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95149 | How would one best dissipate or absorb shockwaves and pressure caused by an explosion within a confined space | I am trying to find a way to limit the effect that detonation of an explosive gas, introduced into a confined space would have when detonated. Can one introduce some form of panelized material or construction that would work to minimize the effect of the initial explosion and shockwave resulting from such? | What are the properties and ideal thickness of a panelized material that would effectively reduce the peak pressure and impulse of a shockwave generated by the detonation of an explosive gas in a confined space? | 19,240 | cqadupstack-physics |
28841 | Wigner-Eckart projection theorem | I'm following the proof of Wigner-Eckart projection theorem which states that: $$\langle \bf{A} \rangle ~=~ \frac{\langle \bf{A} \cdot \bf{J} \rangle}{\langle {\bf{J}}^2 \rangle} \langle \bf{J} \rangle $$ if ${\bf J}$ is conserved. There is an equation: $$ \langle k'jm | {\bf J} \cdot {\bf A} | k j m\rangle = m \hbar \... | In the context of the Wigner-Eckart theorem, given that you have the matrix elements expressed as components of the vector \( \mathbf{A} \), derive the conditions under which the relationship \( \alpha \langle j \| A_0 \| j \rangle + \beta \langle j \| A_{-1} \| j \rangle + \gamma \langle j \| A_{+1} \| j \rangle \equi... | 13,365 | cqadupstack-physics |
47727 | Relation between density and refractive index of medium | Is there any relation between Refractive index and density of a material? It is not found to be proportional in my experimental results. Is there any equation to relate these parameters? | What experimental relationship can be established between the refractive index and the density of a material, and is there a specific equation that defines this relationship? | 19,045 | cqadupstack-physics |
96443 | Is there any role of steering in turning? |  I am aware of the practical requirement of turning the steering wheel to turn a car while going on a straight and even curved road. But in the proofs of turning of car on leveled or banked curves, we see the tyres **straight**. Assuming a road where a ... | In the context of a car negotiating a banked curve at a constant speed without skidding, calculate the angle at which the road must be banked to ensure that the car can maintain its circular path solely through the force of gravity without the need for additional steering. Assume a car speed of 20 m/s, a radius of 50 m... | 10,771 | cqadupstack-physics |
55118 | How can we know the time frames for events in the early universe? | I just finished watching Into the Universe with Stephen Hawking (2010). Specifically the third episode titled 'The Story of Everything.' In the episode Hawking is explaining the mainstream theories of the events just after the Big Bang. What confuses me is that he just said at the beginning that the laws of physics wer... | In the context of the early universe shortly after the Big Bang, how can we quantitatively describe the time spans of significant events when time itself may have been fundamentally different from our current understanding? | 28,368 | cqadupstack-physics |
3635 | Radiation from a pair of charged objects orbiting each other | This question on binary black hole solutions, led to me think about the similar question from the perspective of what we know about the Hydrogen atom. Prior to quantum mechanics, it was not understood what led to the stability of the Hydrogen atom against collapse of the electron orbits due to Bremsstrahlung, i.e. the ... | Given an electron and a proton in a classical hydrogen atom model, calculate the total energy $E$ emitted by the system due to electromagnetic radiation as the mean separation $r$ between the two particles varies from $0$ to a maximum value $r_{\text{max}} \ll d$. Derive the expression for $E(r)$ as a function of $r$ a... | 11,025 | cqadupstack-physics |
17517 | How do formulas get figured out? | Many of the formulas I learn in school are derived from more basic formulas -- as long you your math is right and assuming the more basic formulas you used are correct, you are bound to get to a correct result... But how do people 'invent' the elementary formulas, like $F=ma$; how can you be sure that that's really the... | What experimental evidence can be provided to support the validity of Newton's second law of motion, \( F = ma \), and how can one demonstrate that this relationship holds true for a range of objects and forces? | 11,664 | cqadupstack-physics |
29710 | General equation of motion for elementary particles | Elementary particles can be grouped into spin-classes and described by specific equations, see below: **Is there a general Lagrangian density from which all these equations can be derived?** **A Lagrangian that allows for all types of spin, but after some gauge transformation settles down into a specific type?** **For ... | What is the condition under which a general Lagrangian density can describe particles of different spins, and how does the Higgs mechanism transform a gauge-fixed version of this Lagrangian into specific equations for massless and massive particles? | 6,266 | cqadupstack-physics |
127879 | How do instantons cause vacuum decay? | From what I read about on instantons (Zee, QFT in a Nutshell, pg 309-310), an instanton is a vacuum solution that maps $S^3 \rightarrow S^3$ (the boundary of Euclideanized spacetime), which comes from minimizing the Euclidean action for some Lagrangian with a nontrivial vacuum structure. I've also read (for example in ... | How can instantons, defined as vacuum solutions mapping \( S^3 \rightarrow S^3 \) and minimizing the Euclidean action, mediate quantum tunneling between vacuum states, considering they live at the boundary of spacetime, while solitons and other configurations do not? Additionally, could you provide a quantitative examp... | 13,937 | cqadupstack-physics |
133406 | Restoring Force | Consider a pendulum hanging straight down. Say I pull it to the $\textbf{right}$ some angle $\phi$. Using Newton's laws in polar coordinates, I find that in the that force in the $\hat\phi$ direction is simply the weight in that direction pulling it back down to equilibrium. $$F_{\phi} = -mg\sin\phi$$ I get that it is ... | If a pendulum is pulled to the left at an angle $\phi$ and then released, what would be the expression for the force in the $\hat\phi$ direction, and how does it relate to the reference direction of $\phi$ in polar coordinates? Specifically, is $F_{\phi}$ still negative, and how do the signs of $\phi$ and $F_{\phi}$ ch... | 8,519 | cqadupstack-physics |
103679 | General formula to compute the redshift (first order perturbations) | Consider an expanding universe with the following metric in conformal time/co- moving coordinates: $$ds^2=a^2\left[-c^2\left(1+\frac{2\phi}{c^2}\right)d\eta^2+\left(1-\frac{2\phi}{c^2}\right)\left(dx^2+dy^2+dz^2\right)\right]$$ What would be the formula to compute the redshift $1+z=\frac{\nu_S}{\nu_O}$ of a photon know... | Given the metric for an expanding universe, how can you derive the formula for the redshift \( 1+z=\frac{\nu_S}{\nu_O} \) of a photon based on the provided information for both the observer and the source? Consider the parameters:
- For the observer: \( [\eta_O, x_O, y_O, z_O] \), \( [\frac{d\eta_O}{d\lambda}, \frac{... | 14,036 | cqadupstack-physics |
74113 | Reason for decoherence time's dependence on variables? | Zurek 2001 is a review article on decoherence in quantum mechanics. Equation 5.36 on p. 24 gives an estimate of the decoherence time, which I'll paraphrase as follows: $ \frac{t_D}{t_R} = \left(\frac{\lambda_T}{x-x'}\right)^2 $ . My attempt to interpret the meaning of the variables is: $t_D$ is the decoherence time $t_... | Given the equation for decoherence time \( \frac{t_D}{t_R} = \left(\frac{\lambda_T}{x-x'}\right)^2 \), where \( t_D \) is the decoherence time, \( t_R \) is the thermal relaxation time, \( \lambda_T \) is the de Broglie wavelength, and \( x-x' \) is the difference in position between two states, how does the ratio \( \... | 33,351 | cqadupstack-physics |
