific model of spacetime? | 35,632 | cqadupstack-physics |
95091 | Does rotation cause gravity? | I want to ask that what causes gravity. My opinion is that it is the rotation that causes gravity, when we see a whirlpool in water it takes anything that comes near to it in to the center of it. I have a doubt that is even gravity caused due to rotation of earth. When earth rotates, it takes the atmosphere with it and... | What is the relationship between the Earth's rotation and the force of gravity experienced on its surface, and how does this compare to the effects of centrifugal force produced by the Earth's rotation? | 18,739 | cqadupstack-physics |
83489 | How does light pass through rough glass? | Light incident on a rough surface will be diffuse after passing it. Angular intensity depends on the grinding of the glass surface. I'm trying to find information about the scattering indicatrix of light passing through the rough glass: how to calculate it numerically, which parameters are essential, etc., or at least ... | How can I quantitatively determine the scattering indicatrix of light after it passes through a rough glass surface, and what parameters are essential for this calculation? Additionally, how can this be related to the equations governing electromagnetic fields? | 30,719 | cqadupstack-physics |
46912 | Scalar Field Theory Decay/Scattering | I have a few questions related to the following interaction Lagrangian (no use of crossing symmetry in the following) involving the uncharged scalar $\chi$ and the charged scalar $\phi$: $$\tag{1}\mathcal{L}_{\rm int} ~=~ \sqrt\lambda· g· \chi\phi^\dagger \phi - \frac{\lambda}{4}(\phi^\dagger\phi)^2.$$ Can we use (1) t... | Given the interaction Lagrangian $$\mathcal{L}_{\rm int} = \sqrt{\lambda} g \chi \phi^\dagger \phi - \frac{\lambda}{4} (\phi^\dagger \phi)^2,$$ determine the vertex factors for the following reactions:
a) $\phi\phi\rightarrow\phi\phi$
b) $\phi\phi^\dagger\rightarrow \chi\chi$
c) $\chi\phi\rightarrow\chi\phi$
E... | 7,176 | cqadupstack-physics |
104860 | metastable energy levels | can someone give me a good definition of "metastable energy levels" in a helium plasma (glow discharge). Am I right when I say : "by adding some neon in my helium plasma, I will obtain a molecular plasma of NeHe" ? I guess the metastable energy levels are the reason of forming NeHe, but I don't know why, can someone ex... | In a helium plasma under glow discharge conditions, what are the characteristics and significance of metastable energy levels, and how do they influence the formation of molecular species like NeHe when neon is introduced? Please provide quantitative examples or explanations related to the energy levels involved. | 23,811 | cqadupstack-physics |
15596 | How can we have spinless fermions? | I've read that the Jordan-Wigner transformation changes qubits into spinless fermions. What, exactly, are spinless fermions? I'm guessing it doesn't mean spin zero which would be a boson, so what does it mean? | What are the defining characteristics of spinless fermions, and how do they differ from bosons in terms of spin and statistical behavior? | 34,141 | cqadupstack-physics |
117017 | How do you determine the Lagrangian? | I have always been puzzled by how do you arrive at Lagrangians? That is, how do you know that the functional you need to get Newton's equations is $L$ = $T-V(x)$ Do you derive the Lagrangian first somehow or do you just guess the one which would satisfy the action to give equation's of motion?(because then you would ne... | What is the relationship between the Lagrangian \( L = T - V \) and the equations of motion in classical mechanics, and can the Lagrangian be determined independently of these equations? Additionally, was the Einstein-Hilbert action formulated before deriving the field equations for general relativity, and if so, what ... | 33,249 | cqadupstack-physics |
30838 | Do observers at different speeds perceive other speeds differently? | I was told that if a plane takes less time to travel from the China to US as opposed to the other direction due to rotation of the earth. I suspect this is incorrect however. From this scenario I came up with the following thought experiment. Imagine two people sitting on a train. One person is sitting with his back (A... | In the thought experiment with two people on a moving train, one facing forward and the other facing backward, how do the speeds of the ball thrown between them compare from their perspectives, as well as from the perspective of an observer standing outside the train? Specifically, if the train is moving at a speed of ... | 33,747 | cqadupstack-physics |
90832 | Characteristic waves in a plasma | What does "characteristic wave" mean in the context of plasma waves? For example, when propagating parallel to the plasma magnetic field, the characteristic wave is circularly polarized. Does this mean that only a circularly polarized wave can propagate in this direction? Could an elliptically polarized wave travel in ... | Given the propagation of plasma waves parallel to the plasma magnetic field, define the phase velocity of a circularly polarized wave in a plasma characterized by a magnetic field strength of \(B\) and electron density \(n_e\). Additionally, what conditions determine whether an elliptically polarized wave can also prop... | 4,892 | cqadupstack-physics |
133567 | Calories Burned While Hiking | I want to find out how many calories are burned on any particular hike by any particular by using a formula. I figure it's probably a simple physics question, but since I never took physics, I don't know the math to do it. My premise is that you will expend (A) energy (calories) when moving (B) weight (C) distance on a... | What is the formula for calculating the total calories burned during a hike, taking into account the hiker's weight, the distance traveled, and the elevation gained, while ignoring minor variables like resistance, fitness level, and individual differences? | 33,049 | cqadupstack-physics |
