Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Question about electrochemical reaction in fuel cell The electrochemical reaction on the anode side of a fuel cell can be expressed as hydrogen split into hydrogen protons and electrons. I'm doing some research about the electrochemical reaction in a fuel cell. Is the anode side electrochemical reaction a heat release ... | The answer lies in your question itself. The left hand side of the anode half-cell equation contains H-H, whereas the right hand side contains isolated H⁺ ions.
What do you have to do in order to break the H-H bond to isolate them? Obviously you must supply them with heat energy equal to or greater than the bond enthal... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/461098",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Why did recombination make the universe transparent? It is commonly said that after the universe cooled enough for ionized Hydrogen to settle down into neutral Hydrogen, i.e. recombination, the universe became transparent. A reason I have heard for this is that most photons don’t have the right energy to be absorbed by... | The scattering cross-section for free electrons is known as the Thomson scattering cross-section $\sigma_T$.
It is relatively easy to show that once the electrons are bound, the cross-section can be treated like that of a damped harmonic oscillator. If the oscillator is driven at frequencies below the resonant frequenc... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/461233",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Why do electromagnetic waves have the magnetic and electric field intensities in the same phase? My question is: in electromagnetic waves, if we consider the electric field as a sine function, the magnetic field will be also a sine function, but I am confused why that is this way.
If I look at Maxwell's equation, the c... | The Maxwell equations that relate electric and magnetic fields to each other read (in vacuum, in SI units) as
\begin{align}
\nabla \times \mathbf E & = -\frac{\partial\mathbf B}{\partial t} \\
\nabla \times \mathbf B & = \frac{1}{c^2} \frac{\partial\mathbf E}{\partial t},
\end{align}
where the notation $\nabla \times{\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/461393",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
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Why is blowing so different than sucking? Why is it so easy to blow out a candle from a significant distance, but nearly impossible to suck enough air to do the same?
Even without focusing the airflow through a nozzle or something, this affect seems to be present. For example, it's easy to feel the air coming out of a ... | Your lungs and mouth are designed to generate overpressure, not underpressure. You can barely suck the liquid out of a straw, while you can expel air with way more pressure.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/461572",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 2
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Why are symmetries in phase space generated by functions that leave the Hamiltonian invariant? Hamilton's equation reads
$$ \frac{d}{dt} F = \{ F,H\} \, .$$
In words this means that $H$ acts on $T$ via the natural phase space product (the Poisson bracket) and the result is the correct time evolution of $F$. In other w... | This is essentially statement 3 in my Phys.SE answer here, which also provides a proof and some related statements.
Statement 3: "A constant of motion generates a symmetry and is its own Noether charge."
In more detail:
*
*An off-shell constant of motion$^1$ $Q$ satisfies by definition
$$\{Q,H\} +\frac{\partial Q... | {
"language": "en",
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Electromagnetic field tensor and antisymmetry Why does the inner product between the four force (caused by the electromagnetic field tensor) and the four velocity equaling zero imply that the electromagnetic field tensor is antisymmetric?
This image is from the textbook General Relativity: An Introduction for Physicist... | The premise is that $F_{ab}u^a u^b=0$ for all timelike $u$. I'll abbreviate this as $uFu=0$.
Given any two timelike vectors $x$ and $y$, we can multiply one of them by a non-zero scale factor so that $x+y$ is also timelike. Then the premise implies
$$
xFx=0
\hskip2cm
yFy=0
\hskip2cm
(x+y)F(x+y)=0.
\tag{1}
$$
This combi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/461856",
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Unification of gravity and electromagnetism Have there been any attempts at unifying gravity and electromagnetism at least at classical level since Hermann Weyl's idea of gauge principle (1918)? We now have Standard Model which is very successful and many other theories. But gravity and electromagnetism are long range ... | Yes, classically, we can unify gravity with electromagnetism. The theories that do so are the famous Kaluza-Klein theories. They are theories of pure gravity in $4+1$ dimensions rather than our usual $3+1$ dimensions. When such theories are viewed from a $3+1$ dimensional perspective, the effects of gravity in the four... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/462122",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why can all solutions to the simple harmonic motion equation be written in terms of sines and cosines? The defining property of SHM (simple harmonic motion) is that the force experienced at any value of displacement from the mean position is directly proportional to it and is directed towards the mean position, i.e. $F... | One way of deriving it is using Taylor series (although to be fully rigorous, this requires further justification for restricting to analytic functions). We have that $f(x) = \sum a_n x^t$, so $f''(t)=\sum (n+1)(n+2)a_{n+2}t^n$. If $f''(t)=-\frac k m f(t)$, then $(n+1)(n+2)a_{n+2} = -\frac k m a_n$, so $a_{n+2} = \fra... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/462245",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does the $\phi$-cubed theory have no ground state? In the book of Sredinicki's, he claimed that the $\phi^3$ theory has no ground state, hence this is not a physical theory.
My question is that I can't see why this system has no ground state. And I don't understand either the explaination he gave. For example, what... | In quantum theory we usually require that the Hamiltonian $H$ is bounded from below and that the system has a ground state. This is intimately related to unitarity. The $\phi^3$ theory violates this.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/462496",
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Beta function in $\lambda_0\phi^4$ theory For a real scalar field $\phi$ after performing all the 1-loop renormalization
for dimensional regulator $d = 4 - \epsilon,\ \epsilon \rightarrow 0^+$, I have found that the renormalized coupling $\lambda$ can be related to the bare one by
$$\lambda\Bigg(1 + \frac{3}{(4\pi)^2... | The idea is that the bare quantities explicitly do not depend on $\mu$, thus one has the equation
$$
0 = \mu\frac{d \lambda_0}{d\mu} = \left(\frac{\partial}{\partial\mu}+ \beta(\lambda_p)\frac{\partial}{\partial \lambda_p}\right)\left(\mu^\epsilon\lambda_p \,Z_\lambda\right)= \epsilon \mu^\epsilon\lambda_p Z_\lambda+\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/462605",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Sun's energy and grand unification According to Wikipedia,
The approximate grand unification energy value is equal to $1×10^{25}$ eV or $10^{16}$ GeV
This is equal to $1602176$ J.
Now,
The Earth receives 174 petawatts (PW) of incoming solar radiation (insolation) at the upper atmosphere
This is solar radiation... | You've got a misunderstanding.
The grand unification energy of $10^{16}$ GeV is meant as an energy of a single particle.
But the solar radiation ($1.74 \cdot 10^{17}$ J/s) is the energy of many photons.
A single solar photon has an energy of only a few eV.
By the way: Even the particle energies achieved with our most p... | {
"language": "en",
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Do orbiting planets have infinite energy? I know that planets can't have infinite energy, due to the law of conservation of energy.
However, I'm confused because I see a contradiction and it would be great if someone could explain it.
