All Questions
12,536 questions
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Lectures Notes on Maxwell-Jüttner distribution function
I have been looking online for good notes on the application of relativity to statistical mechanics, in particular about the Maxwell-Jüttner distribution function. Does anyone have some links to ...
- 213k
2
votes
0
answers
377
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Calculation of Maxwell-Juttner distribution integral
I am reading one very good notes on Maxwell-Juttner distribution, but I met some places that puzzled me a lot. Please give me a hand!
The notes:
Let $\Theta = kT/mc^2$ be the dimensionless ...
- 1
0
votes
1
answer
73
views
Apparent Woodhouse Galilean Maxwell Paradox
I don't understand this Maxwell paradox in Woodhouse's relativity. The first equation implies that there are fields working on the moving charge, but the last equation implies that the magnetic field ...
- 3,339
2
votes
1
answer
141
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Embedding diagram of flat spacetime
I am trying to understand how embedding diagrams are drawn and how they are interpreted, so I'd start with the flat spacetime.
In spherical coordinates, metric for the flat spacetime reads
$$ds^2=-dt^...
- 120
-4
votes
1
answer
219
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The relativistic Doppler effect is a function of relative velocity. But does the velocity also have to be non-zero relative to the travelling signal?
The classical Doppler effect is a function of that component of the velocities of source and receiver in the direction of the travelling signal. The relativistic Doppler effect is a function of the ...
- 121
11
votes
2
answers
288
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Does Lorentz transformation affect mass density, pressure or temperature of a physical object?
A cylinder filled with gas and moving along its axis would be Lorentz contracted, diminishing its volume. Viewed from stationary frame, would the pressure of the gas be higher than in the co-moving ...
- 61.8k
1
vote
1
answer
56
views
Does the mean value theorem of the potential on a sphere hold for relativistic charge movements?
Imagine a sphere of radius $R$ centered at the origin, and a charge $q$ at some location on the $z$ axis outside the sphere.
When Laplace's equation $\nabla^2 \phi$ holds, it seems we can use the mean ...
- 915
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0
answers
28
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How should loss of crystal symmetry due to Lorentz contraction be interpreted in the stationary frame?
A crystal with cubic symmetry moving at a relativistic speed would appear to have lost that symmetry as viewed from the stationary frame due to Lorentz contraction of its axis in the direction of ...
- 129
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2
answers
143
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In QFT when performing path integral, why don’t we divide it by the volume of Poincaré group, as what we did for gauge group?
When performing path integral in gauge theory, we naively want to compute
$$
Z = \int DA \exp(iS[A])
$$
But we noticed, that because the action is the same for gauge equivalent conditions, we should ...
- 2,975
1
vote
2
answers
256
views
Coulomb's Law and relative motion
This might be a repeated question but I couldn't find an answer already.
I am told by my teacher that Coulomb's Law is valid for stationary charges. Here are the two validity criteria I am given;
...
CommunityBot
- 1
3
votes
1
answer
257
views
Does the no signalling theorem in quantum mechanics beg the question?
I had always thought similarly and then came across a paper here that argues this.
The abstract is as follows:
Many authors state that quantum nonlocality could not involve any controllable ...
CommunityBot
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8
votes
3
answers
675
views
Cherenkov radiation in the frame of a moving observer
Imagine a medium in which an electron is moving at speeds faster than the speed of light in the medium. Within the same medium an observer moves at the same speed with the electron. Will the observer ...
- 109k
2
votes
1
answer
909
views
Particle momentum in collision expressing in Mandelstam variable
Consider the $s$-channel process. I use the metric convection $(+,-,-,-)$. The constraints are: Conservation of four momentum: $p_{1}^{\mu}+p_{2}^{\mu}=p^{\mu}$ and on mass shell condition $p_{i}^{2}=...
CommunityBot
- 1
6
votes
1
answer
897
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Uses of the Angular Momentum 4-Tensor
The angular momentum 4-tensor has 6 independent components, three angular momentum components and three new guys. Some call these new guys the 'boosts', but since they are the conjugate momentum of ...
- 3,833
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0
answers
40
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Does the Lagrangians in different coordinate systems differ by a total derivative when converted to the same coordinate in special relativity?
According to this post, it seems like we should use the $$\mathbb{L}~=~L \mathrm{d}t~=~ L \dot{t}\mathrm{d}\lambda \tag1$$ rather than $$L(v'^2) = L(v^2)+ \frac{df}{dt}\tag2$$ when working with ...
- 167
1
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1
answer
763
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Prove that relative velocity, momentum, and energy, are related by $E_1E_2v_{rel}=\sqrt{(p_1p_2)^2-m_1^2m_2^2}$
In Chapter 8 of F.Mandl's book Quantum Field Theory, during the derivation of the differential cross-section, the following relation is used:
$$E_1E_2v_{rel}=\sqrt{(p_1p_2)^2-m_1^2m_2^2} \,\, ,$$
...