95217 | Can we have light through out the house with out light being switched on for all the time? | Optical fibres are used to transmit light from one place to the other along curved path in a more effective manner. The optical fibres consist of thousands of strands of a very fine quality glass or quartz of refractive index about $ 1.7$ or so. The thickness of a strand is about $10^{-6}$ cm. The strands are coated wi... | Calculate the minimum angle of incidence required for total internal reflection to occur at the interface between the optical fiber (with a refractive index of 1.7) and its coating (with a refractive index of 1.5). What would this critical angle be, and how does it relate to the efficiency of light transmission in opti... | 16,270 | cqadupstack-physics |
53817 | Muon production in particle accelerator | PAMELA is a particle accelerator which have two concentric rings, protons are accelerated in the inside ring. At ISIS muons are produced when a 800 MeV proton beam collides with a graphite target(carbon 12) can the same be done with this device? The accelerated protons from inside may be sent to the outside ring which ... | What are the magnetic properties of pions, and how might these properties influence the containment and manipulation of pions produced in a particle accelerator like PAMELA after their production from a proton-carbon collision? | 6,743 | cqadupstack-physics |
56595 | Getting pairs of angle and velocity for a projectile to a given destination | I'm trying to calculate the initial velocity $v_0$ and angle $\theta$ for a given destination $(x, y)$ with a launch height of $y_0$. Obviously there will be a set of pairs of velocity and angle that will pass through the destination point. This set is given by $$ \left\\{(v_0,\theta) \middle|y = - \frac{g}{2 v_0^2 \cd... | Given a destination point \((x, y)\) and a launch height \(y_0\), how can I determine the initial velocity \(v_0\) and launch angle \(\theta\) for a projectile to reach that point without exhaustively iterating through all possible pairs of \(v_0\) and \(\theta\)? Specifically, can you provide a method or formula to de... | 36,263 | cqadupstack-physics |
19500 | How can indeterminacy in quantum mechanics be derived from lack of ability to observe a cause? | I don't get this part of quantum mechanics. I get the part that you can't observe particles and not affect their behavior because you are shooting photons to them while you are observing them, but how can this show that while you are not observing them, they behave in indeterministically and that's a feature of nature. | What experimental evidence supports the concept of indeterminism in quantum mechanics, particularly in the behavior of particles when not being observed? Please describe an experiment, such as the double-slit experiment, and the implications it has on our understanding of quantum behavior. | 646 | cqadupstack-physics |
56576 | Most efficient type of heat pump | Can I make a heat pump beat the Carnot efficiency? Why is the Carnot process the most efficient one? If I have a heatpump that is sphere shaped, and cascaded in layers like a onion can I beat Carnot efficiency? Heat would be transferred and concentrated from the outermost layer that is in contact with ambient air, and ... | If I have a spherical heat pump designed with multiple concentric layers that draw heat from ambient air, what is the maximum theoretical coefficient of performance (COP) it can achieve compared to the Carnot efficiency, assuming the temperature of the ambient air is 20°C and the temperature of the heated fluid is 80°C... | 22,130 | cqadupstack-physics |
61001 | The Klein–Gordon equation | As we know that the Schrödinger equation presents basis of Quantum Mechanics and analogy with Newton second law in Classical Mechanics, I thought that relativistic interpretation of Schrödinger equation can make general relativity and quantum mechanics closer $$ \frac {1}{c^2} \frac{\partial^2}{\partial t^2} \psi - \na... | Can the relativistic wave equation \( \frac {1}{c^2} \frac{\partial^2}{\partial t^2} \psi - \nabla^2 \psi + \frac {m^2 c^2}{\hbar^2} \psi = 0 \) be reduced to the non-relativistic Schrödinger equation, and what do the solutions of this equation represent physically in terms of relativistic mechanics? | 21,039 | cqadupstack-physics |
66201 | What are the theoretical prerequisites for experimental work with SEM and TEM? | What level of knowledge and in what areas would be required to perform experimental work with an SEM (Scanning Electron Microscope) and a TEM (Transmission Electron Microscope) respectively? E.g. would a strong background in quantum mechanics be necessary for EELS (Electron Energy Loss Spectroscopy) using a TEM? Assume... | What specific knowledge and skills in materials science, physics, and electron microscopy are essential for conducting experiments with modern SEM and TEM techniques, particularly for analyzing metal alloys using methods like EBSD, Surface Imaging, BSE, EELS, and Electron Diffraction? | 9,798 | cqadupstack-physics |
98798 | What's a good book for an advanced undergraduate/early graduate student to learn about symmetry, conservation and Noether's theorems? | What's a good book (or other resource) for an advanced undergraduate/early graduate student to learn about symmetry, conservation laws and Noether's theorems? Neuenschwander's book has a scary review that makes me wary of it, but something like it would be great. | What is the mathematical expression for Noether's theorem in terms of conservation laws, and can you provide an example of a physical system where it is applied? | 36,677 | cqadupstack-physics |
133466 | Why should an area vector point normal to the surface? | Why is it that the direction of an area vector should be always along the normal drawn to the surface? Can't it also be some other angles with the plane? | What is the mathematical definition of an area vector, and why is its direction defined to be perpendicular to the surface it represents? Can you provide an example where the area vector aligns with the normal of a surface? | 34,019 | cqadupstack-physics |
