Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why is the South Pole Telescope located exactly at the South Pole? I read that there is less atmospheric interference for the telescope at the South Pole because the atmosphere is thin and there is less water vapor in the air. However this seems to be true for many locations on Antarctica? Are there any other reasons t... | There is no scientific reason that the South Pole Telescope is located so close (within a few 100 meters, really) of the geographic south pole. It might as well be located a few hundred miles to either direction, no difference.
The reason is purely practical: On the South Pole, there exists very significant infrastruct... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/327190",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "22",
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Green's function approach in Tight-Binding I am studying single-particle Green's functions using Economou's textbook, and am interested in using them to calculate surface states in tight-binding models. What I don't really understand is what benefit the Green's function method provides Green, as opposed to just using t... | One example quantity that one would like to know from a given Hamiltonian
is the density-of-states (DOS), which is related directly to measurable quantities, e.g. conductance. Instead of diagonalizing the Hamiltonian
to know the DOS, the trace of the imaginary part of the Green function then
gives the DOS.
By the wa... | {
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"source": "stackexchange",
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When the angle of incidence is less than the critical angle, why is some light still reflected? When the angle of incidence is less than the critical angle, why is some light still reflected? When the angle of incidence is greater than the critical all light is reflected, why is not all light transmitted when it's less... | Light is an electromagnetic wave, and as such is governed by the Maxwell equations. These equations (considering only the linear mediums 1 and 2) give certain boundary conditions:
$$
(\text{i})\ \epsilon_1E^{\perp}_1=\epsilon_2E^{\perp}_2\ \ ;\ \ (\text{ii})\ \bf{E}^{\parallel}_1=\bf{E}^{\parallel}_2
$$
$$
(\text{iii}... | {
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What is the difference between $\psi$ and $|\psi\rangle$? My understanding is that $\psi(\vec{r}, t)$ and $|\psi(\vec r,t)\rangle$ are the same thing yet one expressed as a wave function and the other expressed as a vector in the Hilbert space. Is this true? Or is there a deeper difference between the two notations?
| Velut Luna gives the main answer. One can see this because we have the probability expectation $1~=~\langle\psi(t)|\psi(t)\rangle$ and with the completion sum $\mathbb I~=~\int d^3r|\vec r\rangle\langle \vec r|$ we then have
$$
1~=~\langle\psi(t)|\psi(t)\rangle~=~\langle\psi(t)|\left(\int d^3r|\vec r\rangle\langle\vec ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/328055",
"timestamp": "2023-03-29T00:00:00",
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What determines invariant mass? The only answer I have been able to find is that energy determines mass but photons have energy yet are still massless. Furthermore this then leads to the question of what determines invariant energy, which I would think to be mass. So in total what are the circumstances that determine f... | Very succinctly: a system's total energy, as measured from its rest frame, is the invariant mass. The rest frame is determined by the frame wherein a system's total momentum is nought.
You are probably a little confused by the photon and other so-called massless objects. Such objects are always measured to have a speed... | {
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Are there superconformal field theories in 10D? I've heard that there is a belief that interacting conformal field theories do not exist in dimensions greater than 6, and in 6D the only known nontrivial CFTs are superconformal field theories. What is the argument that these theories can't exist in higher dimensions? ... | As said in the comments, there are no superconformal field theories in $D>6$ dimensions. The references for this result are
*
*Werner Nahm, Supersymmetries and their Representations, Nucl.Phys. B135 (1978) 149.
*Shiraz Minwalla, Restrictions imposed by superconformal invariance on quantum field theories, Adv. The... | {
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Partial Derivatives Relation on Thermodynamics and minus sign
My problem is to show that
$$ \left( \frac{\partial C_{V}}{\partial V} \right)_{T} = -T \left[ \frac{\partial (\alpha/\kappa_{T})}{\partial T} \right]_{V}$$
where
$C_{V}$ is molar specific heat capacity of constant volume and $$\alpha := \frac{1}{V}... | I started with $$dU=C_vdT-\left[P-T\left(\frac{\partial P}{\partial T}\right)_V\right]dV$$ So, $$\frac{\partial ^2U}{\partial T \partial V}=\left(\frac{\partial C_v}{\partial V}\right)_T=-\left(
\frac{\partial \left[P-T\left(\frac{\partial P}{\partial T}\right)_V\right]}{\partial T}\right)_V$$
The rest is easy.
| {
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Could a planet with a strong magnetic field exert a diamagnetic force on an orbiting moon? Here is a question from the world building stack exchange.
https://worldbuilding.stackexchange.com/questions/79003/making-a-slow-orbit-around-a-large-gas-giant
Requested: a means to have a moon of Jupiter orbit closely but slowly... | May be if the satellite have some electric charge the Lorentz's force applies, and act in the radial direction.
I think that to have a diamagnetic satellite has any effect in radial acceleration, may be in $\hat{\phi}$ direction (in spherical coordinate system with the origin in Jupiter's center).
| {
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Why energy corresponding to most probable speed is not equal to most probable energy? According to Maxwell speed distribution of molecules of gas at temperature $T$, most probable speed is given by
$$v=\sqrt{\frac{2kT}{m}} \, .$$
The corresponding energy is
$$E= kT \, . $$
According to the Maxwell Boltzmann energy di... | Lets think about exactly what the Maxwell-Boltzmann distribution tells us. If we are being lazy we might say that it gives us the probability that a particle has a speed $v$, however since $v$ can take a continuous range of values, the probability that it takes any given value is $0$. Instead we say that it gives us th... | {
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Crash simulation on Mythbusters I remember an episode of mythbusters where they were busting myths to do with a head on collision between two cars.
They said that instead of crashing two cars into each other at 50mph they would crash a car into a stationary object at 100mph because the energy involved in the crash woul... | The Mythbusters hosts realized that the important issue in a head-on collision is what is happening inside your vehicle. There is indeed twice the kinetic energy involved with one car colliding with an immovable object at 80 mph vs. two cars colliding head-on at 40 mph. However, Newton's third law requires the immova... | {
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"url": "https://physics.stackexchange.com/questions/329831",
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Monopole Spherical Harmonics I was following Yakov Shnir his book about magnetic monopoles, there they derive the monopole spherical harmonics. I will sketch the derivation briefly,
The starting equation is the eigenvalue problem of the total angular momentum,
\begin{align}
\hat{\textbf{J}}^2 Y_{\mu lm}(\theta, \phi) ... | This is not a direct answer to the question asked, but rather a different approach to the problem. It's much easier to derive the monopole harmonics from a geometric consideration of the Hopf map ${\rm Hopf}: S^3\to S^2$, which is the same thing as the Hopf bundle $\pi: {\rm SU}(2) \to {\rm SU}(2)/{\rm U}(1)$. Then ... | {
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Is Frobscottle from the movie 'The BFG' less dense than air? For those who have either read the book, or watched the movie "The BFG", you would know Frobscottle as a green drink the giant uses, and has bubbles fizzing "in the wrong way", which is downwards. Assuming the bubbles to be filled with air, and that gravitati... | It implies that the author made it up without worrying about physics. If Frobscottle was less dense that air, it wouldn't stay in a cup. It would float like a helium balloon.