109053 | What is the meaning of space-time curvature? | What is the difference between the Space-time curvature and Space curvature? | What is the difference in the mathematical representation of space-time curvature and space curvature in the context of Einstein's General Theory of Relativity? | 35,141 | cqadupstack-physics |
131256 | Instantons as a -1 dimensional object | I don't know much about Instantons, and looking through the Wiki page it seems like one must have a lot of knowledge about QFT to understand them. However recently I've encountered a statement (which I cannot refer to or extract more information) that instantons are "-1 dimensional" objects in the context of string the... | In the context of string theory, if a 0-dimensional object (a point-like particle) creates a 1-dimensional worldline, and a 1-dimensional object (a string) creates a 2-dimensional worldsheet, what type of events could a -1 dimensional instanton create in spacetime? | 18,091 | cqadupstack-physics |
12509 | Does decoherence single out a preferred frame? | Environmentally induced decoherence makes wave function collapse unnecessary. But the environment, usually taken to be some heat bath, introduces a preferred frame. (That in which the total (spatial) momentum vanishes.) So, doesn't then the decoherence time depend on the motion of the prepared state relative to the env... | Given that the decoherence time is influenced by the relative motion of a quantum state with respect to its environment, how would you quantitatively determine the change in decoherence time when measured from a frame with a relativistic boost relative to the cosmic microwave background (CMB) rest frame? Consider the r... | 25,994 | cqadupstack-physics |
35195 | What do I call the inverse of a propagator? | Let's suppose I have a theory described by a Lagrangian as follows: $ \mathcal{L} = A_\mu \underbrace{\left( \partial^2 g^{\mu\nu} - \partial^\mu \partial^\nu + m^2 g^{\mu \nu} \right)}_{K^{\mu \nu}} A_\nu $ (What's the actual theory does not matter.) I know that the inverse of $K^{\mu \nu}$ is called the propagator, I... | What is the term used to describe the quantity \( K^{\mu \nu} = \partial^2 g^{\mu\nu} - \partial^\mu \partial^\nu + m^2 g^{\mu \nu} \) in the context of a Lagrangian theory? | 37,710 | cqadupstack-physics |
48305 | Noether theorem and classical proof of electric charge conservation | How to prove conservation of electric charge using Noether's theorem according to classical (non-quantum) mechanics? I know the proof based on using Klein–Gordon field, but that derivation use quantum mechanics particularly. | What is the mathematical relationship established by Noether's theorem that demonstrates the conservation of electric charge in classical mechanics, and how can it be quantitatively verified using a specific physical scenario? | 20,398 | cqadupstack-physics |
103288 | Charging one thing with static electricity by using battery | How can I make one thing to get statically charged by using batteries but not friction ? For example charge a rod so it can attract shredding ? | What is the minimum voltage required from a battery to charge a rod to attract small pieces of paper or shreds without using friction? | 1,024 | cqadupstack-physics |
55622 | How would a Lagrangian be used to recover the Schrodinger equation? | I heard that the Lagrangian is defined in the path integral formulation of quantum mechanics. How would the Lagrangian in this formulation be used to recover the Schrodinger equation that we normally use? | How can the Lagrangian in the path integral formulation of quantum mechanics be expressed to yield the time-dependent Schrödinger equation, and what specific mathematical steps are involved in this derivation? | 31,965 | cqadupstack-physics |
67126 | How can Young's modulus be dimensionless, but still have units? | According to this wikipedia entry: > Young's modulus is the ratio of stress, which has units of pressure, to > strain, which is dimensionless; therefore, Young's modulus has units of > pressure. From my reasoning if something is dimensionless, it should be a unitless ratio. So how come Young's modulus has a unit? | What are the units of Young's modulus, and how do they relate to the physical quantities of stress and strain in materials? | 4,734 | cqadupstack-physics |
45858 | Root mean square value for DC | The mean value of alternating current comes to be zero because of half of the cycle being positive while the other half negative. so, take the root means square value of Alternating current given by: $I_{rms} = 0.707\times I_{max}$ But why do we take "rms" for direct current? if we take the simple average of direct cur... | What is the root mean square (RMS) value of a direct current of 10 A, and how does it differ from its average value? | 11,638 | cqadupstack-physics |
87292 | Lorentz covariance of the Noether charge | The invariance under translation leads to the conserved energy-momentum tensor $\Theta_{\mu\nu}$ satisfying $\partial^\mu\Theta_{\mu\nu}=0$, from which we get the conserved quantity$$P^\nu=\int d^3\mathbf x\Theta^{0\nu}(x)$$But I cannot see explicitly **how this quantity is a four-vector** covariant under Lorentz trans... | How can we demonstrate that the conserved quantity \( P^\nu = \int d^3\mathbf{x} \Theta^{0\nu}(x) \) is a four-vector that transforms covariantly under Lorentz transformations, given that \( d^3\mathbf{x} \) and \( \Theta^{0\nu}(x) \) do not appear to transform covariantly on their own? Additionally, how can we prove t... | 14,825 | cqadupstack-physics |
62607 | Entangled photons creating particle pairs | Two gamma ray photons are entangled and travel through space. The first gamma photon interacts with a low frequency photon and creates an electron positron pair. What happens to the other gamma photon, does it's motion (position, momentum, spin etc) change as well thus creating another electron positron pair? | If one of two entangled gamma ray photons interacts with a low-frequency photon to create an electron-positron pair, what is the expected effect on the second gamma photon in terms of its quantum state, specifically regarding its position, momentum, and spin? Detail any conservation laws that may be applicable in this ... | 10,392 | cqadupstack-physics |
106636 | Can I detect/measure strength of a FM radio wave using a Electro magnetic field meter? | I understand that an alternating current produces an Electro magnetic field . The strength of this magnetic field can be measured by measuring devices. What I wanted to understand is 1. Are the FM waves generated by the radio transmitters a form of Electro magnetic field? 2. Given an EMF meter such as this one, can... | What is the relationship between the frequency of FM radio waves emitted by transmitters and the strength of the electromagnetic field they generate, and how does this strength change with distance from the transmitter? | 17,663 | cqadupstack-physics |
123297 | Why is scattering vector $\vec{q}$ called vector of 'momentum transfer'? | In the world of scattering the angle at which you detect the scattered radiation is known as $q$, where $$ \vec{q} = \frac{4\pi\eta}{\lambda}\sin(\theta/2) $$ I read in a lot of books that this is known as the scattering vector or "momentum transfer". What I am trying to understand is why it is called "momentum transfe... | Can you explain how the scattering vector \( \vec{q} = \frac{4\pi\eta}{\lambda}\sin(\theta/2) \) relates to the momentum transfer during the scattering of light by a particle, and why this concept is important in understanding the behavior of light scattered by dipole oscillations? Additionally, how does changing the a... | 36,081 | cqadupstack-physics |
68194 | Toward the establishment of non-equilibrium (quasi-equilibrium) magnon BEC theory | In 2006, Demokritov et al have reported that they have achieved the observation of quasi-equilibrium magnon Bose-Einstein condensation (BEC) in YIG at finite (room) temperature by using the method called "microwave pumping" http://www.nature.com/nature/journal/v443/n7110/abs/nature05117.html. I know there are various (... | What is the expected form of the macroscopic condensate order parameter, \( a_0 \), in a quasi-equilibrium magnon Bose-Einstein condensate at room temperature, taking into account thermalization effects characterized by dissipation time \(\tau\)? | 15,913 | cqadupstack-physics |