134448 | kinematics question about runner | Here's the question: Your goal is to complete your 10,000-m run in less than 30.0 min. Apparently you've started too slowly because at 27.0 min, you still have 1100 m to go! You can accelerate at 0.20 m/s2 . For how many seconds should you accelerate (and after this have constant velocity) in order to complete the run ... | What is the minimum time in seconds that you need to accelerate at 0.20 m/s² in order to finish a 10,000-m run in less than 30 minutes, given that you have 1,100 m left to run after 27 minutes? | 7,866 | cqadupstack-physics |
103642 | Is every ordinary coloured transparent paper an optical filter? | Can any red coloured transparent paper be used as an optical filter that only allows red colours through it? | What is the wavelength range of light that can pass through red transparent paper, and would it effectively filter out all other colors of light? | 37,488 | cqadupstack-physics |
44664 | Possible colors of fire? | I have learnt that depending on the various gases those are involved in the reaction that produces fire, different colors (yellow, red or blue) of flames become visible. I have a question .. what are the possible colors that fire can possess? and do they (how, if yes) relate to the intensity? like I know blue is more i... | What are the various colors of flame produced by different gases during combustion, and how do these colors relate to the temperature or intensity of the flame? Please provide specific examples and their corresponding temperatures. | 4,569 | cqadupstack-physics |
5094 | Will negatively charged strangelets be produced by the LHC? | Witten (and earlier, Bodner) hypothesized that strange matter (up, down, strange quarks) should be more stable than "regular" nuclear matter(The strange matter hypothesis). That is that the typical hadrons in matter are metastable, and will eventually decay into strange matter because it can exist at lower energy confi... | What is the expected stability of negatively charged strangelets compared to regular nuclear matter, and what evidence supports the hypothesis that they are unlikely to be produced in high-energy collisions at the LHC? | 32,970 | cqadupstack-physics |
99448 | A vertical variation of modern versions of Michelson-Morley | For almost a year now, I have been in the uncomfortable position of having an idea. However, there is one nice thing about this idea. It makes a concrete, exact and relatively easy to test physical prediction. The idea predicts that there is a 11,187 m/s (Earth’s escape velocity) aethereal wind directly into the surfac... | What factors would influence the expected results of a vertically oriented Michelson-Morley experiment, and could you estimate the cost of conducting such an experiment, possibly indicating if it would be around \$10,000, \$100,000, or more? | 19,195 | cqadupstack-physics |
78798 | Galactic flux given magntiudes | **Introduction** I have the following data for a galaxy: apparent magnitude in $U,B$ and $V$ Johnson photometric system: $$m_{U}=17.51 \\\m_{B}=17.08 \\\m_{V}=16.74 $$ The galaxy is such that the galactic hydrogen column has $N(H)=6 \cdot10^{22} \mbox{ cm}^{-2}$. I have to take into account galactic extinction, $A_{J}$... | Given the apparent magnitudes of a galaxy in the Johnson photometric system as \( m_U = 17.51 \), \( m_B = 17.08 \), and \( m_V = 16.74 \), along with the galactic extinctions \( A_U = 0.3017 \), \( A_B = 0.2632 \), and \( A_V = 0.199 \), how can I calculate the specific fluxes \( f_{U_0} \), \( f_{B_0} \), and \( f_{V... | 6,722 | cqadupstack-physics |
19402 | conformal anomaly of free scalar in 2D | I'm trying to calculate the conformal anomaly $c$ of a free scalar on a 2-sphere. I've seen other, indirect ways to do this, but since this is a free theory I feel like it should be possible to see it directly as the anomalous depenedence of the partition function on the radius of the sphere. However, I'm having a diff... | What is the conformal anomaly \( c \) for a free scalar field on a 2-sphere, and how does the dependence of the partition function on the radius manifest when regulating the expression using a momentum cutoff? | 1,299 | cqadupstack-physics |
103803 | Surface current and current density | Hello I want to know when I am asked to find the surface current density and the space current density what should I do? Also what is the difference between the surface and space current? Can the space current density help me to find the latter if I know it? Thanks! | Given a wire with a surface current density \( K \) of 5 A/m, calculate the space current density \( J \) within the wire if its radius is 2 mm. What is the relationship between the surface current density and the space current density in this scenario? | 18,018 | cqadupstack-physics |
70314 | How often can virtual particle/antiparticle pairs form real particles in a space expanding sufficiently fast to do this? | And if the rate of expansion of the universe becomes sufficient for virtual particles to be ripped apart into real particles, what effect would the mass of these particles have on the rate of expansion of space? Would it slow the rate down sufficiently to stop the creation of even more particles? | If the expansion rate of the universe were to increase to the point where virtual particles could transform into real particles, calculate the potential change in the overall mass-energy density of the universe and discuss how this change could influence the rate of cosmic expansion according to the Friedmann equations... | 3,576 | cqadupstack-physics |
21527 | Equivalence principle and radiation from falling particle | I am currently having a hard time solving a problem of GR from Lasenby's book. I can't make it more clear than by quoting the exercise: 7.2 A charged object held stationary in a laboratory on the surface of the Earth does not emit electromagnetic radiation. If the object is then dropped so that it is in free fall, it w... | How does the principle of equivalence explain the contradiction between a charged object at rest on Earth's surface not emitting radiation and the same object emitting radiation when it is in free fall? Quantitatively, what would be the total energy radiated by the charged object over a specific time interval while in ... | 35,157 | cqadupstack-physics |
