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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Lorentz transformation of basis vectors in The geometry of Minkowski spacetime by Gregory L. Naber

Gregory L. Naber's book introduces the Lorentz transformation like this: Now let $L :M→M$ be an orthogonal transformation of $M$ and ${e_1, e_2, e_3, e_4}$ an orthonormal basis for M. By Lemma 1.2.3, ...
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Will an observer see the light hit the same spot as the ones in a spaceship? Why?

In terms of special relativity. An astronaut marks a spot a at the ceiling and shoots a light beam at a in a spaceship. The ...
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Time dilation rotating around the center of mass

If 2 objects connected by a massless rod or wire, rotate around the center of mass, do they experience time dilation ? I'm thinking that the smaller one will move faster so time will pass slowly, but ...
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Show that the dot product of two basis vectors in special relativity gives the metric

I'm reading Schutz's Introduction to GR and came across an exercise problem. The problem is the following: Show that the vectors $\{\vec e_{\bar \alpha }\}$ obtained from $$\vec e_{\bar \beta } = \...
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Two-way tachyonic anti-telephone

Consider the two-way tachyonic antitelephone where the speed at which message is transmitted is $a$. A person $A$ sends a message to $B$ which is moving away with a speed of $v$ with respect to $A$. ...
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Simple question on orthocronous proper lorentz transformation

I've found written in an undergrad textbook on relativity (Barone's, Relativity; italian book, don't actually know if it's been translated in any other language) that proper orthocronous Lorentz ...
Michele's user avatar
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3 answers
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One-way Tachyonic anti-telephone

When you have length contraction in special relativity $$L' = L/\gamma$$ the interpretation is that $L'$ is the length of an object with rest-length $L$ moving with respect to an observer at rest. ...
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$\mathbf F'=\mathbf F$ in special relativity

Assume that an inertial observer $S'$ is moving with a velocity $\mathbf u$ relative to another inertial observer $S$ along the $x-$axis. Now, imagine that the two observers observe a force being ...
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Why has time always a minus sign in standard metric signature? [closed]

I wrote an article about a possible interpretation of the usual metric notation of time expressed with a negative sign (in order to preserve causality). Maybe it's a really meaningful physical require ...
Thomas Villa's user avatar
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1 answer
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Seeking advice from people for my notes on special relativity [closed]

I am writing a notes on special relativity, and I want to ask everyone for their comments on a paragraph I wrote in my work. Here it is : Definition. Let $M$ be a 4 dimensional vector space. A scalar ...
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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 ...
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Trying to understand the motion of a high speed particle?

To start we have a single proton. We place are proton in a circular particle accelerator, and bring the proton up to speed of 0.99C. we then accelerate the entire particle accelerator on the ...
Kyle Howatineck's user avatar
2 votes
2 answers
397 views

Doppler shift of a single photon

I'm curious to understand how the Doppler shift phenomenon occurs and is mathematically expressed for a single photon emitted by a stationary single photon emitter, such as a quantum dot, and observed ...
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How to distinguish a doppler-shifted photon from a non-doppler-shifted photon of the same frequency?

Can one physically distinguish a photon of frequency $\omega$, generated by a stationary laser, from a photon generated by a mechanically moving laser (a different laser from the first one) which, due ...
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Why does an alpha particle traveling at the same speed as a beta particle have 'only' about twenty times the energy? Rather than over seven thousand? [closed]

An alpha particle travels at about half the speed as a beta particle, right? ~5% of light speed versus ~10%? Therefore, if you doubled its velocity, its energy would roughly quadruple, correct? (Or ...
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Doppler shift phenomenon for non-inertia frames

The Doppler shift phenomenon is well understood when the source and observer are in relative constant motion. However, I'm curious to know how the Doppler shift phenomenon is modified when they (i.e., ...
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Why don't the electrons experience length contraction in this scenario?

