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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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
66 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 ...
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2answers
749 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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439 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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59 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
149 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
566 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
111 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
189 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
189 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 ...
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2answers
245 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
304 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
237 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
135 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 ...
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2answers
364 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
143 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
515 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
843 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
661 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 ...
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1answer
198 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 ...
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1answer
170 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 ...
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1answer
66 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
442 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
309 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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550 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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218 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 \\ ...
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2answers
218 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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4answers
847 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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52 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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283 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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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
2k 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
150 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
108 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 ...
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2answers
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Understanding the difference between co- and contra-variant vectors

I am looking at the 4-vector treatment of special relativity, but I have had no formal training in Tensor algebra and thus am having difficulty understanding some of the concepts which appear. One ...
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6answers
3k views

What keeps mass from turning into energy?

I understand the energy and mass can change back and forth according to Einstein. It is fluid; it can go from one to the other. So, what keeps mass from just turning into energy? Is there some force ...
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1answer
239 views

How is Momenergy frame independent?

momenergy = mass * spacetime displacement/proper time for that displacement What I dont understand is how can the momenergy be frame independent? The unit-4 vector always points in the direction of ...
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1answer
2k views

Why does light travel at finite speed? [duplicate]

We have known for quite some time now that light travels at a finite speed of 3x10^8m/s (approx) through vacuum. But why is that? Why can't the speed be infinite? Or at least higher than the current ...
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1answer
313 views

Did the Goudsmit-Uhlenbeck analysis of spin consider relativity?

It's frequently mentioned in introductory quantum mechanics texts that Goudsmit and Uhlenbeck conjectured that the magnetic moment of an electron was due to angular momentum arising from the electron ...
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1answer
3k views

Deriving the Electromagnetic Tensor

The electromagnetic tensor is given as: \begin{equation} F_{\mu \nu} = \partial_\mu A_\nu - \partial_\nu A_\mu \end{equation} How do you derive this? And how come there is a partial derivative in ...
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1answer
122 views

Speed of Light and Special Relativity

If light is travelling vertically upwards and I am travelling horizontally and perpendicular to light, the velocity of light in the vertical direction will get reduced. How does this happen? How does ...
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291 views

Rigorous definition of frame of reference

I'm looking for a mathematical definition of frame of reference. Most of the textbooks I have seen take it for granted and they just refer to some set of spacetime coordinates. A more mathematical ...
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5answers
1k views

What does 99.9% speed of light mean when there is no absolute velocity?

So when people say: 'I am approaching the speed of light, and to get to 100% light I would need infinite energy' they are essentially saying that this situation is impossible? I read this in ...
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80 views

Possible values of energies and impulses of virtual photon emitted by real electron

I need to find the possible values of energies and impulses of virtual photon emitted by real electron. I don't understand how to compute it (look to the text below). Let's introduce the free ...
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4answers
484 views

Speed of light travel

I have just started special theory of relativity. The limiting speed known as speed of light fascinated me most. I asked my teacher: Consider two massless objects moving in the same direction at ...
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137 views

Quantum Eraser under Lorentz Boost

Suppose I am conducting the Quantum Eraser experiment. The results of this experiment are easy to understand with the traditional quantum mechanical interpretation of a pair of entangled photons. ...