99824 | How to choose a location for rocket launching? | What's the relation of earth's magnetic equator with satellite launching? How does the nearness of a rocket launching station to the earth's magnetic equator make it an ideal location for scientists to conduct atmospheric research? But not all stations are near the magnetic equator. why? Are there any special requireme... | How does the distance of a rocket launching station from Earth's magnetic equator affect its launch efficiency and the accuracy of atmospheric research measurements? | 26,257 | cqadupstack-physics |
83699 | Does unitarity imply conservation of energy? | Not too long ago, someone began to discuss the thinking and motivation behind the Lagrangian and its formalism for the Newtonian framework and an intuitive understanding of such formalism. Somehow, it ended in the case that the Lagrangian can be understood in terms of conservation of information (largely) without havin... | Is the principle of unitarity in quantum mechanics a stronger constraint than the conservation of energy in classical mechanics, and can you provide a quantitative example demonstrating this relationship? | 27,741 | cqadupstack-physics |
46200 | Why is energy-momentum 4-vector so much easier to explore/observe than spacetime 4-vector | I have read that spacetime 4-vector is quite difficult to observe/explore and that energy-momentum 4-vector is much more appropriate for CERN etc. **Why is that?** Could anyone give me a brief explanation of the differences regarding exploration and observation? | What are the components of the energy-momentum 4-vector, and how do they relate to observable quantities in high-energy particle physics experiments, such as those conducted at CERN? | 31,883 | cqadupstack-physics |
81976 | Power dissipated in Series versus Parallel | Do two resistors in parallel dissipate more heat per unit time for an applied voltage when compared to two resistors in series? | If two resistors, R1 and R2, are connected in parallel and two resistors of the same resistance value are connected in series, how does the total power dissipated by each configuration compare when the same voltage is applied across both arrangements? | 35,277 | cqadupstack-physics |
19037 | What are the advantages of the ILC over the LHC? | USA Today has an article on Japan's interest as the site for the $10 billion future International Linear Collider. This accelerator will utilize electron/positron collisions (like CERN's former LEP collider) at energies of 500 GeV and will be 30 km long. The ILC site claims precision capabilities over and above those o... | What is the energy of electron/positron collisions at the International Linear Collider, and how does this energy compare to the collision energy of the Large Hadron Collider? | 19,317 | cqadupstack-physics |
80287 | Time period of simple pendulum with varying mass | How do you find time period as a function of time for a simple pendulum that is in the form of a hollow sphere that is filled with mercury and there is a hole in the bottom through which the mercury is constantly falling at a fixed rate? I tried creating a function for the time period to check how it varies with the ma... | What happens to the time period of a simple pendulum, formed as a hollow sphere filled with mercury, as the mercury uniformly drains out of a hole at the bottom? Choose one of the following options: A) The time period becomes erratic, B) The time period increases, C) The time period decreases, or D) The time period fir... | 16,907 | cqadupstack-physics |
133740 | Relative velocity of two cars | Two cars A and B are at $100\,\text{m}$ and $200\,\text{m}$ distance from the origin $O$ at time $t = 0$. They start simultaneously with velocities $10\,\text{m/s}$ and $5\,\text{m/s}$ respectively. A will overtake B at a distance of $x$ from $O$. The answer given: $300\,\text{m}$. What I have tried so far: I tried to ... | Two cars, A and B, start from positions 100 m and 200 m from the origin O at time t = 0. Car A moves at a speed of 10 m/s and Car B at a speed of 5 m/s. At what distance x from the origin O will Car A overtake Car B? | 22,534 | cqadupstack-physics |
73662 | Does $E$ cause $B$ or does $B$ cause $E$ in Maxwell's equations? | From the Maxwell's equations we get $$\frac{\partial E}{\partial x} = -\frac{\partial B}{\partial t}$$ and $$\frac{\partial B}{\partial x} = -\mu_0\epsilon_0\frac{\partial E}{\partial t}$$ My question is: A change in the electric field causes a change in the magnetic field, while a change in magnetic field is causing a... | Given Maxwell's equations, if the electric field \( E \) changes with time at a rate of \( \frac{\partial E}{\partial t} = 2 \, \text{V/m/s} \) and the distance with respect to \( x \) is \( \Delta x = 1 \, \text{m} \), calculate the induced magnetic field \( B \) at that point in space, using the relationship \( \frac... | 26,379 | cqadupstack-physics |
81046 | Ionization Energy and Bohr | I was having problems with ionization energy - but all it is is the energy required to remove first electron that pops off right? In the case of Bohr's atom, there's only one electron, so it's that electron in it's ground state. In the case of a multielectron atom, it's the energy required to remove the outer electron,... | What is the ionization energy of a hydrogen atom in its ground state, and how does it compare to the ionization energy of a sodium atom, which has one more electron and an outer electron in the n = 3 state? | 30,356 | cqadupstack-physics |
35562 | Is a 1D vector also a scalar? | A vector in one dimension has only one component. Can we consider it as a scalar at the same time? Why time is not a vector, although it can be negative and positive (when solving for time the kinematics equation for example)? | Can a one-dimensional vector be considered a scalar quantity, and under what conditions might this equivalence be justified in physics? Explain the rationale behind treating time as a scalar rather than a vector, despite its ability to be represented as both positive and negative in kinematic equations. | 23,672 | cqadupstack-physics |