78552 | Why are there no particles in conformal theories? | In Matt Strassler's recent post (here) he makes the statement that scale invariant (I assume he means conformally invariant, more generally) theories have no particles in them. What's the reason for this? What are the technical and heuristic explanations, apart from what he mentions in his post? | What is the relationship between scale invariance and the existence of particles in field theories, and how can this be explained both technically and intuitively? | 9,722 | cqadupstack-physics |
69124 | What is the physics behind a soap bubble? | A soap bubble is an extremely thin film of soapy water enclosing air that forms a hollow sphere with an iridescent surface. What fluid dynamical process occurs during the popping of a soap bubble? | What specific fluid dynamical process primarily contributes to the rapid collapse of a soap bubble when it pops, and how does this process relate to the concepts of surface tension and pressure? | 9,847 | cqadupstack-physics |
103245 | Resistance of a cylinder contacted by two smaller circular faces | Suppose we have a solid homogeneous cylinder with radius $a$, heigth $h$ and conductivity $\sigma$. The top and the bottom face is contacted with a smaller circular face with radius $b$. How can I calculate the resistance? I know the two boundary cases: * if $a = b$, then $R = \rho \cdot \frac{h}{A}$ simply $\propto ... | How can I derive the electrical resistance \( R \) of a solid homogeneous cylinder with radius \( a \), height \( h \), and conductivity \( \sigma \), when the top and bottom faces are in contact with a smaller circular face of radius \( b \) (where \( b < a \))? What is the expression for \( R \) in terms of \( h \), ... | 31,433 | cqadupstack-physics |
41497 | Can I find a potential function in the usual way if the central field contains $t$ in its magnitude? | I'm working on a classical mechanics problem in which the problem states that a particle of mass $m$ moves in a central field of attractive force of magnitude: $$F(r, t) = \frac{k}{r^2}e^{-at}$$ * $r$ is the distance from the force center, * $t$ is time, * and $k$, $a$ are constants. I am concerned about the $t$ ... | Given the force magnitude \( F(r, t) = \frac{k}{r^2} e^{-at} \), where \( k \) and \( a \) are constants, determine the potential energy function \( U(r, t) \) associated with this force. Show your work and explain how the time-dependent nature of the force affects the potential. | 36,019 | cqadupstack-physics |
69436 | Is the big desert hypothesis a wilder assumption than the see-saw mechanism to explain neutrino masses? | Sometimes I see comments about the big desert hypothesis that I don't understand. For instance in a famous blog : > _...This is based on a renormalization group calculation extrapolating the > Higgs effective potential to its value at energies many many orders of > magnitude above LHC energies. To believe the result yo... | What is the energy scale difference, in orders of magnitude, between the upper limit of the photon mass ($10^{-18}$ eV) and the Planck scale ($10^{19}$ GeV), and how does this compare to the 16 orders of magnitude mentioned in the big desert hypothesis? | 34,398 | cqadupstack-physics |
102170 | Energy in a Solenoid? | > Consider a circuit consisting of a battery, a resistor and a solenoid > inductor. Then, the emf $\mathcal{E}$, is defined as: > > $$\mathcal{E} = L\frac{di}{dt} + iR$$ > > Multiplying both sides by $i$ gives: > > $$\mathcal{E}i = Li\frac{di}{dt} + i^2R$$ > > The term on the left side gives the rate at which the batte... | In a circuit consisting of a battery, a resistor, and a solenoid inductor, the energy stored in the magnetic field is given by the formula \( U_B = \frac{1}{2}Li^2 \). If the inductance \( L \) is 0.5 H and the current \( i \) flowing through the circuit is 4 A, what is the total magnetic potential energy stored in the... | 30,742 | cqadupstack-physics |
113374 | Could we obtain free electrical energy from the Earth's magnetic field? | If there exists a natural magnetic field due to the metallic core of the earth... could we then extract and get free energy from the earth core ?? | Is it possible to calculate the amount of energy that could theoretically be extracted from the Earth's magnetic field, assuming we could harness energy from the natural magnetic field generated by the metallic core? | 23,556 | cqadupstack-physics |
10673 | What does plasmon look like in 3D band structure graph? | Consider metal, and its reciprocal lattice representation with Fermi surface. What is the correct way to represent a plasmon in this system? M.b. rotating points on the surface? Or 3d membrane-like oscillation of surface? Or what? | What is the correct representation of plasmons on the Fermi surface of a metal: as rotating points on the surface or as a three-dimensional membrane-like oscillation? Provide a brief explanation for your answer. | 32,484 | cqadupstack-physics |
123564 | What is the error on measuring the phase of a sine wave? | Let's say I have a wave, with frequency $\omega$ and phase $\phi$, of the form: $$y(t) = 1 + A \sin(\omega t+\phi)$$ where $A < 1$. I have measured this wave N times, and we can assume these measurements are evenly spaced over one period. Each of those measurements has an uncertainty in the y-direction of $\sigma_y$, a... | Given a wave described by the equation $$y(t) = 1 + A \sin(\omega t + \phi)$$ where $A < 1$, if I have $N$ measurements of the wave taken evenly over one period with an uncertainty of $\sigma_y$ in the y-direction, how can I quantitatively determine the uncertainty in the phase $\phi$ of the sine wave? Specifically, ca... | 22,994 | cqadupstack-physics |
73297 | A question for the generalization of gauge transformation with two antisymmetric indices | I have a question about the generalization of gauge transformation with two antisymmetric indices. Starting from Eq. (3.7.6) in Polchinski's string theory book p. 108. $$S_{\sigma} = \frac{1}{4 \pi \alpha'} \int_M d^2 \sigma g^{1/2} \left[ \left( g^{ab} G_{\mu \nu}(X) + i \epsilon^{ab} B_{\mu \nu} (X) \right) \partial_... | How can I show that the variation $$ \delta B_{\mu \nu}(X) = \partial_{\mu} \zeta_{\nu}(X) - \partial_{\nu} \zeta_{\mu}(X) $$ leads to a total derivative when integrated in the context of the action $$ S_{\sigma} = \frac{1}{4 \pi \alpha'} \int_M d^2 \sigma g^{1/2} \left[ \left( g^{ab} G_{\mu \nu}(X) + i \epsilon^{ab} B... | 23,755 | cqadupstack-physics |
132026 | Is it possible for an electrical device to generate more heat than another using less power or the same? | People are claiming that a Plasma TV uses more power which explains why it uses more heat. We refer to power as wattage in this regard. Countering this, is it possible that a device can draw the same wattage or less and produce more heat? Basically, can something create more heat than something else with the same or le... | Is it possible for an electronic device to produce more thermal energy than another device while consuming the same or a lower amount of electrical power? Provide an example and explain the mechanism that allows this to occur. | 17,863 | cqadupstack-physics |
129752 | Higgs field and masses of particles | Interaction of particle with Higgs field provides mass to the particles, then why still some particles are massless? | What are the specific properties or mechanisms that allow certain particles, such as photons and gluons, to remain massless despite their interaction with the Higgs field? | 19,907 | cqadupstack-physics |
87561 | Is there a theoretical maximum for refractive index? | May there be materials yet to be discovered which may have a higher refractive index than today's known materials (for wavelengths within the visible range)? Is there a theoretical limit for the refractive index of a material? | What is the theoretical upper limit for the refractive index of a material, and what are some materials currently known to exceed a refractive index of 2.5 in the visible range? | 34,474 | cqadupstack-physics |
