Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Relationship between the constancy of the laws of physics and conservation principles I have heard it said before in passing (I think it was on Star Talk Radio) that there is some specific relationship between the constancy of the laws of physics and conservation principles such as the conservation of momentum and cons... | You are referring to the theorem of Emmy Noether: "If a system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time". Any such symmetry refers to the constancy of the laws of nature under this symmetry transformation. For example, if you observe a system in a pa... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/411130",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Symmetry groups of 3D systems which are periodic in one direction and homogeneous in the other 2 directions What kind of symmetry groups, analogue of 3D crystallographic space groups, can describe the spatial symmetries of 3D systems which have discrete periodicity in only one direction, but are homogeneous in the 2D t... | If the system is only discretely periodic in one dimension, the only point groups are the trivial group $C_1$ and the group $Z_2$ generated by reflections about a point.
These, combined with the discrete translational symmetry of periodicity, give the 1D line group.
See https://en.wikipedia.org/wiki/One-dimensional_sym... | {
"language": "en",
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Is there any experiment that doesn't have a finite countable number of outcomes? There are a lot of random variables in physics that are, in principle, continuous and unbounded (canonical examples: time, position along each direction). In practice, it is my understanding that the number of outcomes of every possible ex... | All practical physical measurements have a precision associated with them (this is distinct form uncertainty or accuracy). Like the rounding error on your ruler; this limits the number of outcomes to the
$$\frac{\text{Measureable range}}{\text{Precision}} \, .$$
Additionally it is not possible to actually measure an i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/411666",
"timestamp": "2023-03-29T00:00:00",
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What would happen to a 10 meter sphere of room temperature water if released into space? Imagine that we had a space station with a relatively large hangar, and we allowed a ball of water to accumulate that had a 10 meter diameter and a water temperature of 20C. While the hangar is pressurized, someone decides to use a... | It boils, then the vapor freezes.
It doesn't directly freeze because water is great at holding heat, and the only way to dissipate heat in vacuum is radiation, no convection. However there is no constraint on pressure, and as we know low pressure makes water boil. The process of boiling acts to carry away heat and se... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/411829",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Does the fact that $j^\mu$ is a 4-vector imply $A^\mu$ is, as argued by Feynman? Let
\begin{equation}
\boldsymbol{\Phi}=\Bigl(\dfrac{\phi}{c},\mathbf{A}\Bigr)
\tag{01}
\end{equation}
the electromagnetic 4-potential. We know that if its 4-divergence is zero
\begin{equation}
\dfrac{1}{c^{2}}\dfrac{\partial \phi}{\partia... | After searching in Web, in our PSE site and many books, textbooks, papers and so on I end up with this conclusion :
That the electromagnetic 4-potential $\:A^{\mu}(\mathbf{x},t)\:$ is a 4-vector is an assumption.
In $^{\prime}$Quantum Field Theory$^{\prime}$ by Itzykson C.-Zyber J., Edition 1980, we read (in $\S$1-... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/412110",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Triple Delta Potential in Quantum Mechanics I am facing a problem of Quantum Mechanics, and I gently need your help in continuing to solve it.
The problem is the old usual problem of a particle subject to a potential, which this time has the form
$$V(x) = \alpha \delta(x^3+2ax^2-a^2x - 2a^3)$$
And we need to find the e... |
From here, a simple sketch of the potential highlights $4$ regions:
$$\begin{cases}
x < -a \\
-a < x < +a\\
a < x < 2a \\
x > 2a
\end{cases}
$$
This is wrong. A delta function $\delta(x + x_0)$ has a peak at $-x_0$, not at $x_0$. You've flipped the sign of $x$.
But my first doubt is: shall I split the second regio... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/412225",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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If iron can’t undergo fusion, does that mean a black hole is mostly iron? Since stellar fusion can’t progress beyond iron, and a large enough star collapsed into a black hole because an iron core stalled fusion, wouldn’t that mean all black holes are predominantly iron?
| If we are talking about stellar-sized black holes, then the object that collapses to form a black hole will have a high concentration of iron (and other iron-peak elements like manganese, nickel and cobalt) at its core, and it is the core-collapse that begins the black hole formation process, but much more material tha... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/412331",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Dissapation of photon energy For an incident photon to be absorbed by a material, must it exactly equal a difference in the electron energy levels, or does it just have to be more than one such difference. If more is okay, what happens to the remaining photon energy? Does it continue on as a lower energy photon, if s... | The energy of the incident photon must be equal to the difference in energy levels whether it be absorbed or emitted, when a photon is absorbed, the electron moves up one energy level, when emitted, the electron moves down one energy level.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/412465",
"timestamp": "2023-03-29T00:00:00",
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How to derive that $pV^k$ is constant in a polytropic process? This is what we did on the lecture:
$$\delta Q=nC dT$$
$$dU=nCdT-pdV$$
$$dU=\bigg(\frac{\partial U}{\partial V}\bigg)_TdV+\bigg(\frac{\partial U}{\partial T}\bigg)_VdT$$
$$dU=\bigg(\frac{\partial U}{\partial V}\bigg)_TdV+nC_VdT$$
$$n(C_V-C)dT=-\bigg(\bigg(\... | The blue line is what is known as a separable differential equation, where we can move all $T$ values to one side, and all $V$ values to the other. So,
\begin{align}
&\left[(C_V-C)\operatorname{d}T=-\frac{RT}{V}\operatorname{d}V\right] \times\left(\frac{1}{T(C_V-C)}\right) \Rightarrow\\
&\int\left[\frac{\operatorname{d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/412727",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Finding the equation of a chain hanging between two points Say I have a connected at either end to two points, $A(x_A, y_A)$ and $B(x_B, y_B)$ of length $l$, where $l \leq \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2}$, how would I go about finding an equation of its shape?
I guess the chain would be of the form $y = \alpha \c... | Taking the solution you propose, you can make $b=0$ since
$cosh(ax+b)=\dfrac{e^{ax+b}+e^{-ax-b}}{2}$
and you can absorb $\beta$ to the remnant of the expansion for the expression. An analogous can be done for constant $\alpha$, and set $\alpha=1$ (Think out: This problem is about two forces acting in one plane, the we... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Symmetry of ground state electron configuration Take a molecule, whose atoms have a symmetry $S\in \text{O}(3)$ (i.e. S permutes the atoms).
