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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Can the apparent velocity of an approaching spacecraft be faster than light?

Consider watching an alien space ship at Alpha Centauri (at 4.5 light years away) through a telescope from earth. This space ship turns towards us, and starts travelling toward us at what appears to ...
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Generators of Poincare Groups

How can I determine the generators of the Poincare Group, $P(1,3)$ explicitly? Here $P(1,3)$ means a matrix Lie group.
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Does the speed of light in different mediums affect the lorentz transformation?

We know that the Lorentz transformation is derived using the speed of light in vacuum. But if we were to use it in water, would it change since the speed of light in water should also remain constant ...
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A problem with a basic thought experiment in Special Relativity

This is for a class on special relativity I am to give to some school children. Moe is moving at 0.9c. At the instant he passed Joe he emits a flash of light. One microsecond later, Joe(at rest) ...
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do relativistic velocities change the apparent entropy content of the moving object?

Imagine a box of hot gas. It has a certain (large) amount of entropy, which we can relate to the amount of information needed to completely specify the position and velocity of every gas particle in ...
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Breaking the simultaneity

I have expressed my self in a detailed way. I've labeled the points to which I want an answer. I have doubt in the Einstein's rail experiments which he mentioned in his book. In this experiment ...
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Confusion about the (relativistic) mass of objects [duplicate]

According to Einstein's theory the (relativistic) mass of objects depend on speed. Then in an inertial reference frame 2 observers moving at 2 different velocities will calculate different masses for ...
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Can a spinor be defined as any quantity which transforms linearly under Lorentz transformations?

Recently I’ve come across a few papers from China (e.g. Xiang-Yao Wu et al., arXiv:1212.4028v1 14 Dec 2012) that make the following statement: ...any quantity which transforms linearly under ...
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What are the constituents of communicated time differences between moving objects?

In "The Elegant Universe," two individuals, George and Gracie, are noted to be moving relative to one another in space and wearing clocks. They sync their clocks upon passing each other. Each observes ...
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Twin Paradox - different approaches

What was the difference between Langevin's approach to the twin paradox and Max Von Laue's? I don't understand how Langevin tried to use the idea of absolute acceleration to explain the distinction in ...
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Noether Charge For Scalar Fields Under Lorentz Transformations

The conserved charge associated with the Lorentz transfomation of a scalar field is given by $Q^{\alpha\beta}=\int d^3x\frac{1}{2}(x^\alpha T^{0\beta}-x^\beta T^{0\alpha})$. The quantities $Q^{ij}$ is ...
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Does the time for communication between moving objects solely account for each object to perceive the other object's clock to more slowly tick? [duplicate]

In "The Elegant Universe," two individuals, George and Gracie, are noted to be moving relative to one another in space and wearing clocks. They sync their clocks upon passing each other. Each observes ...
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A question about relativistic spin operator

The question comes from Ryder's Quantum Field Theory, 2nd edition. The author was looking for relativistic spin operator. It was concluded that it cannot be $J^2:=\mathrm{J} \cdot \mathrm{J}$, where ...
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Theoretical Upper Bound on Processor Speed?

Barring aside considerations such as heat dissipation, capacitance, etc... (aka any sort of technological issue) what is the fastest speed of a processor? I am told that at distances of 1 planck ...
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Is time travel different from time dilation?

I just wanted to know whether time dilation is different from time travel or not. Personally I believe both are different. If they are the same things I just wanted to know why. According to me time ...
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108 views

Photons and proper time

Why is there no proper time without inertial frame? In question n°95054 I learned that there is no proper time zero and no proper distance zero for photons because they are no inertial frames. That ...
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172 views

Does the velocity of a light source influence the light

I have only just finished High school physics so my understanding is still fairly simple but I'm having trouble with this question. Imagine you are in space traveling at a relativistic speed with a ...
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Space-Time Continuum [duplicate]

In special relativity it is said that " Time and space cannot be defined separately from one another. Rather space and time are interwoven into a single continuum known as spacetime. " What is the ...
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Are covariant components of 4-gradient of scalar product made of contravariant components of vector?

Trying to find normal to hypersurface $p^ip_i=m^2c^2$, I take gradient of corresponding function $F=p^ip_i-m^2c^2$. What I get is: $$n_i=\frac{\partial F}{\partial p^i}=\frac{\partial}{\partial ...
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What does it mean to divide space and time?

Goldstein's mechanics book, on the chapter on relativistic mechanics says that "We cannot assume that all observers make the same division into time and space in the same way." What does it mean to ...
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Relativistic space travel?