There is a liquid less dense than air, but it is nothing you could put air bubbles in. It is 3 monolayers of $He^3$ adsorbed on graphite at temp... | {
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Bell Inequalities - Expectation Values I'm currently reading Loopholes in Bell Inequality Tests of Local Realism by Jan-Ake Larsson
https://arxiv.org/abs/1407.0363
On Page 6, Equation 7, he has a short proof, where I am having a hard time seeing through the math. I'll re-state here for convenience:
$ \lvert E(A_{2}B_{... | From 2nd to 3rd expression:
It is well known that:
$$\left|\int f(x)dx\right| \leq \int \left|f(x)\right| dx.$$
Here you can find the reference for this fact.
Now, you have that:
$$\lvert E(A_{2}B_{1} + A_{2}B_{1}A_{1}B_{2}) \rvert = \left|\int (A_{2}B_{1} + A_{2}B_{1}A_{1}B_{2})\rho(\lambda)d\lambda \right| \leq \\
\l... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Friction on cars It is known that friction is given as :
$F_{friction}=\mu F_n$ , where $F_n$ is the normal force, and $\mu$ is coefficient of friction.
For a car travelling down a hill with constant velocity, the component of the gravitational force which is parallel to the cars velocity must be equal and opposite to ... | When your wheel is powered by the engine the wheel pushes backward and reactionary friction force opposing this pushes your car forward.Same as the case when we walk.The feet push backwards and the reactionary frictional force pushes us forward.The friction is in a direction opposite to the direction we are pushing in ... | {
"language": "en",
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Does an increase in entropy always result in an increase in heat, or can there be increased entropy without an increase in heat? Most situations I can think of where entropy increases also results in an increase in heat, but just wondering if that is a rule. Are there any cases where heat does not increase with entropy... | Your question has one unclear definition: heat. I guess that is temperature.
Here is one simple example. A box is filled with gas and the box wall is well insulated. If, somehow, the box volume can be doubled, the entropy increases and the gas temperature decreases.
| {
"language": "en",
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Metamaterial : Snell's law and Fermat principle How do we deduce Snell's law using Fermat's principal in case of metamaterials? Metamaterials have negative refractive index. This makes the refracted ray of light bend on same side of normal as incident ray. But according to Fermat principle, the light could have take... | What is the "travel time" of a beam of light in a medium with negative refractive index? Do you save time by traveling a greater distance? Time = distance/speed, and speed = c/n. When $n<0$, the part of the trajectory in the meta-material will contribute "negative time" to the over all travel time of the beam.
Remember... | {
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Does energy conservation implies the mass conservation? According to Noether's theorem, every symmetry implies and conserved quantity. And, from Einstein's equation, every mass have an amount of energy associated.
Can it say that the mass conservation is a consequence of energy conservation associated to homogeneity of... | In classical mechanics mass is conserved, conservation of mass is not valid in relativistic physics unless you consider the so-called "invariant mass" of a closed system. The sum of the masses of particles can change due to interactions. In classical mechanics this sum of masses is conserved and this follows from conse... | {
"language": "en",
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How are the constants for the NFW profile determined? I'm trying to understand the NFW profile and how it causes a flat rotation curve.
$$ \rho(r) = \frac{\rho_0}{\frac{r}{r_s}\left(1+\frac{r}{r_s}\right)^2} $$
I think I've got why it causes a flat rotation curve. The density seems to be inversely proportional to $r^3... | Why does it matter what their values are? $r_s$ is some characteristic scale length of the system where it switches from a $r^{-1}$ dependence to a $r^{-3}$ dependence and $\rho_0$ is a normalisation constant that ensures that the total mass within some radius is correct.
The values of these constants are obtained by f... | {
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What is the energy of a single charge system? I will try to limit the question in the case of the electric fields, but is something that applies also to the magnetic ones.
There are two ways to express the energy in a capacitor:
*
*By Voltage : $U = 1/2 CV^2 $
*And by Field : $U = 1/2 \varepsilon E^2Ad$, With Ener... | Besides the things mentioned in the other answers, here is one more thing to consider:
The energy of the single charge at some point in space can be thought of as arrived at by starting with an infinitesimal charge, and adding (from infinity) a little bit of charge. That will take a little bit of work. The next bit of ... | {
"language": "en",
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Size of mercury barometer and effect on its reading I was thinking that since atmospheric pressure is 760mmHg what would happen if I shrink a mercury barometer until it's shorter that 760mm in height. What would happen? Would the barometer retain it's ratio of mercury height? Will the mercury fully fill the barometer? ... | A vacuum must exist above the meniscus of the column so that the mercury
can rise above 760mm (or 30 in.) which is what a mercury barometer reads
at sea level. In other words, the mercury column needs headroom to rise
with increasing ambient atmospheric pressure.
A barometer capillary tube with a ball pediment cistern... | {
"language": "en",
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Why young modulus value doesn't change even if we change the parameters? The Young modulus of steel is determined using a length of steel wire and is found to have the value EE. Another experiment is carried out using a wire of the same steel, but of half the length and half the diameter.
What value is obtained for the... | Young's Modulus is measuring the ratio of stress to strain.
Stress is a measure of the forces in a material. It has units of force per unit area. This is the reason why changing the diameter does not affect the experiment. If the wire is thinner you may have to apply a different force to get the same strain (elongat... | {
"language": "en",
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Field due to internal Induced charge on a conductor to an external point? A charge q is located at a distance r from the center of a conducting sphere with inner radius 2r. The charge induces charges on the inner surface of the sphere according to Gauss' law .
The electric field at point p is to be approximated.
Inside... | The electric field at the point P is solely due to the charges on the outer surface of the sphere [Suppose this was not true, for the sake of contradiction.The only way this can happen is if the magnitude of induced charge on the inner surface of the sphere is not equal to the q itself.If this happens, then by Gauss' l... | {
"language": "en",
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Gauss Law Doubt I have a doubt regarding whether or not I can take a spherical surface as a Gaussian surface when the taken Gaussian surface completely overlaps a symmetrical spherical charge distribution of same radius.
Won't it violate the fact that a Gaussian surface can not have charges on it.
Or would be okay for ... | Gaussian surface is an imaginary plane which we draw so that we would know how much of electric field lines are passing through that imaginary area we took(flux).Hence it will give perfectly correct answer. This can sbe proved by using Coulombs law and Gaussian law for the same surface
And the charge "+q" is already... | {
"language": "en",
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Why do colours of object change due to incident light? A leaf is green, a pen is blue and so on because those objects absorb all colours and reflect only one colour. However when red light is incident on these objects, their colour becomes reddish. Why is that the case?
| In an ideal situation, i.e. if
*
*really all colors except one are absorbed
*your red light is perfect (one wavelength)
the objects should actually appear black, i.e. no light is reflected.
In the real world a blue pen will reflect a small amount of red (and other colors). That's why it appears reddish if you sh... | {
"language": "en",
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Does this make sense from mass-energy equivalence standpoint? Over the weekend I was (in over my head) discussing mass/energy and I proposed this thought experiment.
Given two separate but equal quantities of matter - one being wood, the other being gasoline - do they both have the same total energy? I am being assured... | What is storing energy?