$S$ also acts on the wavefuncion $\psi(x_1,...,x_n)$ of the $n$ electrons in the molecule, by its action on the $x_i$ (maybe the most natural action also permutes the $x_i$, I'm ... | Generally, it need not be the case that the electronic ground state of any given molecule will be invariant under a symmetry transformation $S$ which preserves the overall configuration of the nuclear positions. This can be shown to be the case if the ground state is non-degenerate, but if you have a degenerate ground-... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/413101",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Sign of work done by friction In Goldstein's classical mechanics (3rd ed.) we read:
"The independence of W12 on
the particular path implies that the work done around such a closed circuit is zero,i.e.
$$\oint \textbf{F}.d\textbf{s}$$
Physically it is clear that a system cannot be conservative if friction or othe... | Indeed, it's an errata. You can find a list of them here.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Tracking Spacetime Events In the linked post: Liouville's Theorem For Spacetime, I indicated the need for tracking the evolution of spacetime events. Is it sufficient to track a spacetime event by placing a particle there with zero initial velocity? You would then identify the spacetime event with the location of the p... | If a spacetime is globally hyperbolic, it can be foliated by timelike geodesics, ie it is possible that through each point of the spacetime passes a free particle such that no two such particles ever intersect (this can be shown by using the Hamiltonian flow of a Cauchy surface). It can indeed be a way to track spaceti... | {
"language": "en",
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How do contact transformations differ from canonical transformations? From Goldstein, 3rd edition, section 9.6, page 399 after equation 9.101:
[...] The motion of a system in a time interval $dt$ can be described by an infinitesimal contact transformation generated by the Hamiltonian. The system motion in a finite tim... | In the 2nd (but not the 3rd!) edition of Goldstein, Classical Mechanics, the word contact transformation appears in its index, and there is a 13 line long footnote on p. 382, which (among other things) states
[...] In much of the physics literature the term contact transformation is used as fully synonomous to canoni... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/413589",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Misunderstanding of the functioning of the reflective diffraction grating Suppose we have a sawtooth diffraction grating, as depicted below:
where the angle $\beta$ is the angle of inclination of the 'teeth' of the grating with respect to the plane of the grating and incident plane monochromatic waves normal to the pl... | Your question concerning the law of reflection is a good one, and it still applies here. This is what's known as the 0th (zeroth) order, or specular, pattern. There are other orders, or reflection peaks, that occur at different angles due to diffraction and interference. I think your problem asks you to find those o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/413776",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Incorporate spinor in field equation I got problem understanding the concept as it state
1. Spinors do not work with the principle of General covariance. But how and why?
2. Contracting spinor into the tetrad solves this delemma.
Anybody explaining this concept would be helpful.
| The short answer: spinors transform nontrivially under local Lorentz boosts/rotations.
Spinors do not work with the principle of General covariance.
More precisely, it's the local Lorentz covariance that is the focus point here.
Contracting spinor into the tetrad solves this delemma.
In addition to tetrad $e$, we... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/413973",
"timestamp": "2023-03-29T00:00:00",
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Electric potential concept Imagine having two charged plates, one positive and one negative, and a negative point charge is placed at the negative plate. Let's set the negative plate to zero potential. The distance between the negative point charge and the negative plate is zero, so $V$ is zero in the equation $V=Ed$. ... | The value of the potential energy doesn't matter, just the change in potential energy. You can set any level of potential to be the zero point. Think of gravitational energy $mgh$, what is $h$? You could measure it from sea level, or you could measure it from the center of the earth. If you're right at sea level, then... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/414086",
"timestamp": "2023-03-29T00:00:00",
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Expectation value of quantum annihilation operator I already know the expectation value of a quantum annihilation operator $\hat{a} $. I want to find the expectation value of quantum creation operator $\hat{a}^\dagger$. Is it equal to following?
$$\langle\hat{a}^\dagger\rangle = \langle\hat{a}\rangle^* $$
$\langle\hat{... | It is helpful here to remember that the expectation value $\langle \hat{a} \rangle$ is taken with respect to a quantum state $|\psi \rangle$ (or a density operator, but let's keep it simple). In this case,
$$
\langle \hat{a} \rangle = \langle \psi | \hat{a} | \psi \rangle
$$Recall now that $\langle \phi | \hat{O} | \ps... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/414237",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Virial expansion in terms of pressure I'm studying thermodynamics and I found two forms for the virial expansion:
$$pV~=~RT[1+\frac{A_2}{V}+\frac{A_3}{V^2}+\ldots] \tag{1}$$ and
$$pV~=~RT[1+B_2p+B_3p^2+\ldots]\tag{2}$$ my problem is that I can not find the correct procedure to express the coefficients $B_k$ in terms o... | Hints:
*
*Define a "density/inverse volume"
$$\alpha~:=~\frac{RT}{V}, \tag{A}$$
and rescale the $T$-dependent virial coefficient functions
$$ A_k^{\prime}~:=~\frac{A_k}{(RT)^{k-1}} . \tag{B}$$
*Then OP's 2 virial expansions (1) & (2) read
$$p~\stackrel{(1)}{=}~\alpha[1+A^{\prime}_2\alpha+A^{\prime}_3\alpha^2+\ldo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/414386",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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What's the reaction force on a charge moving in a magnetic field? According to newtons third law, all forces occur in pairs. What is the reaction force that the third law predicts when a magnetic force acts on a charged particle moving in a magnetic field?
| In general, Newton's third law is not valid when EM forces due to distant bodies are involved. Two charged moving particles act on each other via electromagnetic forces, but these are not related as action and reaction in Newton's 3rd law; they may even have different directions and magnitudes.
Instead, there is a law ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/414873",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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How do fusion reactors deal with blackbody radiation? The plasma of the ITER reactor is planned to be at 150 million K. Using the Stefan-Boltzmann law, setting the surface area as $1000\,\mathrm{m}^2$ (the plasma volume is $840\,\mathrm{m}^{3}$ so this is being generous), and the emissivity as $0.00001$ (emissivity is ... | In ITER the average electron and ion temperatures are about 8 keV and the electron density is about $10^{20}$ m$^{-3}$.
At such a low density, the plasma is optically thin (see for example How large should an optically large fusion reactor be?) and therefore does not emit blackbody radiation.
The primary means of emiss... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/415028",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How does the electric field produced by a simple circuit look? I have not seen anywhere a description of how the electric field looks inside and around a simple circuit. For example let's say we have the circuit shown below. One DC voltage source, two resistors, and a constant current flowing around.
We know that the ... | Close but not quite. Here's a very similar circuit from CircuitSurveyor. (I tried to input yours but it wouldn't calculate.) The background grid & flowlines are the Poynting vector $\mathbf S$. For the haphazardly scattered points, blue is $\mathbf E$, green is $\mathbf B$ (always into the screen here), and orange is... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/415160",
"timestamp": "2023-03-29T00:00:00",
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Correlators for space-like photon bouncing Consider the diagram below of two detectors-emitters exchanging photons: Thin lines are null-paths between detectors. Detectors are also synchronized in such a way that measurements outside the blue or red windows are ignored. So first detector can only react to photons receiv... | I have 2 questions plus an optional third, as I’m not sure I’ve fully understood the problem:
1) what does it mean that the probability of second apparatus to shoot a photon from C depends on the detection of a photon in B?
Do you mean that there the emission from the second device is not causal and the second photon ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Physical intuition behind Poincaré–Bendixson theorem The Poincaré–Bendixson theorem states that: In continuous systems, chaotic behaviour can only arise in systems that have 3 or more dimensions. What is the best way to understand this criteria physically? Namely, what is is about a space of dimension 1 or 2 that canno... | There's not enough room for chaos in a 2D flow.
