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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Fierz identity for chiral fermions [closed]

First of all I define the convention I use. The matrices $\bar{\sigma}^\mu$ I will use are $\{ Id, \sigma^i \}$ where $\sigma^i$ are the Pauli matrices and $Id$ is the 2x2 identity matrix. I will use ...
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Strange implication of the relativistic invariance of the Dirac equation

At least as normally formulated, the law of transformation of a wave function solution of the Dirac equation to another inertial frame seems to indicate that if observer 1 is certain the particle is ...
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By special relativity, a particle can only couple to an EM field? [closed]

By special relativity, the Lagrangian for the coupling must be $$ u_i A^i . $$ Here $u_i $ is the four-velocity, and $A^i$ is the four-potential. So, a particle can only couple to an EM field? ...
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What is physical meaning of Lorentz boost?

Physical meaning of spatial part of Lorentz transform is, obviously, rotations in R-space. Does anybody have a nice physical interpretation of boosts though? I can understand to some extent off-...
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Symmetry, Space-Time interval, and Coordinate Time

I had the following question I was working from a book: Question: A physics professor runs across the hallway covering 120 ns of distance in 150 ns of time as measured in the frame of the earth....
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How does the comparison of rates depend on mutual speed?

If I'm moving with a considerable fraction of speed of light, the time and any process in my system will be going slower. If B is an outstanding person that is watching me passing by, he will see ...
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From gauge invariance to charge conservation in covariant electrodynamics

I tried to solve the equations of motion using the action for the electromagnetic field interacting with a current, like $$ L = F_{\mu\nu}F^{\mu\nu} + A_{\nu}j^{\nu} $$ getting the right Maxwell's ...
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53 views

Speed of light when accelerating

I'm studying special relativity and saw the 2 postulates of Einstein. The most remarkable one for me is the universal speed of light. Einstein postulated that the speed of light in vacuum is the same ...
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Can the momentum of a system be spacelike?

For a particle, we always have $Eu=p$ where $u$ is the speed of the particle and correspondingly the momentum is always timelike. For a system of particles, if the potential energy is not considered ...
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Does increasing the energy of a relativistic particle increase thrust?

I know this particular chestnut has been asked before, but I have a specific variation on the theme: Particle accelerator space thrust. Specifically, cyclotrons to generate the thrust. They are ideal ...
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Is it really possible to break the speed of light by flicking your wrist with a laser pointer?

Minutephysics has a popular YouTube video called "How to break the speed of light". In the video it states that if you flick your wrist while pointing a laser that reaches the moon, that the spot of ...
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Special Relativity, refractive index and catching up with a wave

Einstein was partially motivated by the following: With Maxwell's equations, a plane wave is a sinusoidal wave that varies in space in time and moving with speed $c$. These variations are linked by ...
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A method of showing how mass increases with higher velocity. I don't get it

I am a high schooler interested in physics and recently started reading a book about relativity. The name of the book is "What Is Relativity" by Jeffrey Bennet. In page 54 there is a paragraph that ...
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206 views

Herbert Dingle's paradox modified

Suppose two spaceships A and B have on them clocks A and B move along the same straight line at uniform speeds differing by 161 miles per second. And suppose they are at positions A and B in space ...
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Can special relativity be derived from the invariance of the interval?

As far as I know, the classical approach to special relativity is to take Einstein's postulates as the starting point of the logical sequence, then to derive the Lorentz transformations from them, and ...
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Another Special Relativity Paradox inspired by Herbert Dingle's Paradox

Suppose spaceships A and B with clocks A and B move along the same straight line at uniform speeds differing by 161 miles per second. At the moment when B passes A, their clocks both read noon. ...
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Is this the correct method for deriving E=mc^2?