I watched this Minute Physics video on how current produces a magnetic force on a moving charge because of relativity. In the video (timestamp is around 2 minutes), he explains that when the charge is ...
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Can Special Relativity's Effect on Proton Diameter Explain Magnetic Fields? [closed]

I've recently delved into the concept that magnetic fields might be understood as an effect of special relativity, inspired by explanations seen in resources like this video. This perspective suggests ...
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Isolated atom absorbs photon at relativistic speeds

I've been studying a type of problem wherein we initially have a photon (with (lab frame) energy $E_L$) and atom, both moving in the $+\hat{x}$-direction, with respective speeds $c$ (of course) and $...
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Energy Loss of protons travelling through gas

I wanted to calculated the energy loss of protons traveling through a gas medium such as helium and hydrogen.At energy range of about 10 Gev there should be two effects:1.Coulumb interaction,2....
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Pressure as momentum flux versus momentum of fluid flow

I've read in multiple sources (for example, Thorne and Blandford, Modern Classical Physics, pg 83 and Schutz, A First Course on General Relativity pg 92) that the stress components of the stress-...
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4 answers
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Why "time part" represents energy in Four-momentum?

I was going through Spacetime Physics by Taylor and Wheeler and came to a point where they said, and I quote, In what follows we find that momenergy is indeed a four-dimensional arrow in spacetime, ...
Plague's user avatar
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Confusion with Weinberg's QFT book, Volume I, Equation 2.5.3 (one-particle states as irreps of Poincare group)

I am reading Sec. 2.5 of Weinberg's Quantum Theory of Fields, Volume I. There he talks about the classification of relativistic one-particle states according to their transformation under the Poincare ...
Solidification's user avatar
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Entangled particles and the Andromeda paradox experiment

I know there are other questions linking the two subjects. I am not asking about an explanation, rather I am curious whether an experiment would be possible. To explain the experiment let's start with ...
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Proof of Invariance of Spacetime Interval?

I was going through Spacetime Physics by Taylor and Wheeler and came to a point where they showed a proof of Invariance of Spacetime Interval. You can find the proof Here and Here is the second part ...
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Does light accelerate? [duplicate]

If considering the general formula for acceleration, ie. Δ V/ΔT, we would get zero as the velocity of light is constant and does not change. However, what about when photons travel through different ...
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Unusual example of Compton Scattering (+Four-momentum approach, +nonrelativistic) [closed]

An electron of kinetic energy $k=100 keV$ (first note, doesn't this mean that its energy is much lower than $0.511 MeV$, and thus that it is a nonrelativistic electron we are dealing with?), collides ...
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Why the $(1/2,1/2)$ representation of the Lorentz group is a four-vector? [duplicate]

The finite dimensional $(\frac{1}{2},\frac{1}{2})$ representation of $SL(2,C)$ or $SO(3,1)$ is the four-vector representation. Why? One way to argue this is as follows. As a representation of $SO(3)$, ...
Solidification's user avatar
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How we can deduce from symmetry of $ θ^{μν} $ that total energy-momentum due to field spin is zero?

I am self-studying the book “James H. Luscombe, Core Principles of Special and General Relativity”. In “CHAPTER 9 : Energy-momentum of fields” of the book, it starts by introducing Noether’s theorem ...
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Taking the non-relativistic limit of the Dirac Lagrangian

I know the usual derivation (as well as the Foldy–Wouthuysen derivation) to obtain Schrödinger equation from the Dirac equation. See for example U Alberta Phys 512. But it it possible to go from $$i\...
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Weyl spinors under the Lorentz transformation

I am reading An Modern Introduction to Quantum Field Theory by Maggiore. On page 28, it says Using the property of the Pauli matrices $\sigma^2 \sigma^i \sigma^2 = -\sigma^{i*}$ and the explicit form ...
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Could we measure the one-way speed of light with two connected rotating apertures? [duplicate]

Can we measure the one-way speed of light by passing light through angularly shifted apertures in two disks solidly connected and spinning at a known angular velocity? Here is the apparatus I would ...
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Poincaré group conservation laws: 10 of 7? [duplicate]

According to the Wikipedia page about the Poincaré group, we get 10 conservation laws using Noethers theorem. 10 generators (in four spacetime dimensions) associated with the Poincaré symmetry, by ...
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On the conditions defining physically acceptable motions in special relativity

Let $ x^\mu(\lambda) $ be a curve in Minkowski spacetime parametrized by some parameter $ \lambda\in \mathbb R $. For $ x^\mu(\lambda) $ to represent a physically acceptable motion we usually require ...
GeometriaDifferenziale's user avatar
2 votes
2 answers
197 views