There is a mass-energy equivalence, which since they have the same mass is equal. We have no idea how to get anything but trivial fractions of this energy through the below mechanisms.
There are nuclear bonds, which since they are both mostly hydrocarbons are probably pretty similar, though havi... | {
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Would a handspinner spin indefinitly in space? I'm having a argument with a colleague, I don't know how to explain to him that if you spin a handspinner in space it will spin indefinitly (if you don't hold it). I agree that if you hold it, it will slow down because of the friction with the center part.
Would it theoret... | Space is not a perfect vacuum, there are gases, electromagnetic fields and so on. The rotating object would be slowing down its rotation and in time, its motion will get erratic, driven by fluctuations of the environment.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/332646",
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How to evaluate the critical exponents of modified van der Waals equation? The given modified van der Waals equation is $$(P+(a/v)^{n})(v-b)=RT$$ where $(n>1)$. What is the physical significance of the power $n$ in the above equation. How could one evaluate the critical constants and exponents for this modified equatio... | The modified Van Der Walls Equation is
$(P+\frac{an^2}{V^2})(V-nb)=nRT$......... $(1)$
where $a$ is a Van Der Walls constant whose value depends upon intramolecular forces of attraction within the gas. $b$ is the correction term for Volume of gas.
Putting $n=1$ in $(1)$,
$(P+\frac{a}{V^2})(V-b)=RT$......... $(1)$ or... | {
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Master Equation under a classical fluctuating noise I have a system as a qubit with Hamiltonian
$H_S = \frac{\Delta}{2}\sigma_z$
The interaction Hamiltonian is
$H_I = \frac{V(t)}{2}\sigma_z$ where $V(t)$ is a stochastic fluctuating variable. One can for example assume it as a random telegraph noise(RTN). In this case, ... | The book by Klyatskin discusses general functional methods for dealing with gaussian and telegraph noises.
However, let me make a few general remarks:
*
*Telegraph noise is not delta-correlated (white), which means that one would get an integral equation, rather than usual master equation.
*Including noise as an ext... | {
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Correct definition of an 'acoustic mode'? I am reading 'The Oxford Solid State Basics' by S.H.Simon in which on page 92 defines an acoustic mode as:
... any mode that has linear dispersion as $k\rightarrow 0$.
Whilst on page 94 he defines it as:
... one mode will be acoustic (goes to zero energy at $k=0$).
Unless a... | No, one does not imply the other, and I disagree with the first definition.
For example, the dispersion relation of the ZA mode in graphene goes to zero like $x^2$, so energy goes to zero as $k \to 0$ but does not do so linearly.
The 'A' in 'ZA' stands for acoustic, so that's an example of a nonlinear acoustic mode.
(T... | {
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How to explain the relationship between wave's amplitude and intensity? I have the following statement which I don't know how to explain:
Suppose I have 2 identical monochromatic waves (same intensity and phase) shooting into the same receiver. If each wave's intensity is I, based on energy conservation I would expect ... | Your initial assumption that you can simply sum intensity (power) is incorrect.
The law of superposition of Maxwell's equations says that you can sum electric fields and magnetic fields -- or voltage and current in a transmission line or circuit context. So if you consider total voltage $V(t)=V_1(t)+V_2(t)$ and total ... | {
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How to calculate altitude from current temperature and pressure? In a certain project, I need to calculate the altitude of the current location given the current location temperature and current location pressure. Temperature, pressure and altitude of a 'reference-level' could be provided if necessary (using a fixed se... | All these formulas are actually equivalent when $P_b = P_0$, $T_b = 273.15 + T$, $T = 15$, $h_b = 0$ (sea-level), $L_b = -0.0065$ the standard lapse rate, and hence $\frac{g_0M}{R^*L_b} = -5.25579$.
| {
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Where does the force actual act?
Why are the two mass of $m_1$ and $m_2$ not multiplied by minus one?
I know that two minus multiplied gives you plus by but I mean the two masses are attracting so they should have a sign like so $$F_g=\frac{G(-m_1) \times (-m_2)}{r^2}$$
I ask these because equation would actual give t... |
but I mean the two masses are attracting so they should have a sign like so $F_g=\frac{G(-m_1) \times (-m_2)}{r^2}$
I am not following the logic. Attraction implies reduction in distance, and not reduction in mass. Therefore the distance related quantities should contain the negative and not the mass ones. Maybe if y... | {
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Experimental proof pions are pseudoscalar particles In nuclear physics lessons I've been taught that pions are pseudoscalar particles and thus their intrinsic parity is odd. The professor said that an experimental proof of this can be derived observing the process:
$$
\pi^- + D \quad \longrightarrow \quad n + n
$$
w... | The answer is based on a comment by Cosmas Zachos.
The pion has no spin, and so can't flip the spin of either nucleon in the deuteron. The nucleons in the deuteron have their spins aligned ($S=1$), so the two neutrons in the final state must be in a spin triplet as well. In order for the final two neutrons to be antisy... | {
"language": "en",
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Easily approximate center of mass of a person when sitting What is the simplest way to get the center of mass of a human body when sitting? I'm especially interested in getting this when sitting in a chair, so this center of mass would include the chair. I'm trying to make an exercise device for myself that attaches ... | This link should help:
https://www.faa.gov/data_research/research/med_humanfacs/oamtechreports/1960s/media/AM62-14.pdf
For a natural sitting position with hands in the lap, the center of gravity is about (from what I can make out from the text - it is not clear) 8 3/8" and 9 1/8" from the horizontal and vertical refere... | {
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Time-dependent harmonic oscillator I am dealing with the problem to solve the following Schroedinger equation:
$$i\hslash\partial_{t} \Psi = ( -\nabla^2 +w^2(t) )\Psi$$
where the frequency of the oscillator depends on time. I tried to resolve it by using the Kruskal approach, as described in the following paper
"An ... | (No mass term and no factors of 1/2? It is weird to me that you included $\hbar$ and not these other factors)
It seems like you may be able to use separation of variables. Just assume (I am going to just use 1 dimension right now as it should be the same process for 3)
$$\Psi = \psi(t)\phi(x)$$
This gives:
$$i \hbar... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How does the addition of two wavefunctions develop in time? Two time dependent wavefunctions:
$\Psi _1(t)= \psi_1*exp(\frac{-i * E_1}{\hbar}*t)$
$\Psi _2(t)= \psi_2*exp(\frac{-i * E_2}{\hbar}*t)$
Both a solution to the timeindependent (note "in") Schrödinger eq. with the same H. We know they are solutions. Furthermore ... | You obviously mean that
$$\begin{aligned}
H\psi_1 &= E_1\psi_1,\\
H\psi_2 &= E_2\psi_2.
\end{aligned}$$
Then, the solution of the Schrödinger equation (I will use units such that $\hbar=1$ throughout: old habit of a former theoretical physicist!!)
$$H\Psi_k = i\dfrac{\partial \Psi_k}{\partial t}$$
with the initial con... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/334368",
"timestamp": "2023-03-29T00:00:00",
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Are all atomic collisions elastic? If this is the case, why? In kinetic theory of gases it is considered all atomic collisions to be elastic. But if collisions are non-elastic the molecules must lose energy.
|
Are all atomic collisions elastic? If this is the case, why?
