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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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Inertial frames?

This is from a book. A traing is moving on earth. A ball is sitting at rest (relative to the train) on the floor of the train which is moving at constant velocity relative to a tree. If the ...
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Velocity addition formula derived from velocity boosts

I understand the derivation for the equation the velocity in a boosted frame by taking the boosts of the differentials such that: $v'^{\mu}= \frac{dx'^{\mu}}{dt'} $ where $x^{\mu} = \Lambda^{\mu}_{\, \...
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Aging while traveling faster than speed of light? [closed]

theoretically, if organic matter was able to travel faster than the speed of light, without becoming "pure energy", and since theoretically traveling faster then the speed of light would travel ...
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Does special relativity causes magnetism? [closed]

And if yes, according to amperes law when the magnetic force beetween two current-flowing conductors the force is in linear reverse connection beetween the distance and the force, but if magnetism is ...
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Dirac equation in 1+1D spacetime compared to “standard” 3+1D Dirac equation

In the past couple of weeks I've been studying the Dirac equation and its solutions. During a discussion with a tutor it was pointed out to me that one could formulate something similar to the Dirac ...
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How does special relativity account for intrinsic magnetic moments and orbital magnetic fields?

I've just watched this video: https://www.youtube.com/watch?v=hFAOXdXZ5TM And it makes perfect sense to me. The only thing that I don't understand is how orbital magnetic fields or intrinsic magnetic ...
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How do time-like separated points preserve temporal ordering under orthochronous Lorentz Transformations?

How do time-like separated points preserve temporal ordering under orthochronous Lorentz Transformations? This question has already been asked in this Phys.SE post but I want to derive this result in ...
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Speed of light and time dilation vs. mass and time dilation

Time slows for an observer the faster they come to the speed of light, large amounts of mass also also have an effect on time. How much mass would be needed to have the same effect on time as moving ...
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Physical interpretation of Mandelstam variables with negative value

Reading the text by Peskin-Schroeder "An introduction to Quantum Field Theory" the use of the Mandelstam variable as a function of angle of scattering in the center-of-mass frame I was surprised that ...
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Why are time dilation and length contraction needed to fix time? [duplicate]

In many textbooks and online answers I have heard people go on about how time dilation accounts for the gap of time experienced between two observers. However, they continue that in reality this is ...
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Formula for all the Lorentz boosts that result in $E$ parallel to $B$?

This is a follow-up question to a previous question regarding a minimum-energy invariant of the electromagnetic field. @ChiralAnomaly showed that there is indeed an invariant minimum energy density ...
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How the Earth observer would see (time-ticks wise) a traveller rushing away or towards Earth at near-light speed?

There is an observer on the Earth. 1) There is a traveller moving away from the Earth at a speed approaching the speed of light. 2) There is a traveller moving towards the Earth at a speed ...
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At black-hole horizon time stops…for whom? The traveller itself or for an observer from the Earth? [closed]

1) Time slows-down in strong gravity field. But I cannot understand for whom (in which reference frame) What about the paradox that time stops for an observer at earth who thus would never see the ...
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Why, when going from special to general relativity, do we just replace partial derivatives with covariant derivatives?

I've come across several references to the idea that to upgrade a law of physics to general relativity all you have to do is replace any partial derivatives with covariant derivatives. I understand ...
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Why does four-momentum have to be tangent to the worldine?

In relativity, we define momentum for a particle as a vector that is always tangent to the particle's worldline. I am wondering what is the exact reason this is necessary. For a massive particle of ...
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The ladder paradox - with equal lengths

Take the usual ladder paradox in special relativity, but this time the ladder and the barn have the same length, at rest. Since each one of them contracts when viewed in the rest frame of the other, I ...
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The chain rule and velocity transformation in relativity

From elementary calculus, we have that the chain rule occurs when we differentiate a function like $f(y(x)) \equiv f(x)$: $$\frac{\mathrm{d}}{\mathrm{dx}}[f] = \frac{\mathrm{d}}{\mathrm{dx}}[f(y(x))] ...
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Relativity: moving space shuttles [closed]

Two space shuttles $A$ and $B$ are moving in opposite directions. A person on Earth measures $v_A = 0,75 c$ and $v_B = -0,85 c$. What is the velocity of $B$ relative to $A$ (= $v_{BA}$)? So my first ...
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How do the creation operators transform under Lorentz transformation?

