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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Einstein's train, considering the thunder

From Einstein's "easy" explanation https://www.bartleby.com/173/9.html (Yes, I have reviewed 8 other answers to similar questions. Please bear with me.) M is on the platform, T (aka M') is on the ...
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Relativistic constant acceleration in the framework of general relativity

Regarding the constant acceleration of a spacecraft towards relativistic velocities, the general equations are found at the following link: Baez However, if the distance covered is in excess of 1 ...
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Relativistic Doppler Effect between rotating bodies

The Wikipedia article "Relativistic Doppler effect - One object in circular motion around the other" confused me. There they say that when the light source orbits the observer, the observation of ...
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$z$ component of angular momentum under Lorentz transformation for massless particle

This question is related to this Helicity states Suppose we have $k=[\omega,0,0,\omega]$. In Weinberg's book The Quantum Theory of Fields: Volume I he defines the state $|k,\sigma\rangle$ as an ...
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Which frame to consider for time dilation? [duplicate]

Clearly for constant motion we cannot define absolute rest or motion. So ,when dealing with time dilation problems for example twin paradox , how do we define which frame is in motion? If we ...
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Basic Special Relativity Question [on hold]

I am trying to understand the implications of c being relative to the frame of reference. Is the following analysis correct? N is on a slow train moving 3 m/s and M on the platform next to N both ...
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Helicity states

On page 71 of Weinberg's book The Quantum Theory of Fields: Volume I, he defines the operators $$A=J_2+K_1$$and $$B=-J_1+K_2$$ where ${\mathbf{J }}=(J_1,J_2,J_3)$ are the rotation generators and ${\...
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Sagnac Effect and clocks synchronization

I read this from "The Sagnac effect and its interpretation by Paul Langevin", in cylindrical coordinates $$ ds^2=c^2t^2-dr^2-r^2d\theta^2 $$ ...This transformation means that the observer O (...
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Helicity under rotation

Suppose that the state $|p,\sigma\rangle$ (for a massless particle) has 3 momentum ${\bf p}=p_3$ (that is the momentum is in the $z$ direction) and that $J_3|p,\sigma\rangle=\sigma|p,\sigma\rangle$ ...
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Why I think the Michelson-Morley experiment was originally flawed, and would have failed either way [on hold]

I was recently reading about how physicists were heavily relying on the existence of Luminiferous Aether for their physics to work. I read about how the Michelson-Morley experiment attempted to prove ...
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Elapsed time between two events is greater for moving observer

Lorentz's equations show the elapsed time between two events in moving frame is greater than rest frame. But moving observer's clock ticks slower. Isn't that an inconsistency? Consider two observers, ...
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Using Lorentz transformations with variable velocity

A particle is moving in a system of reference $S$. In its proper system of reference, say $S'$, the particle is still and it is described by the event $(c\tau,0,0,0)$. In the inertial frame $S$, the ...
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Four-velocity of an accelerating particle

In the rest frame of a particle, the acceleration four-vector is $$ \mathbf{a} = (0, g) $$ (see https://users.physics.ox.ac.uk/~smithb/website/coursenotes/rel_A.pdf , Eq.3.51). By definition $$ \...
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Difference between position of indexes in tensor notation (SR) [duplicate]

I am learning SR, and don't understand the difference between the following notations of a Lorentz transformation $\Lambda$ $$\Lambda_{\mu\nu} , \Lambda_{\mu}\ ^\nu , \Lambda^{\mu\nu}$$ I know that ...
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Why can't we measure the one-way speed of light?

I believe the problem is because we need to synchronize clocks. But ok let's assume we can't do that. Can't we just use some external reference - Eg The Sun & Solar Noon? For example given the ...
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Can a person from different universe which has its “own different laws of nature”, can go into our past in our Universe? [on hold]

Suppose There is a Universe, which has different laws of nature than ours galaxy and they have much greater speed of light than $3* 10^8 $ m/s ,so some person from their universe visits our universe ...
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Doesn't the speed of light limit imply the same electron can be annihilated twice?