Energy is defined as the capacity to do work. Work is defined as Force x Distance. Fo... | Your definitions are incorrect. Force is rate of change of momentum and is a vector. More importantly, the work done by a force is not force x distance, it is the force resolved in the direction of the displacement x the magnitude of the displacement. This is more formally known as the scalar product of force and displ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/462768",
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Quantum logic gates (2-inputs 1-output) Is there a quantum logic gate (or any sequence of QLGs) that takes as input two Qubits and outputs one Qubit?
*
*If yes, could you please write it down in the simple example?
*If no, could you explain why?
PS: Sorry for stupid question
| Quantum gates are reversible and hence must have a one to one correspondence between the input and output bits. Another way of thinking about reversibility is that there is a way to run the circuit backwards from the set of outputs and get back all possible inputs. This means that you have the same number of input and ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/462912",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Electric charge of the Higgs field The Higgs field is
\begin{equation}
\Phi = \frac{1}{\sqrt{2}} \left( \begin{array}{cc} \phi_{1} + i\phi_{2} \\
\phi_{3} + i\phi_{4} \end{array} \right) \tag{1}
\end{equation}
with $\phi_{1}$ and $\phi_{2}$ carrying electric charge $+1$ respectively, while $\phi_{3}$ and $\... |
Besides, if two components of the Higgs field carry positive electric charge, the whole space (even the whole universe) is electrically positive since the Higgs field permeates the whole space. This is very doubtful and seems not reasonable to me. Is this case true?
You are confusing the fields of quantum field theor... | {
"language": "en",
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"source": "stackexchange",
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Symmetry operations on an infinite uniform sheet of charge My book has a section on symmetry operations.
It says, (if the plane of charge is the yz plane) translation symmetry along the y-axis and z-axis implies that the electric field is constant if one translates along the y and z axes respectively. Also, due to rota... | Scale symmetry. An infinite plane looks the same no matter how far away from it you are.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How do I determine the components of a cinematic jump, for vertical and horizontal velocity? I have been tasked with determining the feasibility of The Rock's jump in the movie 'Skyscraper' I am using projectile motion equations to determine it, but have gotten stuck whilst calculating my horizontal and vertical veloci... | The initial vertical velocity $v_{y0}$ can be found by using $$0 = v = v_{y0} - gt.$$ The initial horizontal velocity is going to be the sum of the velocity due to the jump and the velocity due to the run. You correctly solved for the horizontal velocity due to the run: $v'_{x0} = 8.58 \, \textrm{m/s}$. The horizontal ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/463251",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Does theoretical physics suggest that gravity is the exchange of gravitons or deformation/bending of spacetime? Throughout my life, I have always been taught that gravity is a simple force, however now I struggle to see that being strictly true.
Hence I wanted to ask what modern theoretical physics suggests about this... | Both.
General relativity describes gravity as curvature of spacetime, and general relativity is an extremely successful theory. Its correct predictions about gravitational waves, as verified directly by LIGO, are especially severe tests.
Gravity also has to be quantum-mechanical, because all the other forces of nature ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/463327",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Does a colored filter reflect their color of light? At the moment I'm somewhat confused by the concept of colored filters; common sense states that they allow only their color of light to pass through(i.e. red filter lets red light through), but, if they appear to be a specific color, wouldn't that indicate that they r... | You're right, an ideal filter can either absorb or reflect the spectrum it should not pass, and thus for that ideal filter we should not see that pass-band color reflected from the filter. Unfortunately, practical materials are less efficient and typically reflect a little of the spectrum they are supposed to pass (the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/463474",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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How do you measure the chemical potential? It is clear how to measure thermodynamics quantities such as temperature, pressure, energy, particle number and volume. But I have no idea how to measure chemical potential.
Could someone please provide some examples of how one could measure the chemical potential?
| We can't measure chemical potentials but that's OK because the actual value of the potential is not important, what matters is its difference from some other state. So, chemical potentials are compared. For example, in vapor-liquid equilibrium the chemical potential of the liquid component is equal to the chemical pote... | {
"language": "en",
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Can an atom be split and put back together? I had recent came across this question when unintentionally tearing a piece of my journal paper. These atoms' bonds are pulled apart when the paper is torn, but is there a way to put them back together?
Now i know that, depending on the object, the method can vary. According... | When you tear a piece of paper, I don't think the atoms are being splitted along the break line because it's far more easy and consumes far less energy separating the atoms into the two pieces that having to cut through every individual atom along the break line. If by splitting you mean something like disintegrating a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/463780",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Why the entropy change is not zero in the irreversible adiabatic process? Why the entropy change is not zero in the irreversible adiabatic process?
...while it is defined as the integral of the heat added to the system over its temperature.
| If you have an irreversible adiabatic process between two thermodynamic equilibrium end states of a system, there exists no possible reversible adiabatic process between these same two end states. So to get the entropy change for the irreversible adiabatic process, you need to devise an alternative reversible path bet... | {
"language": "en",
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When the voltage is increased does the speed of electrons increase or does the electron density increase? I am just a high school student trying to self study, please excuse me if this question sounds silly to you.
I know that current is a product of the speed of electrons and the electron density.When current is incre... | In a conductive material such as a metal, for all practical purposes, current depends only on the speed of the electrons. The electron density does not change because each metal atom has already given up all of its valence electrons; releasing further electrons would require a very large energy input.
In an insulator ... | {
"language": "en",
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What is the Kitaev Model and why has it become so popular? I am seeing Kitaev Model everywhere. It feels like the spin-glass model of our time. How the Kitaev model differ from spin-glass and why it can be used everywhere? Looking at equation 1 here suggests it's basically a spin-glass model.
| The paper linked in the original post already answers some of the post's questions.
*
*What is the Kitaev Model?
It's a lattice model where
nearest neighbor spin degrees of freedom interact via a strongly anisotropic nearest-neighbor Ising exchange [...] The Kitaev interactions along neighboring bonds cannot be sa... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why is air pressure higher in winter than in summer? At the top of a mountain, say Mt Everest, atmospheric pressure is low.
So shouldn't the same thing be true for winter season.
I.e air pressure in winters should be lesser than that in summers.
But it's the opposite.
Can someone please explain why ?
| One of the reasons the air pressure is higher in winter is because the air is colder so the molecules stick closer together building more pressure. Also Mt. Everest is the highest elevation above sea level so it would seem like it would be cold, BUT there are many things that factor into it that make that statement wro... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/464355",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Cavity optomechanics Hamiltonian In cavity optomechanics the radiation pressure exerted by light moves a mirror in a cavity. Because of that the resonance frequency of the cavity changes due to change in length of the cavity (cavity frequency, $\omega_{cav} = n\pi c/L$, $L$ is the length of the cavity). The Hamiltonian... | This is beacause, it is based on the assumption that only one optical and mechanical mode interact. Each optical cavity supports in principle an infinite number of modes and mechanical oscillators have more than a single oscillation/vibration mode. The validity of this approach relies on the possibility to tune the las... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/464724",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Is every open circuit a capacitor? I think that even open-ended wires can let AC current flow through them, just with a low capacitance. I also think an antenna could be a capacitor and open ended. Am I thinking correctly?
| Yes. If two non-insulators (in the Universe) are connected to any emf source, current will flow between them regardless of the source frequency (eg. 60Hz or 60GHz). At DC, the leakage current flow depends on the circuit conductance. At AC, the leakage current flow depends on the circuit admittance. Of course, the curre... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/464850",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "30",
"answer_count": 10,
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Demonstration of the completness of an orthonormal set of functions I find this concept of completness a little bit dense when it comes to prove this property of some set of orthonormal functions. In one of my classes, my professor proved this for the orthonormal set of functions $\left\{ \sqrt{2/L} \sin( n \pi x/L) \r... | Sorry, I really don't under what the question is in the first part.