So lately I tried to deriving Einstein's $$ E = mc^2$$ which later I found from this website : http://www.emc2-explained.info/Emc2/Derive.htm They use calculus based method, so I tried another way. ...
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Lorentz transformation of an antisymmetric tensor

I'm trying to find the infinitesimal Lorentz transformation of a rank 2 antisymmetric tensor. Looking through Peskin, all I can see is the transformation of a vector, and even there it is simply given....
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Invariant upper bound for velocity of a particle

In the book Relativity book by Wolfgang Rindler, he explains that the Galilean and Lorentz transformations exhaust all the possible transformations. And explaining that he says, "Now, either there is, ...
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96 views

Why $F_\mu V^\mu=0$ in special relativity? [closed]

I'm trying to prove why $F_\mu V^\mu=0$. Where $F^\mu$ is the four force and $V^\mu$ is the four velocity. Can anyone help me?
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Relativity theory - lower end of falling to Earth object moves slower or faster than higher end?

According to relativity, time slows close to gravitational field (I prefer to say the processes with which we measure Time slows). (https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment) - "...
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Interpretation of terms in the Lorentz Transformation

What is the physical significance of the term "${vx}/{c^2}$" in $$ t' = \gamma \left(t- \dfrac{vx}{c^2}\right) $$ It has got something to do with clock synchronization but cant derive the 'correction ...
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61 views

Relativity on a universal scale

Imagine there was a clock on a planet the same size as earth, travelling at the same speed through space, and that this planet was at the most distant part of the universe from earth. If we had a ...
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72 views

Why does $k^z/E$ have dimensions of inverse velocity rather than velocity?

I'm studying quantum field theory and I want to prove the cross section. In Peskin's book, equation 4.77 says that: $$ \frac{1}{\left | \frac{k_{A}^{z}}{E_{A}}-\frac{k_{B}^{z}}{E_{B}}\right |}=\frac{...
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Special relativity: is this a known paradox, or one at all?

Two ships of the same proper length $L$ move towards each other, as in the diagram below (which shows it in the reference frame where the ship at the left is at rest). The fronts (noses) are pointing ...
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Lorentz contraction (or not) of an accelerated electron bunch

It's a well-known fact from special relativity that moving objects are subject to a length contraction: an object with a proper length $L_0$ moving at a high velocity $v$ will appear to a stationary ...
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Anti-commutator relation of supercharges

Reading mutiple references on SUSY (e.g. Baer and Tata's Weak Scale SUSY and A SUSY Primer by S.P. Martin, arXiv:hep-ph/9709356), there seems to be different anti-commutation relation conventions for ...
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Does $E=mc^2$ mean that an object with mass $m$ travels at the speed of light in empty space? [closed]

I cannot wrap my head around this (Im new to physics), and this concept is troubling me. I think no, but im not sure why?
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If we traveled at almost the speed of light would objects appear the same?

We see objects with our eyes as object emits/reflects light. Say if we travel at almost the speed of light can we see the objects normally?
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Is there a physical upper limit on how fast a physical object can rotate?

Objects can not travel faster than the speed of light. Angular velocity is $\omega = \frac{s \times v}{|s|^2}$ It seems to me that for infinitely small objects (like electrons) there is no limit on ...
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167 views

The norm of the vector sum of two 4-momentum vectors before and after pair production

Two photons traveling along the x-axis (in a lab frame of reference) of different frequencies are about to collide. Their 4-momentum vectors are (h$\nu_1$/c , h$\nu_1$/c , 0, 0) and (h$\nu_2$/c , -h$\...
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Difference between KE “relativistic” mass and heat mass

I have been told in several answers that the term "relativistic mass" is no longer considered adequate wrt. the mass/energy increase in KE. Yet, I read that 1 Kg of gold's mass ingreases by 10^-14 Kg ...
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Difference between space of reference and system of coordinates

In the book "The meaning of the relativity" by A. Einstein, it is referring to two different concepts: space of reference and system of coordinates. What it is the difference? It says: "we ...
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What is meant by rest in rest-mass?