If I understand correctly, there is a small probability the same electron to be found anywhere in the universe. Suppose that an anti-electron collides with an electron, annihilating it and producing ...
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A More Inspired Derivation for Time Dilation

I've always believed the classic derivation you see for time dilation in a intro physics course, however I also have always had the uncomfortable feeling that some things were getting brushed under ...
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What is the point of sub and superscripts in metric tensor

I am new to QFT and have to catch up with some things that I did not learn from my SR courses. I am learning about the tensor notation, in particular the metric tensor, $$g_{\nu\mu}=g_{\mu\nu}=\begin{...
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Condition for Lorentz transformation

Today I had my first class of a QFT course, and there were some things that apparently I am supposed to know, but I don't. One of them is regarding Lorentz transformations. My teacher stated that: $\...
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Relative velocity between 2 frames of reference [duplicate]

In special relativity formulas for changing coordinates x,t into x',t' are based on the relative velocity of the 2 frames. What is the base for assuming that if v is the velocity of frame O' relative ...
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Gamma traceless

I read this Under what conditions is a vector-spinor gamma trace free. And also read many papers about higher spin, but no one explains why irreducible spinor is gamma traceless spinor? Can anyone ...
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Are laws of Physics same in frames having zero relative acceleration?

If two frames have the same acceleration, then they'll be moving with a uniform speed with respect to each other. Are laws of Physics the same in these two frames?
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Is there any known experimental violation of Einstein's $E=mc^2$?

Note that I am not talking about $E_0= m_0c^2$ but $E=mc^2$, where m is the relativistic mass. I know that one holds for stationary particles, moving particles, even light, I read that it even holds ...
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What will happen first: the rod's front end will hit the back wall of the cave or the left end of the rod will enter the cave? [duplicate]

A rod flies into a cave at the speed of 0,8c relative to the cave. In the reference frame of a stationary observer, the cave is 30 meters deep. According to the observer, who "sits" on the rod, the ...
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Grasping (Inertial) Frames of Reference [duplicate]

I am new to studying Special Relativity and have some trouble truly understanding what the phrase (Frame of Reference) tries to imply. So I understand that an inertial frame of reference, for example,...
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Why does FTL not leave behind a motion blur? [closed]

I once thought anything traveling faster than light would leave behind a motion blur that on one end recedes at the speed of light and at the other increases at the velocity of the object. If an ...
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If clocks themselves are based on light signals, wouldn't we expect the measured speed of light to always be the same constant?

I'm trying to work out if there is an alternative starting point for the second postulate of special relativity. My main observation is that all "clocks" are, internally, based on light signals. So ...
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Spacetime rotation matrix using mostly minus conventions

When trying to find the Lorentz transformation in matrix form in the $x^2+x^3$-direction, I tried simply mapping the Lorentz boost in the $x^2$-direction to the $x+x^3$-direction by rotating it $45°$ ...
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Show that $c^2 B^2=E^2$ is invariant under Lorentz transformations [closed]

Hello to every one please help me for this question, Show that $c^2 B^2=E^2$ is invariant under Lorentz transformations I try but can't.
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Meaning of time derivative of the Lorentz factor $\gamma$?

This question about the Lorentz factor $\gamma$ in special relativity. I know what $\gamma$ means and how to drive. I'm wondering if I have time derivative of $\gamma$, what dose it mean conceptually?
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Does a uniformly moving charge induce electric quadrupole moment densities in surrounding space?

The electric field of a uniformly moving charge is cylindrically symmetric around an axis parallel to its velocity vector. It varies inversely to the square of the distance. The electric field of a ...
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What does Ethan Siegel mean by “The fact that there are no stationary, oscillating in-phase electric and magnetic fields led to Special Relativity.”