121830 | Does Earth really have two high-tide bulges on opposite sides? | # The bit that makes sense – tidal forces My physics teacher explained that most tidal effect is caused by the moon rotating around the Earth, and some also by the Sun. They said that in the Earth and Moon system, the bodies are are in free fall about each other. But that points on the surface of Earth, not being at Ea... | How can there be high tides and low tides occurring simultaneously at two locations, such as Holyhead and Whitby in the UK or Westport and Kaikoura in New Zealand, when tidal bulges are caused by the gravitational pull of the moon? What is the mechanism that allows for these opposing tidal conditions to exist? | 31,576 | cqadupstack-physics |
59232 | Thermal conductivity affected by electrical current | Does anyone know of any materials whereby the thermal conductivity can be changed by passing an electrical current through the material? | What are some materials whose thermal conductivity can be altered by the application of an electrical current, and how is this phenomenon quantitatively measured? | 16,547 | cqadupstack-physics |
19218 | Certain material heating water in a recipient | I don't know how to resolve a problem, but I don't want the answer since I'm almost going to have it resolved. What the problem says is we have 85 liters of water at 7ºC in an iron pot of 29kg. We want the water to be at 86ºC. The temperature of the iron pot is 12ºC. The water is heated by fire wood (65% of the thermal... | How much firewood, in kilograms, is required to heat 85 liters of water from 7ºC to 86ºC, taking into account that 65% of the thermal energy from the firewood is wasted during combustion and that the heating value of the firewood is 12 MJ/kg? | 16,468 | cqadupstack-physics |
126492 | What does it mean to expand a Hamiltonian using perturbation theory? | On UC Davis chemwiki website, the Hamiltonian for quadrupolar coupling in NMR is analyzed. (The details of this aren't important.) It is said in the analysis that: > _The expansion of the Hamiltonian is done usingperturbation theory._ It then proceeds to "expand the Hamiltonian" according to first and second order term... | What are the mathematical forms of the first-order and second-order perturbation corrections to the energy levels of a quantum system described by the Hamiltonian \( H = H^0 + H^1 \), and how do they relate to the original unperturbed Hamiltonian \( H^0 \)? | 24,121 | cqadupstack-physics |
60804 | Why did increasing the Ackermann geometry in my race car make it faster in corners? | Ackermann geometry is used to account for the different radius arcs that the front tires follow when the steering wheel is turned from center. It's often expressed as a percentage: e.g. 25% Ackermann, 100% Ackermann. I had observed the following physical phenomena: increasing the Ackermann geometry in my race car made ... | How does increasing the Ackermann geometry by a certain percentage, such as from 25% to 100%, affect the speed and handling dynamics of a race car during cornering, and what are the underlying physical principles that explain this effect? | 25,124 | cqadupstack-physics |
127460 | My basis set isn't orthonormal? | I'm implementing a little QM calculation just for fun and to make sure I understand how it works (calculating the helium ground state energy). My problem is that my basis set doesn't seem to be orthonormal. I'm using the spherical harmonics for the angular part and the Slater type radial function. If I integrate just t... | What is the exact normalization condition for the integrals of Slater-type functions combined with spherical harmonics, and how does the presence of the radial component affect the orthonormality condition across different principal quantum numbers \( n \) and \( n' \)? | 8,372 | cqadupstack-physics |
29528 | Semiclassical QED and long-range interaction | I'm interested in the (very) low energy limit of quantum electrodynamics. I've seen that taking this limit does not yield Maxwell equations, but a quantum corrected non-linear version of them. 1. If quantum phenomena are responsible for what we see in the macroscipic world, it is expected that there is a limit which ... | What conditions must be met for quantum electrodynamics to approximate classical Maxwell's equations in the low energy limit, and how can we mathematically demonstrate that these conditions differ from those of the strong and weak interactions, which are mediated by short-range forces? | 34,050 | cqadupstack-physics |
47446 | Gravitation force- Attraction and repulsion | Gravitation force is always attractive. Now assume(not a practical one): I took our Earth in my hand and started shaking up and down. This will create a disturbance in space-time warp and it moves like a wave outward direction. So when the crest part of this disturbance comes in touch with another mass, it should carry... | If I hypothetically shook the Earth and created gravitational waves, what would be the expected effect on a nearby mass, and how would this illustrate the nature of gravitational fields being inherently attractive? | 30,673 | cqadupstack-physics |
44120 | What are Wightman fields/functions | Simple question: What are Wightman fields? What are Wightman functions? What are their uses? For example can I use them in operator product expansions? How about in scattering theory? | What are Wightman functions in quantum field theory, and how do they relate to operator product expansions and scattering theory? Provide an example of their application in these contexts. | 16,722 | cqadupstack-physics |
34946 | What is the significance of action? | What is the physical interpretation of $$ \int_{t_1}^{t_2} (T -V) dt $$ where, $T$ is Kinetic Energy and $V$ is potential energy. How does it give trajectory? | Given the expression $$ \int_{t_1}^{t_2} (T - V) dt $$, where \( T \) represents kinetic energy and \( V \) represents potential energy, what does this integral physically represent in the context of motion, and how does it relate to the trajectory of an object? Calculate the value of this integral if \( T = 5t^2 \) Jo... | 32,856 | cqadupstack-physics |
46185 | Origin of exchage interactions | Can someone explain to me the origin of the exchange interaction between two electrically charged spin 1/2 fermions? Quantitative or qualitative accepted. | Calculate the energy of the exchange interaction between two electrically charged spin-1/2 fermions as a function of their separation distance, considering both Coulombic interactions and the Pauli exclusion principle. Provide a detailed derivation of your answer. | 18,769 | cqadupstack-physics |
130397 | Constructing SUSY algebra via index structure | Often in literature the SUSY algebra is simply given, but various books, for example Bailin and Love, goes through the trouble of showing how the SUSY commutation relations are the only possible ones that you can write down. This is the content of my question. SUSY adds two spinor generators to the Poincare algebra, ou... | What are the reasons that the only permissible commutation relations for SUSY generators are expressed as linear combinations of the form \(c \sigma^\mu_{\alpha \dot{\beta}} \bar{Q}^{\dot{\beta}}\), and how can one systematically demonstrate that this structure leads to unique constants (up to scaling) in the algebra? ... | 36,274 | cqadupstack-physics |
32382 | Could we build a super computer out of wires and switches instead of a microchip? | I thought of this question; would too much wiring make a computer burn down? Or can you build an actual full-speed supercomputer computer using switches and wires? In other words, could simply adding wires and switches into a computer already composed of switch and wire, can you achieve a calculation speed which is lim... | If you were to design a supercomputer using only wires and switches, what is the theoretical maximum calculation speed achievable based on the limitations imposed by the speed of light, and how would adding more wiring affect the system's risk of overheating or failure? | 21,355 | cqadupstack-physics |
