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 ...
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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 ...
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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-...
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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 ...
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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 ...
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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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Spinor transformations as representations of $\mathrm{SL}(2, \mathbb{C})$

Background In the Weyl representation of the Dirac $\gamma$-matrices, the spinor transformations $S=e^{\frac{1}{2} \omega_{\alpha \beta} \Sigma^{\alpha \beta}} \in \,\mathrm{G}_{\mathrm{L}} \leq \...
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Dirac equation derivation

I am working through a set of lecture notes containing a derivation of the Dirac equation following the historical route of Dirac. It states that Dirac postulated a hermitian first-order differential ...
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Explain the last paragraph of this text

First, look at the first paragraph of the second page. It says: The things that you can see at some time are the inside of the light-cone at o. I don't get it. Suppose an event happened outside ...
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Particle physics threshold energy

I read the article Threshold energy on Wikipedia about colliding particles and their threshold energy. Consider the case where a particle 1 with lab energy $E_1$ (momentum $p_1$) and mass $m_1$ ...
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Generators of the Poincaré group

I am specifically interested in constructing the generators of an Poincaré group for a 2+1 dimensional Euclidean field theory. But I am pretty new to the subject, so I would like to ask some basic ...
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When to apply Lorentz transformations and laws of time dilations and length contractions: explanations

In the laboratory we are observing the motion of a particle moving in the positive direction of the axis $x$ of a frame system attached to it. At the initial moment, the particle is in the origin and ...
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Is relativity of simultaneity being violated in accelerated frames?

Consider relativity of simultaneity in SR, where 2 observers S and S' are inertial. With the Lorentz transformation $$t=\gamma(t'-vx'/c^2)$$ we can see that the relativity of simultaneity comes from $...
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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 ...
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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 ...
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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 ...
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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 $b$ ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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Derivation for relationship between rest mass, kinetic energy and momentum

I am trying to find a particle's rest mass in terms of its kinetic energy and momentum. Is this following derivation correct? $(E_{0}+K)^2=E_{0}^2+(pc)^2$ $2E_{0}K=p^2c^2-K^2$ $2m_{0}c^2K=p^2c^2-K^...
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Does the Doppler effect happen instantly?

Assume that a far star sends light toward a receiver. If we move this antenna such that it accelerate first for a moment, and then it moves with constant speed, we can see that the frequency of the ...
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Would possibility of instant communication break physics? [duplicate]

I recently read a sci-fi book, where some (very few) people can communicate telepathically, which happens to be instantaneous. So, every spaceship has a crew member who telepathically communicates ...
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Shooting someone's past self using special relativity

Suppose A and B are a long distance apart initially. B takes off in a spacecraft in A's direction at a really high speed. Both were aged 0 when B took off. When B about to cross paths with A, A ...
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Gravitons and self-interaction

In the book quantum field theory and standard model by Schwartz, there is a problem 9.4 that says by considering lorentz invariance of Compton scattering, you can prove that for spin 1 massless field ...
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Loss of simultaneity in special relativity

I was recently reading Introduction to Classical Mechanics by David Morin and while reading special relativity I came up with a paradox I am not able to resolve. It is basically related to the loss in ...
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Timelike, spacelike etc. for higher-order tensors

Vectors $V^\mu$ in relativity can be classified into those which are timelike, spacelike and null. A similar classification is available for tensors: A tensor $$T^{\mu_1\mu_2...\mu_p}_{\phantom{\mu_1\...
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Why is the onboard trip shorter when riding on a relativistic rocket as compared to a Newtonian rocket? [duplicate]

In the top answer for this question on the Space Exploration StackExchange, it's calculated that a rocket traveling at constant 1g of acceleration over 100,000 light years would, under Newtonian ...
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In Special Relativity, is it allowed to ask 'How much time has elapsed in a second inertial frame at a particular moment in the first inertial frame'?

Or is it a meaningless question? For example, A and his friend B are the same age initially. B travels relative to A at a very high speed. A keeps observing B from his frame. At one moment, A ...
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D'Inverno Exercise: velocity between reference frames given angle of a rod

I'm trying an exercise from D'Inverno book "Introducing Einstein's Relativity" that says S and S' are in standard configuration with $v = \alpha c$ $(0 < \alpha < 1)$. If a rod at rest in S' ...
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A query on group velocity of light in a vacuum of 30c

I have read that the speed of information propagation in a light packet is equal to the group velocity. But here I wonder if that is always correct. This article below that claims to have ...
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To prove: the integration measure is Lorentz invariant (Schwartz's problem 2.6b)

I am stuck on Schwartz's ("Quantum Field Theory and the Standard Model") problem 2.6b, and would be grateful for clarification. (I'm aware that this question has been asked and answered elsewhere (...
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Why has Einstein gotten the credits for “inventing” Special Relativiy, while Lorentz wrote down the Lorentz tranformations first? [closed]

At the heart of Special Relativity lie the Lorentz transformations, invented by the Dutch physicist Hendrik Antoon Lorentz (the name of the transformation was given by Poincaré in 1905). He wrote them ...
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Help understanding the speed of light in media with refractive index < 1

I have read the standard explanations on this, but I still have trouble with convincing myself that information is not propagating at faster than the speed c in media of refractive index less then ...
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How fast can we get to Alpha Centauri?

Suppose in the near future we send an Antimatter rocket that is capable of constant $1g$ acceleration to our nearest star, Alpha Centauri, $4.3$ light years away and suppose we want the spacecraft to ...
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How does a particle move under a constant 4-force?

This question pertains specifically to the case of a constant pure 4-force in special relativity, of the form $\textbf{F} = (f_0, f_x, 0, 0)$, where $f_0 = \frac{γ}c \frac{dE}{dt}$. I understand how ...