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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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Is there a situation in which two photons/particles violate Lorentz transformation?

It does not necessarily have to be a pair production or anything with a name. Consider two photons moving away from or moving towards each other in the void. If imagining photons in relativity is ...
Raymond's user avatar
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A puzzle about relativistic spin

I'm suffering from a confusion about relativistic spin. I don't believe my question has been asked before, and I'm sure I've made some silly mistake somewhere, but I can't spot it. So I'm appealing to ...
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Meaning of general Lorentz transformations

According to Wikipedia, the Lorentz transformations for two inertial frames are written:$$\begin{cases} t'=\gamma(t-\frac{\mathbf {r}_{\parallel }.\mathbf{v} }{c^{2}} )\;\;\;(*)\\\mathbf {r'...
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Relativity problem about light signals and rockets equipped with mirrors [closed]

I find in a relativity book a problem that states: "A rocket with its own length $L$ moves away from Earth at a constant velocity $v$. A radar signal emitted from a ground station is reflected ...
idefix's user avatar
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Some confusion about understanding the relativistic quantum mechanics

S. Weinberg in his book "The quantum theory of fields" chapter 2 introduced the notion of symmetry in quantum mechanic as follows: Physical states are represented by rays in Hilbert space. ...
Mahtab's user avatar
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Where can I publish a paper on an overhaul of quantum mechanics and relativity, for peer review? [closed]

I am working on a theory that combines quantum machanics and special relativity, the paper is by no means ready, I am just wondering where I could publish it for peer review when it is. I have never ...
Xeno's user avatar
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When is the Lagrangian a Lorentz scalar?

The Lagrangian $\mathcal{L}$ can be defined as the Legendre transform (when it exists) of the Hamiltonian $\mathcal{H}$, a non-Lorentz scalar quantity (as $\mathcal{H} =T^{00}$). My questions are, ...
Gabriel Ybarra Marcaida's user avatar
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Magnetic Field Generation in a Vacuum Through Special Relativity

The way special relativity explains electromagnetism is that when electrons move, their lengths contract due to relativistic effects, even though they do not move at extremely high speeds. This ...
Gopal Kaushik's user avatar
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Wikipedia states that the relativistic Doppler effect is the same whether it is the source or the receiver that is stationary. Can this be true?

According to Wikipedia, the relativistic Doppler effect is simply the classical Doppler effect for a stationary source, $1-v/c$, times the relativistic time dilation, $1/\sqrt{1-v^2/c^2}$ (where v is ...
John Hobson's user avatar
1 vote
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Resolution of Ehrenfest paradox using only special relativity

It was my understanding the solution to the Ehrenfest paradox requires non-Euclidean geometry. Observers riding the rotating disk measure small distances according to the Langevin-Landau-Lifschitz ...
Aiden's user avatar
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On definition of time in non-inertial frames [closed]

Strictly speaking we can only compare times and lengths in inertial frames of reference because the measuring tools are in the same conditions and aren't subject to G-force. So they are identical ...
Марат Рамазанов's user avatar
2 votes
3 answers
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Question on special relativity

I am trying to learn special relativity. If we consider two inertial reference frames with spacetime co-ordinates $(t,x,y,z)$ and $(t',x',y',z')$ and let there be 2 observers who measure the speed of ...
morpheus's user avatar
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Co-ordinates and change of frame in relativity [closed]

Given an inertial co-ordinate system, and observer at the origin.  I'll make it concrete, for simplicity. He sees an object at the point $x = +10$, moving at velocity $v = +1$. He's subjected to a ...
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Derive Minkowski metric from Lorentz transformation

I am trying to learn special relativity. My goal is to prove that given the fact that a 4-vector $\mathbf{x}$ is transformed as $\mathbf{Lx}$, between two inertial reference frames where $\mathbf{L}$ ...
morpheus's user avatar
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Mandelstam variables sign

I am self-studying the book "Quantum Field Theory and the Standard Model" by Schwartz, on page 99 (paragraph "Mandelstam variables"), the context is the $2\rightarrow 2$ scattering ...
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About momentum states covariant normalization

I'm following QFT of Schwrtz and I have a doubt about Eq. (2.72). In particular, from Eq. (2.69): $$[a_k,a_p^\dagger]=(2\pi)^3\delta^3(\vec{p}-\vec{k}),\tag{2.69}$$ and Eq. (2.70): $$a_p^\dagger|0\...
Albus Black's user avatar
2 votes
2 answers
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Time dilation in Einstein's train example (lightning strike)

In Einstein's famous thought example involving a fast-moving train (say with a velocity of $c/2$), we assume that lightning strikes occur simultaneously at the front and rear end of the train as ...
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Apparent violation of Newton's Third Law in relativistic force transformation

In special relativity, we know that, relativistic force is defined as F = dp/dt, where p = γmv. For forces perpendicular to the direction of relative motion, force transforms as F' = γF. Consider two ...
Kenshin's user avatar
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Einstein's notion of "covariant"

In his The Meaning of Relativity, pg. $11-12$, Einstein explains the notion of "covariant" along the following lines: Consider a point $\mathbf x$ on a straight line $\mathbf x -\mathbf A=\...
Awe Kumar Jha's user avatar
11 votes
3 answers
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Can a big mass defect make the mass negative?