For the second part, let
$$|v>=\sum_n c_n |\phi_n> \tag{1} $$
where $|v>$ is a vector (ket) in a finite dimensional space with an orthonormal basis $|\phi_n>$ and
$$<v|=\sum_n c^*_n <\phi_n|$$
is an adjoint or dual vector (bra).
Orthonormality of the... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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plane vs diverging waves michelson itnerferometer I'm wondering if there's a difference in the interference pattern achieved in the michelson interferometer if the source of light is sending plane waves vs sending diverging waves (for example by putting a diverging lens between the source and the first plate, the one w... | Plane waves are a theoretical construct as every aperture produces divergence, so you need an infinite amount of empty space to keep a plane wave plane.
As such every Michelson interferometer deals with diverging waves. These interferometers will take a divergent beam and collimate it before reciprocating the process s... | {
"language": "en",
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Why does a car's steering wheel get lighter with increasing speed I've noticed it is difficult to turn the wheels of a car when the car is stationary, especially cars without power steering, which is why the power steering was invented. However, I've noticed it becomes feather light when traveling at speed (some model... | The work to turn the wheel is roughly proportional to how much you turn the wheel, and inversely proportional to the distance the car traveled. You feel less resistance at higher speed because the car moved farther for the same amount of steering wheel turn. This is because when the wheels on the ground are rolling, th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/465280",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "19",
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Does total $\hat{S}^2$ always commute with total $\hat{S}_z$ even for interacting spins? I was given the following operator $\hat{f}$ describing the interaction of two spin-$\frac12$ particles:
$$\hat{f}=a+b{\hat{\bf S}_1}\cdot{\hat{\bf S}_2}.$$
I was told that I can prove that $\hat{f}$ does commute with the total spi... | The form of the intersction is invariant under spin rotation, so we do expect commutativity with total spin operator.
Algebraically, $S_1 \cdot S_2 = \frac{1}{2} \left((S_1+S_2)^2 - S_1^2 - S_2^2\right)$, so we see that $S^2$ and $S_z$ commutes with all the terms. We use the fact that $[S^2, S_z] = [S^2, S_y] = [S^2, S... | {
"language": "en",
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Virtual images - Work of a brain or work of a lens? I am just a high school student trying to self study, so please excuse me if this question sounds silly to you.
Many people tell me that virtual images are formed when two rays that are diverging appear to come from a point, therefore our brain thinks that it is comin... | Our brain just gets signals from the retina. The visual cortex interprets these signals, I am guessing, using an image recognition and matching. If a match is found then the owner of cortex believes that that is the reality behind the original signals. All reality is virtual...
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/465680",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Work when there is more than 1 force I know that for an object with an applied force, the work done is
$$W = Fd \cos \theta.$$
I was wondering what would happen when there is another force (e.g. friction)? Is it better to say that the work done for a general case is
$$W = F_{net} d \cos\theta.$$
| First, you must recognize that your formula only works for constant forces and motion in one dimension.
So, if all of those conditions are met, then just add up the work done by each force.
$$W=F_1d\cos\theta_1+F_2d\cos\theta_2$$
If both forces act in the same direction ($\theta_1=\theta_2=\theta$), then you can combin... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Variance of a hermitian operator Take an hermitian operator $O$ such that $O|\psi\rangle = x|\psi\rangle$. The variance of an operator $O$ is defined as
$$ (\Delta O)^2 = \langle{O^2}\rangle - \langle{O}\rangle^2.$$
Let's consider the first term, I would write it as
$$ \langle{O^2}\rangle = \langle\psi|O O|\psi\rangle... | As you have written things, the variance is indeed $0$ because $\vert\psi\rangle$ is an eigenstate of $O$: thankfully this is so as it means the outcome with eigenvalue $x$ is not uncertain and we can use the eigenvalue $x$ to label the state.
| {
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"url": "https://physics.stackexchange.com/questions/465923",
"timestamp": "2023-03-29T00:00:00",
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Why do prism split light at angle instead of curving it? I assume that when light goes through matter, it doesnt really slow down, but the waveform is pushed back due to some resonance with the atoms.
EDIT: Interference is probably a better word than resonance here
I also assume that the above effect is responsible for... |
I also assume that the above effect is responsible for the refraction index of materials.
Yes. The index of refraction is a quantification of how the speed of light changes due to the medium it is propagating through. So whatever mechanism slows the light down is what is responsible for the index of refraction.
But ... | {
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Do gluons interact with each other by the strong foce? I learned that strong force between quarks are mediated by gluons. What does this say about interactions between gluons? Do they interact with each other by the strong force?
| If you take a look at the QCD Lagrangian describing the strong force
\begin{align}
\mathcal{L}_{QCD}= \overline{q}(i D_\mu \gamma^\mu - m) q - \frac{1}{4} G_{\mu \nu}^a G_a^{\mu \nu}\, ,
\end{align}
you can see in the term $\frac{1}{4} G_{\mu \nu}^a G_a^{\mu \nu}$ we have a contraction of the gluon field strength tenso... | {
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"source": "stackexchange",
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Seebeck coefficient of metals In some metals such as Platinum Seebeck coefficient is taking for 0 conditionally.
https://en.wikipedia.org/wiki/Seebeck_coefficient#Seebeck_coefficients_for_some_common_materials
Or graphite.
How it is possible to explain it physically? Why exactly it is "0"?
The Seebeck coefficient of p... | This is explained in the very same article that you linked. The absolute Seebeck coefficient is simply difficult to measure because the voltage probes with which you measure also experience a temperature gradient. Hence, the measured voltage is influenced by both the Seebeck coefficient of the sample material and the S... | {
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Are Electrons in a Circuit Subject to Newton's Third Law? Consider a simple electrical circuit made up of a battery, an incandescent bulb, and wire. The battery and bulb are equal in mass and are on opposite sides of a circle made up by the wire. Lastly, the circuit is operating and floating freely in microgravity.
Si... | Yes, conservation of angular momentum applies and the system will not rotate. I assume that the bulb radiates isotropically and also that any other radiation effects are isotropic. The electrons cannot be set into motion without a reaction force on the battery.