It comes down to the system's solutions being smooth 1D curves in a 2D space: due to uniqueness, these curves cannot cross (they can meet at special points [homoclinic or heteroclinic], but only asymptotically), and that strongly limits the possible end states. Particular... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/415971",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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How to mathematically prove that point charge and infinitesimal volume charge are same? In electrostatics, while deriving certain elementary equations, I have seen all the books just assuming that point charge and infinitesimal volume charge are same.
How can we rigorously, mathematically and formally prove that point ... | Maxwell's equations, which are regarded as the fundamental equations governing the evolution of electromagnetic fields, are constructed in terms of charge density and current density. As such, electromagnetism is fundamentally described not in terms of point charges, but a continuous charge distribution.
In the languag... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/416193",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How are high-energy detectors able to to distinguish between $m_{e}$ and $m_{\mu}$? I had a teacher pose this interesting question yesterday:
Suppose you're running a high-energy scattering experiment at the LHC. For concreteness, let's suppose it's a 2 to 2 scattering event which involves electrons and/or muons.
The t... | The usual way to identify an electron vs a muon in a high-energy detector is via their interactions with matter:
- an electron will dump all its energy quickly in an "electromagnetic shower" and quickly stop
- a muon will interact minimally and go far through the material.
In pictures, these look like:
Note that we ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/416498",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Pauli exclusion responsible for "solidity"? I have heard Frank Close say that the reason you can't put your hand through a solid object is the Pauli exclusion principle. However Richard Feynman in his "Fun to Imagine" series attributes it to electrostatic forces.
I have two questions: Firstly, who is correct here (or m... | Without Pauli exclusion your hand would go through a glass table or even fuse with it. There would be no chemistry as we know it. It seems unbelievable that the universe is stabilised by something regarded to be a mere consequence of symmetry.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/417626",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Why is a fermion field complex? The Lagrangian of a fermion field is
\begin{equation}
\mathcal{L} = \overline{\psi} (i\gamma_{\mu} \partial^{\mu} - m)\psi
\end{equation}
It is said that the fermion field $\psi$ is necessarily complex because of the Dirac structure. I don't quite understand this. Why is the fermion fiel... | Classical fermions in $3+1$ or higher dimensions are not complex. They are Grassmann number-valued. i.e. $\theta_{i}\theta_{j}+\theta_{j}\theta_{i}=0$ for any two fermions $\theta_{i}$ and $\theta_{j}$. There can be no difficulties regarding fermionic fields as complex numbers as long as you don't consider the product ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/417886",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does this paper use 1/cm for units of frequency? Reading this paper from 1963 $^*$, they use units of cm$^{-1}$ for frequency.
Here is an excerpt:
It doesn't seem like wave number, as they clearly call it frequency. What's going on here?
$^*$ Sievers III, A. J., and M. Tinkham. "Far infrared antiferromagnetic reso... | A frequency is a number of oscillations, but you need to specify the unit you're refering to : is it oscillations per a given duration (temporal frequency) or per a given length (spatial frequency). Today "frequency" implies a temporal frequency, and we use the word "wave number" for the spatial frequency, allowing us ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Understanding what it means that gravitation is proportional to the product of the masses Newton's gravitational law states that
$F = G*\frac{M*m}{d^2}$
Intuitively it means that the greater the masses, the stronger the force, but it is more precise than that, it is proportional to the product of the masses not, for ... | The most intuitive way of thinking of it seems to be to picture two objects each made up of 100 "particles" (imagine indivisible points of equivalent and constant mass) at a given separation $d$. We can build up to this picture and see why the product of masses makes sense.
First, imagine the simplest picture: 2 partic... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Integrals involving Bose-functions (Computational) In short, I'm looking for some advice/literature how to deal numerically with Bose function.
My physical problem is to calculate a coupled set of Self-energies, thermal loop integrals, self consistently. These integrals involve Bose and Boltzman distributions.
There ... | There is a great paper On the Relativistic Bose-Einstein Integrals by Weldon and Haber which I have found useful in the past. It focuses on asymptotic expansions of generic Bose-Einstein integrals in the high-$T$ and low-$T$ limits, but maybe it will be useful for you.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/418895",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Relative motion and time When someone reaches to a speed which is close to the speed of light with respect to earth, will he see the things actually moving faster than when he is in low speeds?
| I'm of two minds about answering this because, on the one hand, it's a straightforward homework exercise, but on the other hand, it seems to me that the other two posted answers are at best misleading.
Michele Grosso's answer says that earth clocks tick slowly in the spaceship's frame, but that's not what I think you'r... | {
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Can the fact that dark energy increases with volume be explained by classical thermodynamics? Considering adiabatic process in classical thermodynamics, a normal substance with (positive) pressure must do work on its environment in order for the volume to increase by $ dV $(like pushing the walls of a piston) so it's i... |
Isn’t it illegal to use classical thermodynamics to conclude that the energy of dark energy increases with volume?
According to thermodynamics the internal energy $U$ doesn’t change in case of adiabatic free expansion (means outside the piston is vacuum) of an ideal gas, so $dU = o$. What changes is density of the ga... | {
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How does tilting a bike make it turn sharper? Note that my question is not why do you tilt your bike when on a curve. It's about the reduction in turning radius when one tilts the bike inwards.
Short to-the-point answers are welcome.
| With the bike upright and either no turn or a very slight one the most outer circumference is in contact with the roadway.
When you lean in a sharp turn the inward torque will balance the outward torque created by the centripetal force (preventing tipping over) and the bike moves off the outer circumference and contact... | {
"language": "en",
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Decomposition of the symmetric part of a tensor The rate of strain tensor is given as $$e_{ij} = \frac{1}{2}\Big[\frac{\partial v_i}{\partial x_j}+ \frac{\partial v_j}{\partial x_i}\Big]$$ where $v_i$ is the $i$th component of the velocity field and $x_i$ is the $i$th component of the position vector. From what I rea... | There are many different answers to your question (since usefulness is subjective), but here's what I would consider the "main" one.
Very often we assume fluids are incompressible: that is, that the density $\rho$ is constant, and consequently $\nabla \cdot \mathbf{v} = 0$ from the mass continuity equation. By splittin... | {
"language": "en",
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What does it mean if the dot product of two vectors is negative? If the dot product gives only magnitude, then how can it be negative?
For example, in this calculation:
$$W = \vec{F}\cdot\vec{r} = Fr\cos\theta = (12\ \mathrm{N})(2.0\ \mathrm{m})(\cos 180^\circ) = -24\ \mathrm{N\,m} = -24\ \mathrm{J}$$
Why is there a ne... | The formula you have supplied in your question says it all:
$$\vec F\cdot \vec r=Frcos(\theta)$$
$F$ and $r$ are both positive (vector magnitudes), and so the negative sign comes from $cos(\theta)$
$\theta$ is the angle between the vectors, and $cos(\theta)$ is negative when $\frac {\pi}{2}<\theta<\frac{3\pi}{2}$. This... | {
"language": "en",
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Euler equations in primitive form for a real gas For an ideal gas, it is relatively easy to express the Euler equations in primitive form (variables $\rho$, $u$, $p$), starting from their expression in conservative variables ($\rho$, $\rho u$, $E$).