52894 | How did Lord Rayleigh derive/determine the phase function for his scattering model? | I've been researching the question for quite some time, as I understand it the phase function is actually an approximation due to the particle-wave duality inherent in participating media such as the atmosphere or anything else. As they are reemitted from particles, some EM waves mingle with their neighbours and amplif... | Can you derive the Rayleigh scattering phase function $$\Phi_R(\theta) = \frac{1}{4\pi}\frac{3}{4}(1 + \cos^2\theta)$$ and explain how it relates to the particle-wave duality of electromagnetic waves in the atmosphere? | 28,566 | cqadupstack-physics |
34393 | How empty of fuel are spacecraft booster rockets typically? | A recent XKCD What-if article mentions the situation where each additional kilogram of cargo to LEO requires an additional 1. 3 kilograms of fuel, which in turn requires fuel to carry (simplification). I wonder then, if an additional half-kilo object, such as an iPod will have a large impact on the amount of fuel that ... | What is the typical amount of excess fuel carried by a rocket when the payload is separated, and how does this relate to the rocket's design and mission requirements? | 6,123 | cqadupstack-physics |
19464 | Does an interaction of entangled particles with each-other cause decoherence? | I'll apologize in advance if this is not an appropriate place for my question. My background is not in physics, and my understanding of quantum mechanics is extremely rudimentary at best, so I hope you'll be forgiving of my newbish question. Given a system of entangled particles (eg, 2 or more electrons), possibly in a... | In a system of two entangled electrons initially in a superposition state, if they interact with each other, how does this interaction affect their quantum state? Specifically, does the interaction lead to a collapse of the superposition, making their state determined (while still unknown until observation)? Please pro... | 15,752 | cqadupstack-physics |
56855 | Homework-Problem solved using Force but unsolved using Energy considerations | > A chain of mass $M$ and length $l$ is suspended vertically with its lowest > end touching a table. The chain is released and falls onto the table. What > is the force exerted by falling part of the chain on the table?(Neglect the > size of individual links) Here's what I did. Momentum of a size $dx$ of chain, which w... | When a vertical chain of mass \( M \) and length \( l \) is released from rest and falls onto a table, what is the total force exerted on the table by the chain when the entire chain comes to a stop? Use the Work-Energy Theorem to derive your answer and explain any discrepancies that arise if you also attempt to analyz... | 32,158 | cqadupstack-physics |
127928 | can we get electrical energy from gravitational energy? | Now I'm trying to give an answer of the question. Satellite rotates about earth by the gravitational force of earth. Now if we place the satellite in such an orbit so that it rotate in opposite to earth rotation and having a greater angular rotational speed. Now there is an existence of earth magnetic field. Though it ... | Is it possible to extract energy from a satellite orbiting the Earth in the opposite direction of its rotation by utilizing the Earth's magnetic field, and if so, how effective would this method be in terms of energy storage? | 20,027 | cqadupstack-physics |
4746 | Glass melting at near absolute zero? | I read this report and summarise here but my question is - if quantum mechanics will make glass melt at temperatures near absolute zero and it is near absolute zero then wouldn't this be a huge issue for satellites and space shuttles? http://www.sciencedaily.com/releases/2011/02/110202102748.htm Scientists Use Quantum ... | What is the effect of temperature on the structural integrity of common glass materials used in satellite construction, considering recent findings that suggest glass can melt near absolute zero due to quantum mechanical effects? | 7,545 | cqadupstack-physics |
98839 | Timelike Shell Collapsing into a Black Hole | Does anyone know where I can find the solution for a spherically symmetric thin shell of timelike matter falling into a Schwarzschild black hole? The matter should be pressureless, so that each particle on the shell follows a radial geodesic. I am interested in the case where the shell is released from rest at a given ... | What is the radial geodesic equation governing the motion of a pressureless spherically symmetric thin shell of matter released from rest at a Schwarzschild radius \( r_0 \) and time \( t_0 \) as it falls into a Schwarzschild black hole of mass \( M \)? | 24,754 | cqadupstack-physics |
101591 | Determining if a particle is bounded or unbounded with motion in polar coordinates |  Firstly, I determined the equation for the particles path for $k <-mV^2a^2$ as $u = {Ae^{\sqrt{\alpha}\theta}+Be^{-\sqrt{\alpha}\theta}}$ where $ \alpha = 1 + \dfrac{k}{mV^2a^2},$ $u = 1/r$ I have two questions; (1) Could I solve for the constants $A,B$ with t... | Given the equation for a particle's path in the form \( u = Ae^{\sqrt{\alpha}\theta} + Be^{-\sqrt{\alpha}\theta} \) where \( \alpha = 1 + \frac{k}{mV^2a^2} \) and \( u = \frac{1}{r} \), determine the conditions under which the motion is bounded or unbounded as \( \theta \to \infty \). Specifically, can you identify val... | 9,473 | cqadupstack-physics |
126085 | Drake's equation | Some years ago i read about this equation that helps us estimate the number of active, communicative extraterrestrial civilizations in the Milky Way galaxy.  Now, i am wondering if there are results from Drake's equation (given that some parameters are ... | Based on the parameters of Drake's equation, estimate the number of active, communicative extraterrestrial civilizations in the Milky Way galaxy, assuming the following values: the average rate of star formation per year is 1.5, the fraction of stars that have planetary systems is 0.5, the average number of planets tha... | 1,514 | cqadupstack-physics |
89434 | Variation of power factor with impedance in a series RLC circuit | I am solving this problem from a previous year question paper > A series RLC circuit has resistance of 1k at resonant frequency and half > power frequencies are 20kHz and 100kHz. Determine (i) The bandwidth (ii) The > value of L and C iii) Show the nature of variation of impedance and power > factor in a series resonan... | In a series RLC circuit with a resistance of 1 kΩ and half-power frequencies at 20 kHz and 100 kHz, calculate the following: (i) What is the bandwidth of the circuit? (ii) Determine the values of inductance \( L \) and capacitance \( C \). (iii) Describe and provide a graph demonstrating the variation of impedance and ... | 30,695 | cqadupstack-physics |
61389 | How to create visible reflections in shallow water? | Assumption: The only lights I have are candle, table lamp, and sunlight. What would I need to create _visible_ reflection of an object in the shallow water contained in a 5 liter bucket? Is it even possible anyhow? What kind of light out of the three will maximize the visibility of the reflection in this case? | What type of light source—candle, table lamp, or sunlight—would produce the most visible reflection of an object in a 5-liter bucket of shallow water, and why? | 2,380 | cqadupstack-physics |
134138 | How to calculate the kinetic energy of supernova ejecta? | I believed I could use $0.5\times M_{ej} V_{ej}^2$, with $M_{ej}$ being the ejected mass and $V_{ej}$ being the velocity of the ejected mass. But I noticed in this and this that the the mean velocity is somehow calculated as following : $V_{mean}=(3/5)^{0.5}\times V_{ej}$. And so the kinetic energy was calculated as : ... | How can the factor of \( \frac{3}{10} \) in the kinetic energy expression \( \frac{3}{10} \times M_{ej} V_{mean}^2 \) be derived from the mean velocity \( V_{mean} = \sqrt{\frac{3}{5}} \times V_{ej} \), and what implications does this have for understanding the kinetic energy of a mass ejected at varying velocities? | 23,236 | cqadupstack-physics |