However the magnetic field will polarise electron spins, f... | {
"language": "en",
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"source": "stackexchange",
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Peskin & Schroeder eq. 9.26 and functional methods I have been reading chapter 9 in Peskin & Schroeder's QFT book and has been stuck in transition from equation 9.26 to 9.27. Equation 9.26 reads:
$$\frac{1}{V^2} \Sigma_{m,l} \exp{[-i(k_m.x_1+k_l .x_2)]}(\prod_{k_{n}>0}\int{d\ Re\phi_{n}\ d\ Im\ \phi_{n}}) * (Re\ \phi_{... | Consider the case when $k_l=-k_m$. Peskin and Shroeder equation 9.26 would then read
$$ \frac{1}{V^2} \sum_m e^{-ik_m.(x_1-x_2)}\left(\prod_{k_n^0>0}\int d\mathrm{Re}\phi_n\ d\mathrm{Im}\phi_n \right)\times (\mathrm{Re}\phi_m\ \mathrm{Re}\phi_{-m} +i\ \mathrm{Re}\phi_m\ \mathrm{Im}\phi_{-m}+i\ \mathrm{Im}\phi_m\ \mathr... | {
"language": "en",
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Is 1 liter always equal to 1 cubic decimeter, independently of temperature, pressure, etc? I recently found this conversion table for the unit conversion $\rm mmol/m^3 \ \leftrightarrow\ \rm mmol/L$ (millimoles per cubic meter to millimoles per liter)
My physics is very rusty, but just to be sure, is it true that a lit... |
is it true that a liter of liquid always corresponds to a particular volume?
Yes, this is correct. The relationship
$$
1\:\mathrm{L} = 10^{-3} \:\mathrm{m}^3
\tag 1
$$
(i.e. one cubic meter is a thousand liters) is universal and it does not depend on anything. The liter is a unit of volume - by definition, it's a cub... | {
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Metric for a Collapsing Disk and FLRW I have to obtain a time-dependent metric for a disk which satisfies a simple differential equation but I am stuck with making sure that the physics is correct.
To be explicit, I'll first describe a shrinking disk:
Suppose that we are working in a $4D$ Minkowski spacetime $(\mathca... | The metric
$$ds^2=-dt^2+dx^2+dy^2$$
with:
$$x^2+y^2=R^2\,\quad \Rightarrow \quad y=\sqrt{R(t)^2-x^2}$$
$$dy=-{\frac {x{\it dx}}{\sqrt { \left( R \left( t \right) \right) ^{2}-{x
}^{2}}}}+{\frac {R \left( t \right) \left( {\frac {d}{dt}}R \left( t
\right) \right) {\it dt}}{\sqrt { \left( R \left( t \right)
\right... | {
"language": "en",
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"source": "stackexchange",
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Maxwell Tensor Identity In Schawrtz, Page 116, formula 8.23, he seems to suggest that the square of the Maxwell tensor can be expanded out as follows:
$$-\frac{1}{4}F_{\mu \nu}^{2}=\frac{1}{2}A_{\mu}\square A_{\mu}-\frac{1}{2}A_{\mu}\partial_{\mu}\partial_{\nu}A_{\nu}$$
where:
$$F_{\mu\nu}=\partial_{\mu} A_{\nu} - \par... | Hint: Try introducing an integral to the expression so it becomes $$-\frac{1}{4}\int F_{\mu\nu}F^{\mu\nu}\text{d}^d x$$
and take the total derivative terms to vanish at infinity. A much more careful argument can be made here in the presence of boundaries, but this should get you started.
| {
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Why parity required symmetry? I'm studying parity for the first time but there is something I don't understand.
I read that a system conserves parity if every experiment is the same in a mirror that is also $180^{\circ}$ flipped.
When I look myself doing something in a mirror everything is the same and so I'm a syste... | rubbish You are not a system that conserves parity. Maybe you need a more rigorous definition of a parity transform: https://en.wikipedia.org/wiki/Parity_(physics) /rubbish
Parity transform means that you mirror the system in three perpendicular planes. So lets see. First we mirroring: your left and right hands swap p... | {
"language": "en",
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Poisson's ratio in analytical beam deflection equations After looking at some of the analytical expressions for analyzing beams, I noticed that none of the equations depend on the material's Poisson ratio. Some analytical expressions can be found in https://www.linsgroup.com/MECHANICAL_DESIGN/Beam/beam_formula.htm
I be... | One of the assumptions of Euler-Bernouli theory is that the cross sectional plane remains rigid.
Consider a cantilever beam (slender) with rectangular cross section. The above assumption implies that breadth and height can NOT change even though there is extension in the longitudinal direction (unrealistic but that is ... | {
"language": "en",
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How does the green function for the wave equation in three dimensions preserve the ordering of noises between a speaker and a listener I was provided with the following equation in class for the Green's function of a three dimensional wave equation:
However, I am confused as to how this form of the Greens function pre... | This Green’s function is for a single sound pulse emitted from $r=0$ at $t=0$. It doesn’t explicitly describe a sequence of sounds.
However, from it you can see that the sound arrives at distance $r$ at a time $r/c$ after it is emitted. So noises emitted later are going to arrive later.
For a better understanding of th... | {
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Principle of friction force When two equal and opposite forces act on a body at rest or in motion we say it is rest or in its state of motion. But when a body kept on a table starts moving uniformly due to a force applied, it overcomes force of friction.Does it really overcome the force of friction or is just equal to ... | It's just that the scenario "when a body kept on a table starts moving uniformly due to a force applied, it overcomes force of friction" is a bit nastier than the simple sentence would lead us to believe. It makes us think of an object which (i) immediately starts moving, and (ii) keeps a constant speed. Well, it would... | {
"language": "en",
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Propagation of light Suppose we are able to make any place free from the magnetic and electric field; then we turn on a light source at any place in that region (where there is no electric and magnetic field). Does light propagate in that region?
| There is the scientific method of limit value analysis. Let’s see what happens to the light in extreme situations.
The local speed of light is influenced by the local gravitational potential. About an influence of electric or magnetic fields on the speed of electromagnetic radiation is nothing published. So even the th... | {
"language": "en",
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In a pilot-wave model, is knowing the position of the particle sufficient for predicting its behavior? Suppose that we somehow exactly know the position of an electron before hitting the double-slit structure (for example we know it's 20cm away from the structure and it's closer to the left slit). In fact we are no lon... | Yes.
To expand: (I am going to use Bohm's pilot wave theory for concreteness).
In normal Newtonian physics, predicting the path of a billiard ball in say a gravitational field requires knowing its position and velocity.
In Bohm's pilot wave theory, the velocity of the particle is defined by the Bohmian velocity formul... | {
"language": "en",
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"source": "stackexchange",
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Flux received by a negative charge Consider two charges $+q$ and $-Q$ placed at a distance, note charge $q$ and $Q$ are different in terms of magnitude.
My question: is number of flux lines received by $-Q$ proportional to its own charge, or does $+q$ charge have anything to say at all?
As according to gauss law
Sour... | The number of flux lines of each charge is proportional to its own charge.
The other charge has nothing to do with that.
