# Questions tagged [special-relativity]

The special theory of relativity describes the motion and dynamics of objects moving at significant fractions of the speed of light.

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### Why is the stress-energy tensor for electromagnetic radiation traceless?

A photon gas obeys the equation of state $\rho=P/3$ and hence $T^{\mu}_{\quad\mu}=3P-\rho=0$. (Can also be seen by expressing the stress energy tensor in terms of of the electromagnetic tensor as ...
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### What will happen if a stick and a beam of light is to race [duplicate]

I don't know whether the question is asked before on not on this website as I can't found it anywhere so I have to ask. What will happen if a place a long stick with a length of a light year. Rather ...
1answer
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### Wouldn't gravitons themselves theoretically be affected by gravity? [duplicate]

(I wrote this using the assumption that the graviton exists, which I know is not necessarily true; this is asked from a theoretical standpoint) It is my understanding that General Relativity states ...
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### Equation of Motion for a Test Particle

I have a question regarding Misner, Charles W.; Thorne, Kip S.; Wheeler, John Archibald (1973), Gravitation ISBN 978-0-7167-0344-0. It is a book about Einstein's theory of gravitation. At the page ...
2answers
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### How does the watch orbiting Earth “know” it has to be the slower one?

Pardon me for asking in layman's terms, but I find it the quickest. When an astrounaut's watch has orbited earth in high speed for a sufficient amount of time, it is delayed by a detectable amount of ...
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### Why does the pythagorean theorem contradict the geometrical interpretation of length contraction?

While I was taking a course in SR, we derived the length contraction formula using Lorentz transformations, however, when I tried to graph the space-time diagram of a ruler at rest being observed by a ...
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### Uncertainty regarding MTW Exercise 3.6 and 3.9

I am currently working through the exercises in "Gravitation" by MTW. I am a little unsure about my approach to Exercise 3.6 and I feel stuck at Exercise 3.9: Exercise 3.6 reads: An observer with 4-...
1answer
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### Why using time-ordering causality? and what is Difference between Locality and Causality?

In QFT, the time-ordering causality is generally used. There are 4 ways to bypassing the pole called time-ordering, anti-time-ordering, retarded and advanced. But in many case only time-ordered ...
2answers
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### Is spacetime in special relativity hyperbolic?

I thought the spacetime diagrams were usual flat planes just with a new formula for distance. But the source I was reading suddenly started talking about hyperbolic angles in triangles ( I don't know ...
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### Regarding notation used for infintesimal parameters of the Lorentz algebra and generators of the Lorentz group

I have a confusion regarding the notation that is used for infintesimal Lorentz transformations and the parameters that define the Lorentz transformation (used in various books such as Srednicki's and ...
1answer
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### Does the CPT theorem hold for all spacetime dimensions?

I can't find any reference which mentions the dependence of the theorem on spacetime dimension, but it would be very interesting to know what if any it has!
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### Relativistic Doppler Effect from source’s frame

Could someone please help me understand the derivation of the relativistic Doppler effect of light for objects moving away as derived from the source's reference frame? There’s no problem for me to ...
2answers
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### Question on kinematics and theory of relativity [duplicate]

If two particles A and B travel in opposite directions with the velocity of 0.6c and 0.7c respectively, the particle A sees particle B moving with a speed of 1.3c in the opposite direction (c is the ...
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### Relativistic doppler efect

I got a little confused with the derivation of doppler effect for light as showed on wikipedia. The derivation states that when the source of light and the receiver are moving away from one another, ...
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### Deriving expressions for momentum in relativistic elastic collision

I have the following question from D'Inverno book 'Introducing Einstein's Relativity': A particle of rest mass $m_0$, energy $e_0$, and momentum $p_0$ suffers a head on elastic collision with a ...
1answer
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### Lorentz Force Equation

We know that from relativistic Lagrangian for a charged particle is $$L = - m_0 c^2 \sqrt{1 - \frac{u^2}{c^2}} + \frac{q}{c} (\vec u \cdot \vec A) - q \Phi$$ leads to the Lorentz force equation, but ...
1answer
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### What does this mean by 'if the point p has same co-ordinates'?

I was learning Special Relativity from this pdf. I'm talking about this part (second paragraph) in the screenshot (the whole screenshot is for more context): "Seen from the point of view of the ...
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### Why to we take the Minkowski vacuum to calculate the thermal Unruh distribution?

Looking at a derivation for the Unruh effect, this generally ends with a calculation of the particle distrubution: $$\langle{0_M}|b^\dagger b|0_M\rangle=\frac{1}{e^{\hbar\omega/k_BT_U}-1}$$ where $b$ ...
2answers
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### Is it possible to use two different metrics for one observer in distinct times (related to twin paradox)

I am not going to rewrite another twin paradox, what i am interested now is that if we assume an observer who moves with acceleration first (during $0<t<T_0$), then he stops his acceleration and ...
3answers
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### Is it possible writing conservation of relativistic energy in this naive way?

Conservation of charge or rest mass can be written in this way and it is Lorentz invariant $$\nabla \cdot (\rho \mathbf{u}) + \frac{\partial \rho}{\partial t} = 0$$ So we could be tempted to naively ...
3answers
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### The interference paradox

This is a thought experiment I created myself. Imagine two radio sources fixed at the ends of a rocket and they produce signal of same frequency such that they arrive at the center simultaneously and ...
2answers
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### In which sense equations of motion are covariant?

I read lots questions about what covariance is and I found out that, according to this topic Lorentz invariance of the Minkowski metric, we say an object is covariant if it doesn't take the same value ...
2answers
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### How can the spacetime interval be negative?

It’s my understand that the spacetime interval is analogous to the distance squared between two points in euclidean space. If the spacetime interval is the distance squared between two events in ...
4answers
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### Can the Schrodinger Equation be Relativistic in it's General Case?

So as we all know the Schrodinger equation is not relativistic when written (constantless) as$$i\partial_t\psi=-\partial_{xx}\psi+V\psi$$due to it not being Lorentz invariant. However, if we consider ...
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### Collision of accelerated particle [duplicate]

If two particles, accelerated by a particle accelerator, collide together when they are individually very close to speed of light, so when they collide their relative speed will be more than the speed ...
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### Representation of Poincaré group

Let's consider the most general Lorentz transformation: $x'^{\mu} = \Lambda^{\mu}_{\ \ \nu} x^{\nu} + a^{\mu}$. These transformations form the Poincaré group. The generators of translations of this ...
2answers
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### Silly doubt about tidal effects and Einstein Field Equations

Suppose I give you the following line element: $$ds^{2} = -(1+2\phi)dt^{2}+(1-2\phi)(dx^{2}+dy^{2}+dz^{2}) \tag{1}$$ Without saying anything you might think that this is just another line element ...
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