Scalar multiple of inertial frame

Consider an inertial frame of reference $S$. Now take a second frame $S'$, defined as follows: If a point $P$ has coordinates $$(t,x_1,x_2,x_3)$$ in $S$, then it has coordinates $$(t,2x_1,2x_2,2x_3)$$ ...
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Motion equations of moving magnetic dipole in electric and magnetic field

I would like to find motion equations $m\frac{\text{d}^2}{\text{d}t^2}\vec{x} = -\vec{F}(\vec{x},\dot{\vec{x}},\vec{E},\vec{B})$ or Hamiltonian $\mathcal{H}$ or Lagrange function $\mathcal{L}$ of ...
Adam Červenka's user avatar
1 vote
0 answers
26 views

Generalizing the Galilean law of addition of velocities using the Lorentz transformation [closed]

I am reading about how to generalize the Galilean law of addition of velocities using the Lorentz transformation, but I am confused about one step. Here, I have the following equations for Lorentz ...
Gene's user avatar
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1 answer
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Taylor Approximation for Time Dilation and Lorentz Contraction

I don't know why the taylor expansion for the time dilation and lorentz contraction look like this. Here, the velocity $\mathbf v$ of $\overline{\mathit O}$ relative to $\mathit O$ is nearly that of ...
Gene's user avatar
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What if an object is rotating near light speed? [duplicate]

lets say that we have a cube made of say 1kg, and using some means, managed to impart enough angular momentum to make it rotate at the speed of light or at least 99% of light speed. ignoring the fact ...
Shanmukha Evani's user avatar
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1 answer
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Relativistic case recoil of the target by emission of a photon

Generally, text books cover the recoil of a target after absorption of a photon. What happens when a target, it might be an atom, recoil after emission of a photon? The scientific literature shows a ...
Ennio's user avatar
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1 vote
2 answers
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Apparent "centrifugal" like force on a uniformly accelerating relativistic object

So this is more of a special relativity question as it comes from someone who's only savvy in special relativity. What I mean by this is if the answer is only describable in terms of general ...
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Valence electron energy and scattering angles in Compton scattering

The Compton scattering of the X-ray from electron is depicted below with x-axis being the dir. of the incident photon: Its wavelength shift amounts to: $$ \lambda_f - \lambda_i = \frac{h}{m_ec}(1-...
Leon Chang's user avatar
1 vote
3 answers
132 views

What exactly is weird about waves propagating without a medium? What does it violate? [closed]

I can not seem to grasp, why exactly does light travelling through space without the need of any medium was baffling for the scientists of 1800's.
Sumir's user avatar
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2 votes
1 answer
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Relativistic Time Dilation and Experienced G-forces

My question is this; does time dilation, or do any other effects of relativistic-velocity travel, effect the experience of the effects of acceleration in any way? So, for instance, if an Astronaut is ...
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1 answer
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Ehrenfest Paradox

If an observer is inside a carousel in circular motion and turns on a light after the light rays complete one full rotation around the carousel, will the light rays reach the observer simultaneously ...
Ricardo Melo's user avatar
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3 answers
59 views

Can anyone help me explain this Loedal diagram scenario? (Special Relativity)

I'm just confused as to what it says in the diagram. Could somebody please explain?
Lauren.0's user avatar
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2 answers
113 views

Do the Lorentz transformations contradict reality by implying time had no beginning? [closed]

Consider the following two points, or events as they are more commonly called, in SpaceTime: Event 1: $(x,t) = (0,0)$ Event 2: $(x,t) = (a,0)$ Take t=0 to correspond to the first moment in time. As ...
lee pappas's user avatar
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1 answer
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Acceleration in flat space-time and gravitational redshift

Consider two observers in flat space-time, of which one, called Terrence, is stationary, while the other, called Stella, moves in an accelerated way. I am particularly interested in the case where ...
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1 answer
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Why does $S$-matrix theory end up being a covariant formalism when it is not obvious that it is?

A principle of QFT that is frequently invoked, repeated, and potentially subject to rigorous verification is that the theory in question must exhibit Lorentz covariance and be invariant under the ...
Davius's user avatar
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1 vote
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How did the author get these three expressions?

I am reading Nonplanar Relativistic Flow by Peter G. Eltgroth, Phys. Fluids 15, 2140–2144 (1972) doi. I do not understand how the author arrives at expressions (12), (13) and (14) at page 2. Equation (...
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