I did not find any example of such derivation for a general real gas, ... | In general, you can always convert between any two variable sets using the Jacobian that connects them. For example, if we define our conservative variable vector as:
$$ \mathbf{W} = \lbrace \rho, \rho u, \rho E \rbrace^T $$
and our primitive variable vector as:
$$ \mathbf{Q} = \lbrace \rho, u, p \rbrace^T $$
then we w... | {
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does tension in the string affect its equilibrium? In my textbook (Sears and Zemansky's University Physics), it is written that the vector sum of the forces on the rope is zero, however the tension is 50 N. Then is tension different than the force? And if not, then why force is zero while tension is not?
A body that h... | Each element of the rope is subjected to two forces which are equal in magnitude and opposite in direction so the net force on each element of the rope is zero.
One of the forces on the left side of the element is due to the left hand part of the rope adjacent to the element pulling left and the other force on the righ... | {
"language": "en",
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Newbie question: Atom identity. How can you talk about two electrons if electrons are identical? How can you talk about two electrons if they are identical (indistinguible)? Does it make sense to let an electron to have an identity by itself?
If they are on diferent places the place they are is a diference (they are no... | You can label billiards balls, ping pong balls, marbles and even BBs. But there is no way you can label electrons, even in principle. Think about 2 identical electrons in a head on collision. Before the collision they move in opposite directions along the same straight line. After the collision, 2 electrons move away f... | {
"language": "en",
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A question over Liouville’s Theorem I have some doubts about Liouville theorem, probably its just something conceptual.
So: I know that for a system in which Liouville’s theorem holds, the volume in the phase space is conserved.
But the conservation of the volume does immediately imply the absence of asymptotically st... | Liouville's theorem holds for all Hamiltonian systems.
If your definition of an asymptotically stable point $\boldsymbol{x}^*$ means that trajectories from points $\boldsymbol{x}$ in some neighbourhood of $\boldsymbol{x}^*$ tend to $\boldsymbol{x}^*$ as $t\to\infty$, then
*
*phase-space volume and/or density near $\... | {
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What does electrical potential at a point mean? From my understanding, potential difference (or voltage) between point A and point B is the difference in electrical potential at the two points. The potential difference is also, the work done per unit charge in moving charges from point A to point B.
But apparently, the... | In common introductory textbooks, voltage is defined as the electric potential difference (say, between A and B) between two points in space. They say that A and B have a potential difference, and both A and B are at unique electric potentials.
This is completely narrow viewpoint.
Electric potential, electric potential... | {
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How is work transferred to the system recognised? For example, a potato initially at room temperature $25 \sideset{^{\circ}}{}{\mathrm{C}}$ is baked in an oven that is maintained at $200\sideset{^{\circ}}{}{\mathrm{C}}.$
I made potato as the system and the outer surface of the skin as the system boundary. While the ove... | Well, it is not strictly true that the volume stays fixed. The potato actually gets dilated in the oven, and the change in volume means that a part of the heat transferred has been converted to work (rigorously speaking the work is not pressure by volume because the potato is a solid body, so you should instead conside... | {
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What is the relation between a symmetry and the invariance of the Lagrangian? While proving that homogeneity of space implies conservation of momentum, we use the fact that homogeneity of space means that the Lagrangian of the system remains invariant under translation. Why is it so? I know that homogeneity of space me... | I'll just add a little to Valter Moretti's excellent answer to explain why in particular momentum conservation is connected to translation invariance. Given the continuous symmetry $\delta\mathbf{q}=\epsilon\mathbf{K}$ with $\dot{\epsilon}=0$, on-shell $$\delta L=\epsilon(\mathbf{K}\cdot\frac{\partial L}{\partial\mathb... | {
"language": "en",
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What would happen if total energy of electron in bohr's orbit were positive? I have read somewhere that if electron had positive total energy in orbit it would not follow a closed orbit.
why is that so?
| If the electron had a positive energy, it would mean that the electron would no longer be bound to the nucleus.
Why does the electron have negative energy?
This is because the electron has lost some energy and thus has been successfully attracted by the nucleus. Energy is released which implies that it is negative.
Pos... | {
"language": "en",
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Principle of reversibility of light in case of refraction at the critical angle In the case where light is moving from denser medium to a rarer medium, at the critical angle, the refracted ray will be parallel to the surface. Now according to the principle of reversibility of light, if we reverse the direction of light... | Light beam is not an ideal ray and is not perfectly collimated, so, in real life, only its small fraction will be exactly at the critical angle for any given incidence angle.
Another factor, making the transition between refraction and reflection gradual is the dispersion, which makes the refractive index and, therefor... | {
"language": "en",
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Arithmetic of Hamiltonian in canonical transformation I have the following Hamiltonian:
$$ \mathcal{H} = \frac{p^2}{2m} + V(q-X(t)) + \dot{X}(t)p, $$
and I make the usual canonical transformation for the momentum:
$$ p \rightarrow p' = p + m\dot{X},$$
and complete the square, which should give the following:
$$ \mathc... | Hint: Try a type-2 generating function $$F_2(q,P,t)~=~\left(P-m\dot{X}(t)\right)q,$$
for a CT $$(q,p,t)~\to~ (Q,P,t),$$ such that
$$K-H ~=~\frac{\partial F_2}{\partial t}~=~\color{red}{-m\ddot{X}(t)q}, \qquad Q~=~\frac{\partial F_2}{\partial P}~=~q, \qquad p~=~\frac{\partial F_2}{\partial q}~=~P-m\dot{X}(t). $$
| {
"language": "en",
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Does measured mechanical power and work change between inertial frames? Imagine a car A is accelerating.
Two observers at constant speed, B and C, analyse the change of A's kinetic energy over a same time interval.
B sees A going from 10 to 30 m/s
C sees A going from 100 to 120 m/s
As both see A having the same mass (... | The car is pushing against the Earth. Calculate $K_{tot} = K_{Earth} + K_{car}.$ You will find that $K_{tot}$ changes by the same amount in both frames.
As a simpler example, consider two boxes, masses 10 and 1, attached by a compressed spring. The spring is released, pushing the masses apart.
In frame A, they are both... | {
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Electric field of an infinite sheet of charge I am trying to derive the formula for E due to an infinite sheet of charge with a charge density of $ \rho C/m^2$. I assumed the sheet is on $yz$-plane. I used Coulomb's law to get an equation and integrated the expression that over $yz$-plane. But, I have not succeeded in ... | Are you looking to do the integrations by hand? Because
$r = x \hat{x} + y \hat{y} + z \hat{z}$
$r^\prime = y^\prime \hat{y} + z^\prime \hat{z}$
Should yield the correct answer, but the integrations are messy, unless you go to cylindrical coordinates
| {
"language": "en",
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The term "Coherence" is overloaded! I have troubles with modern terminology in the field of quantum information technologies. There are a lot of new terms that everyone is using and no-one takes time to explain, even though modern textbooks did not catch up to these yet. Two of them are optical coherence lifetime vs sp... | For a quantum system such as an atom, or rare earth ion in a bulk crystal, the coherence lifetime is defined relative to two states of the system. 'Spin coherence' typically would refer to the situation when the two states are the same up to different nuclear or electronic spin orientations. For example, in a typical a... | {
"language": "en",
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"source": "stackexchange",
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Pascal's law - Glass Flask Experiment (doubt)
This image was of my book and written below this image was that when the piston is pushed down, it is observed that liquid flow out with equal pressure from each hole. But, I think that pressure at the lowermost hole should be the most as pressure increases with depth and ... | Ur question is right but in a flask the effect of gravity is negligible so the pressure on all points will remain same.