No, this is one of the key approximations for an Ideal Gas.
I will quote you the very first line on that page word for word; it says "An ideal gas is a theoretical gas composed of many randomly moving point particles whose only interaction is perfectly ela... | {
"language": "en",
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How to prove the constant speed of light using Lorentz transform? I read the light-clock example in my book which proved the time dilation formula by assuming that the speed of light is constant for all observers. But I've trouble in understanding it the other way around. Lorentz transformation is just a correction to ... | In short yes. You can try to solve it yourself. Take 2 observes A and B, moving at velocity v wrt each other. A sees a light pulse, traveling as x = ct (which means light's velocity as seen by A is dx/dt = c). Now use Lorentz transformation to find out coordinates of the pulse as seen by B. you'd see it comes to be c a... | {
"language": "en",
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Is there any Electric Current on (Solar) Coronal Loops? I'm studying Plasma Astrophysics and now I have came across the following problem, which I have been trying to solve on my own, and came to a "non-logical" conclusion?
Here is the Problem:
Let the Coronal Loop have the following Magnetic Field:
$$ B_{x} = B_o e^{... |
One can find that J=0 ??
Your math is okay. What you are being asked to examine is a special case of a coronal loop constructed from what is called a potential field. You often see the converse, namely a non-potential field, in discussions of dynamo theory.
It is perfectly fine, mathematically, to have $\nabla \tim... | {
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Gauge covariant derivative I have seen distinct definitions of gauge covariant derivative (in Yang-Mills theory)
$$ D_\mu \phi = (\partial_\mu + igA_\mu) \phi $$
vs
$$ D_\mu \phi = \partial_\mu \phi + ig[A_\mu,\phi] .$$
I guess the first is the common definition, which is the same as the covariant derivative in QED. Wh... | As AccidentalFourierTransform points out, the second expression is the non-abelian generalization of the former. The first one is only valid for the abelian case (QED), while in general Yang Mills the fields are matrices transforming in some representation of the gauge group and the correct form is the latter.
| {
"language": "en",
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Heisenberg Uncertainty Principle Applied to an infinite square well I appreciate the statement of Heisenberg's Uncertainty Principle. However, I am a bit confused as to how exactly it applies to the quantum mechanical situation of an infinite square well.
I understand how to apply Schrödinger's equation and appreciate ... | Provided that we have an infinite square well with potential
$$
V(x)=\begin{cases}
0, \text{ if }0<x<L,\\
+\infty, \text{ otherwise}
\end{cases}
$$
we obtain the wave functions as
$$
\psi_n(x)=\sqrt{\frac{2}{L}}\sin\left(\frac{\pi n x}{L}\right),
$$
where $n$ is a positive integer.
it is now straightforward to calculat... | {
"language": "en",
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Will a Cylinder placed on a frictionless inclined plane keep on slipping at its place or skid and slide down the plane? I've been wondering after learning about rolling without slipping and how it needs static friction for an object to start rolling but my question is that if theoretically the surface is frictionless t... | The cylinder won't experience any torque, because gravity can be though of as acting at the cylinder's center and the normal force from the ramp points directly toward the center. So the cylinder's angular velocity won't change. If it is released without any rotation, then it will simply slide down the ramp without e... | {
"language": "en",
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Evaluating Potential Energy Integral in Quantum Chemical Calculations My question is what are the steps for taking an integral of the following form?
$$\int e^{-\alpha|\mathbf r- \mathbf R_a|^2} {1\over|\mathbf r- \mathbf R_b|} e^{-\beta|\mathbf r- \mathbf R_b|^2} dV$$
This integral is commonly seen when attempting to ... | Let's call this integral $C = C({\bf R}_a,{\bf R}_b,\alpha,\beta)$, since the arguments are the free variables in the integral. Let's also assume that we're working in $\mathbb R^3$.
Our first attack consists of performing the substitution ${\bf r}\rightarrow{\bf r}+{\bf R}_b$. This won't change the volume element, so ... | {
"language": "en",
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Scintillator for adjusting sputter gun lenses What do you use to adjust the beam of you sputter cannon?
We have a test plate with a scintillating coating, that is now almost completely worn out, and I would like to replace it, but I am unable to find out what the luminescent coating was, or any supplier of similar plat... | One simple way is to use a tarnished (oxidized) copper plate, you will see the spot where the ions clean the surface by observing a color change.
other crystals that show luminescense from dopant atoms are commonly called "phosphors". You can find a few names here
http://www.proxivision.de/products/phosphor-screen.html... | {
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Why do different letters sound different? If one sings the letter "A" and "M" at the same volume and pitch, the two letters are still differentiable. If both pitch and volume are the same however, shouldn't the sound be the exact same?
| The basic frequency is determined by the vocal cords. They make the air flow pulsate with a frequency of 100 Hz to 200 Hz. The pulses are short, so there are overtones upp to several kHz.
The mouth and tongue make the vocal tract resonant at different frequency ranges. Those are called formants. Have a look at the form... | {
"language": "en",
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Definition of conjugate momentum in QFT My lecture notes define the conjugate momentum of a scalar field via:
$$\pi = \dot{\psi}$$
Where
$$\psi = \int \frac{d^3p}{(2\pi)^{3}}\frac{1}{\sqrt{2E_p}}\left(a_p e^{i\vec{p}\cdot \vec x} + a_p^\dagger e^{-i\vec p \cdot \vec x}\right) $$
and claim that this gives
$$\pi = \int... | I think I know what your problem is. You are forgetting that the time dependency can be implicit and doesn’t have to only be explicit. For instance, $\psi$ might depend on time because $x$ and/or $p$ depend on time. In this case the derivative will not be zero.
Also, the definition must be valid in both pictures since ... | {
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Can the 7-10 rule of thumb for radiation be understood theoretically? Is there a way to understand where the 7-10 Rule of Thumb for nuclear radiation comes from? A seven fold increase in time after explosion results in a 10 fold reduction in exposure rate.
From a FEMA page on responding to "nuclear threats":
From the... | Theory behind the rule? Local fallout from a groundburst is a million parts irradiated dirt (light elements) and one part plutonium nastiness. Each component has its own half-life, so the only way to estimate decay is empirical observation. My bet is that someone in the late 1950s plotted radiation versus time on lo... | {
"language": "en",
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"source": "stackexchange",
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Schwarzschild coordinates beyond the event horizon We can write down the metric of the Schwarzschild black hole in Schwarzschild coordinates.
On page 6 of the notes by Leonard Susskind of a course given at the Perimeter Institute titled 'Black Holes and Holography.' we find the following:
However, note that the Schwar... | Coordinates are not sacred objects in GR. Any coordinate system is just as good as any other coordinate system. So to ask whether the Schwarzschild coordinates are valid or not is a meaningless question ${}^1$.