See this image with two unequal charges. The right negative charge ($-3Q$)
has three times the size of the left positive charge ($+Q$):
(image from Chegg Study: physics questions and answers)
This i... | {
"language": "en",
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"source": "stackexchange",
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Self-interaction in spin-orbit coupling? In spin orbit coupling, in an atom motion of electrons about nucleus generates magnetic field and we consider this field to interact with magnetic moment of electron. It sound strange as in electrostatics a field is generate by a charge particle but this field does not interact ... | It's in the name $\textbf{spin-orbit}$ coupling. The source of the magnetic field is the orbital angular momentum, whose origin was discussed by Andrew's answer. And the dipole that is interacting with it is due to the spin. So the field does not interact with the origin of the dipole as the source of the two are diffe... | {
"language": "en",
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Difference between voltage, electrical potential and potential difference I am having hard time to visualize these two concepts in my mind seriously.
First of this confusion came from two parallel plates that was connected to a power supply, charged then disconnected from power supply and then separated from each othe... | In a parallel plate capacitor, the electric field is homogeneous between the plates (we neglect boundary effects here) and given by
$$ E = \frac{\sigma}{\epsilon\epsilon_0},$$
where $\epsilon$ is the relative dielectric constant of the medium between the plates, and $\sigma$ is the charge density on one plate. The dire... | {
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Does a vacuum solution to the Einstein equation imply flat spacetime? I have read that a solution to the vacuum Einstein equation has a vanishing Einstein tensor, and therefore a vanishing stress-energy tensor. This means that there is no matter to generate spacetime curvature. If there is no matter to generate spaceti... | No, a vacuum solution does not imply flat spacetime.
It is possible, as in a Schwarzschild metric, to have a zero Einstein tensor but a nonzero Riemann tensor. The Riemann tensor is the most detailed indicator of curvature, with 20 independent components (out of 256 nominal components) at each point in spacetime. The E... | {
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"source": "stackexchange",
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Lattice gauge theory under a Lorentz transformation Taking a grid of 'evenly-spaced' space-time points. e.g. at integer values of (x,y,z,t). Now do a Lorentz boost on this grid. We end up with a grid of points which are much closer together.
It is bothering me that the grid of points only looks evenly distributed in ce... | Lattice theories are not invariant under Lorentz transformations. They are usually defined in Euclidean signature (imaginary time) so the symmetry woud be ${\rm SO}(N)$ rather than ${\rm SO}(N-1,1)$ --- but apart from this the lattice breaks the rotational symmetry down to a discrete subgroup of 90 degree rotations.... | {
"language": "en",
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"source": "stackexchange",
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Weak Energy conditions for Perfect fluid derivation
I want to derive the restraints $$\rho + p \geq 0\qquad\text{and}\qquad \rho \geq 0$$ which correspond to applying the weak energy condition ($T^{\mu \nu} v_\mu v_\nu \geq 0$ for $v_\mu$ timelike) on the stress energy tensor $T_{\mu \nu}$ of a perfect fluid given by
... | The statement of the weak energy condition is that
\begin{equation}
T^{a b} v_a v_b \geq 0
\end{equation}
holds for any timelike vector $v$.
The first important step is to prove that the weak energy condition implies the null energy condition, if the previous inequality holds for any timelike vector $v$, it will also ... | {
"language": "en",
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What are equations of state in thermodynamics? So I am having real trouble understanding what equations of state are and how we form them. My issue stems from reading multiple sources. So I understand that an equation of state is used to build a relationship between variables to describe a state of a system.
For exampl... | An equation of state is simply an equation that shows the relationship between the properties of a system when the system is in equilibrium, that is, when the properties (Temperature, Pressure, Volume, etc.) are not changing in time. For example, the equation of state of an ideal gas is given by
$$PV=NRT$$
Where $P$ is... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How can a day be exactly 24 hours long? The longest solar day of year is approximately 24 hours 0 min 30 seconds (occurs at mid to late December) while the shortest solar day of year is approximately 23 hour 59min 38 seconds. If I average out both of these I come up with average solar day of 24 hour +4seconds. Why then... | The original definition of an hour was 1/24th of a day, no matter how long the day was at the time. The durations you're quoting are only possible with the help of extremely modern definitions made possible by redefining the second (keeping the minute and hour fixed as 60 seconds, and 3600 seconds, respectively).
| {
"language": "en",
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"source": "stackexchange",
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How can I calculate the speed at which a gas flows from one volume to another? Suppose that there are two rigid Volumes A and B. Each of these contains a gas with know properties (pressure, temperature, number of moles, volume, composition). Suppose also that there is a pipe with a valve that connects the two Volumes.
... | The ideal gas equation of state that you've mentioned or the equation of heat transfer provided in the other 2(!) self-advertising answers don't help in this case. Heat transfer only talks about.. well the heat of the fluid, not its bulk movement.
For your problem, you need a variant of the Euler equations, which contr... | {
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Can someone provide to me an intuitive explanation of the second integral of position with respect to time? I am aware of what the first integral of position, absement means (at least to a very superficial level).
However, I can find nothing regarding the physical intuitive meaning of absity, the second integral of pos... | You can say that the position is the second derivative of it, so that the relation between this quantity and the position is the same between the position and the acceleration.
I've never seen this quantity be used for a physical purpose, it carries indeed very redundant information.
| {
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"source": "stackexchange",
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Longitudinal magnification I want to prove that if an object is small in length and lying along the principal axis then
$$M = -\frac{dv}{du} = -\left(\frac{v}{u}\right)^2$$
Where, $M$ is the longitudinal magnification.
| In geometrical optics the following relation between the longitudinal positions of object and image (respectively $u$ and $v$) together with the focal length $f$ is valid:
$$\frac{1}{u} + \frac{1}{v} = \frac{1}{f}$$
If the object is small and it has one of its ends at $u_1$, with the corresponding image at $v_1$, we ca... | {
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Why the time period of pendulum with infinite length is $84.6$ minutes? In a book I was reading about SHM it stated:
If the length of a simple pendulum is increased to such an extent that $\ell\to\infty$, then its time period is given by,
$$T=2\pi\sqrt\frac{R}{g}\approx84.6\text{ min}$$
Now I have many confusions like:... | $\def\PD#1#2{{\partial#1 \over \partial#2}}$
I would suggest a different approach. If $l$ is very large the circumference of radius $l$ becomes a straight line, tangent to a circumference centred in Earth's centre C and radius $R$. If $x$ is bob's displacement along this line, bob's distance from C is $D=\sqrt{R^2+x^2}... | {
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If a downed power line hits your car, why should you shuffle away from it? A bit of fun! My colleague showed me a video at work about what to do if a downed power line lands on your car.
https://www.youtube.com/watch?v=Psv3ySUoF3Q&feature=youtu.be&t=54
In the video, the narrator says this about how to get out of the ca... | A downed power line can create a voltage gradient across the ground. If your two feet touch areas that have a voltage difference, a current can flow up one leg and down the other, electrocuting you. By keeping your feet close together, you are minimizing the potential for this to happen, as nearby points on the ground ... | {
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Why doesn't Newton's third law mean a person bounces back to where they started when they hit the ground? When we drop a ball, it bounces back to the spot where we dropped it, due to the reaction forces exerted on it by the ground. However, if a person falls down (say, if we push them), why don't they come back to thei... | Energy is not lost, but it is expended in different ways when different objects collide.