In This One ‘Anomaly’ Is Driving Physicists To Search For Light Dark Matter, what does Ethan Siegel mean by "The fact that there are no stationary, oscillating in-phase electric and magnetic fields ...
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Can I get a single matrix from Einstein’s summation

A simple question guys, I have this equation $ g^{m \bar{n}} g^{r\bar{p}} \partial_t {g}_{m r} \partial_t {g}_{\bar{n}\bar{p}} = X_{i\bar{j}}~ \partial_t{f}^i (t) ~ \partial_t{f}^\bar{j} (t) $ ...
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Spacetime interval calculation - What am I doing wrong?

I'm calculating spacetime intervals in standard setup with frames A and B where t = t' = 0 and x = x' = 0, and all the motion is going only in x direction. Objects A and B move in relative velocity ...
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Lorentz group in 1+1 dimension

Consider the Minkowski 2D metric $\eta = \text{diag}(-1, 1)$. The Lorentz group is the set of matrices such that, for a transformation $\Lambda$, we get $$\eta = \Lambda^T \eta \Lambda$$ This means ...
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Is the mass needed to create a black hole greater if the black hole is moving? [duplicate]

So my argument goes like this: say we have an object that is nearly at the density required for a black hole. Then we Lorentz boost into a new frame, the object is Lorentz contracted and therefore ...
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Lorentz boost in light-cone coordinates

Consider a particle with momentum $p^{\mu}=(p^+,p^-,p_{\perp})$, where the momentum is written in light cone coordinates defined as, \begin{align} n^{\mu}&=(1,0,0,1)& \bar{n}^{\mu}=(1,0,0,-1) ...
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Can an observer perceive a single source of light as multiple sources because of curved spacetime?

Is it possible that some of the stars and galaxies we observe here on Earth are actually replicates of other stars and galaxies we are observing from different angles because of curved spacetime? Let'...
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Time measured by a person vs Time measured by the same person as observed from another frame

I'm talking about the last few lines in the image. It says : $t_A$ (time measured by A1 as seen by A1) = $t’_A$ (time measured by A1 as seen by Bob) Why are these two times equal? The reason given ...
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Lorentz Transformation Perpendicular Photons

I'm trying to derive the Lorentz Transformation on my own but I'm stuck. This is probably something stupid, but I cannot figure out why I am not getting this right. enter image description here Here'...
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Why does the charge conjugation of the spinor transform as a spinor?

I have come across (in QFT Nutshell, A. Zee) how the charge conjugation of the spinor, $\psi_c \equiv \gamma^2 \psi^*$, transform (where $\gamma^2=\sigma^2\otimes i\tau^2$ is the component of the ...
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Why does everyone seem to think that moving clock appear to tick slower? [duplicate]

I'm getting interested in special relativity and almost all people and explanations about the subject I found on the internet seem to think that when A and B would be in relative motion, they would ...
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Is rest mass determined by the kinetic energy of inner particles?

I haven't studied physics in many years, please forgive my lack of proper formalism. With that being said... The total energy is a function of rest mass energy and the velocity of the object, and is ...
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Causality under relativity [duplicate]

If simultaneity is relative; meaning that for each any events A and B and we can find a reference frame in which two events A and B occur in inverse order, how does our notion of 'causality' withholds?...
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If I want to spin a disc or rod with an objective of high tip/edge velocity (of .1c) what are my limitations?

What are our limitations on being able to spin a disc or rod to create a relativistically fast tip/edge speed? My thoughts are you should be able to increase the radius of the spinning object to ...
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Higher spin field?

Ok, Bosons transformed as $(n,n)=n\times n=2n+(2n-1)+\cdots+3+2+1$, where $+$ is direct sum, and $\times$ is tensor product of representations.This tensor is traceless because every representation of ...
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A question about Lorentz invariant argument when writing down the Dirac equation [duplicate]

According to the chapter II.1 in "Quantum Field Theory in a Nutshell" by A. Zee, Dirac was trying to write down the relativistic wave equation linear in spacetime derivative. The author stated that ...