However it is reasonable to ask if coordinates have an intuitive meaning for some specified observer. So for ... | {
"language": "en",
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Electron concentration in compensated semiconductor - different from intrinsic? I am having trouble understanding the formula for total electron concentration in the conduction band (under the Boltzmann approximation):
$$n_{0}=\frac{N_{d}-N_{a}}{2}+\sqrt{\left(\frac{N_{d}-N_{a}}{2}\right)^{2}+n_{i}^{2}} $$
While I unde... | As it turns out, according to this explanation (section 2.6.4.1 'Dopants and impurities'), in room temp the donor electrons more readily "migrate" (energetically) to the acceptor states than to the valence band. Therefore, contrary to the OP, donors and acceptros do 'cancel' out. This is indicated by the red arrows in ... | {
"language": "en",
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Ohm's law and current due to magnetisation I'm reading Landau's Electrodynamic of continuous media, specifically the following paragraph of section §29 (The magnetic field of a constant current):
If a conductor carries a non-zero total current, the mean current density in it can be written as $\rho{\bf v}= c\ {\bf cu... | Ohms law applies to free charges. The magnetization current applies to bound charges. The total current is the sum of the two.
| {
"language": "en",
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"source": "stackexchange",
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What am I failing to understand about a light in a material? In a material, a photon's velocity becomes slower, photon's wavelength becomes shorter, but photon's frequency doesn't change.
If there is a material that makes low frequency photons have very short wavelength photons, and if I stick my finger in the material... |
In a material, a photon's velocity becomes slower, photon's wavelength becomes shorter, but photon's frequency doesn't change.
The photon always travels with velocity c and its frequency and wavelength are fixed unless there are inelastic interactions.
The classical wave emerges from a confluence of photons, and it i... | {
"language": "en",
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Simultaneity in Newtonian mechanics How would Newtonian mechanics answer the train and moving light question?
The setup is:
A train is moving in the positive x_axis with speed c/2. A person stands in the middle of the train. There are two light bulbs at both ends of the train. The light goes off at the same time (ab... | Rather than think in terms of what someone will observe, think in terms of what would be measured in their frame of reference assuming the frame to be equipped with suitably distributed clocks.
As an example, even in the Newtonian realm, suppose an someone is at the origin of his frame of reference and there are lamps ... | {
"language": "en",
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Changing magnetic flux In the figure, there is a metallic ring inside which there is a dotted region through which constant magnetic field is passing. A wire with sliding contact is moved from position (1) to (2). Will the galvanometer show any deflection?
In this problem, when we take wire from (1) to (2) there is a c... | Imagine a wire configuration between 1 and 2, where the sliding contacts are not touching one another. Since you want to evaluate the emf along the conductor, you'd have to choose one closed path encompassing the galvanometer, the wires and one of the two sections of the ring, in order to connect the two sliding contac... | {
"language": "en",
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How to tell if a thermodynamic cycle is reversible without calculating entropy change? Consider the Carnot cycle, consisting of two reversible, isothermal processes and two isentropic processes. It is reversible, pretty much by definition.
Now consider the Lenoir cycle, consisting of an isochoric compression (heat addi... | If the isochoric and isobaric transformation are performed reversibly, i.e. quasistatically and without heat dissipation caused by friction or other effects, then your cycle will be reversible.
This is true for every thermodynamic cycle you can draw in the $PV$ plane: if every step is performed reversibly, then the cyc... | {
"language": "en",
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Is the classification of particles into matter and anti-matter arbitrary? It is well known that every fundamental particle has a corresponding antiparticle, and that – except for particles which are their own antiparticle – for practically every pair of particles and antiparticles, one type of particle predominates. W... | You are confusing two things at least.
This is the particle table:
There exists a mirror antiparticle table such that when the quantum numbers of particle and antiparticle are added each sum is identically zero, and particle and antiparticle have the same mass.
When a particle meets an antiparticle , and both are at r... | {
"language": "en",
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Classifications of quasiparticles Different particles can be represented as different irreducible representations of Poincare group. Can we classify quasiparticles using irreducible representations of some group? Also, quasiparticles are low energy excitations of the system, and it is closely related to the ground stat... | The group representation argument can not be applied to those excitations of topological origin. Group theory is not the most general classification criterion of quasiparticles. Group theory is useful when symmetry plays an important role in the discussion. For example, Goldstone modes in the symmetry breaking phases c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/337728",
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Why is light bent but not accelerated? Light is bent near a mass (for example when passing close to the sun as demonstrated in the famous sun eclipse of 1919). I interpret this as an effect of gravity on the light.
However, it seems (to me, at least) that light is not accelerated when it travels directly toward the (ba... | Currently, there is no evidence that photons have mass, and it is generally accepted that they are massless particles.
Nonetheless, gravitation does affect the path of photons, because the bending of space-time causes all particles to travel on curved paths, including massless ones. But that does not mean than light wi... | {
"language": "en",
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"source": "stackexchange",
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Does Violating Cosmic Censorship Really Mean Violating Causality? As I understand it, the basic motivation behind ruling out a naked singularity is that we don't know what is happening at a singularity and thus, we won't be able to predict anything in the universe if there is no horizon around such an unknown region. B... | There are closed timelike curves in the interior of the Kerr horizon. The obvious way to see this is if you go through the center of the ring singularity (thus, not intersecting the ring singularity), the Boyer-Lindquist $r$ goes negative, and the Boyer-Lindquist $\phi$ becomes timelike. Since, by construction, the o... | {
"language": "en",
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How does one come up with the model of torque? In school, we learn that $T = Fd$, where $T$ is the torque, $F$ is the force perpendicular to the moment arm, and $d$ is the length of the moment arm. If I was the first physicist to come up with this model for torque, what might my train of thought be? In other words, how... | The way you worded the question sounds to me like you're asking more for an intuitive understanding of why someone thought Fd would be a useful enough quantity to give it its own name, why it's taught to kids as a sort of fundamental equation rather than just another step in a derivation, and also where it fits into th... | {
"language": "en",
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Equation of motion for a falling slender bar
I have a few question about equations of the uniform slender bar motion.
The bar is released from rest on a horizontal surface as shown in the figure and falls to the left. The surface is rough so friction forces are applied at bottom end of the bar. The coefficient of fric... | Given that the bar is narrow, it would not have to tip very far for the center of mass to be vertically outside the base and therefore topple.
Hint for calculating alpha: consider how fast the top of the bar would have to accelerate in order for the bottom to lift off of the ground, and that it should rotate around the... | {
"language": "en",
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Why are we able to break a vector along it's components or in other words why is it that a vector exists along $x$, $y$ and $z$ axis? Does a 3 d vector exist in three dimensions at once? It seems to me that a vector always changes axis along which it is to fit into the scenario. For example: Electric field in $x-y$ pla... | Yes, a vector exists in three dimensions at once. Imagine we apply force to a body diagonally then it will also move diagonally, which means it is moving in both x and y directions. If you block that object from moving in only y direction then you will see it is moving in only x direction while we are still applying t... | {
"language": "en",
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A question related to time and motion I have a theory, I think that we cannot travel at speeds faster than light because, as we know,when you travel at speeds near light time passes slowly and that if we go further than light time may pause perhaps and that if time pauses its impossible to have motion because in 0 seco... | PBS Spacetime's YouTube channel has several videos related to your theories. There are specific methods physicists use to examine Light and Time. One of them is the Penrose diagram:
Here are some of the videos where they talk about Time, Black Holes, and Superluminal Travel... all of which examine how the geometry o... | {
"language": "en",
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Why does the annihilation operator acting on the ground state in Quantum Field Theory gives a zero? One of the main motivations for Quantum Field Theory after Dirac Equation is that the Dirac equation predicts negative energy states which leads to the ground state being unbounded which ultimately leads to the sea of ne... | For the Klein Gordon equation, when we interpret it as being the equation for a wavefunction of a particle, we have the negative energy states as a solution.