Ur point could be considered while dealing with large volumes under gravity.
I feel it might be helpful.
| {
"language": "en",
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Real Lagrangian with complex variable I have a general question concerning real valued Lagrangians that take complex arguments. I have seen in many works of physicists and lecture books where extremal problems are discussed in Lagrangians that are real but depend on complex fields.
But, according to the Cauchy-Riemann ... | Complex variables in physics are often real differentiable (=smooth) but rarely complex differentiable (=holomorphic/analytic). The simplest example in field theory is a complex scalar field.
| {
"language": "en",
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"source": "stackexchange",
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Galilean transformations of velocity If I perform a Galilean boost $$x' = x - vt \\ t'=t$$ between two frames $S$ and $S'$, observers in each frame would disagree on the velocity of a particle because
$$ \frac{dx'}{dt'} = \frac{dx}{dt} - v. $$
Well Galilean transformations preserve the spatial intervals $\Delta x$ and... | You are mixing two things. $dx$ and $\Delta x$. When you say "Gallilean Transformation preserves $\Delta x$ it means when measured by any observer", the relative distance between any two fixed points is same. But that is not the $dx$ in the definition of velocity. Its the change of position of a particle when we measur... | {
"language": "en",
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In a vacuum can a cooler body radiate Infrared radiation to a warmer body? I mentioned vacuum, because I want to discount the effects of conduction or convection. I simply want to know if some of the infrared radiation(IR) goes from the cooler body to the hotter body? How does each body know how much to radiate at any ... | Yes, both bodies radiate, including the cooler one. The warmer one puts out more power in its radiation, proportional to $T^4$ just as you say. The amount of radiation depends on absolute temperature, not temperature difference. But since the colder body has a lower absolute temperature, it radiates less than the hot o... | {
"language": "en",
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How can a transformer produce a high voltage and a low current? I understand that in ideal transformers, power is conserved. Because of this the product of voltage and current in the secondary winding is a constant.
This means that voltage and current are inversely related, which seems unintuitive because they are dire... | Actually the emf induced per turn in both of the primary and secondary windings are equal due to the conservation of energy. Now if you increase the secondary windings with respect to the primary windings then you will get high voltage than the primary circuit for an ideal transformer. And consequently the current in t... | {
"language": "en",
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Orthonormal Basis integration and Kronecker delta Given that this integral I'm trying to solve is
$$\frac{2}{\pi}\sum^{\infty}_{l=0}\sum^{l}_{m=-l}\int_{r=0}^{\infty}\int_{k=0}^{\infty} R_{nl}(r)b_{lm}(k)j_{l}(kr)k^2 r^2 \int_{\theta = 0}^{\pi}\int_{\phi=0}^{2\pi} Y^*_{lm}(\theta,\phi)Y_{l'm'}(\theta, \phi)\sin\theta \... | The Kronecker Delta in a sum acts like the Dirac Delta function in an integral. So basically you can drop the sums and remove the delta terms. Your integral will be the integrand without the Kroneker Deltas. You technically can make the $l$s and $m$s primed if you wanted to, but that's unneeded primes (unless the conte... | {
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Woodworking clamps, does force add up? I was watching a woodworking video about glue, and the guy was clamping two pieces of wood together using a total of 8 clamps. He argued that by doing so he would apply 8 times the maximum force of 150N (a property of the clamp), resulting in 1200N in total.
I think he's wrong. I ... | You're both wrong.
Although I would say you are more right than the expert. When you apply a force to an object's surface, the stress (a.k.a pressure) on the object clearly can't be constant across the surface; it must have a maximum closest to the point of contact and then dissipate as distance from the point of conta... | {
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Why do vehicles with a higher center of mass roll more easily considering that they have a higher moment of inertia? It is a well known fact that cars with a higher center of mass roll over more easily, but why is this true considering that higher center of mass = higher moment of inertia?
I understand that the higher ... | The moment of inertia tells you rate of rotation given a net torque. But for cars, we don't care how fast they tip over, we care if they tip at all. So the question isn't the moment of inertia, but the net torque. Is there something about a high center-of-mass vehicle that makes it more likely to enter a regime wher... | {
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All central forces are conservative forces, but are all conservative forces central forces? I have just been introduced to the concept of central forces, and to the fact that they are per definition conservative forces. I have looked up several examples of central forces (gravity, electric, and spring), but they cover ... | If $\phi=-xy$, and ${F}=-\nabla \phi=y \hat{i}+x \hat{j}$ is conservative but not central
| {
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Why do we use $m\frac{dv}{dy} = -b(v-v_{ter})$ while determining how the terminal velocity is changing for an object falls down in linear drag force? Why do we use $$m\frac{dv}{dy} = -b(v-v_{ter} )$$ while determining how the terminal velocity is changing for an object falls down in linear drag force . I was Jr Taylor'... | Consider the downward direction to be positive. The equation of motion is, $m \frac {dv}{dt} = mg -bv$, where $bv$ is the upward drag force.
The net force will be zero when $v = v_{ter} =mg/b$
Substituting back, we get $ F_{downward} =- b(v-v_{ter})$.
Note that this is the net force (so it becomes zero when the body ... | {
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The definition of the hamiltonian in lagrangian mechanics So going through the "Analytical Mechanics by Hand and Finch". In section 1.10 of the book, the Hamiltonian $H$ is defined as: $$H = \sum_k{\dot{q_k}\frac{\partial L}{\partial \dot{q_k}} -L}.\tag{1.65}$$
And then author affirms that this quantity is constant and... | *
*Ref. 1 is confusingly calling the Lagrangian energy function $H(q,\dot{q},t)$ for the Hamiltonian. We stress that the whole Section 1.10 is purely within the Lagrangian formalism. Eq. (1.68) follows after time differentiation of the definition (1.65) and use of Lagrange equations (1.60).
*In contrast, the function... | {
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The work-energy principle for particles reversing direction I've been trying to find an answer to this question, but have really been stumped so far.
The work-energy principle says that work done on a single particle is equal to its change in kinetic energy. Now let's say a particle is moving in the +x direction at con... | The answer is that it doesn't actually require work. Using the equation $dW=\vec{F}\cdot d \vec{x}$, we can see that the work done on the object is positive if the force is pushing in the same direction as the object is moving, (speeding the object up) while it is negative if the force points in the opposite direction ... | {
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Do compact symplectic manifolds play a role in physics? In classical mechanics, the phase space is the cotangent bundle of the configuration space, and it is a symplectic manifold, but not compact.