Can two particles with small masses and a strong attractive interaction have a total negative mass when brought together? Let $m_1, m_2$ be the (rest) masses of two particles when infinitely distant. ...
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Proper Time Along a Trajectory with Changing Velocity

I'm relatively new to SR and just encountered the Twin Paradox. I don't think I had trouble understanding the resolution to the paradox, but I was curious how an observer in an inertial reference ...
Lambda's user avatar
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Testing the twins problem with an accelerator

Re the twins paradox in relativity: has anyone performed an analysis of a pair of identical particles, inside a storage ring? Specifically, we posit that one is stationary - the 'home twin' - while ...
Rich D's user avatar
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2 votes
5 answers
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Is a photon truly massless? [duplicate]

First of all, I am not a physicist or mathematician, not even a hobbyist but the following statements have always puzzled me: $E=mc^2$ A photon is a desecrated particle of energy. A photon is ...
AUser's user avatar
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What effect would relativity have for an objective with absolutely no momentum? [closed]

I know as you near the speed of light time slows down and mass increases to near infinite. What I'm curious about is what would happen if an object lost all momentum. No movement at all not even the ...
joshua landry's user avatar
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2 answers
61 views

Interpretation of degenerate metrics

I was studying the metric tensor and saw all about degenerate metrics. I would like what is the physical or geometrical intuition of a degenerate metric. What is the meaning of $g(v,w) = 0$ for a ...
JL14's user avatar
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1 answer
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Physical intuition for the Minkowski space?

As the title suggests, I am looking for physical intuition to better understand the Minkowski metric. My original motivation is trying to understand the necessity for distinguishing between co-variant ...
user10709800's user avatar
-2 votes
3 answers
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Clocks are not synchronized in moving system (book of David J. Griffiths) [closed]

In the electrodynamics book of David J. Griffiths, in section 12.1.2, there is a paragraph about the synchronization of the clocks on a moving train. I don't understand why " Clocks that are ...
Smith Jack's user avatar
2 votes
1 answer
76 views

How to properly combine kinetic and gravitational time dilation effect?

I developed a time dilation calculator that includes both kinetic (Lorentz Factor) and gravitational (Schwarzschild Metric Formula) factors to assess the time difference between Earth and satellites. ...
Eliot Mallamo's user avatar
2 votes
2 answers
125 views

Given a representation $(n, m)$ of the Lorentz group, is the little group representation just the tensor product $n \otimes m$?

I've been reading Weinberg's QFT Vol 1. and more specifically section 5.6. I would like to know if my understanding is correct or if I missed something. He starts with the full Lorentz group $\mathrm{...
Wihtedeka's user avatar
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Split Pauli Four-vector as quadratic terms of spinors

If I have the Pauli Four-vector $$x_{\mu}\sigma^{\mu} = \left(\begin{array}{cc} t+z & x-i y \\ x+i y & t-z \end{array}\right)$$ with $\sigma^0$ as Identity Matrix. Is there some way to write ...
Alexandre Masson Vicente's user avatar
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1 answer
55 views

Length Contraction: is $t'$ or $t = 0$?

To demonstrate my confusion - let's say there is a rod traveling with velocity +v relative to S, and in S, the length of the rod is measured to be $L$. If I want to go from S to S', the frame where a ...
Emil Sriram's user avatar
1 vote
0 answers
61 views

Where does the angular momentum of relativistic objects go? [closed]

Suppose you are floating in outer space and there is a massive sphere of mass $1 \text{kg}$ next to you and radius $1$ meter and an angular velocity of $1$ revolutions a second. Using the formula for ...
Sidharth Ghoshal's user avatar
2 votes
1 answer
113 views

Physical meaning of $vx/c^2$ in Lorentz transformation

In Lorentz transformation, this is the formula of time dilation $$ t' = \gamma \left( t - \frac{vx}{c^2} \right) $$ It can be derivated from the formula of length contraction and be proved ...
Rojan's user avatar
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1 vote
2 answers
91 views

Who will die first between two people on different spaceships, where both are in inertial frames? [duplicate]

Here's something that's really been confusing me. If two people on separate spaceships pass each other by, where both are in inertial frames, person A (on spaceship 1) could say that he is at rest and ...
Andrew Flynn's user avatar
2 votes
1 answer
56 views

Causality for gauge dependent operators in quantum field theories

Suppose that $\mathcal{A}_{ij...}(x)$ and $\mathcal{B}_{ij...}( x')$ are two gauge dependent (so non-observable) operator in some theory. If they are spacelike, should I impose the causality ...
Ervand's user avatar
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What are the characteristics of a non-relativistic collision?