This problem vanishes when we move to field theory and think of KG eqn as the differential equation for a classical field. Write the Hamiltonian for it and it is... | {
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"url": "https://physics.stackexchange.com/questions/338875",
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Non-constant tension in rope Could somebody explain to me intuitively how tension is not the same in a rope with mass? My physics teacher (when regarding a massless string) told me that the tension is always equal because if you pull at one side more then the other side has to pull just as much to keep it in equilibriu... | Imagine a rope having a finite mass and is placed in gravity free space and having a constant velocity.Now take the rope as your system and exert an external force on one end of the rope then the rope will bear some tension at the point of application of force.As rope is the system tension is the internal force.The who... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/339000",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Brownian motion in a box It is often said that the Brownian motion for a particle in a box, thus a finite domain, is described by a uniform probability distribution in the longtime limit. One may easily imagine this maybe intuitively, but is there actually an easy way of showing this? How is it that even though there a... | I think the distribution remains flat for diffusion in a box, unless the boundary conditions are really strange or unphysical. Let me try with this not-so-accurate argument. Free diffusion gives a probability distribution which starts at $t=0$, for a single particle, as a delta function centered at the initial position... | {
"language": "en",
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"answer_id": 3
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Tipping point on fence panels? I deal in temporary fence panels - and my concern is the tipping point of our product out in the field.
Panels are 6' tall x 12' long (63#)
Stands are 23" long x 6" wide
We use sand bags (30#-40#) on the bases, but for whatever reason, they don't always stay on (or people take them).
Is a... | If the height of the fence is increased by a factor $k$, this will increase the area by the same factor, and also the wind force on it. (I assume for simplicity that windspeed does not vary with height, which is probably not true.) The average height at which the wind force is applied is also $k$ times as large. So ove... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How to integrate out the $W$-boson fields? What does it mathematically mean to 'integrate out' the $W$-boson fields to obtain the Fermi Lagrangian from the electroweak theory? How does one achieve this mathematically? It will be helpful if someone can explain this both in the path integral formalism and the operator fo... | Heuristically, there are two ways.
*
*In the electroweak Lagrangian, you substitute for W by its classical solution. That is, you find the Euler-Lagrange equation for W, solve for it, and plug the solution in Lagrangian. In doing this, the W fields are "integrated out".
*When an internal line of the W boson is pr... | {
"language": "en",
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Meanings of the word "phase" I have been confused at points due to multiple uses of the word "phase".
*
*Mainly, when I think of a phase diagram, I think of a graph relating temperature to pressure, and segments the possible combinations of these values into regions in which a particular substance is "solid", "liqui... | Right. Other than the generic meaning of phase being the state of a system, these two specific meanings are independent. As a third example, the phase associated with wave motion would be another separate definition.
| {
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Why large excavated holes can create air currents? My friend shared this post on my wall, but I got doubt: How can a hole like this create air currents which suck helicopterss also? I didn't really understand.
| In the link that reproduces the photo it is said that temperatures in Siberia on the ground can be as low as -40C.
The chimney effect is used for generating power , so this might act as a solar updraft tower :
The solar updraft tower (SUT) is a renewable-energy power plant for generating electricity from low tempera... | {
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In summer, should I close curtains during the day? In summer, that is when it's warmer outside the house than inside, one want to prevent the air in the house to warm up too much. Let's consider that all the windows are kept closed, that they are double panes and made of "Low-E" glass. During the day, does closing the ... | Windows are transparent to visible light, but opaque to infrared. If your curtains are dark, they will absorb the visible and emit infrared. This will cause your house to warm as the light doesn't escape so easily. If they are lighter, they will be more reflective to visible light and will bounce it back through the... | {
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Help in an integration step in QFT by Lewis H. Ryder There is an integration step I can not figure out and is frustrating.
We start from the equality
$$ \dfrac{\partial^2\phi}{\partial x^2} = \dfrac{\partial V}{\partial \phi} $$
and by integration process we are supposed to get (eq. 10.8 in the textbook):
$$ \... | Another possible way which might be more clear for you is to do the following:
Begin with
$$ \frac{\partial^2 \phi}{\partial x^2} = \frac{\partial V}{\partial \phi}.$$
Multiplying the above by $\partial \phi / \partial x$ and moving $\partial V/\partial \phi$ to the other side yields
$$ \label{eq:1} \tag{**} \frac{\... | {
"language": "en",
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Why does a massless, frictionless piston move from high pressure to low pressure? Consider an ideal gas kept in a rigid cylinder with a movable massless, frictionless piston at the top. Let the pressure inside the cylinder be $P$ at pressure exerted by the surrounding on the cylinder be $p$. Let $$ P>p $$
Now since the... | Piston being massless never makes sense because it is the same as talking about thin air.
Massless in the context that any force due to the elastic collisions between the particles and the piston can move the piston, i.e. the piston is maneuverable.
| {
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Why do we say Sun curves space and the Earth moves following the geodesic? Why do we say sun curves space even if the Ricci Scalar for a Schwarzchild metric, the solution of Einsteins Equations for the Sun, is equal to zero.
The Ricci scalar for the constant time slice is also zero.
Can we define curvature using a sin... | According to the mathematical definition of the curvature, it represents the commutator of covariant derivative. More precisely, $$[\nabla_\mu,\nabla_\nu]A^\rho=R^\rho_{\kappa\mu\nu}A^\kappa$$
Where $R^\rho_{\kappa\mu\nu}$ is the Riemann curvature tensor. It is the single quantity that defines (or represents) the curva... | {
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Why is the Schwarzschild radius associated with the tiniest micro black hole formed by a Planck mass twice the Plank length? If one calculates the Schwarzschild radius, $r_s$, of a Plank mass $m_p=2,18*10^{-8} (m)$ one gets:
$$r_s=2{\frac{G{m_p}}{c^2}}=1,48*10^{-27}*2,18*10^{-8}=3,22*10^{-35}(m)$$
Now the Planck length... | Things like the Planck mass, the Planck length, etc. are order of magnitude estimates of when certain effects should be important. You shouldn't take it literally that Quantum gravity becomes important at EXACTLY $\ell_{p}$, and is completely irrelevant at any longer distance. It's a heuristic to help us think. In r... | {
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Are pointlike massive particles naked singularities? If elementary particles (specifically, those with mass, such as the electron or other leptons) are pointlike particles, wouldn't that mean they are naked singularities?
But these particles have spin- wouldn't that make them naked ring singularities, thus giving them... | If you consider only classical physics, an electron can be seen as a Kerr-Newman black hole, that is a rotating charged black hole, violating the naked singularity bound since it's "rotating" too fast.