73079 | Can we create a small black hole? | Suppose we create very large spherical body by using gamma rays generator and they will concentrate on a single point at the centre of sphere.We will place this spherical body thousands of kms above the sun so that it can draw energy from sun.Can the centre of the sphere create a Mini Black hole by the energy from the ... | If a very large spherical body is created that concentrates gamma rays at its center, and this body is positioned thousands of kilometers above the Sun, what is the minimum energy concentration required in order to form a mini black hole, considering the known equations for black hole formation and the properties of ga... | 8,753 | cqadupstack-physics |
7051 | Are there notable cases of anomalies in the mass-decay rate relationship? | As a general rule of thumb, massive particles (both composite and fundamental) tend to decay rapidly through the weak force, while less massive particles tend to be more stable. Hence, taus are shorter lived than muons, top quarks are shorter lived than charm quarks, and all mesons and baryons except protons and neutro... | What are some examples of particles that exhibit a decay rate that deviates from the expected relationship with their mass according to the Standard Model, and how do their experimental decay rates compare to theoretical predictions? | 1,676 | cqadupstack-physics |
48537 | Energy levels in perturbation theory | Hi guys I have a quick question about perturbation theory in quantum mechanics, particularly about energy shifts. We write: $E_n = E_n^{(0)} + \delta E_n$ where $E_n^{(0)}$ is the unperturbed hamiltonian. If I now have to calculate the first order energy i.e. $E_n^ {(1)}$ I have to calculate $\delta E_n$ to first order... | Given the first-order energy shift in quantum mechanics is calculated using the formula $\delta E_n = \int \psi_n^* \delta H \psi_n \, dx$, if the unperturbed energy level is known to be $E_n^{(0)} = 5 \text{ eV}$ and the integral $\int \psi_n^* \delta H \psi_n \, dx = 1 \text{ eV}$, what is the first-order corrected e... | 24,289 | cqadupstack-physics |
34395 | How does a car turn without any skidding? | The rear wheels of a car always face in the direction the car is moving. The front wheels are able to turn left or right and thus can point in the direction the car is moving towards. What I don't understand is how a car can turn with all four wheels rotating (not skidding). That is, how is it possible that the front t... | How can a car turn smoothly without skidding when its front wheels are aligned in a different direction from its rear wheels, considering all four tires are connected by rigid suspension and are rotating? What are the physical principles that allow for this movement? | 6,673 | cqadupstack-physics |
73953 | Is it correct to say "like poles attract, unlike poles repel" while two magnets are placed such that one is inside another? | As we know a solenoid is considered as a electromagnet(magnet) if there's a current flowing through it. if a soft iron core is placed inside the solenoid, the former get magnetised. Consider the solenoid as a hollow bar magnet, and the magnetised soft iron core inside as a bar magnet. The poles of the magnets next to e... | If a soft iron core is placed inside a solenoid with current flowing through it, how does the interaction between the solenoid and the magnetized core demonstrate the principle that "like poles attract, unlike poles repel"? Specifically, what is the magnetic behavior when the north pole of the solenoid faces the north ... | 3,783 | cqadupstack-physics |
57941 | How large must the Quantum teleportation fidelity have to be in order for it to be useful? | This question relates and stems from my original question. Please read this one and the comments before answering this question. Quantum Teleportation Fidelity I know that for discrete variables quantum teleportation, one needs a fidelity greater than 50%, otherwise you could produce that state by classical means. For ... | What is the minimum fidelity required for quantum teleportation to be considered practically useful in terms of transferring the quantum state of a diatomic molecule, given that a 97% fidelity might yield similar behaviors due to environmental interactions? | 23,844 | cqadupstack-physics |
6887 | effective theory of graphene | This is a question about deriving effective mass theory for graphene. For the two sub-lattice atoms, the wave equation can be written as the massless Dirac equation: $ \displaystyle -i\hbar v_F \begin{pmatrix} 0 & \partial_x -i\partial_y \\\\\partial_x +i\partial_y & 0 \end{pmatrix} \left(\begin{array}{c} \Psi_A \\\ \P... | What is the effective mass of charge carriers in graphene, and how is it derived from the massless Dirac equation? Please provide a brief explanation of the physical implications of this result. | 27,427 | cqadupstack-physics |
131013 | Will the Universe eventually stop expanding | Sorry if this is a naive question, not being even a part qualified physicist in any way shape or form. I've read that the universe is expanding and the rate of expansion is increasing. The assumption being that it will continue expanding indefinitely. However isn't there another possibility. Let me illustrate my questi... | What are the conditions under which a universe experiencing an initial phase of acceleration might eventually transition to a phase of deceleration and subsequent contraction, and what current cosmological models would support or refute this possibility? | 27,856 | cqadupstack-physics |
5224 | Why is it necessary to represent Schrodinger's equation as a partial differential equation? | The Schrodinger equation governs the possible time evolution of a wave function, expressed as a partial differential equation. Isn't this equivalent to the simpler equation $$\omega = \hbar k^2/2m$$ i.e. any wave function that satisfies this dispersion relation will also satisfy Schrodinger's equation, and the equation... | Given the dispersion relation $$\omega = \frac{\hbar k^2}{2m}$$, derive the corresponding wave function that satisfies the Schrödinger equation for a free particle and identify the conditions under which this wave function is normalized. | 19,233 | cqadupstack-physics |
113006 | Is $4 \pi G$ the true most fundamental gravitational constant? | Newton's law of gravitation is: $$F = G m_1 m_2 \frac{1}{r^2}$$ It looks simple and natural. But that's only in 3 dimensions. Let's look what happens in $n$ dimensions: $$n=2 : F = 2 G m_1 m_2 \frac{1}{r}$$ $$n=4 : F = \frac{2}{\pi} G m_1 m_2 \frac{1}{r^3}$$ $$n=5 : F = \frac{3}{2 \pi^2} G m_1 m_2 \frac{1}{r^4}$$ $$n=6... | Calculate the gravitational force \( F \) between two masses \( m_1 \) and \( m_2 \) at a distance \( r \) in five-dimensional space, given that the gravitational constant is defined as \( G^* = 4 \pi G \). Use the surface area formula for a five-dimensional sphere in your calculations. | 3,609 | cqadupstack-physics |
102625 | How do magnetic objects exhibit attraction/repulsion across empty space? | Magnets will attract or repel over a distance before physically touching each other. What makes this effect possible? My best guess is that the forces generated by the angular momentum of the electrons in the outer shell produce a "wind" of force that is similar to the draft you feel when a fast moving object passes yo... | What is the principle behind magnetic forces that allows magnets to attract or repel each other at a distance before physical contact, and how can this phenomenon be quantitatively measured in terms of magnetic field strength? | 2,529 | cqadupstack-physics |
111743 | Is there an equation to calculate the average speed of liquid molecules? | I seem to remember from first year physics that we can calculate the RMS speed of a stationary, ideal gas with $v=\sqrt{\frac{3RT}{M}}$. Does a similar equation exist for liquids? | Is there an equivalent formula for calculating the average speed of molecules in a liquid, similar to the RMS speed equation for gases, and if so, what factors does it depend on? | 14,091 | cqadupstack-physics |