- 15.2k
0
votes
1
answer
39
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Can a reverse-parabolic screen in the double-slit experiment test local vs. nonlocal interference formation?
Suppose that in a double-slit experiment, the slits open just in time for a photon to pass through, and a reverse-parabolic screen is used, with edges positioned much farther from the slits than the ...
- 2,859
2
votes
2
answers
75
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If electrically charged particles transact virtual photons, why aren't said virtual photons subject to the rules of general and special relativity?
For instance, if there exists an electron at sea level, and an electron in orbit, why don't the virtual photons which mediate their electrical field contract and expand as they move across the ...
- 10.7k
1
vote
1
answer
75
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Potential Textbook Typo in Calculation of Lorentz Transformation
In the 3rd edition of Goldstein's Classical Mechanics (pp. 283-284), the authors consider three inertial frames $S_{1}$, $S_{2}$, and $S_{3}$ where the Lorentz transformation from $S_{1}$ to $S_{2}$ ...
- 13k
-1
votes
1
answer
105
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Is relativistic action too restrictive?
When I was studying special relativity, I've learned that the relativistic action for a free particle is defined as
$$
S = \lambda \int_{\tau_0}^{\tau_1} d\tau
$$
Where $\lambda$ is a constant that is ...
- 3,339
2
votes
0
answers
44
views
Lorentz invariance in statistical physics
Given a function $f=f(p^\mu)$ with $p^\mu$ the four-momentum I can integrate it over the full phase-space with $\int\mathrm{d}^{d+1}p\ f(p^\mu)$. This, however, is usually not very useful, since the ...
-6
votes
2
answers
114
views
Are high-energy neutrinos subject of relativistic time dilation like muons are?
Synchrotron experiments and cosmic-rays hitting our atmosphere have proved many times that high-energy massive muons moving with speeds close to the speed of light are subject to relativistic length ...
- 45.7k
1
vote
1
answer
67
views
Gauge charge of the spin connection
When dealing with quantum field theory in curved spacetime, a spin connection field is introduced as a result of the Lorentz symmetry. I'm wondering what would be intuitively considered as "...
- 213k
0
votes
4
answers
194
views
Time-like separated and Space-like separated events
I am trying to get an intuition about Time-like separated and Space-like separated events. I understand the definition of these terms, but I lack intuitive understanding of what these concepts ...
- 39.6k
0
votes
2
answers
108
views
Time dilation of distant stars changed by walking or standing still, paradox?
Disclaimer, using generalized numbers here to illustrate the question, not to be mathematically accurate.
Based on my understanding, if you were standing still vs. walking towards a distant star, say ...
- 10.7k
0
votes
2
answers
620
views
Quantum Field Theory: infinitesimal Lorentz transformation
In the Brandhuber lecture notes, it says at the section about Dirac equation under lorentz transformation that we can consider an infinitesimal Lorentz transformation like this one,
$$
\Lambda^{\nu}_{\...
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-2
votes
1
answer
112
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Not "understanding" the Twin Paradox? [closed]
Many of the explanations that I've seen of the Twin Paradox seem to rely on the role of acceleration to explain the differences between the twins. But why can't we simply resolve it just via "...
- 269
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0
answers
32
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On the distinction between Lorentz group and proper orthochronous group via Jacobian determinants
The group $O(1,3)$ is defined as the set of matrices which are orthogonal with respect to the Minkowski metric $\eta$, i.e. those matrices $\Lambda$ satisfying
$$\Lambda^T \eta \Lambda = \eta.$$
...
- 1
8
votes
4
answers
693
views
Why is imaginary time "outdated"?
I was looking at reviews for Sakurai's Quantum Mechanics textbook, and some mentioned it being outdated, specifically mentioning his use of imaginary time. Is this idea deliberately avoided in modern ...
- 71.5k
3
votes
2
answers
663
views
Symmetry between inertial reference frames
So my textbook says the following - roughly translated - in the context of Special Relativity:
"Assume we have two observers, A and B, moving relative to each other. Observer A measures a velocity ...
- 1
0
votes
3
answers
122
views
Does a clock at the rear end of a train is ticking faster than a clock at the front end of a train?
When a train zooms past us, we observe a clock at the rear end of the train ahead of a clock at the front of the train. I wonder if it implies that the clock at the rear end is ticking faster than the ...
- 16.2k
212
votes
11
answers
273k
views
If photons have no mass, how can they have momentum?
As an explanation of why a large gravitational field (such as a black hole) can bend light, I have heard that light has momentum. This is given as a solution to the problem of only massive objects ...
- 3,833
3
votes
2
answers
811
views
D'Alembertian of a Dirac delta function of a spacetime interval (i.e. with support on the 3+1D light-cone)
How one differentiates a delta-function of a spacetime interval? Namely,
$$[\partial_t^2 - \partial_x^2 - \partial_y^2 - \partial_z^2] \, \delta(t^2-x^2-y^2-z^2) \, .$$
Somewhere I saw that the result ...
- 213k
6
votes
1
answer
311
views
What are the conditions for a force field to be "consistent with special relativity"?