In Weinberg's QFT book In chapter 4, the change of creation operator under Lorentz transformation is describe by (4.2.12), $$\begin{aligned} U_{0}(\Lambda, \alpha) a^{\dagger}(\mathbf{p} \sigma n) ...
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As our velocity changes shouldn't the span of time taken change [duplicate]

We all know the variation in the velocity of an individual causes different time periods . If we move with the speed of light ,then the time stops for us. Then why does sunlight take time to reach us?
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Sending Information With Entangled Particles

I learned from my quantum mechanics course that if you measure a quantum state twice, two things can happen: 1) You take the second measurement just after the first on. In this case, the result will ...
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1answer
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How to determine particle energies in center of momentum frame?

I want to show for the following process that, except for the angle $\theta$, all momenta and energies are fixed by energy-momentum conservation. Namely: $$p_A=\frac{1}{2\sqrt{s}}(s+m^2_A-m^2_B\space,...
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A question about Lorentz transformations in spinor representation

For $$\Lambda^{\mu}{}_{\nu}= \frac{1}{2} Tr(\bar{\sigma}^{\mu} S \sigma_{\nu}S^{\dagger}) $$ We need to prove that $$\Lambda (S)= \Lambda (-S)$$ Am I naive to say that by adding $-S$, $S^{\dagger}...
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Behaviour of a star as it approaches Ultrarelativistc limit

By considering the potential energy of a degenerate star of mass $M$ and radius $R$, I can use dimensional arguments to show that the radius of the star depends on its mass as: $$ R ∝ M^\frac{2-n}{...
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What motivated Einstein's postulate on the speed of light? [closed]

I know that there are several experiments (conducted after Einstein's formulation of Special Relativity) that confirm to some extend Einstein's postulate that nothing can travel faster than light. But ...
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Relativity and Quantum Mechanics

I have been thinking about the problem of relativistic path integrals and I encountered several difficulties. Let's assume we have a particle initially a position $x_i$ at $t_i$ in a certain reference ...
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2answers
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Does the electromagnetic field have a “rest mass” that is conserved?

In an answer to this Physics SE question, @ChiralAnomaly demonstrated that, indeed, there is a minimum field energy density observable at any point in an EM field. With a bit more calculation, it's ...
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2answers
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Is Einstein's train-lightening thought experiment consistent with Special Relativity? [closed]

Einstein’s train-lightening thought experiment contains only inertial motion so SR says we can ascribe relative motion and relative rest to either reference frame. Although it is not stated in the ...
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Infinitesimal parameter of Lorentz transformation

I'm working through the SUSY lecture notes by Lambert, and he does something which seems strange to me during the calculation of the Wess Zumino model. He says the spinor $\psi$ has the ...
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If infinitesimal transformations commute why don't the generators of the Lorentz group commute?

If infinitesimal transformations commute as proved e.g. on this mathworld.wolfram page, why are the commutators for the generators of the Lorentz group nonzero?
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SR time dilation discussion meaningless when there is gravity?

Let us say you have three clocks fixed to the spinning earth at the equator. If you set one of this clocks on a plane going eastwards around the globe it will have measured a lesser amount of time ...
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What creates the physical difference in ageing when travelling close to the speed of light? [duplicate]

I probably have a fundamental misunderstanding, so correct me if I'm wrong. When travelling close to the speed of light, movers experience time dilation, which is what results in the phenomenon of ...
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Is there a “special” inertial frame determined by the value of E and B at a point in an EM field?