Do compact symplectic manifolds have physical meaning? Or just of mathematical interest?
| The other two answers do indeed give examples of compact symplectic spaces that can appear in physics. I would like to give some comments about how such things might arise in general, rather than an example thereof.
Starting with an arbitrary Lagrangian system, we construct the conjugate momenta and can construct from ... | {
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Determining conservation of isospin I am trying to understand a worked example. The problem is to determine if all conservation laws are conserved in
$$
\pi^-+n \rightarrow K^++\Lambda^0
$$
The answer says that isospin is conserved, which I don't understand. Isospin for $\pi^-$ is $1$, the isospin for $n$ is $\frac{1}{... | The isospin quantum number $I$ is not additive. Isospins combine like angular momenta so in your example you have $I_\pi=1$ and $I_n=1/2$, so the possible values of isospin for the left hand side of your reaction is
$1\otimes 1/2= 3/2\oplus 1/2$, i.e. the output channels must have either isospin quantum numbers $3/2$... | {
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What direction does electric current flow in when the voltage drop is negative? We were given the below diagram, and we needed to determine whether the unknown component is supplying energy into the system.
$\hspace{200px}$
I thought the unknown component was supplying energy since charge is flowing to a higher potenti... |
I just wanted to know what the -2v actually means.
Operationally, it means that if you place the red (positive) lead of your voltmeter on the $+$ labelled terminal and the black (negative or reference lead) of your voltmeter on the other, the voltmeter will read $-2\,\mathrm{V}$.
This tells you that the $-$ labelled ... | {
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Is the force which throws a body on a rotating disk outwards centrifugal force? If some object is kept in a radial groove made on a disk and the disk is rotated with say constant angular velocity.
Now as we know that the object moves outwards ie away from the centre of the disk. I want to know which force is it which ... | No force throws it outwards.
There is also no force pulling it inwards. Therefore it doesn't follow the circular motion. Such a force would have been friction for example. Instead it just continues straight ahead, away from the disk.
All in all, when an object has a speed, then it keeps going at that speed until a forc... | {
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What is wrong with my deformation gradient calculation? I created two ellipses,$\hspace{150px}$,where the red ellipsis is as the blue one, except translated to the right and rotated by ${30}^{\circ} .$ Using rotation matrix,
$$
\left[
\begin{array}{cc}
x \\[2px]
y \end{array}
\right]
\
\phantom{F} ~=~
\le... | In component form,
$$x=F_{xx}X+F_{xy}Y$$
$$y=F_{yx}X+F_{yy}Y$$
In your example, there is a mapping of 2 vectors:
X = 0, Y= 2 ---> x = 1, y = 1.732
and
X = 1, Y = 0 ---> x = 0.866, y = - 0.5
Solving for the components of the deformation gradient tensor gives:
$F_{xx}=0.866$, $F_{yx}=-0.5$, $F_{xy}=0.5$, and $F_{yy}=0.86... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Forms of transformation Suppose $O$ is an object to be transformed, and $S$ is the transformation operator. Sometime the transformation is in the form
\begin{equation}
O \rightarrow SO. \tag{1}
\end{equation}
But sometime the transformation is in the form
\begin{equation}
O \rightarrow SOS^{-1}.\tag{2}
\end{equation}
I... | This is a question where the bra-ket notation is truly useful. When $O$ is a column vector, think of it as a ket $\vert O\rangle$. Then the transformation matrix $S$ acts in the usual way
$$
\vert O’\rangle=S\vert O\rangle\, . \tag{1}
$$
Now think of $O$ as an operator, i.e an object of the form $\vert m\rangle\langl... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Electrical potential with a combination of bodies 1) what would occur with respect to electrical potential if a +1 charged body is brought close to a -2 charged body?
2) a positively charged body next to an earthed conductor
For the 1st one I'm not too sure to make an educated guess. For the second one I'm thinking t... |
1) what would occur with respect to electrical potential if a +1
charged body is brought close to a -2 charged body?
The potential of -2 body will be getting less negative, while the potential of +1 body will be getting less positive. At some point, the potential of the +1 body will become zero and than negative. W... | {
"language": "en",
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Does 'special relativity + newtonian gravity' predict gravitational bending of light? It seems to me that special relativity (SR) already predicts that gravity will bend light rather than this effect being a proof of general relativity (GR). Photons have energy proportional to their frequency and according to $E = mc^2... | As mentioned in tfb's answer, the deflection treating photons with an "effective mass" is half that of general relativity. While photons have zero rest mass in special relativity, one can consider them with infinitesimal mass for the purposes of a Newtonian approximation (a "gravitational force" interacting directly an... | {
"language": "en",
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"source": "stackexchange",
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What do string theorists mean when they say that little is known about M theory?
*
*It’s often said that we don’t know what M theory is, but what does that actually mean?
*And how long until M theory becomes somewhat of an understood theory?
*Where are we at now with M theory?
| So far, it is known the low-energy limit of the theory. This means that when the energy scale is not high enough to resolve the typical length of the theory, then we will just see point-like objects. Namely, at that energy scale, our system is effectively a set of particles and it will be described by standard quantum ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Torque acting on car trailers My question: "Which car trailer below will be moved in a straight forward line?"
Relevant info: All forces (represented by the arrows) in the diagram are equal in magnitude. The car trailer diagrams below seem to me very similar in terms of the net torque that acts on each of them. The net... | The drawing is not particularly accurate. For instance, although it does not affect the answer, $0.25$m and $0.5$m on the second drawing have about the same length.
Apart from that (without going into the details of the hook-up), it appears that the idea here is that the forces acting on trailer $1$ appear to be symme... | {
"language": "en",
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Could black holes be formed by highly energetic gravitational waves? Could the gravitational waves released by two merging black holes contain enough energy to produce another black hole?
| In theory, yes, any concentration of energy that is suitably high will form a black hole. In particular, according to general relativity, if any energy is concentrated within about a volume equal to its own Schwarzschild radius or less, it will form a black hole, and given that gravitational waves transmit energy there... | {
"language": "en",
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How can the solutions to equations of motion be unique if it seems the same state can be arrived at through different histories? Let's assume we have a container, a jar, a can or whatever, which has a hole at its end. If there were water inside, via a differential equation we could calculate the time by which the conta... | Everyone keeps saying all these things but really the issue here is so much more succinct and I think it has a lot more to do with science itself. The purpose of science is to construct models that attempt to predict future behavior based on previously observed behavior. So while yes the differential equation might be... | {
"language": "en",
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How can a particle's position be random and uncertain in quantum mechanics if it is already pre-determined in relativity? In relativity, to my knowledge, the path of an object is described by its worldline in spacetime, and since time is a part of the spacetime geometry, an object's worldline--in a sense--always exists... | So when a particle's position is measured, we can say that the particle is really located in some region of space. As time progresses without measurements, the region of where it could be grows according to the uncertainty in its momentum. A first understanding of relativistic QM just makes sure that this region is bou... | {
"language": "en",
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What happens if a neutron flies towards a nucleus? Rutherford experiment shows that alpha-particles when they fly towards metal foil sometimes (in minority of cases) can bounce. An explanation proposed was that atoms in fact have positively charged nuclea and majority of space is covered by fields of negative charge ca... | The place to go for neutron scattering data is The Evaluated Nuclear Data Files site, hosted in the US at Brookhaven National Laboratory. There one can get data for a wide range of neutron scattering possibilities, including the cross section vs energy.