A more visceral statement of these principles:
Drop a rubber ball on the floor. As it hits the floor it stores up spring energy inside itself, and then bounces back almost as high as the start point, losing only a little energy to... | {
"language": "en",
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"source": "stackexchange",
"question_score": "18",
"answer_count": 6,
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If atmospheric pressure is 76 cm of $\text{Hg}$ , why won't 76 cm of mercury stay in an open tube when suspended in air? If we keep an hold a tube in air with the closed end up and open end downwards, containing mercury upto a length of 76 cm, why does the mercury not stay in place? Shouldn't atmospheric pressure exert... | You probably mean this:
Let we fill the tube with closed end at the bottom with 76 cm of mercury. Then we will turn the tube upside down. The mercury will flow out from it.
It happens because during the rotation of the tube some amount of mercury flowed off, and is instantly replaced with air, which moves up to the c... | {
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Minkowski space
*
*In Minkowski space, coordinates which satisfy
$x^2 = t^2 - X^2 > 0$
are in the region of spacetime that is time-like.
*If it's
$x^2 = t^2 - X^2 < 0$
the region is space-like.
*But if
$x^2 = t^2 - X^2 > 0$
then its "trajectory of light-like particles".
I have understood the first two points abou... | Only particles with zero mass can travel between two events which are separated by a light-like distance. The trajectory is called light-like because photons (light) are massless, and historically the first example of a massless particle, as well as the only example in the 1910's. There are other massless particles, li... | {
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Geometrical Optics: Infinite Rays Normally in ray optics, we draw a parallel line from the top of the image to the lens and stop when this line intersects an angled line (drawn from the height of the real object) and intersects. However, why do we stop? We can draw infinite rays from this object and they should be able... | I have added some more rays onto your diagram and omitted the arrowhead to make the diagram clearer. I have also ignored the effects of spherical aberration.
Every point on the object produces light which travels along rays and after reflection from the mirror meet at a corresponding point on the image - neighbouring... | {
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Why is normal force at the bottom dependent on normal force on top?
Why does the normal force on bottom of the track have anything to do with the normal force on top of the track? Why isn't the normal force at the bottom simply $mg$?
| You need to know that a motion can be accelerated in two independent ways or any combination of these; either when there is a change in velocity, or when there is a change in direction of motion.
The above problem has a constant velocity but the direction of car at every point of the loop changes, which mean the motio... | {
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Why does $\sqrt{\frac km}$ represent angular velocity and not frequency? When I break down $\omega = \sqrt{\frac km}$ (angular velocity for a simple harmonic oscillator) into its units, I get:
$$\omega = \sqrt{\frac{kg * \frac {m}{s^2}}{kg *m}}$$
which simplifies to:
$$\omega = \frac 1s$$
If I'm not mistaken, that is t... | Looking into the equation of motion of a mass attached with a spring of spring constant, we get
$$\frac{d^2x}{dt^2}= - \left( \sqrt{\frac{k}{m}} \right)^2 x \;,$$
which is analogues to the equation
$$\frac{d^2x}{dt^2}=-(\omega)^2 x \;.$$
(Obtained by double differentiating $x=ACos(\omega t+\phi)$). Here $\omega$ is... | {
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Does the Central Limit Theorem hold for position measurements? A friend asked me recently if the Central Limit Theorem holds for quantum systems: i.e., if the distribution of measurements (e.g., of position) for any wavefunction would prove approximately normal, given enough samples.
My gut response was no, because I'v... | Let's be clear here: You're asking whether the probability distribution of the normalized sum of many individual quantum measurements of the same quantity necessarily tends to a normal distribution, not whether the probability distribution of the possible outcomes of any single quantum measurement is necessarily a norm... | {
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Why the source function is equal to Planck function when we have a local thermodynamic equilibrium? I understand that the source function $ S_λ $ for the special case of blackbody radiation is equal to the Planck function $B_λ $.
However, in the broader case of a local thermodynamic equilibrium (and not the special ca... | The source function is a property of the body itself and not the radiation field it is immersed in. If the object is in local thermodynamic equilibrium then the source function only depends on temperature.
In principle you could put the body in a cavity filled with black body radiation at a given temperature and it wou... | {
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What does 'coupling' mean? (Laser) I assume this question is so basic that no YT-video or paper I found answers it. But in order to understand I have to know what it refers to.
I'm talking about laser coupling to be exact. I have a 'coupler' device. What does it do with the laser?
| Coupling is the term used to describe the coupling of laser equipment together in the same way as a mechanical coupling.
One such laser coupler is the laser to fiber-coupler as can be seen in this youtube video.. The goal in this device is to get the laser output beam coupled as good as possible into the fiber cable.... | {
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Derivation of length contraction in Einstein, Relativity: The special and general theory I was reading the book, "Relativity: The special and general theory" by Einstein. At some point it discusses the awkwardness of "relativity of simultaneity" with using universal time axis for all inertial frames. And to fix it uses... | From the first equation, at time t , we can write $$x= x' \sqrt{1-\frac{v^2}{c^2}}+vt.$$ Substitute for $x'=0$ and $x'=1$, and do $x_{(x'=1)}-x_{(x'=0)}$. You will get the answer.
| {
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Light in classical electrodynamics I am starting to learn elementary electrodynamics with Griffiths.
In the book, he has shown the natural correspondence between light and electromagnetic plane waves.
The problem that has agitated me is that plane waves are "global solutions", i.e. they have non-trivial EM field almost... | The reason is that light in real life is better approximated as "spherical", although when you zoom in, it looks like planes.
Spherical waves expand as they propagate, and therefore decrease in intensity due to conservation of energy. So if a wave carries a certain amount of energy power P (Joules per second), the inte... | {
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Infinite Electricity from Photon Inside Closed Box with Magnet Attached in a Coil? (Thought-experiment) Let's say I have a very large box with a magnet attached to the outside. Inside the box there is a perfect mirror on each side.
I open my box and quickly shoot in one photon before shutting it. After some time the ph... | Effectively, what you're doing is Compton scattering with a very massive object rather than a subatomic particle. In particular, this means that when the photon collides with the walls of the box, its energy will decrease slightly. This means that the photon will slowly lose energy to the box; and as time goes on, i... | {
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How does light 'choose' between wave and particle behaviour? Light exhibits wave behaviour in phenomenon such as interference but particle behaviour in the photoelectric effect. How does light 'choose' where to be a wave and where to be a particle?
|
How does light 'choose' where to be a wave and where to be a particle?
It doesn't. It always behaves as a wave (obeying the principle of superposition), and it always behaves as a particle (particle number being quantized).