Given the facts that $(E^2 - B^2)$ and $(E\cdot B)$ are Lorentz invariants of the EM field, and that the energy density $(E^2 + B^2)$ is not invariant, it seems that at each point in an EM field there ...
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An invariant for transformations of Lorentz

Exist a physical demonstration why $$E^2- p^2c^2 =m^2c^4=E'^2- p'^2c^2 $$ is an invariant for transformations of Lorentz? N.B.: $m$ is mass; $E$ is the energy and $p$ is momentum in the frame $\...
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Inverse of metric tensor

The Minkowski metric tensor have the relation $\eta_{ij} \eta^{jk}=\delta_i {^k}$. That is the inverse of the Minkowski matrix is the matrix itself. Analogously, is it true that $g_{ij} ...
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Lorentz contraction of the wavelength of light

I couldn't find this question on the suggested "similar questions". If this has been asked before please direct me to answer. My question is "why isn't the wavelength of light,which is in the ...
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Reconciling classical mechanics with special relativity - energy lost as heat in an inelastic collision

If a particle of rest mass $m_0$ travelling with a velocity $u$ collides with a stationary particle also of rest mass $m_0$ and then coalesces to form a new particle with invariant rest mass $M_0$ ...
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Radiation emitted by collision of two photons

Using Lamor's formula, can someone tell me how much radiation is emitted by a particle accelerator or by the collision of two photons? It requires a 4 momentum vector which I'm not very acquainted ...
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1answer
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Is it speed or acceleration that leads to time dilation? [duplicate]

Is it acceleration or speed that leads to time dilation or both? For example, when a spaceship accelerated to (almost) the speed of light, then reversed course to come back towards earth, does this ...
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The transformations of Lorentz as a general case of the transformations of Galileo

Starting from the transformations of Lorentz, $$ \left\{\begin{aligned} x&=\gamma (x'+\beta ct)\\ y&=y'\\ z&=z\\ ct&=\gamma (ct'+\beta x')\\ \end{aligned}\right. \quad \tag{*}$$ I ...
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Why can't a particle decay into a higher mass particle?

I mean, why can't the initial particle (decaying particle) give some of its initial energy to the final particle such that the particle in the end will have a greater mass?
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How to Construct Proper Spherical Coordinates in Minkowski Spacetime?

In $n$ dimensional Euclidean space, we only need one radial coordinate, and $n-1$ angular coordinates, where one ranges from $[0, 2π)$ and the rest range from $[0, π]$ Spherical Minkowski coordinates ...
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Length Contraction of a rotating object

When observing an object, such as a spinning ring, what velocity is used to calculate its length contraction? I know it depends on the observer, but let's say theoretically an observer is just ...
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2answers
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What happens to the energy of an absorbed photon?

Photons are electromagnetic wave fields that travel at the speed of light. When they are absorbed by an object, their momentum and energy is transferred to the absorbing object. What is that ...
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How does the momentum conservation law hold for gravitational interactions in special relativity with Newton's third law being invalid?

Griffiths' argument that Newton's third law is invalid in special relativity The selected answer to the post above talked about momentum conservation in electrodynamics – Newton's third law ...
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3 variations of the Twin Paradox [duplicate]

Here I state and try to answer three variations of the twin paradox 1) "Classical" problem, no acceleration, no turn around Consider the case where there's a stationary planet, and a moving ...
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Is the Lorentz transform of a bound current - a bound current?

The bound (magnetization) current is $\mathbf{J}_\mathrm{M} = \nabla \times \mathbf{M}$. The charge density of a moving magnet that is electrically neutral in its own rest frame satisfies the ...
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Have there been any papers on a relativistic relative state (“MWI”) interpretation of QM with continuous spectra?

I've read the original papers on the relative state interpretation ("MWI") of Quantum Mechanics. They seem compelling, but they only addressed a nonrelativistic system and operators with discrete ...
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Query about using lorentz transforms to describe muon decay

Image from https://brilliant.org/practice/cosmic-ray-muons/?p=5. On the above diagram, $T$ and $X$ correspond to the axis of an observer on Earth and $T'$ and $X'$ correspond to the axis of the ...
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Length contraction and electromagnetism [duplicate]

No physics guy so forgive any stupid questions or incorrect wording. I think I get the length contraction, looking at a moving train, the light coming to my eyes are really emitted at different points ...