Since fission was mentioned in the comments, lets look at U-235. ... | {
"language": "en",
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Why is it much more difficult to horizontally throw a toy balloon than a football? If you horizontally throw a sphere of radius $R$ it will feel, in this direction, a drag force due to air. Assume the drag is given by Stokes law, $F_D=6\pi\eta R v$, where $\eta$ is the air viscosity and $v$ is the horizontal speed. Thi... | Let's say you get your object to some initial speed $v$ and then let it go so that only the drag force is acting on it (ignoring gravity for now).
Then by Newton's second law:
$$a=\frac{F_D}{m}=\frac{F_D}{\rho V}=\frac 1\rho \cdot \frac {F_D}{V}$$
Where $\rho$ is the density of the object. Since $\frac {F_D}{V}$ depend... | {
"language": "en",
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What is state variable and full differential? e.g. in entropy? I am studying basic concepts of entropy and statistical physics. And red a lot what is entropy, and that it is integrative factor of heat; and getting it with the full differential._
Anyway, what I am trying to grasp in all that story, actually to gain a fe... | A function of state is one that depends only on the state of the system, which for a gas means that it's a function of the pressure $p$, volume $V$, and temperature $T$, and not dependent on the path by which the system got there. They're also only defined in equilibrium; if there's no defined $p$, $V$ or $T$, there's ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Reducing multi body system to a single body using reduced mass A two body system can be treated as a single body using reduced mass and the motion can be described using one generalized coordinate.
Can this concept be somehow used to reduce a body of say 3 or more particles to a single body?
| The two dof of the system reduces to one because the other one ends up with constant velocity solution and a co-moving reference frame can be constructed that is still inertial. For three bodies, no such co-moving inertial frame exists.
| {
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Cast metal vs. machined metal Why is it, that machined metals, milled out of a primitive shape, tend to bend upon impact rather than crack or shatter? Why do they behave differently to stresses when they are cast into the final shape?
I find this rather confusing. Don't they have the same lattice? Are there more defect... | Jon Custer is right- this is a very broad question, about which whole chapters in materials science textbooks have been written. I'll furnish a broad perspective which I hope will get you pointed in the right direction.
First of all, all common metals begin their useful (i.e., engineering) lives as raw solids that were... | {
"language": "en",
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If the path integral formulation includes future events, why doesn't that imply retrocausality? I know that such events would cancel out in the math, but if an extreme event were to happen in the future (say a black hole forming or something on that par), would a particle in the present react to it? If not, why?
| The path integral is a broad idea, which comes in several different flavors. In non-relativistic quantum mechanics for one particle, you calculate the propagator matrix element $\langle {\bf x}_f| U(t_f,t_i) | {\bf x}_i \rangle$ by summing $\exp(i\, S[{\bf x}(t)]\, /\hbar)$ over paths connecting $(t_i, {\bf x}_i)$ to $... | {
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Why does light bend towards the normal when passing through a denser medium? When light passes from a medium with less refractive index to a medium with higher refractive index, it bends towards the normal. But why normal . Of course we can take an example of a car moving from the road to the mud in an angle. Its first... | This is due to Fermat's principle, which states that light travels between two points along the path that requires the least time, as compared to other nearby paths. Light travels more slowly in a denser medium, and hence will bend more toward the normal.
Why then does light follow this path, and not other paths? This ... | {
"language": "en",
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Half-life of $W$ and $Z$ bosons $W$ and $Z$ bosons should decay through weak interaction. But their half-life is around $\tau = 10^{-25} s$ which is a typical value for particles decaying through strong force (instead of a $10^{-12}-10^{-6} s$ for a weak interaction decaying particle).
Why this can be?
| Yes, it is
correct to say that the W boson is decaying through weak interaction despite its very small lifetime.
The weak interactions were dubbed such in the last century because, at low energies compared to the mass of the W, about 80GeV, the large mass of this particle appeared squared in the propagator of this v... | {
"language": "en",
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Confusion about how an electron gun works I'm a little unclear about the charge balance aspect of an electron gun. Referring to this diagram and similar diagrams I've seen, what I don't get is wouldn't the target of the electrons have to be connected to the positive anode so that the electrons fired at a target can b... | I cannot comment on the construction of a specific electron gun, but in a typical CRT, the internal surface of the tube around the screen is coated by graphite, forming the final anode electrode.
This electrode is connected to high positive voltage and one of its functions is to collect electrons arriving to the scree... | {
"language": "en",
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Is continuum mechanics a generalization or an approximation to point particle mechanics? Newtonian Mechanics is usually presented as a theory of point particles (and forces). My impression of the status of continuum mechanics is that it is mostly taken as an approximate description for certain situations, where many pa... | It's neither a generalization of, nor approximation to, the classical mechanics of particles, it's simply a different perspective. As described by Walter Noll in discussing the connection in The foundations of classical mechanics in the light of recent advances in continuum mechanics (1959):
It is true that the mechan... | {
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Confusion about the meaning of steady current I am trying to learn some elementary EM, but I have some confusion about the basic concepts of steady current.
Suppose I have a wire of uniform cross section area. The current is always flowing from left to right.
I imagine that I can cut a segment of this wire (with the ar... | $\frac{\partial}{\partial t}\rho = 0$ implies $\nabla\cdot\mathbf{J} = 0$. Then, $I = \oint_S \mathbf{J}\,d\mathbf{S} = \iiint_{\Omega} \nabla\cdot\mathbf{J}\,d\Omega = 0$
If you consider $S$ as a cylinder, you will see that the current density does not depend on the cross section you take.
| {
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What is a 'spacelike surface' in relativity? I am studying Noether's theorem in field theory and I am not understanding what spacelike-surfaces mean. I will reproduce the bit of the argument below that contains the term "spacelike-sufaces" in the context I am not understanding.
There will be a conserved ccurrent for e... | Your definition of the surface is correct. I think you misread the text. They are talking about a volume that is bounded by two such surfaces "in the time direction" and unbounded "in the space directions".
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/428088",
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What is a complex phase shift? In a complex methods course I am taking, we were given an equation for a particular driven harmonic oscillator where the driving force is trigonometric. I have worked out the math and obtained an equation that tells me that the driving frequency at resonance is the natural frequency multi... | If your oscillating function is of the form $e^{i\omega t}$, a phase shift looks like $e^{i(\omega t+\phi)}$, which can be rewritten as $e^{i\omega t}e^{i\phi}$.
Now, recall that $e^{i\phi}=\cos\phi + i\sin\phi$. A 90 degree phase shift corresponds to $\phi=\frac{\pi}{2}$.