It sounds like you may have been influenced by someone who told you that light behaves like a ... | {
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Why do stars appear so close in universe photos? I saw an extremely sharp picture (from NASA/ESA) of the Andromeda Galaxy recently, and it made me wonder why the stars appear so close together, when I know in fact that they are not.
Is it simply because there are many stars behind stars, so that even if two stars are ... | Your guess is correct; the stars appear close together because they are far away.
Relatively nearby stars are resolvable as distinct points, but in very distant galaxies it is often not possible to resolve individual stars.
Dark spaces between individual stars are actually full of stars and galaxies full of stars. T... | {
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Uniqueness Theorem and the 1D Infinite Square Well Consider the 1D infinite square well problem: $$\frac{d^2\psi (x)}{dx^2} = -k^2\psi (x)\tag{1}$$ along with the boundary conditions $\psi (0) = \psi (L) = 0$. This seems to be a well posed problem with enough information to have a unique solution but the solution $\psi... | The 1D square well is quite different from the classic harmonic oscillator. You need to remember that the wave function in the square well is actually a function of $x$ and $t$. While it is normal to compute the amplitude from normalization, we could compute it from specifying initial conditions.
If you want to compa... | {
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If a satellite speeds up, does that make it move farther away or closer? If a satellite is in a stable circular orbit and goes about 41% faster (escape velocity) then it leaves its host forever. I get that. However, what if it speeds up by less than 41%?
Intuitively, it would seem to make the satellite move farther awa... | What you are missing is that as the satellite moves farther away from the Earth, it slows down because of work done by the gravitational field.
Since you have given the satellite more total energy (kinetic plus potential) and because the total energy of a bound orbit is $-GMm/2a$, where $a$ is the semi-major axis, then... | {
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How did the Intersecting Storage Rings Actually Perform Tests I am reading the book written in 1982 titled "Quarks, The Stuff of Matter" by Harald Fritzsch. In it he writes about the ISR at Cern, that slammed protons together and in some of those collisions, 2 quarks bounced off each other at right angles to the proto... | The ISR was, in large part, built as an experiment in accelerator technology. When it succeeded, CERN considered it a "facility for experiments". Unlike modern colliders, which are built along with detectors aimed at specific physics, the ISR was well along on construction while the physics was still being discussed. ... | {
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Location of free charge in insulators I'm going through the introductory section to Electrostatics in Materials in Griffiths, and I have a question that I can't seem to find a satisfactory answer to.
If I have an insulator with free charge, is it necessarily confined to the surface?
In the case of a conductor, Gauss' l... | The question is not entirely clear; I wonder if you are really asking about bound charge (polarization charge).
Free charge is charge that is free to move macroscopically; bound charge is charge that can only move on a microscopic or submicroscopic scale. Free charge ends up on the surface of a dielectric medium unde... | {
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Calculating percentage error with significant figures I have a problem with significant figures. In an assignment, the paper gives us data to $3$ significant figures to calculate some values but afterwards requires us to calculate the percentage difference given an accepted value that is to $4$ significant figures. If ... | That's the point, you weren't meant to round it up. Approximation of numbers comes with error because you are, for instance, adding .005 to 2.545 to approximate it to 2.55. The .005 has a value and adding it when it never existed generates error. Now the question is requesting you to calculate the percentage error (.00... | {
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Lorentz Transformation: Message sent before finish line As she wins an interstellar race, Mavis has a “hooray” message sent from the back of her 300m long ship as she crosses the finish line at v=0.6c. Stanley is at the finish line and at rest relative to it. He claims the message was sent before she crossed the line... | Here's a spacetime diagram drawn on rotated graph paper (so that one can more easily measure displacements in time and space along segments and so that one can visualize the orthogonality between an observer's time and space axes).
It encodes the calculation (without explicit use of the Lorentz Transformation formulas)... | {
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What would happen if we use two of Schroedingers cats? I am worrying about Schroedinger's cat's experiment and I am wondering about the phenomena. First of all, I have to say that I am not a physicist and I have no clue about more than advanced high-school physics.
As far as I understood the experiment there is a chan... | If the experiment is set up in such a way that the quantum mechanical event that kills a cat is guaranteed to kill both cats (e.g., it releases poison gas into a chamber containing both cats), then the experiment entangles the cats' alive/dead states in such a way that either both cats live or both cats die. That's th... | {
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Variation of Refractive index We know that refractive index, for any medium,
$$n=1/\sqrt{\epsilon\mu}.$$
Also, according to Cauchy's relation
$$n=A+B/\lambda^2,$$
where $A$ and $B$ are constants related to the medium.
According to the first relation, refractive index isn't in any way related to the wavelength of the li... | There is no discrepancy. Generally speaking, the permittivity of the medium depends on the wavelength, which means that $n=1/\sqrt{\mu\epsilon}$ also depends on the wavelength. (The magnetic permeability could also depend on the wavelength, but this is much less frequent.)
It's also important to note that Cauchy's rela... | {
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Why do we observe the nuclear force only in scatterings and decays? Why, at first glance, are the only forces we perceive to be gravity without quantizing, electromagnetism and nuclear forces only in disintegrations?
| Gravitational and electromagnetic potentials of a point source both fall of with the distance $r$ as $1/r$. This is a "long-range" characteristic compared to the effective nuclear forces that are mediated by massive particles (pions) and have a Yukawa potential, where the $1/r$ Coulomb behaviour is screened by an expon... | {
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How is the relative force of the fundamental forces measured? My physics textbook includes the following table:
My question is about the fourth row, where it compares the relative strengths of the fundamental interactions. How are these determined? Is the ratio of electromagnetic and gravitational simply the ratio of ... | Here is another table of fundamntal forces as used in particle physics.
Fundamental means the basic framework, and the basic framework is quantum mechanics, from which macroscopic forces emerge which can be demonstrated mathematically. These forces exist at the particle level, and their strength relative to each other... | {
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Will sound be generated by the capture of air from a vacume? I have a thought experiment. If I had a box sized vacuum sitting on the floor in front of me and I were to instantaneously remove all the walls of my box. Would the capturing of air from that vacuum make a noticeable sound?
| Yes. Once the walls are magically removed, the air surrounding the box will suddenly rush inwards toward the center of the box volume- thereby propagating a rarefaction wave outwards at the speed of sound- which you will hear. Very soon thereafter, all the inrushing air will meet at the center of the box volume and reb... | {
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Why is the neutron magnetic moment negative? I understand that the magnetic moment is due to the quarks, but specifically why is it negative? Is it due to the two down quarks or something?
| Because the "large" pieces in the baryon octet wavefunctions usually win.
Bég,Lee,&Pais, PRL 13 (1964) 514, a historically significant demonstration that the naive constituent quark model with a symmetric wavefunction was there to stay, one way or another-- and thus led to the inference of color to antisymmetrize it c... | {
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Why are there rings (halos) around street lights? Especially when it's foggy I was in a car that was turned off last night for some time and the windows became foggy via condensation (moisture droplets building up on one side of window). Looking outside, I could see that street lights which were near me had a halo or a... | A couple of years ago a little piece of debris met my left eye. Later that day at night I started to notice a halo around streetlights as seen by my left eye. After an eye doctor visit and some treatment and time, they were gone for good. That made me ask myself the same question.