But this analogy is flawed in many ways, mainly not taking into account quantum physics. You cannot have a black hole... | {
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Bounds of Integration (with respect to something that is not time) I have been reading Richard Feynman's lectures and came across an interesting proof regarding the Earth's gravitational force. At one point in the proof, Feynman uses the following the integral:
$\int_{R+a}^{R-a} dr$
(13.18 on http://www.feynmanlectures... | The problem has nothing to do with change of variable. It is just about orientation, where you are choosing to put your zero potential energy. He is putting it at $r=\infty$. This is just a convention, no math. You can put the zero anywhere you like. The integral is then from $r=\infty$ to $0$. So, the integral is real... | {
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On a derivative of the Poynting vector's derivation I'm studying the Poynting theorem (the mathematical proof). It starts considering the energy held by the electromagnetic field inside a surface $S$, which is:
$$
U_{em} = \int_{\tau}\frac{1}{2}(\vec{E}\cdot\vec{D})\ \mathrm{d}\tau + \int_{\tau}\frac{1}{2}(\vec{H}\cdot... | Look to the product rule. First, what is $\mathbf{D}$? $\mathbf{D}(\mathbf{x}, t) = \epsilon(\mathbf{x}, t)\, \mathbf{E}(\mathbf{x}, t)$, right? Thus:
\begin{array}
\ \frac{1}{2} \frac{\operatorname{d}}{\operatorname{d}t} \left(\mathbf{D} \cdot \mathbf{E}\right) & = \frac{1}{2}\frac{\operatorname{d}}{\operatorname{d}t}... | {
"language": "en",
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What produces an electromagnetic field? A charge that moves, or a charge that changes over time? I've learnt an electromagnetic field is produced by moving charges, i.e. a current.
Is it the case, or is it actually the fact that the charge is changing at a given location?
I mean: imagine I have a charge $q_1$ locat... |
I have a charge ... located at a given point of the space. Then imagine the charge changes ..., but without moving (this is probably impossible? ... Does it produce an electromagnetic field?
Elementary charges (electron, proton and their anti-particles) in unbounded state have unchangable charges and by this electric... | {
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Is there any qualitative difference between the WZW $SO(2)_1$ and the WZW $SU(2)_1$ CFT? Consider the anisotropic spin-$\frac{1}{2}$ Heisenberg chain $$H = \sum_{n=1}^N S^x_n S^x_{n+1}+S^y_n S^y_{n+1} + \Delta S^z_n S^z_{n+1}$$
which for $\Delta = 0$ realizes the Wess-Zumino-Witten (WZW) $SO(2)_1$ conformal field theor... | They are very different. First of all the free fermion is fermionic. Then $SU(2)_1$ has non-chiral fields coming from the left and right primary fields with $h=1/4$ (spin 1/2), namely the Hilbert space decomposes as
$(\mathcal{H}_0\otimes\bar{\mathcal{H}}_0)\oplus (\mathcal{H}_{1/4}\otimes\bar{\mathcal{H}}_{1/4})$.
| {
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Quantum systems: three-level vs qutrit Is there a difference between a three-level atomic system and a qutrit? If yes, please tell me what it is and how to relate both quantum systems.
| In a qutrit, every transition between pairs of levels is independent, in the sense that $\vert 1\rangle \leftrightarrow \vert 2\rangle$ is independent from $\vert 1\rangle \leftrightarrow \vert 3\rangle $ which is independent from $\vert 2\rangle\leftrightarrow \vert 3\rangle$.
Thus, not every three-level system is a q... | {
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First law of thermodynamics as conservation of energy We have that $\Delta U = Q + W$. What I don't see is how this formula relates to the law of conservation of energy. Can someone please clarify?
Does this mean that $\frac{dU}{dt}=\frac{dQ}{dt}+\frac{dW}{dt}=0$, so that $\frac{dQ}{dt}=-\frac{dW}{dt}$?
| The equation of the first law of Thermodynamics does not directly imply the conservation of energy; rather the first law of Thermodynamics is a consequence of the conservation of energy when applied to Thermodynamics( systems involving heat, temperature etc.)
The conservation of energy was known somewhat by scientists ... | {
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Are special relativity calcs affected by media? Time dilation, increase in mass, Lorentz contraction calcs all involve velocity of light in vacuum. But in optical media light slows down. So what of relativity calcs in media? Do we ever need to adjust the speed of light?
| No, because in a dielectric medium light isn't light, and that's why its speed isn't $c$.
The speed of light in a dielectric medium remains unchanged. You'll find lots of questions discussing exactly what goes on with light in a medium, but basically the EM field of the light interacts with electrons in the medium to f... | {
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How is it that in a car crash, four 8mm bolts can anchor the seat to the car? In a car crash at for example twenty metres per second. I used suvat equations and newtons second law to work out the force as as body accelerates(negatively). I estimated that the distance travelled in the crash by the body would be roughly ... | It isn't uncommon for the breaking load for M8 bolts to be 1800 kg or more. That puts four at 7200 kg, enough to statically support the weight of many vehicles with passengers.
Also important is that the bolts are not the only thing transferring the force. In any good design, much of the force will be transferred acro... | {
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Estimate of the effect of quantum disturbances on a macroscopic object I am self-studying P. Davies, D. Betts, Quantum Mechanics. Exercise 4 of Chapter 1 says:
"A snooker ball of mass $0.1$kg rests on top of an identical ball and is stabilized by a dent $10^{-4}$m wide on the surface of the lower ball. Use the uncertai... | If one uses the position-momentum uncertainty relation $\Delta x\Delta p\sim h$, one arrives at a time of $\tau\sim 10^{25}$ s. If, on the other hand, one uses the energy-time uncertainty relation $\Delta E\Delta t\sim h$, one arrives at a time of $\tau\sim 10^{29}$ s.
Let's just take the geometric mean of these answer... | {
"language": "en",
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How is the equation of Mach number derived? Wikipedia states that for a pitot-static tachometer, the mach number for subsonic flow equates to
$$M = \sqrt{5\left[\left(\frac{p_t}{p_s}\right)^\frac{2}{7}-1\right]}.$$
How did they get to that result? Is there a derivation, or is it just from a polynomial fit of a tabulate... | If you want to know more about calculating a Mach number, it helps to read Wikipedia's article on Mach number. As explained here, the Mach number for subsonic compressible flow is obtainable from Bernoulli's equation (Wikipedia cites this source). The result you cited then follows from $\gamma=\frac{7}{5},\,p_t=q_e+p$.... | {
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(Why) is it necessary to invoke Newtonian Gravity to fix normalization constants in General Relativity? I'm studying GR on Carroll's book. In Chapter 4 the constant appearing in Einstein's equation is fixed by requiring to obtain Poisson's equation in a Newtonian framework.
In chapter 5 the constant of the Schwarzschi... |
Is it actually necessary to use classical results?
Of course. Any new theory in physics must replicate current theories in those areas where those current theories already do a very good job of predicting behaviors. This is true in quantum mechanics as well.