Thus,
$$e^{i\frac{\pi}{2}}=\cos\frac{\pi}{2} +... | {
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Speed of sound in a gas and speed of a typical gas molecule Why is speed of sound in a gas less than the average velocity of the gas molecules? Is there an intuitive way to explain this?
| I know the derivation of $v_\text{sound}=\sqrt{\frac{\gamma p}{\rho}}\ $ from macroscopic principles, but I've always thought that there must be a way of deriving it on a molecular level. And I've sometimes wondered about the question being asked here: not so much that $v_\text{sound}\ $ is less than $v_\text{rms}$, as... | {
"language": "en",
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What’s wrong with my cloud chamber setup? For my setup, I am using a fish tank, lined with black felt and with one side open for viewing and a slit on a side for the light. I have a pretty bright multi led flashlight. I am using dry ice blocks inside a stryofoam container that is separated from the chamber by a metal c... | Try and make the black flat metal base which is sitting close to the dry ice (solid carbon dioxide) as horizontal as possible.
If the bottom plate is not approximately horizontal convection currents will be set up within the chamber which will ruin the experiment.
The felt soaked in isopropyl alcohol (IPA) is placed ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/428412",
"timestamp": "2023-03-29T00:00:00",
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Why does work depend on distance? So the formula for work is$$
\left[\text{work}\right] ~=~ \left[\text{force}\right] \, \times \, \left[\text{distance}\right]
\,.
$$
I'm trying to get an understanding of how this represents energy.
If I'm in a vacuum, and I push a block with a force of $1 \, \mathrm{N},$ it will move... | When a weight is sitting on the floor, the floor is applying a force to the weight (and vice versa), but no distance. And it should make intuitive sense that there's no work being done.
For your example of a weight in a vacuum: if you push it with force 1N for distance 1m, and then stop pushing, it will move forever a... | {
"language": "en",
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what is effective index method which is used to solve modes in rectangular waveguide? I actually want to know the basics of effective index methods for solving the optical modes in slab/rectangular waveguides.
| The effective index method is an analytical method applicable to complicated waveguides such as ridge waveguides and diffused waveguides.
The ridge waveguide, such as shown in Figure Below, is difficult to analyze with simple method since the waveguide structure is too complicated to deal with by the division of wavegu... | {
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What to do with an extra index in the definition of a tensor? I came across this definition of a tensor while reading some vector calculus literature
This definition contains the index $\ell$ in the last term, however the tensor itself only depends on $j$ and $k$. What am I supposed to do with this extra index? Do I s... | Yes, generally these sorts of expressions follow the Einstein summation convention. This says that whenever you see an index repeated in a multiplication expression, it means to implicitly sum over that index. So $(x_a - X_a)$ is a vector subtraction, but $x_a X_a$ is an inner product.
This is then made a little bit mo... | {
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Why doesn't a charged particle moving with constant velocity produce electromagnetic waves? A charged particle moving with an acceleration produces electromagnetic waves. Why doesn't a charged particle moving with a constant velocity produce electromagnetic waves? As far I understand, the electric and magnetic fields i... | Okay, I'll try with a poor but "intuitive" explanation.
According to relativity theories, "it is impossible to tell if you're at rest or moving with constant velocity".
We know that a charge at rest does not emit any wave.
If you were moving at constant velocity and you saw a static charge emitting a wave, you'd think ... | {
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Why isn't Rayleigh scattering a concern in analog communication? The Rayleigh scattering effect applies to 'light' signals, and the scattering of a signal when passing through a material medium, the amount of light scattered is proportional to 1/$\lambda^4$. I am curious as to why(or if) this wasn't considered when we ... | Rayleigh scattering affects light passing through air, and the light wavelengths range from ~650 nm (red) to ~420 nm (blue) compared to the sizes of the gas molecules in air of ~$4 \unicode{x212B}$ (0.4 nm). That is, the air molecules are about 1/1000 of the wavelength of blue light, which is much strongly scattered th... | {
"language": "en",
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Why stress always flows through the shorter/stiffer path? Why load has a preference at which way to act? What is the reason behind this preference?
Any link or comment would be welcome
| The majority of the load tends to be carried by a stiffer member. Stress is load per area, so if the stiffer member has a larger cross-sectional area then the stress is not necessarily higher.
As to why... imagine two springs hanging in parallel from the ceiling. Both have an unloaded length of 1 meter. Both are att... | {
"language": "en",
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Ray sun heating I recently got a curious question about the sun rays. Is there a material that can absorbs most of them and turn it into pure heat?
For example, we all know that dark material (black t-shirts) get much hot than white material, Although, I've heard that there is some metals that can get much hotter from ... | The sun emitts a whole spectrum of wavelengths, so what we'd like in this case would be a material that has a low reflectivity for a large bandwidth. Black t-shirts absorp more heat because they simply absorp the more wavelengths, including most of the visual ones, and that's why they appear black. As we know, white li... | {
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Velocity of separation and velocity of approach Can I have a clear cut dimension or difference between velocity of approach and velocity of separation?
In just simple 1D motion.
Considering two rigid spherical masses of different masses and moving with different velocities.
| I have not seen any formal definition, but this might work.
Let's assume that two bodies, left and right, move along $x$, with positive direction to the right.
Let's define the velocity of approach as positive and the velocity of separation as negative.
Then, the velocity of approach or separation could be determine as... | {
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What do the points on a Dalitz plot represent I have read that a Dalitz plot is nothing but the plot of $m_{12}^2$ vs $m_{23}^2$, and that the dots correspond to "events". However, this doesn't really tell me anything. My question can boil down to exactly what phase space variable the dots represent. I am currently try... | Dots on a Dalitz plot should be datapoints (I say "should" because many are drawn with the "SCAT" option in ROOT, which actually fills bins with a number of randomly-placed dots proportional to the bin content). These can come from real or simulated data. Even if you want to draw the functional form of the decay rate (... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/429963",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Simple question about change of coordinates Suppose we have two coordinate systems (Cartesian and spherical)
$$x^{\mu} = (t,x,y,z)$$
$$x'^{\mu'} = (t',r,\theta,\phi)$$
where $r= \sqrt{x^2 + y^2 + z^2} , \theta = \cos^{-1}(z/r), \phi = \tan^{-1} (y/x)$. My question is, in general, what are the components of a vector $A_... | The GR vector transformation you cite applies to elements of the tangent space at a point. Positions are not vectors in any tangent space, so coordinates $x^\mu$ do not transform as vectors.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/430071",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Under what circumstances are general relativistic coordinate transformations physically meaningful? Although the field equations of GR are covariant under arbitrary coordinate transformations, such as the transformation given by Dirac (in Princeton Landmarks pp 34) that eliminate the singularities in the Schwartzschild... | As an example of a possible virtual coordinate transformation consider the Schwarzschild metric for r less that the Schwarzschild radius. Then make the space-time switching transformation indicated to get the inside metric:
$$ds^2=\Big(1-\frac{r_s}{r}\Big)\ c^2dt^2-\Big(1-\frac{r_s}{r}\Big)^{-1}dr^2$$$$d\rho = cdt$$ $$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/430180",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 1
} |
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