110584 | Two-dimensional atomic trap--how to set up the problem? | > It is possible to trap neutral atoms between two solid surfaces in a > potential of the form $V (x, y, z) = ax^2 + by^2$ where a and b are > parameters. The allowed space for the gas extends to infinity in the $x$ and > $y$ directions but is limited in the z-direction by the two solid surfaces, > which are located at ... | Given a system of neutral atoms trapped between two solid surfaces at \( z = 0 \) and \( z = L = 2 \) with a potential \( V(x, y, z) = ax^2 + by^2 \), where \( a \) and \( b \) are parameters that can be changed slowly and adiabatically, what will be the final temperature \( T_f \) of the gas in terms of the initial te... | 2,780 | cqadupstack-physics |
76880 | Virial Theorem and the Energy in a Gas | I clearly am interpreting the Virial Theorem incorrectly, but I don't know how. In dipole gases, the molecules can exhibit five kinetic modes, while they can only experience 2 potential modes. Doesn't the Virial Theorem say the two must have an equal distribution of energy? | In a dipole gas where molecules exhibit five kinetic modes of motion and only two potential modes, how does the Virial Theorem help us understand the distribution of energy among these modes? Calculate the expected ratio of kinetic to potential energy based on the number of modes. | 25,346 | cqadupstack-physics |
19653 | How does a receiving antenna get an induced electric current? | From this **question**, I've noted that an electromagnetic field carries _no electric charge_ but it has two components: * Electric field * Magnetic field Now what I failed to understand is how does the receiving antenna get an induced small voltage. Is it due to the electric or the magnetic field component of EMF?... | How does a receiving antenna generate an induced voltage from an electromagnetic field, and which component of the electromagnetic field, electric or magnetic, is primarily responsible for this induction? Please explain the underlying principles involved. | 17,908 | cqadupstack-physics |
54063 | Shift operator (integral calculus involving Hermite polynomials) | I didn't know whether to pose this question on _Physics.stackexchange_ or _Math.stackexchange_. But since this is the last step of a development involving the eigenfunctions of an Harmonic oscillator and a _shift operator matrix_ , I thought it'd be better to post it here. I have to calculate the integral $$\frac{1}{2^... | Calculate the integral
$$I(n, l, k) = \frac{1}{2^n n! \sqrt{\pi}}\int_{-\infty}^{+\infty} H_n(x) e^{-x^2 + kx} H_l(x) \;\mathrm{d}x$$
where \( H_n(x) \) and \( H_l(x) \) are the nth and lth Hermite polynomials, respectively. Prove that
$$ I(n, l, k) = \sqrt{\frac{m_<}{m_>!}} \left( \frac{k}{\sqrt{2}} \right)^{|n-... | 19,012 | cqadupstack-physics |
65524 | Physical interpretation of changing variables $S(T,V)$ to $S(T,p)$ | I'm confused in this situation. In an example of this book (Example 16.5. Thermal Physics, by Blundell) they ask to prove that $$C_P - C_V = VT\frac{\alpha^2}{\beta_T}\tag{1}$$ but using the fact that $S=S(T,V)$. Then they use the fact that $$C_V = T\biggl(\frac{\partial S}{\partial T}\biggr)_V\tag{2}$$ and that $$C_P ... | Given the equation \( C_P - C_V = VT\frac{\alpha^2}{\beta_T} \), where \( C_V = T\left(\frac{\partial S}{\partial T}\right)_V \) and \( C_P = T\left(\frac{\partial S}{\partial T}\right)_P \), explain how you can derive \( C_P \) from \( S = S(T,V) \). What is the physical significance of transitioning from the dependen... | 37,362 | cqadupstack-physics |
88905 | Acceleration of a car in a collision? | For example because of newton law $F=ma$ force is acceleration times mass but if I go at a high constant velocity ($900\: \mathrm{miles/hour}$) in my car for examples I have $0$ acceleration but if I hit an obstacle by newton's law it will have no effect on me because $F=ma$ and mass of my car x 0 = 0 But if I do the e... | If a car traveling at a constant velocity of \(900 \, \text{miles/hour}\) suddenly collides with an obstacle, what is the role of momentum in determining the effect of the collision on the car and its occupants, considering that the car's acceleration is \(0\) before the impact? | 9,772 | cqadupstack-physics |
79923 | Paralel light conditions after passing from a sphere |  Is it possible to get such result that light will be parallel after passing from the sphere? what is the total condition for such result if possible? Thanks for answers | If a beam of light enters a glass sphere with a radius of 10 cm and an index of refraction of 1.5, at what angle of incidence must it strike the surface of the sphere in order for the emerging light beam to be parallel to the original beam? Assume the light enters the sphere from air. | 1,305 | cqadupstack-physics |
60726 | Einstein's theory tells us that gravity is a curve in space and time but how does that causes attraction in mass? | The sun is incredibly massive object and it causes the space around it to bend. This causes the planets to pulled to the sun or the planets move in an elliptical path around the sun. But I don't understand how the curvature in space can cause the pulling or what cause the planets to move in elliptical path? | How can the curvature of spacetime around a massive object like the sun lead to the planets moving in elliptical orbits, and what mathematical principles describe this relationship? | 38,138 | cqadupstack-physics |
134384 | Lightspeed (invariance) measurement methods | I would like to know, how measurements of the speed of light are conducted these days, especially in the context of the invariance of $c$. Do all the methods involve mirrors to redirect the photons back to the place where they were emitted from? If not, could somebody, please, describe the method briefly? Again, what I... | What is the current method used to measure the speed of light, and how do these methods test the invariance of the speed of light \( c \)? Specifically, are there experimental setups that do not utilize mirrors for redirecting photons, and can you describe one such method? | 8,452 | cqadupstack-physics |
33589 | What does the concept of phase space mean in particle physics? | I came across the concept of phase space in statistical mechanics. How does this concept come about in particle physics? Why was it introduced and how is it used? What does it mean when textbooks say there is no enough phase space for that reaction to take place? | In particle physics, if the phase space is defined as the set of all possible states a system can occupy, how is the total phase space volume for a two-particle reaction calculated, and what conditions must be met for the reaction to occur based on the available phase space? | 19,547 | cqadupstack-physics |