Newtonian gravity predicts behaviors quite nicely in the li... | {
"language": "en",
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Two-point correlation function in Peskin's book I am reading Peskin's book on QFT and I reached a part (in chapter 4) where he is analyzing the two-point correlation function for $\phi^4$ theory. At a point he wants to find the evolution in time of $\phi$, under this Hamiltonian (which is basically the Klein-Gordon - $... | I think the question is related with the answer given by Valter Moretti from
Here
Clearly, you cannot say that the field $\phi(x)$ can be decomposed as creating and annihilation part.
| {
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Will overlapping two different beams of coherent light with different wavelength cause interference? If I use two different wavelength lasers to transmit light into a single mode optic fiber will they interfere with each other? If so, how much will be that interference.
| Yes, light from the two lasers will interfere, but the light will interfere temporally, not spatially. The result, when the light is incident on a detector, is a beat frequency: a signal whose frequency is equal to the difference between the frequencies of the two lasers.
The phase of the signal will wander relatively... | {
"language": "en",
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Is there a case when it is better to use the integral form of the Maxwell equations rather than the differential form? I was wondering if there is a case where the integral form of the Maxwell equations is preferred over the differential form?
If you could provide with an example for each one of the equations I would ... | The integral form of Maxwell's equations is the most general form.
You may ask, why? Aren't both of them equivalent statements. No, they are not, the integral form is more powerful, yet it's underappreciated.
The first condition for a function to be differentiated is differentiable, if there's a single point which is n... | {
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Determining mass radius and charge radius of electrons First the mass radius problem:
Why can't the mass radius of electrons be determinded by shooting neutral particles on it. Similar to Rutherford's gold model only a bit more sophisticated.
Secondly the charge radius problem:
I often hear the term charge radius and... | Rutherford used $\alpha$-particles as projectiles. Compared to the gold foil they have "little" mass and they interact "heavily" via the electro-magnetic force. Furthermore, compare to the size of a gold atom (incl. the electronic shells) the $\alpha$-particles are small. All three properties were important:
*
*smal... | {
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Non-local field redefinition and $S$-matrix It is known that for local field redefinitions for which the LSZ formula is valid:
$$\langle 0|\phi(x)|p\rangle \neq 0$$ field redefinitions don't change the S-matrix.
(See QMechanic's answer to Equivalence Theorem of the S-Matrix)
But is it true for non-local field redefint... | Claim 1. If $\psi(x)$ is an arbitrary operator that satisfies
\begin{equation}
\langle 0|\psi(x)|p\rangle\neq 0\tag1
\end{equation}
then it is a valid interpolating field, and as such, it can be used in the LSZ formula. The proof can be found in any introductory text, such as Weinberg.
Claim 2. If we assume that
\begin... | {
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Does stream function hold only for steady flow? This is just a basic question about streamline, equation of streamline and stream function. I am used to perceiving that the stream fucntion is just another form of the equations of streamlines. Since streamlines can be obtained at an "instant time" of an unsteady flow fi... | Generalizing your mathematics (which are all correct), the 2D stream function automatically satisfies continuity for any 2D case where $\partial\rho / \partial t$ is zero. In flows other than these, you must independently confirm that your results satisfy continuity.
| {
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Deformation of a self-gravitating sphere from two forces I have a fluid sphere (say a gas or a liquid of uniform density, under its own gravity) on which forces is applied to its surface. I would like to find its approximate shape (most probably an oblate ellipsoid), from the forces applied on its (initialy) spherical... | If the deformation is minimal, I think you can approximate the problem by just increasing the radius of the sphere by the amount that it is deformed outwards (of course on the poles this gives the wrong results then).
Then you can require the increased gravitational force to be equal to the force acting on the equator ... | {
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How can we show Power = $\mathbf{F}\cdot \mathbf{v}$? How can we say that $$\text{Power} = \mathbf{F}\cdot \mathbf{v}$$
We know that small work done by a force $\mathbf{F}$ to displace an object by '$\mathbf{x}$' is
$$W = \mathbf{F}\cdot \mathbf{x}$$
So derivating wrt time, we get
$$\begin{align}
P=\dfrac{dW}{dt}&=\fr... | The work $W$ is not equal to $F\cdot x$ generally. The correct form is
$$W=\int F \cdot dx$$
So $dW=F\cdot dx$ and $P=\dfrac{dW}{dt}=F\cdot\dfrac{dx}{dt}=F\cdot v$
| {
"language": "en",
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When short circuits are not exactly short circuits?
Here $R1 = 2 \Omega$, $R2= 4 \Omega$ and $R3= 4 \Omega$
Though there looks to be a short circuit in this diagram, my teachers say that this circuit can easily be redrawn into simple parallel circuit. As far as I know a short circuit is an alternate way for current to... | The wire which joins the points $A$ and $B$ is essentially a short circuit. Assuming the wire to be ideal (no resistance), the electric potential at point $A$ is equal to the electric potential at point $B$.
Therefore, the circuit is equivalent to the circuit where $R_2$ and $R_3$ were connected to point $A$.
With simi... | {
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Why does the Sun appear larger during the sunrise and sunset? Why does the Sun appear larger during sunrise and sunset compared to its size during midday even though its distance from the Earth remains fixed all the day? It is only during the Winter when the Sun is away from the Earth and that too is due to the motion ... | I spent over 30 years at sea, and I can tell you that when you're out in the middle of the ocean the setting and rising sun sometimes seems to be much larger. Atmospheric conditions seem to influence this. If you wake up to a red sky and the sun looks huge on the horizon you can expect some nasty weather.
I think tha... | {
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Why can a regular infrared camera not show temperature (thermography)? There are a lot of questions here dealing with infrared cameras and thermographic cameras. I think I understand the reason why a thermographic camera is able to retrieve the temperature values from any object and convert them to a falsecolor represe... | It depends on the sensor. If all that makes a camera "infrared" is that it is capable of detecting light with a lower frequency than red light, that is not enough to identify temperature. Objects of different temperature emit different frequencies of infrared light at different amounts. In order to accurately determine... | {
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Renormalization and canonical commutation relations My question is whether canonical commutation relations hold for renormalized quantum fields. Below I show reasoning which caused by doubts.
Consider a relativistic scalar QFT. We have spectral decomposition of two-point function
$$ \langle \Omega | \phi(x_1) \phi(x_2)... | The commutation relations for renormalized fields are different then those of the bare fields by factors of the wavefunction renormalization. As an example, consider a complex scalar field, $\phi$. The bare fields obey, e.g.,
$$
\left[ \phi (x) , \phi (y) ^\dagger \right] = \int \frac{ d^3p }{ (2\pi)^3 } e ^{ i p \cd... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/348328",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 2,
"answer_id": 0
} |
Buoyancy Force and Density I am doing a practice problem about buoyancy force. If there are two objects, (one made of wood and one made of metal), and we hold them underwater, will the buoyancy force of both objects stay the same? That's what I believe at least.
| The buoyant force will be same if the fluid density is the same and the volume of liquid displaced by both objects is the same. The formula to calculate upward buoyant force is ρ × V × g , where ρ is the density of the liquid the object is immersed in, V is the volume of the displaced liquid and g is the gravitational ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/348430",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Current experimental evidence of lepton flavour violation other than neutrino oscillation Is Lepton Flavour Violation (LFV) experimentally established in processes other than neutrino oscillation? This answer by Luboš Motl points out that
Interestingly, CMS has detected a 2.5 sigma excess of Higgs bosons that seemingl... | The answer is no :)
(At least thus far.)
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/348613",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
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