# Tagged Questions

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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### Reunion condition in the Twin Paradox

In the Twin Paradox two twins initially at rest in the same reference frame are separated and take different journeys through spacetime. Eventually they are reunited. What is the condition for the ...
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### Mandelstam variable equality derivation for $s$-channel process

I am supposed to show that the Mandelstam variable $s=(p_1^2 + p_2^2) = 4(P_{cm}^2 + m^2)$ for an electron/positron interaction, where $p_1$ is the incident 4-momentum of the electron and $p_2$ is ...
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### Proving Lorentz invariance of Maxwell equations

I've read somewhere that one does not need to prove Lorentz invariance of the Maxwell equations $F_{\mu\nu,\sigma}+F_{\nu\sigma,\mu}+F_{\sigma\mu,\nu}=0$ because it is "manifestly Lorentz invariant" ...
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### According to relativity, can a statement be true and false in same time?

Say I write following statement on a paper: It's year 2014 at earth. Then I give it to my friend. My friend then starts to leave me and earth to outside with velocity of light. Einstein says the ...
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### Relativity and speed of light again - two opposite light sources [duplicate]

Two light sources emit light at the same moment but in opposite directions. At what speed the distance between two light fronts is increasing? c or c * 2? Note, that there is only one coordinate ...
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### Clock synchronization and dilation

This is a question on the synchronization of clocks. If a girl on a train has the same clock that a guy has on the platform and they synchronize their clocks at 12am together when the train and the ...
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### Proper time along path in Minkowski Space

Consider the path $x^\mu(u)$ in Minkowski space; such that: $$t = \frac{a}{c} \sinh(u) , \quad x = a \cosh(u) ,\quad y = 0 ,\quad z = 0$$ where $a$ is a positive constant and $u$ is a parameter ...
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### Acceleration reaches speed of light? [duplicate]

Hi, I am thinking about acceleration. Let's think we have a force of $1$ N and a particle of $1$ kg, then acceleration will be $1$. So the speed gets higher every second and $c$ seconds later, in ...
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### A confusion in the Derivation of Lorentz Transformation

My doubt is in the equation (1) and (2). Aren't x,y and z also the radiuses? EDIT Thank you guys for trying to give a wonderful explanation but I figured out the answer myself and it was just my ...
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### Speed of light energy

Considering the amount of energy necessary to accelerate a particle to the speed of light (ie; half the energy in the entire universe) how could we have so many things already going the speed of light?...
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### Electric charge is lorentz invariant

I know that electric charge is lorentz invariant quantity and I can easily think of experiment to check that. Is a though experiment that can prove that also?
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### Interpretation of rank 2 spinors

While inspecting the $(\frac{1}{2},\frac{1}{2})$ representation of the Lorentz group and defining a right-handed spinor with upper dotted index and a left-handed spinor with lower undotted index and ...
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### Moving Clocks Time Problem

http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/Special_relativity_rel_sim/index.html Talking about the situation of clocks shown on this page. Clocks A&B. Now suppose clock B is moving ...
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### Can a revolving body self-gravitate?

If a body is revolving around a point at radius R with tangential velocity V, does General Relativity predict that at some tangential speed, the body will revolve around the point without any external ...
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### Questions on 4-vector velocities and invariance [closed]

Unfortunately, I missed a few lectures on four-vectors and I am pretty confused on how to go about solving the below question. I would be extremely grateful for any responses or solutions to enlighten ...
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### Why do we use the complexification of the Lorentz group?

I do understand why we are using the double cover, but why exactly do we make the transition to complex Lorentz transformations? Where and why are they needed? To be precise: The double cover of ...
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### Relativistic momentum and mass [duplicate]

Is there even a relativistic mass or just relativistic momentum? How does one reason to prefer one over another? What is the problem with saying a hot gas will have more mass/inertia to it?
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### Problem understanding a step in derivation of Lorentz Transformation

I need to understand a step in the derivation of Lorentz Transformation. I cannot understand how can we equate the equations 1 and 2. I am talking about the relation between ct, x, y, z. Where ...
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### Synchronisation of clocks

How can two clocks be synchronised with each other at some instant without being at the same place and same time $?$ considering that simultaneity is a relative concept .
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### Twin paradox an simultaneity [duplicate]

Suppose there are two observers A & B, separated in space and one is moving towards the other. Their clocks were somehow synchronised at the beginning meaning they both started from $0$ or just ...
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### Recovering 4-vector Lorentz transformation from spinor formalism

I'm trying to recover the 4-vector transformation laws using spinors. I have defined $$v^{\dot{a}b} = v^{\nu} \sigma_{\nu}^{\dot{a}b}$$ as usual, with $\sigma_0=1$. Now with the rules for dotted ...
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### is action integral Lorentz invariant?

I need to find the Lagrangian for charged particles in EM fields considering relativistic effects. Is action integral Lorentz invariant. $$A = \int_{t_1}^{t_2} L (q_i, \dot q_i, t) dt$$ According ...
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### Field of moving charge / Lorentz;Lienard-Wiechert

First question here. I'm really confused at the moment. An electron moves at constant velocity, no acceleration Wikipedia says here Lorentz: Which yields something like this: Wheras here, ...
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### Paradox Regarding Time Dilation at the Speed of Light

Consider the following scenario: On earth, I pulse a laser focused at a far away mirror such that the time it takes for the light to reflect off the mirror and arrive back at me is at least a few ...
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### Why Sun light can reach us if Time is dilating?

I understand that if something is moving with constant speed in respect to an observer, the time of the moving one runs slower, so the more your speed is, the more your time ticks slower. Which ...
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### What speed should have an alone planet to have a habitable zone due to relic radiation?

What speed should have an alone planet to have a habitable zone due to relic radiation, without any star involvement? How much time the planet will be able to remain in the habitable zone before the ...
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### Spacetime and uncertainty principle

I only have limited knowledge of relativity and quantumphysics but as far as I know, the uncertainty principle relates the uncertainty of space and momentum of a particle. Einstein however, explained ...
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### Why can't matter pass the speed of the light? [closed]

I have the following questions. Why can't matter pass the speed of the light? What happens to an object when it comes close to the speed of the light? What makes the object unable to surpass this ...
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### Increase in Mass with Velocity [duplicate]

I just had a confusion. Does the mass of the body actually increase when it is moving with a certain velocity? Or does it only look like the mass has increase to another observer. How can the actual ...
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### Time-Independent Gravitational Equation?

Is it possible to calculate gravitational induced position change without requiring the use of time (and therefore, acceleration) anywhere in the equation? If such an equation were to be discovered, ...
Two questions regarding the Rindler diagram: 1) Does the vertex of a given hyperbola in the diagram have physical meaning? I know it is the inverse of the constant proper acceleration ($\alpha$) ...
Equation 1.2 of 't Hooft's Introduction to General Relativity gives the Lorentz transformations: $$(x^\mu)' = \sum\limits_{\nu = 1}^4 {L^\mu}_\nu x^\nu$$ Is this the sum of four square matrices ...