122626 | Are only 2 bits of information transmitted in quantum teleportation? | Prompted by the recent success in Delft, I've been reading a number of papers and articles about quantum teleportation. I'm comfortable with my understanding of most aspects but haven't found much reliable discussion about the interpretation and if anything "spooky" might be happening. Let me try to explain as clearly ... | Is there a way to experimentally verify that a qubit, rather than just two classical bits, is transmitted during quantum teleportation, and if so, what specific measurement or outcome would indicate this? | 36,037 | cqadupstack-physics |
63005 | The weight of a cavity of radiation | A sealed cavity full of light weighs more than an empty one. So consider a cavity consisting of parallel mirrors, with a pair of beams bouncing between the mirrors. The question is whether that weight will change if we arrange for the beams to completely cancel one another at every point along their length? | If two beams of light are bouncing between parallel mirrors in a sealed cavity and can be arranged to completely cancel each other out at every point along their length, what is the net effect on the weight of the cavity compared to when the beams are not canceling each other? | 11,898 | cqadupstack-physics |
3531 | Photon wave packets from distant stars | A distant star like the sun, thousands of light years away, could be so faint that only one photon might arrive per square meter every few hundred seconds. How can we think about such an arriving photon in wave packet terms? Years ago, in a popularisation entitled “Quantum Reality”, Nick Herbert suggested that the phot... | Given the scenario where a distant star emits photons that arrive at Earth at a rate of one photon per square meter every few hundred seconds, how would you calculate the wave packet dimensions of the photon upon arrival, particularly focusing on the transverse width and the relationship between the width and the photo... | 14,099 | cqadupstack-physics |
112447 | Photoelectric Effect Problem | Say in a photoelectric experiment, we find a stopping potential of 1.85V for $\lambda=3000\overset{\circ}{A}$ and of 0.82V for $\lambda = 4000 \overset{\circ}{A}$. 1. How can I get the Planck's constant from the above information? 2. Determine the work function of the sodium in electron-volts. 3. Determine the th... | In a photoelectric experiment, a stopping potential of 1.85 V is measured for a wavelength of \(3000 \, \text{Å}\) and 0.82 V for a wavelength of \(4000 \, \text{Å}\).
1. Calculate Planck's constant using the given data.
2. Determine the work function of sodium in electron-volts.
3. Find the threshold wavelength fo... | 32,352 | cqadupstack-physics |
75398 | How to model perfectly elastic collisions using force? | I want to have elastic collisions in my Newtonian physics simulator, but in the one physics class I've taken we only used momentum when analyzing elastic collisions, and my simulator is totally force-based. If two pointlike objects are colliding with given velocities and masses, what forces should I have them exert on ... | What are the magnitudes and directions of the forces that two pointlike objects with masses \(m_1\) and \(m_2\) should exert on each other during a perfectly elastic collision, given their initial velocities \(v_{1i}\) and \(v_{2i}\)? | 18,763 | cqadupstack-physics |
52101 | Is a large system just a set of smaller systems? | All particles exhibit wave-particle duality. And I have a strange question. Why does a larger system, liken an atom that is just a set of smaller systems, itself exhibit wave-particle duality? In principle all large systems can be defined as a set of smaller systems. An atom is a set of nucleus (a smaller set of up and... | How can wave-particle duality be quantitatively demonstrated for a composite system like an atom, considering it is made up of smaller systems such as protons, neutrons, and electrons? Can you provide a mathematical framework or example that illustrates this phenomenon in terms of their wavefunctions? | 7,461 | cqadupstack-physics |
83056 | What is known about the statistical mechanics of systems with normally distributed energies? | Consider a system taking on N states with energies $\epsilon \sim \mathcal{N}(\mu,\sigma^2)$. Are such systems well-studied in any context? I ask because I'd like to be able to take certain expectations related to the partition function. For example, one can show that: $<Z> = Ne^{\mu + \frac{\sigma^2}{2}}$ without too ... | Given a system with N states described by energies $\epsilon$ that follow a normal distribution $\mathcal{N}(\mu, \sigma^2)$, can you calculate the variance of the partition function $Z$, defined as $Z = \sum_{i=1}^{N} e^{-\beta \epsilon_i}$, and provide the expression for $Var(Z)$ in terms of $N$, $\mu$, and $\sigma^2... | 452 | cqadupstack-physics |
27625 | Question from Schutz's | In q. 22 in page 141, I am asked to show that if $U^{\alpha}\nabla_{\alpha} V^{\beta} = W^{\beta}$, then $U^{\alpha}\nabla_{\alpha}V_{\beta}=W_{\beta}$. Here's what I have done: $V_{\beta}=g_{\beta \gamma} V^{\gamma}$ so, $U^{\alpha} \nabla_{\alpha} (g_{\beta \gamma} V^{\gamma})=U^{\alpha}(\nabla_{\alpha} g_{\beta \gam... | Why does the term \( U^{\alpha}(\nabla_{\alpha} g_{\beta \gamma})V^{\gamma} \) vanish in the expression \( U^{\alpha} \nabla_{\alpha}(g_{\beta \gamma} V^{\gamma}) \) when showing that \( U^{\alpha} \nabla_{\alpha} V_{\beta} = W_{\beta} \) given that \( U^{\alpha}\nabla_{\alpha} V^{\beta} = W^{\beta} \)? | 19,194 | cqadupstack-physics |
95970 | Under what conditions is a vector-spinor gamma trace free | I came upon the concept of irreducible vector-spinors while trying to simplify an expression involving the gravitino field. It is claimed that an _irredicible_ vector-spinor is gamma-traceless, i.e. $$ \Gamma^M \psi_{\alpha M} = 0.$$ Are there conditions on the irreducibility besides the above equation? When can I use ... | What are the necessary group-theoretic conditions for a vector-spinor to be considered irreducible, and how do these conditions relate to the gamma-traceless property given by the equation \( \Gamma^M \psi_{\alpha M} = 0 \)? Additionally, in which physical contexts can this relation be applied? | 16,380 | cqadupstack-physics |