31552 | Dirac equation as canonical quantization? | First of all, I'm not a physicist, I'm mathematics phd student, but I have one elementary physical question and was not able to find answer in standard textbooks. Motivation is quite simple: let me fix some finite dimensional vector space $V$. Then we can think about Clifford algebra $Cl(V \oplus V^*)$ as algebra of od... | Is it possible to construct a Lagrangian for a classical fermionic field on spacetime \(\mathbb{R}^{3,1}\) such that the canonical quantization of this field results in the Dirac operator as the quantum Hamiltonian? If so, what would the form of this Lagrangian be? | 30,174 | cqadupstack-physics |
94631 | Understanding voltage | I understand that water flows because of height difference and current flows because of potential dfference. Now, in this analogy, I can understand height but I fail to realise what potential is. Is it the number of electrons? Say, A has 10 electrons, B has 20 and C has 100 electrons. So, can I say AC has more potentia... | If point A has 10 electrons, point B has 20 electrons, and point C has 100 electrons, how would you calculate the potential difference between points A and B, and between points A and C, based on the concept of electric potential? Additionally, which point has the highest electric potential, and why? | 9,234 | cqadupstack-physics |
127004 | is there a metatime required for space-time to change | Space- **time** is thought to curve and ripple. Is a kind of metatime required in or during which such events take place? | Given that space-time is described as curving and rippling, calculate the potential energy of a test mass m placed in a fluctuating gravitational field generated by such curvatures. Assume the mass experiences a gravitational acceleration of g = 9.81 m/s². What would be the potential energy at a height h of 10 meters? | 501 | cqadupstack-physics |
14753 | Old Russian Physics Papers? | Where can one find old Russian scientific papers in physics, say, in the Proceedings of the Russian Academy of Sciences or Zhurnal Eksperimentalnoy i Teoreticheskoy Fiziki? Can they be found online somewhere? | What is the total number of old Russian scientific papers on physics published in the Proceedings of the Russian Academy of Sciences and the Zhurnal Eksperimentalnoy i Teoreticheskoy Fiziki that are currently available online? | 30,059 | cqadupstack-physics |
10463 | Understanding the cause of sidebands in Amplitude Modulation | I've read it many places that Amplitude Modulation produces sidebands in the frequency domain. But as best as I can imagine it, modulating the amplitude of a fixed-frequency carrier wave just makes that "louder" or "quieter", not higher-frequency or lower-frequency. That is, I believe I could sketch, on graph paper, a ... | When a carrier wave is amplitude modulated with a signal frequency \(f_m\), what are the frequencies of the upper and lower sidebands produced in the frequency domain? Provide your answer in terms of the carrier frequency \(f_c\) and the modulating frequency \(f_m\). | 33,407 | cqadupstack-physics |
103328 | Effect of linear terms on a QFT | I was always told when first learning QFT that linear terms in the Lagrangian are harmless and we can essentially just ignore them. However, I've recently seen in the linear sigma model, \begin{equation} {\cal L} = \frac{1}{2} \partial _\mu \phi _i \phi ^\mu \phi _i - \frac{m ^2 }{2} \phi _i \phi _i - \frac{ \lambda }{... | In the context of the linear sigma model with the Lagrangian given by \(\mathcal{L} = \frac{1}{2} \partial_\mu \phi_i \partial^\mu \phi_i - \frac{m^2}{2} \phi_i \phi_i - \frac{\lambda}{4} (\phi_i \phi_i)^2\) where \(m^2 = -\mu^2 > 0\), what are the implications of adding a linear term in one of the fields \(\phi_N\) on... | 7,416 | cqadupstack-physics |
82644 | Does pure electric dipole have higher order moments? | Of course for the standard configuration(i.e. two opposite charges separated by some distance), there exist higher order multipole moments. However for an ideal dipole(those dipoles associated with point mass, which means the separation is zero), are there any higher order moments? | For an ideal dipole, characterized by zero separation between two point charges, are there any higher-order multipole moments that can be defined, and if so, what implications do they have on the dipole's field? | 27,026 | cqadupstack-physics |
108503 | Approximation of skeleton diagrams | I'm studying the diagrammatics for a Bose system (in the superfluid phase) developed by Gavoret and Nozieres (Annals of Physics 28 349 (1964)). In this paper, they show how to solve the problem using skeleton diagrams. In other words, they give equations for the two-point, three-point and four-point functions, involvin... | In the context of skeletal diagrams for a Bose system in the superfluid phase, how can one systematically approximate the skeleton diagrams to recover Bogoliubov theory, while ensuring that conservation laws are still respected? Specifically, could you outline the steps or techniques needed to achieve this approximatio... | 4,982 | cqadupstack-physics |
23049 | How to express the heat capacity in terms of heat? | The first law of thermodynamics divides the internal energy change into contributions of heat and work. $$\text dU=\omega_Q-\omega_W,$$ Here I chose the notation to emphasise that the two parts are in general not exact differentials, i.e. that there is no heat counting function. > What would be the proper way to expres... | How do you express the heat capacity \( C_V \) in terms of the heat transfer \( \omega_Q \) given that the first law of thermodynamics states \( \text dU = \omega_Q - \omega_W \)? | 18,147 | cqadupstack-physics |
20335 | Costa Concordia shipwreck: why can't they right the ship with pingpong balls? | So I guess I don't really understand the situation in question... I heard a radio piece about the Costa Concordia shipwreck in Italy taking 7-10 months to remove the vessel from its place of resting, and I was reminded of the Donald- Duck-ping-pong-balls-solution for raising a sunken ship. How come they're not using th... | What are the key physical and structural challenges that would make the "ping-pong ball" method impractical for raising a large cruise ship like the Costa Concordia compared to a smaller object? | 14,269 | cqadupstack-physics |
12290 | A moderate introduction to Hanbury Brown Twiss interferometry in particle physics | For astronomy, as originally invented, the Hanbury Brown Twiss interferometer is good for finding the angular diameter of stars and is not a rapidly fluctuating observable like the amplitude in ordinary interferometry. The same concept in particle physics is not so straightforward. When I measure the 2 particle correla... | How does the Hanbury Brown and Twiss interferometry technique allow for the determination of the angular diameter of stars, and what are the implications of measuring two-particle correlations in particle physics? | 15,283 | cqadupstack-physics |
89307 | How does the expectation value of the square of angular momentum transform under translations? | In quantum mechanics the angular momentum operator is defined as $$ \mathbf{\hat L}=\mathbf{\hat x} \times \mathbf{ \hat p} $$ This definition explicitly depends on the choice of the origin of the coordinate system. For a state $|\psi\rangle$ that does not move, i.e. has a vanishing expectation value of momentum, it is... | In the context of the hydrogen atom problem, how does the expectation value of the square of the angular momentum operator, $\langle \psi | \mathbf{\hat L^2} |\psi\rangle$, change when the origin of the coordinate system is shifted to a point located a distance \( r_0 \) from the nucleus? Specifically, calculate this e... | 27,569 | cqadupstack-physics |