I'm trying to gain a deeper understanding of a certain exercise I came across (Source: "Problem Book In Relativity and Gravitation", Exercise 2.15):
A new force field $F^\mu(x^\nu)$ is ...
- 3,313
6
votes
1
answer
460
views
Can we use local proper time instead of global coordinate time in special relativity?
In special relativity we have:
$$dt^2-dx^2-dy^2-dz^2 = d\tau^2$$
Where $d\tau$ is the change in local proper time of the object (the change in the clock ticks).
I've always wondered why we can't just ...
- 109k
-4
votes
1
answer
76
views
Problem of deriving time dilation in different way [closed]
I tried to derive the time deliation equation in different way,but I got a ridiculous result.
Could somebody point out the problem in my derivation?
The derivation in situation 1 (stationary source &...
- 19
3
votes
2
answers
276
views
Difference between these two Rindler metrics
I am uncertain about the difference between these two Rindler metrics:
$$ds^2 = -\left(1 + \frac{\alpha x}{c^2}\right)^2 c^2dt^2 + dx^2+dy^2+dz^2$$
$$ds^2 = -\left(\frac{\alpha x}{c^2}\right)^2 c^2dt^...
- 711
0
votes
1
answer
47
views
Units for proper distance
The proper distance for a spacelike path $P$ between two spacelike-separated events is defined as
$$L=c\int_P\sqrt{\mp ds^2}=c\int_P\sqrt{\mp g_{\mu\nu}dx^\mu dx^\nu}$$
assuming $(\pm,\mp,\mp,\mp)$ ...
- 109k
0
votes
0
answers
31
views
Lorentz algebra representation
In my QFT lecture the following was derived, but I have no idea how:
We consider a scalar field : $\phi(x^\mu)$.
$\phi(x^\mu)=\phi'(x'^\mu)$
Then:
$\phi'(x'^\mu)=\phi((\Lambda^{-1})^\mu_{\ \ \nu}x'^\...
- 338
1
vote
1
answer
89
views
How do you describe a light wordline using affine parameter?
One can parametrize wordline of objects with nonzero mass in spacetime using $x^\alpha(\tau)=(ct(\tau), x(\tau), y(\tau), z(\tau))$ where $\tau$ is object's proper time.
I learned that wordline of a ...
- 3,313
3
votes
0
answers
82
views
How does potential energy become relativistic mass?
I know that during certain nuclear reactions, the rest mass of the components is greater than the rest mass of the matter results because it lost potential energy. The implication is that the ...
- 213k
3
votes
2
answers
238
views
Confusion over the electric field produced by an infinite, neutral, and current-carrying wire
I have a lot of trouble in attempting to understand several aspects of the relativistic explanation of the magnetic field produced by electric currents. To be more specific, my problem is not in the ...
- 17.1k
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vote
6
answers
3k
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What do clocks measure?
I recently asked a question about the measurement of time, and it has become apparent that I'm really asking a set of related questions, the premises of which need to be shored up and articulated ...
- 28.4k
1
vote
4
answers
141
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Confusion about relativity and length contraction and time dilation?
So I know the equations of time dilation and length contraction given by:
$$L' =\frac{1}{\gamma}L_0$$
$$t' = \gamma t_0$$
However, I am confused about how the speed of light stays the same in all ...
- 39.6k
-4
votes
1
answer
99
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How does the theory of relativity point to a block universe? [closed]
Please explain in layman's terms how Einstein's theory of relativity points to a universe that is eternal and non moving, where past, present and future all coexist simultaneously.
- 39.6k
3
votes
1
answer
335
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Physical intuition for the Geodesic Equation derivation via a Variational Principle: Why maximum proper time instead of minimum?
The most commom derivation I've seen of the geodesic equation of a massive particle is by the use of the Variational Principle. My problem is that I can't realize what the meaning of find a spacetime ...
- 213k
0
votes
2
answers
81
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Invariance of spacetime interval when using Rindler coordinates
In the previous question I asked why it is not possible to derive Rindler coordinates using Lorentz transforms and I think I found an answer.
Lorentz transforms in standard configuration
$$t'=\gamma\...
- 711
2
votes
1
answer
636
views
Maximization of proper time between two timelike events in Minkowski space
So it is accepted that the path that maximizes the proper time between two timelike separated events in Minkowski space is a straight line (in Minkowski space). I am having trouble deriving this from ...
- 213k
2
votes
0
answers
64
views
Combined SR and GR effects for time dilation in uniform gravitational field
I was reading David Morin's "Classical Mechanics" Chapter 14 and he claims that the combined effect of time dilation on a body moving at speed $v$ is $$d\tau=(1+gx)\sqrt{1-v^2}dt$$ ($c=1$). ...
- 213k
-3
votes
1
answer
103
views
A Computer Moving Close to the Speed of Light
I'm a computer science student with a limited physics background and was recently introduced to special relativity. I have a question I haven’t been able to answer, and I would appreciate your help.
...
- 213k