54301 | Electric field lines | If electric field lines cannot terminate in empty space, in the simple example of two equal charges what happens to the line starting from one of the charges toward the other in the middle? | In a system with two equal positive charges separated by a distance \( d \), how many electric field lines originate from one charge and terminate on the other charge at their midpoint, and what can you deduce about the behavior of electric field lines in this configuration? | 32,745 | cqadupstack-physics |
3871 | Is causality a formalised concept in physics? | I have never seen a “causality operator” in physics. When people invoke the informal concept of causality aren’t they really talking about _consistency_ (perhaps in a temporal context)? For example, if you allow material object velocities > c in SR you will be able to prove that at a definite space-time location the ph... | What are the implications for the consistency of Special Relativity if an object were to exceed the speed of light, particularly regarding the defined state of physical objects at any given spacetime location? | 28,618 | cqadupstack-physics |
13263 | Can the distance of a quasar be determined accurately? | As noted in A doubt about the age of the universe, the wiki about quasars still contains the following misleading sentence: "The highest redshift quasar known (as of June 2011) is ULAS_J1120+0641, with a redshift of 7.085, which corresponds to a proper distance of approximately 29 billion light-years from Earth." But e... | What is the significance of the rotational motion of a black hole on the measured redshift of a quasar, specifically in the case of ULAS_J1120+0641, which has a redshift of 7.085? | 10,631 | cqadupstack-physics |
132836 | Why potential energy of external force on particle attached to spring is equal to full force multiplied by full displacement? | I am having quite difficult time to understand the meaning of total potential energy on spring. All references I read say that the total potential energy on particle attached to spring is: total potential energy (U)=elastic potential energy (from spring) + potential energy from external force The wo... | If a particle is attached to a spring with a spring constant \( k \) and is displaced by a distance \( x \) from its equilibrium position, how much work is done by an external force \( F \) that is applied gradually to move the particle from position \( A \) to position \( B \) such that the force \( F \) remains great... | 2,582 | cqadupstack-physics |
105659 | Why does the gas cloud of an underwater gunshot pulse? | I have been watching some slow motion video and I was intrigued by the slow motion underwater gunshot. The first moments of the video go as expected. The gun fires and a cloud forms in front of the gun. Then the bullet rips through the water, leaving an open space (which I assume is a cavitation vacuum.) Soon after, th... | What is the physical phenomenon that causes the gas bubble created by a bullet traveling underwater to pulse and emit light, and what are the underlying mechanisms responsible for these observations? | 29,666 | cqadupstack-physics |
92506 | Classical systems with strong coupling | I would like to have some examples of classical systems with "strong" coupling coefficient (in their action term). Specifically, I am looking for intermediate or cross-over ranges of coupling (~$\mathcal O(1) $), where it is neither possible to describe them by effective (composite) field theories with small coupling (... | Can you provide examples of classical systems that exhibit a strong coupling coefficient of approximately \(\mathcal{O}(1)\) in their action term, and also have a negative beta function, indicating that the coupling increases in the infrared (IR) limit? | 4,042 | cqadupstack-physics |
119630 | How does a (near) elastic collision work at a microscopic level? | Suppose a large mass $M$ travelling at $v$ impacts a small stationary mass $m$, then following through the elastic collisions from high school, we get that the smaller mass can exit the collision FASTER than $v$. In the limit of huge $M$, we can change reference frame and make $M$ basically stationary, and $m$ simply b... | In an elastic collision between a large mass \( M \) and a small mass \( m \), if \( M \) is effectively stationary and \( m \) bounces off with a velocity of \( 2v \), how can we mathematically demonstrate that the smaller mass \( m \) can exceed the initial speed \( v \) after the collision? Additionally, what princi... | 21,116 | cqadupstack-physics |
132384 | Dashed lines in Feynman diagram | In this article, in e.g. figure 2, what does these dashed lines across the Feynman diagram mean?  | In a Feynman diagram, what is the physical significance of dashed lines, and how do they differ from solid lines in representing particles or interactions? | 32,690 | cqadupstack-physics |
66006 | Is a particle subject to dissipation proportional to its velocity a Hamiltonian system? | Why or why not? I'm pretty sure that this isn't a Hamiltonian system because it involves a dissipation term, but using the Hamiltonian flow it gives me that the system is Hamiltonian. | Is a system with a dissipation term considered a Hamiltonian system, and if it is not, under what conditions can it exhibit Hamiltonian-like behavior? Provide a mathematical example to support your answer. | 36,076 | cqadupstack-physics |
3645 | Can someone give a simple expose on Coleman Mandula theorem and what Mandelstam variables are? | Can someone give a simple expose on Coleman Mandula theorem and what Mandelstam variables are? Coleman-Mandula is often cited as being the key theorem that leads us to consider Supersymmetry for unification. An overview discussion with sufficient detail is missing in many popular texts. So how does Coleman Mandula theo... | What are the main implications of the Coleman-Mandula theorem in the context of particle unification, and how do the Mandelstam variables relate to this theorem? | 10,565 | cqadupstack-physics |