I have a physics test tomorrow on special relativity and one of the questions on the previous test was as follows: "A particle of mass m hits another particle of the same mass that was originally ...
fiene's user avatar
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0 votes
1 answer
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Is the Dirac adjoint in the representation dual to Dirac spinor?

As seen in this Wikipedia page, the Lorentz group is not compact and the Dirac spinor (spin $\frac{1}{2}$) representation is NOT unitary. Therefore, the complex conjugate representation does NOT ...
Keith's user avatar
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Can you ever obtain a pure rotation from composing Lorentz transformations?

An exercise asks one to show that given $v, u$ speeds much smaller than $c$ and oriented orthagonally, the composition of the lorentz boosts $B(\mathbf{v})B(\mathbf{u})B(\mathbf{-v})B(\mathbf{-u})$ is ...
Y G's user avatar
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4 votes
1 answer
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Energy of moving Sine-Gordon breather

A few days ago I stumbled across the formula for the energy of a moving breather for the sine-Gordon equation $$ \Box^2 \phi = -\sin\phi.$$ The energy in general is given by ($c=1$) $$ E = \int_{-\...
Ash's user avatar
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2 votes
0 answers
93 views

Relativistic Schrödinger Equation: How is it relativistic and can it be useful? [duplicate]

As is well known, the usual Schrödinger equation, $$\mathrm{i}\hbar\frac{\partial}{\partial t}\psi=-\frac{\hbar^2}{2m}\Delta\psi+V\psi,$$ is not relativistic. It can be derived formally by applying ...
Caesar.tcl's user avatar
-2 votes
0 answers
37 views

Black hole production via light speed [duplicate]

As a test particle with rest mass approaches $c$ relativistic mass increases to infinity, does this mean that the energy required to continue the acceleration will create a black hole (as time also ...
John Pryme's user avatar
1 vote
1 answer
37 views

Relative speed in unpolarized cross-section

In section 5.1 of Peskin and Schroeder, we are presented the computation of the amplitude for the $e^+e^-\to \mu^+\mu^-$ reaction and then the computation of the unpolarized cross section. After ...
Rafael Grossi's user avatar
1 vote
0 answers
72 views

Kinematics of a two-body decay [closed]

I suspect a flaw in the reasoning below, but am unable to pinpoint it: Is there something inconsistent in terms of the application of conservation of momentum and energy? Thanks for any hints in ...
Leonardo's user avatar
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11 votes
3 answers
723 views

How does special relativity lead to anti-particles?

Anti-particles and spinors pop out of the Dirac equation very naturally, yet the Dirac equation is only a modified version of the Schrödinger equation which includes the relativistic energy-momentum ...
eli morhayim's user avatar
1 vote
1 answer
65 views

Why does the mass-energy equivalence apply to binding energy when it is derived purely through kinematic means?

I understand that by defining the four velocity, multiplying it by the rest mass and taking the entire thing's norm we get $E^2=m^2+p^2$, but how does this apply to binding energy, or in general ...
Y G's user avatar
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1 vote
1 answer
97 views

Magnetic field in different frames

If I move at the same velocity as that of a charge Q, I wouldn't be able to feel its magnetic field because it is stationary with respect to me. However, if I am to place a magnetic compass needle ...
Mel's user avatar
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0 votes
2 answers
68 views

How to prove $ g^{\mu\nu}\Lambda^{\rho}{}_{\mu}\Lambda^{\sigma}{}_{\nu}=g^{\rho\sigma} $ for the inverse metric?

In Srednicki's book, we have \begin{align*} g_{\mu\nu}\Lambda^\mu{}_\rho\Lambda^\nu{}_\sigma=g_{\rho\sigma} \end{align*} and let $ \Lambda \to \Lambda^{-1} $, use the relationship $ (\Lambda^{-1})^\...
liZ's user avatar
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0 answers
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How is potential energy incorporated into mass in special relativity? [duplicate]

I've seen it said before that we often ignore potential energy in relativity because it can be included in the mass term. It is commonly said that a hydrogen atom has less mass than the sum of its ...
Aidan Beecher's user avatar
-4 votes
1 answer
99 views

In SR, why do we claim length contraction rather than faster than $c$ travel in the rocket frame? [closed]

In special relativity, a rocket traveling at .5c will take .86 years (in the astronauts frame) to travel 1 light year (in a stationary observer frame). There are two possible ways to look at this ...
foolishmuse's user avatar
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0 votes
0 answers
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Meaning of of inertial frames in special relativity [duplicate]

One of the postulates of special relativity is The laws of physics are the same in all inertial frames There is a mention of inertial frames in the postulate. But the predictions of relativity are ...
Niladri Sarkar's user avatar

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