The rings are not around the street li... | {
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What is the definition of beam energy in particle physics? For example, the proton beams in the LHC collider have 7 TeV energy. Does this mean that the individual protons in the beam have 7 TeV energy or that the energy of all the protons in the beam add up to 7 TeV?
| In the LHC, each individual collision has a center-of-mass energy of roughly 14 TeV. Since the collisions are symmetric (two protons with equal energy, moving in opposite directions, collide), we can say that each individual proton has roughly* 7 TeV of energy.
As you can probably tell, adding up the energy of all of t... | {
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Is throwing dice a stochastic or a deterministic process? As far as I understand it a stochastic process is a mathematically defined concept as a collection of random variables which describe outcomes of repeated events while a deterministic process is something which can be described by a set of deterministic laws. Is... | Physics models rarely hint at ontological level. Throwing dice can be modelled as deterministic process, using initial conditions and equations of motion. Or it can be modelled as stochastic process, using assumptions about probability. Both are appropriate in different contexts. There is no proof of "the real" model.
| {
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Does a particle exert force on itself? We all have elaborative discussion in physics about classical mechanics as well as interaction of particles through forces and certain laws which all particles obey.
I want to ask,Does a particle exert a force on itself?
EDIT
Thanks for the respectful answers and comments.I edited... | What even is a particle in classical mechanics?
Particles do exist in the real world, but their discovery pretty much made the invention of quantum mechanics necessary.
So to answer this question, you have to set up some straw man of a "classical mechanics particle" and then destroy that. For instance, we may pretend ... | {
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Can you change the wavelength of light keeping frequency constant and can you do the opposite as well? Can you change the wavelength of light keeping frequency constant and can you do the opposite as well?
I understood the basics but please don't hesitate to go deeper into the concept. Also, If you happened to have an ... | Frequency: acoustic optics can change the frequency.
Wavelength: the speed of light $=3\cdot 10^8 m\cdot s^{-1}$ in vacuum, change a material with different reflective index change the wavelength.
| {
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Displacement currents, aren't really currents? I'm confused with this definition of displacement currents within capacitors via Wikipedia:
However it is not an electric current of moving charges, but a
time-varying electric field.
It's a time-varying electric field, but there isn't any actual flow of current, while... | In the absence of current the Maxwell equation reads $\partial \vec E = \vec \nabla \times \vec B /c^2$. This equation means that both sides denote the very same thing. It does not mean that E induces B or vice versa.
| {
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Why hydrogen lines are less visible in the Sun spectrum than in supernovae clouds? Supernovae clouds are very colorful, and if I trust documentaries I watched, the colors are due to excitation of elements, as in fireworks. Since the Sun is mostly made of hydrogen, I suppose those lines should be very apparent but they ... |
What contributes to the rest of the spectrum up to the point it masks
hydrogen lines?
It's basically due to the optics.
In the case of the sun, you're seeing the energy of the gas in the outer shell. This is highly random, moving in all directions and over a huge distribution of speeds. So everything is being blurr... | {
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Resource recommendation for spintronics What are some good beginner level books to understand spintronics. I am looking for some sources in which basic mathematics of spintronics is properly explained.
| You should start with books on solid state physics, obviously. Beginner level material is "Kittel" or "Ashcroft/Mermin". You may continue with mathematically more involved books as, for instance, Bruus/Flensberg to understand the modern solid state physics notation. There some basic spintronics phenomena are already me... | {
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Does kinetic energy warp spacetime? My interpretation of GR leads me to think that energy (namely kinetic) also adds to the curvature of space-time. Which, has raised a thought experiment. If a $10000$ kg ship closely passed a $1$ kg glass ball at $0.8c$ relative to the glass ball, would the glass ball be moved in the ... | The answer is yes, and this is actually an important point when considering extremely high-energy physics. As a result of this effect, gravity is the dominant interaction at sufficiently high energies, at least if we can trust the most straightforward extrapolation of the current foundations of physics. This is highlig... | {
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Why are solar panels kept tilted? I have noticed that, in my country India, most of the solar panels are tilted southward at an angle of ${45}^{\circ} .$ Even on buildings with inverted V-shaped roofs, solar panels are still oriented southward on both the sides of roof.
Research
Many sites suggests that the tilt aids ... | *
*Because in northern hemisphere sun is at the south (it moves from east to west - but always on the south side of the sky), by tilting the solar panel towards the sun (to the south) you increase energy generation. Solar panel at 90° angle towards the sun gives you near 0 energy, at 0° (directly looking at the sun) y... | {
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Why is it that magnetic fields(or any field)not move in space? When I imagine a magnetic field produced by a magnet, or the electric field produced by a charge, I've learned that the fields are stationary, however, their value(across space) changes.
If I placed the magnet at a point $P$($0,0,0$), and then moved the m... | The fields are stationary with respect to a coordinate system fixed to the magnet.
| {
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Simple harmonic motion as projection of circular motion Can we consider $\omega$ (angular frequency) in equation of simple harmonic motion (SHM) as the angular velocity of the object in circular motion, when we see simple harmonic motion as projection of circular motion?
|
Yes. The point on the circle with radius $R$ revolves around the centre, with angular velocity:
$$\omega=\dot{\theta}=\frac{\mathbf{d}\theta}{\mathbf{dt}}$$
The projection on the RHS axis, call it $y$, is:
$$y(t)=R\sin(\omega t+\phi)$$
where $\phi$ is the angle $\theta$ at $t=0$.
| {
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Grassmann-even action I am currently studying supersymmetric quantum mechanics with the help of the book Mirror Symmetry by Kentaro Hori (and others). On page 155 where they introduce Grassmann variables they say that the action is Grassmann-even without an explanation. But i do not quite understand why this is the cas... | *
*At the classical level, the action $S$ can have any Grassmann-parity.
*At the quantum mechanical level in a path integral/partition function, it would be rather strange/exotic$^1$ to consider a Boltzmann factor $$\exp(\frac{i}{\hbar}S)~=~1 +\frac{i}{\hbar}S$$ for a Grassmann-odd action $S$. In particular, the Bolt... | {
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"answer_id": 1
} |
Why aren't satellites disintegrated even though they orbit earth within earth's Roche Limits? I was wondering about the Roche limit and its effects on satellites.
Why aren't artificial satellites ripped apart by gravitational tidal forces of the earth?
I think it's due to the satellites being stronger than rocks?
Is th... | The Roche limit is a limit on objects being held together by their own gravity. Satellites are held together by much stronger forces. Different parts of the satellite are ultimately connected by chemical bonds, which are electromagnetic.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/480190",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "39",
"answer_count": 6,
"answer_id": 3
} |
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