108506 | From a cross section to a probability | This is homework problem: Given the cross-section of a neutrino-electron scattering, what is the probability for a solar neutrino to scatter with a electron as it goes through the center of the Earth? I'm quiete confused: the dimensions of a cross section are of $L^{-2}$, to get a probability one has to multiply with t... | What is the probability that a solar neutrino will scatter off an electron as it travels through the center of the Earth, given the cross-section for neutrino-electron scattering is \( \sigma \) and the radius of the Earth is \( R \)? | 26,160 | cqadupstack-physics |
109774 | Cooling power for cloud chamber | I'd like to build a small Peltier cell cooled cloud chamber. The cold surface would be a copper sheet with a surface of 200x200 millimeters. Is there a way to even guess the cooling power needed to bring the copper sheet below -30°C ? | What is the minimum cooling power requirement needed to lower the temperature of a copper sheet with dimensions 200 mm x 200 mm to below -30°C, assuming the initial temperature of the sheet is room temperature (20°C) and considering the properties of copper? | 18,608 | cqadupstack-physics |
92648 | Polarization in Nicol prism | My book reads "When unpolarized light is incident on nicol prism (made of 2 crystals joined by Canada balsam a type of glue) it divides into 2 rays, both rays are plane polarized and electric field vectors of one of the rays are perpendicular to plane. These ray is Ordinary Ray. And electric field vector of another ray... | Given that the refractive indices of the ordinary and extraordinary rays in a nicol prism made of calcite are 1.658 and 1.486, respectively, what is the angle of incidence at which total internal reflection occurs at the interface between the ordinary ray and Canada balsam, assuming Canada balsam has a refractive index... | 13,075 | cqadupstack-physics |
77925 | Is there an upper limit on the radius of a rotating wheel? | Is there an upper limit on the radius of a real wheel which is rotating at an Angular frequency of $\,\omega \,$ along its axis, such that we just require a finite amount of energy to rotate it? Why/why not? e.g. if a wheel which is rotating at an angular speed of $\omega = 3 \times {10^5}\,{{rad} \over {\sec }}$ could... | What is the maximum radius of a wheel that can rotate at an angular frequency of $\omega = 3 \times 10^5 \, \text{rad/s}$ without requiring an infinite amount of energy, and how does this limit differ between an inertial frame and a non-inertial frame located at the center of the wheel? | 13,693 | cqadupstack-physics |
16297 | Is decoherence due to coarse graining or coupling with the environment? | In the literature, sometimes one reads that decoherence is due to the coupling of the system to the external environment, and sometimes one reads that it is due to coarse graining over the microscopic degrees of freedom. Are these two different cases of decoherence, or is one more fundamental than the other? | Is decoherence in quantum mechanics primarily driven by the system's interaction with the external environment, or can it be equivalently explained by the coarse graining of microscopic degrees of freedom? Provide a quantitative example to support your answer. | 15,506 | cqadupstack-physics |
107841 | Sign convention for EMF | When we define the field generate by EMF, why there is not negative sign in $\mathcal{E} = \oint \vec{E} \cdot d\vec{l}$? Usually we talk about potential, there should be a negative sign, right? | In the context of electromotive force (EMF), can you explain why the equation for EMF is defined as \(\mathcal{E} = \oint \vec{E} \cdot d\vec{l}\) without a negative sign, while the electric potential difference is typically expressed with a negative sign, \(\Delta V = -\int \vec{E} \cdot d\vec{l}\)? What is the physic... | 13,128 | cqadupstack-physics |
123879 | Since "coordinate time" has a very specific meaning, how to call more general parametrizations? | Recently I've learned that " _coordinate time_ " assigned to a particular time-like spacetime path is not only required (1) to be monotonous and continuous and even differentiable wrt. the " _proper time_ " corresponding to that path, but also that (2) _In the special case of an inertial observer in special relativity,... | What is the common name for a parametrization of the time-like spacetime path of an inertial observer that is continuous, monotonous, and differentiable with respect to proper time, but does not require that the coordinate time is the same as the proper time? | 8,375 | cqadupstack-physics |
64849 | Power transfer in a transformer | Can it be proved using the concept of induced emf that power supplied at the primary coil equals power consumed at the secondary. I tried following. Let primary coil be called 1 and secondary be called 2. Assuming there is no resistance in the primary and a purely resistive load on the secondary. Kirchoff's eqns for th... | How can we derive the condition that the power input at the primary coil equals the power output at the secondary coil in an ideal transformer, considering no losses and a purely resistive load? Specifically, can you show the mathematical relationship and provide a clear explanation of how the induced emf and Kirchhoff... | 31,697 | cqadupstack-physics |
105001 | Solving the 1-d time-independent Schroedinger's equation with an infinite boundary | In my introductory modern physics class we have examined time-independent solutions to the Schrödinger equation in 1 dimension. We looked at a few cases without finite boundary, e.g., free particles and step potentials with $V_{\mathrm{max}} < E$. In each example, in class and in all introductory material I've found, i... | What criteria can be used to determine the physical acceptability of solutions to the time-independent Schrödinger equation, particularly regarding the presence of complex exponential terms, and how can this be mathematically justified? | 3,201 | cqadupstack-physics |
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