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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1answer
1k views

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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1answer
3k views

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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3answers
346 views

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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2answers
303 views

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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0answers
87 views

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 ...
3
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1answer
219 views

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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1answer
88 views

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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2answers
165 views

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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1answer
67 views

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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2answers
846 views

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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1answer
457 views

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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0answers
62 views

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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2answers
152 views

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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0answers
65 views

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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1answer
627 views

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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1answer
113 views

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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1answer
141 views

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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2answers
192 views

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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1answer
198 views

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 ...
2
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2answers
249 views

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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2answers
344 views

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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2answers
266 views

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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1answer
138 views

Proof: Conservation of a 4-vector in one frame implies conservation in another

I came across a proof that says if a 4-vector $P$ is conserved in one inertial frame $$P_{before}=P_{after} \text{ (sum)}$$ then Lorentz transforming to another frame gives $$P'_{before}=\Lambda P_{...
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2answers
393 views

Special Relativity Time Dilation Misconception

Imagine a boxcar with a lamp on the left end and a mirror on the right end, so that a light signal can be sent down and back. The boxcar is moving to the right with velocity v. They find the length of ...
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2answers
1k views

Nothing can travel faster than the speed of light. In what frame of reference? [duplicate]

Since frames of reference are arbitrary, I can define a frame of reference that moves backwards with a speed greater than $c$, then any static object in that frame of reference is already traveling ...
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1answer
146 views

Special Relativity Time problem

Suppose there are two observers, they each own a light clock which were synchronised in the beginning and are moving relative to each other. So each of them accuses that the other person's clock is ...
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3answers
546 views

Does the Relativity Principle of Special Relativity imply homogeneity and isotropy of all the reference frames?

In Rindler's book: Relativity, Special, General and Cosmological, is stated on page 40 that the Relativity Principle (RP), when applied to just one Inertial Frame (IF), guarantees the homogeneity and ...
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2answers
944 views

Exact definition of momentarily comoving reference frame (MCRF)

Consider a particle $P$ in the framework of special relativity with position $r(t)=(ct,x(t),y(t),z(t))$ respect to an inertial reference frame $\Sigma=(ct,x,y,z;O)$. I need to know if the following ...
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5answers
678 views

What distinguishes time from space in Quantum Field Theory?

Consider the following expression for a general QFT action: $$ S ~=~ \int_0^t\mathrm dt~L ~=~\int_0^t\mathrm dt\int_\mathbb {R^3}\mathrm d^3x~\mathcal L ~=~\int\mathrm d^4x~\mathcal L.$$ Here we ...
4
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1answer
201 views

Twins paradox “corrected”

If you know a bit of special relativity, probably you've heard of the twin paradox. I would like to know: what happens if we take acceleration into account in the paradox. Usually we consider an ...
5
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1answer
203 views

Hidden momentum

I'm trying to learn about hidden momentum. After reading what I could find with a google search, I understand that it is equal to the momentum carried by radiation, calculated with the Poynting vector....
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1answer
67 views

Energy of electron accelerated by a magnet

In the YouTube video Monster magnet meets computer, the south pole of a 1 T (roughly) neodymium magnet is held in front of a CRT. Assuming the CRT produces electrons of 30 keV, and that the screen is ...
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2answers
470 views

Do photons see shorter distances due to space contraction?

I may be wrong, but this is just what I've heard. People often talk about what would happen if we, humans, were able to make a spaceship travel at the speed of light. If I'm not mistaken, then we ...
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3answers
320 views

How can the Lorentz transformation cause two objects' masses to both increase?

Suppose there are two people A and B. A is standing on the earth and B is on a rocket in space. Now B passes by the earth at a speed of 0.9c and A sees him. According to A, B's mass would have ...
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0answers
585 views

Relativistic elastic head-on collision: The momentum just reverses direction

Consider a relativistic elastic head-on collision between a projectile, with mass $m_a$ and velocity $\mathbf{v}_a$, and a stationary target of mass $m_b$. Here "head-on" means that the two particles ...
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0answers
226 views

Translational and Rotational Energy in Special Relativity

In non-relativistic classical mechanics: $$\tag{1} \begin{eqnarray} \text{KE}&=&\frac{1}{2}\sum_i m_i v_i^2=\frac{1}{2}\sum_i m_i (\vec{v}_{cm}+\vec{v}_{i,rel})^2 \\ &=&\frac{1}{2}\...
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2answers
223 views

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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5answers
921 views

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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0answers
53 views

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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3answers
314 views

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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2answers
2k views

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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2answers
3k views

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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0answers
98 views

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, ...
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1answer
154 views

Physical meaning of the Rindler hyperbola vertex and the Rindler lines

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 ($\alpha$) ...
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2answers
109 views

What does this summation mean in relativity?

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 ...