40957 | Number of Grassmann generators for Dirac field? | How many Grassmann generators are sufficient for the description of a Dirac spinor in 4 dimensions? _i.e._ The Dirac field is a map to $\Lambda_N$, the space of supernumbers with $N$ real Grassmann generators. What is $N$? This is a follow up question to my previous question Grassmann Paradox Weirdness. I am following ... | How many Grassmann generators \( N \) are required to describe a Dirac spinor in 4 dimensions, given that the Dirac field is represented as a map to \(\Lambda_N\), the space of supernumbers? | 13,287 | cqadupstack-physics |
112679 | Classical and Semi-classical treatments of the ideal gas | In the semi-classical treatment of the ideal gas, we write the partition function for the system as $$Z = \frac{Z(1)^N}{N!}$$ where $Z(1)$ is the single particle partition function and $N$ is the number of particles. It is semi-classical in the sense that we consider the indistinguishability of the particles, so we div... | Calculate the difference in entropy between a monatomic ideal gas and a diatomic ideal gas at room temperature, using the provided entropy formulas for each case. What does this difference indicate about the relationship between the degrees of freedom for monatomic and diatomic molecules, and how does it manifest in th... | 17,536 | cqadupstack-physics |
52778 | Charged quantum particle in a magnetic field - choosing a different gauge leads to different wavefunctions | Consider a charged quantum particle confined to the $xy$ plane, subject to a magnetic field $\mathbf{B}=B\hat{z}$. The Hamiltonian is: $$ H = \frac{1}{2m} \left( \mathbf{p} - \frac{e \mathbf{A}}{c}\right)^2~, $$ where $\mathbf{A}$ is the vector potential, for which we have a freedom of gauge in choosing. One possible... | What is the relationship between the gauge choices for the vector potential \(\mathbf{A}\) in a magnetic field and how do the resulting wavefunctions \(\psi(x,y)\) for a charged quantum particle reflect this relationship? Specifically, can you demonstrate that while the expressions for \(\psi(x,y)\) appear different, t... | 30,937 | cqadupstack-physics |
59929 | What prevents bosons from occupying the same location? | The Pauli exclusion principle states that no two fermions can share identical quantum states. Bosons, one the other hand, face no such prohibition. This allows multiple bosons to essentially occupy the same space, a phenomenon that has been theorized responsible for superconductivity. Bosons do not, however, occupy exa... | What physical principles or characteristics of bosons prevent them from occupying the exact same position in space, and how do these principles contribute to phenomena such as Bose-Einstein condensation? | 19,463 | cqadupstack-physics |
59729 | Is a purely vertical or almost vertical orbital launch possible? | Is it possible, for the sake of argument, to launch a payload into an orbit around the earth by putting almost all the energy going at a 90 degree angle? What velocity would it take, and what horizontal orbital burns would you need? | What is the minimum velocity required to launch a payload into a stable low Earth orbit by initially applying thrust at a 90-degree angle to the surface, and what subsequent horizontal velocity adjustments would be necessary to achieve and maintain that orbit? | 15,384 | cqadupstack-physics |
95982 | What force keeps electrostatic charge from exiting a metals surface | I understand that in electrostatics all charges are 'static' due to equal forces acting upon them. This then leads to the fact that the arising electric field must be perpendicular to the metals surface at the surface. What i don't understand is what force is counteracting the electric field. I have read that there is ... | In the context of electrostatics, how does the concept of electric field perpendicularity at a metal surface relate to the forces acting on free charges in equilibrium? Specifically, calculate the magnitude of the electric field at the surface of a charged conductor with a surface charge density of \( \sigma \). What i... | 23,552 | cqadupstack-physics |
62003 | Why is the Planck length the shortest measurable length? | I quote from the Wikipedia article on Planck length: > _According to the generalized uncertainty principle, the Planck length is in > principle, within a factor of order unity, the shortest measurable length – > and no improvements in measurement instruments could change that._ I also link to an answer provided to this... | Is the Planck length (approximately \(1.6 \times 10^{-35}\) meters) the smallest measurable length in physics, and can this be derived from the principles of quantum mechanics and the uncertainty principle? If so, provide a simplified explanation of the reasoning or proof behind this assertion. | 26,423 | cqadupstack-physics |
117266 | Would it really require 44 car batteries to heat my pool? | After doing some research and math, I 'discovered' that it would take 44 (give or take 20%) car batteries to heat 1,000 gallon pool by 10 degrees. Is this right or am I missing something? It seems a little crazy! * It takes 8.3 BTUs to heat one gallon of water 1 degree F. * Thats 83,000 BTUs to heat the entire pool... | How many car batteries would be required to heat a 1,000-gallon pool by 10 degrees Fahrenheit, given that it takes 8.3 BTUs to heat one gallon of water by 1 degree Fahrenheit and that a car battery holds 2,000,000 joules (which is approximately 1,900 BTUs)? | 35,113 | cqadupstack-physics |
54334 | What are the units of the Bekenstein bound? | Working with the Wikipedia definition of the Bekenstein bound: $S \leq \frac{2 \pi R k_bE}{\hbar c}$ $2\pi R \ $ is $m^2$ $k_b$ is $\frac{J}{K}$ $E$ is $J$ $\hbar$ is $J*s$ $c$ is $\frac{m}{s}$ $\frac{m^2 \frac{J}{K} J}{(Js \frac{m}{s})} = m \frac{J}{K}$ Am I overlooking something? | Calculate the maximum entropy \( S \) that can be contained within a spherical region of radius \( R = 1 \, \text{m} \) when the energy \( E = 1 \, \text{J} \) is confined inside it. Use the Bekenstein bound formula \( S \leq \frac{2 \pi R k_b E}{\hbar c} \) and provide your answer in joules per kelvin (\( J/K \)). Giv... | 13,642 | cqadupstack-physics |
54491 | Can the speed of an electromagnetic wave be measured in the absence of neutrinos? | Let me explain better: from what I understand neutrinos are so pervasive they are literally everywhere. And since they have such a tiny electric charge they barely interact with anything and cannot be "removed" or "shielded" from an area in order to take a measurement of light speed in their absence. However, all three... | What is the estimated average number of neutrinos passing through a human body every second, and how does this vast number of neutrinos relate to the measurement of the speed of light? | 9,775 | cqadupstack-physics |
103458 | Definition of a non-pertubative Quantum field theory | How do you define a non-perturbative Quantum field theory. What does it mean? I was just digging around some math about the meaning of $Z_1$, and such in terms of probabilities. It turns out these and associated counter terms are derived via perturbation theory. So the question is , if you associate meaning to things l... | What are the main differences in the description of self-interacting quantum fields in non-perturbative quantum field theory compared to perturbative quantum field theory, and can you provide an example of a non-perturbative model that illustrates these differences? | 9,040 | cqadupstack-physics |
4789 | What is the usefulness of the Wigner-Eckart theorem? | I am doing some self-study in between undergrad and grad school and I came across the beastly Wigner-Eckart theorem in Sakurai's _Modern Quantum Mechanics._ I was wondering if someone could tell me why it is useful and perhaps just help me understand a bit more about it. I have had two years of undergrad mechanics and ... | Consider a quantum system with a total angular momentum quantum number \( j = 3/2 \). Using the Wigner-Eckart theorem, determine the matrix element \( \langle j', m' | T^{(k)}_q | j, m \rangle \) for a tensor operator \( T^{(1)}_1 \) that connects state \( | j = 3/2, m = 3/2 \rangle \) to \( | j' = 3/2, m' = 1/2 \rangl... | 11,341 | cqadupstack-physics |
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