As far as I know only photons are considered to have no rest-mass. In common words when it doesn't move it 'disappears'. Electrons and quarks should have a rest-mass. But are they really at rest? ...
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The criteria of light

My question is regarding if the "speed of light" 299,792,458 m/s should only apply to certain frequencies of light/colors/amplitude and most the medium in which it travels at 299,792,458 m/s . Shouldn'...
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Time dilation: time shortest where events occur at same place?

In his book Simply Einstein Richard Wolfson describes time dilation this way: "The time between two events is shortest when measured in a reference frame where the two events occur at the same place." ...
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Observer travelling near speed of light observing a laser pointer seeing photons at speed of light?

I'm a little confused by the following classic example about the speed of light being constant for all observers (paraphrasing): Jack and Jill are both travelling at a significant portion of the ...
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How do I draw the Minkowski diagram of a event in two inertial systems when t=t'=0?

An Introduction to Mechanics" by David Kleppner & Robert Kolenkow, 1st Edition, 12.1 Assume that v= 0.6c . Find the coordinates in S' of the following events: a). x=4 [m], t= 0[s] b). x=4 [m], ...
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What is relationship between electromagnetic mass and rest mass?

Is there a direct equation which compares rest mass $m_°$ and electromagnetic mass $m_{em}$? Nothing on web I found. $m_{em} = \frac{4 E_{em}}{3c^2}$ 4/3 problem The final solution of the ...
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Relevance of spinor in relativistic (classical) electrodynamics

I'm following a course about relativity and electrodynamics (not the "quantum" one), and the lecture notes introduces the concept of spinor by a map between an orthogonal basis in Minkowski spacetime ...
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Is the speed of light constant in all directions?

Consider the shape of the waveform emitted by a moving source: (with the horizontal axis "x" and the vertical axis "y"). According to the stationary observer, the wavefront of a short pulse ...
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Do we know why there is a speed limit in our universe?

This question is about why we have a universal speed limit (the speed of light in vacuum). Is there a more fundamental law that tells us why this is? I'm not asking why the speed limit is equal to $c$...
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Special Relativity: Verifying a general boost matrix is in the Lorentz group

I'm attempting the problem shown below. Using the hint, I have so far found: \begin{align}B^T \eta B &= \begin{pmatrix}\gamma & -\gamma\beta^j \\ -\gamma \beta_k & \delta_k^j+\frac{(\...
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Action of a massive free point-particle in relativistic mechanics

I was reading about the formulation of mechanics in special relativity and found that the action for a massive free point-particle as $$ S = -mc\int_a^b ds $$ So, I did a few observations, ie. $$ S =...
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Are gravitational time dilation and the time dilation in special relativity independent?

There are two kinds of time dilation: One because the other clock moves fast relative to me (special relativity). Another one because the other clock is in a stronger gravitational field (general ...
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Is Young's Modulus a Lorentz Scalar?

If a spring is at rest and lies along $X$ axis in a frame $O$ with a spring constant $k_{0}$ then its spring constant in a frame $O'$ which is moving with a speed $v$ at an angle $\theta$ with the $X$ ...
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Is it possible to determine maximum frequency of a disc using a relative circumference?

On Wikipedia there is an article that shows how to calculate the relativistic effects on a rigid spinning disc, I am referencing the formula under the "Ehrenfest's argument" section in the link. The ...
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Speed of Dark experiment, does it *really* travel faster than light? [duplicate]

I have seen many folks doing this Moon shadow experiment concluding that shadow from point A on the Moon can travel to point B on the Moon faster than light. What I fail to understand here (and I am ...
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Can't reach speed of light, but relative to who?

Imagine a stationary person (with respect to a spaceship) floating in space and looks at a clock on the spaceship going 0.5c and sees it's clock ticking slower than his own, and concludes that it is ...
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Were the Michelson-Morley results a surprise?

How unexpected were the Michelson-Morley experiment results? Did physicists have theoretical reasons to predict that the speed of light would result to be invariant?