If one travels in a spaceship at speed V, the time elapsed for the traveller relative to an observer on earth is dilated by, $$ t' = t(1 - v^2/c^2)^{1/2} $$ Does this mean that a space traveller, ...
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327 views

Time dilation formula and example

What is the time dilation formula by constant velocity? Is the right formula $$t'=t\times \sqrt{1-v^2/c^2}$$ or is it $$t'=\frac{t}{\sqrt{1-v^2/c^2}}$$ ? And can someone show me a computational ...
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Special Relativity moving in space

Given that time is 'just another' dimension and people get hung up on the fact that we cannot go back and forth in time like the other dimensions. Is there any proof that the corner of 8th Avenue and ...
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Idea of Covering Group

$SU(2)$ is the covering group of $SO(3)$. What does it mean and does it have a physical consequence? I heard that this fact is related to the description of bosons and fermions. But how does it ...
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Does action really have to be Lorentz-invariant in SR?

From Landau & Lifshitz The Classical Theory Of Fields it is said: To determine the action integral for a free material particle (a particle not under the influence of any external force), we ...
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If one is travelling at a significant fraction of $c$, will the length of the trip be shortened?

Assuming two stars are 1 light year apart and a traveler is travelling at 0.75 of $c$, from the point of view of the traveler what would be the observed time en route? Also, if a vehicle is constantly ...
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Why does a Lorentz scalar field transform as $U^{-1}(\Lambda)\phi(x)U(\Lambda) = \phi(\Lambda^{-1}x)$?

This problem is from Srednicki page 19. Why $U^{-1}(\Lambda)\phi(x)U(\Lambda) = \phi(\Lambda^{-1}x)$? Can anyone derive this? $\phi$ is a scalar and $\Lambda$ Lorentz transformation.
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Why is $U(\Lambda)^{-1} = U(\Lambda^{-1})$ for a unitary representation?

This is from the beginning of Srednicki's QFT textbook, where he writes (approximately): In QM we associate a unitary operator $U(\Lambda)$ to each proper orthochronous Lorentz transformation ...
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Derivation of rest energy in Landau & Lifshitz

In Landau & Lifshitz The Classical Theory Of Fields there's a statement: $$\mathscr E=\frac{mc^2}{\sqrt{1-\frac{v^2}{c^2}}}\tag{9.4}$$ This very important formula shows, in particular, that ...
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What is the real meaning of length contraction?

Suppose one inertial observer measures a rod at rest w.r.t. him and another observer is moving w.r.t. rod. We then say that length will be shorter for moving observer but at the instants the first ...
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Textbook on the Geometry of Special Relativity

I am looking for a textbook that treats the subject of Special Relativity from a geometric point of view, i.e. a textbook that introduces the theory right from the start in terms of 4-vectors and ...
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Is aging independent of time progression when relativistic effects are taken into account? [duplicate]

I have been trying to understand Einstein's principle of relativity for quite some time. I have at least I believe, understood the notion that time is relative and can actually 'change' relative to ...
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81 views

Implications of Formula for Stellar Aberration

I am studying relativity and was working on deriving stellar aberration using relativity. My derivation is as follows: Suppose that the observer is traveling at a velocity $v$ in the $x$-direction. ...
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Time dilation and relativity

We've just started with relativity and I got a question regarding an exercise we got. A spaceship passes by earth on its way to planet X, at the moment it passes by Anna is born on the spaceship. Can ...
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Application of $E = mc^2$ [duplicate]

We very well know that mass-energy equivalence is given by $E = mc^2$. My question however is how would we actually convert an object or some mass into its pure energy state and then if possible even ...
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2answers
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Dirac spinor and Weyl spinor

How can it be shown that the Dirac spinor is the direct sum of a right handed Weyl spinor and a left handed Weyl spinor? EDIT:- Let $\psi_L$ and $\psi_R$ be 2 component left-handed and right-handed ...
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Why does special relativity talk about the speed of light in a vacuum?

What's the importance of the speed of light being in a vacuum? Does not being in a vacuum cause a difference?
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K-factor in special relativity

A sends out a series of flashes of light to B, where the interval between flashes is denoted by T according to A's clock. Then it is plausible to assume that the intervals of reception by B's clock ...
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158 views

Pole and Barn Paradox

I'm having trouble reconciling two different versions of the Pole and Barn paradox. Version 1: Consider a pole 10 m long and a barn 5 m long with a front and rear door. A runner carrying the pole ...
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There can be nothing with zero mass [closed]

Zero mass has no meaning and is an outcome of 2nd postulate of STR .The STR can be developed without this postulate and thus the postulate is redundant besides being contradictory to 1st postulate.The ...
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Einstein's Postulates: Simultaneity

Okay, I still don't get the solution (which I will lay out) to the following problem: Suppose that A', B', and C' are at rest in frame S', which moves with respect to S at speed v in the positive ...
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How does Spacetime Curvature increase the velocity of particles falling towards the earth?

Two particles fall side by side, towards the earth. The horizontal distance between them is 10m. As they advance nearer and nearer to the earth's surface, the horizontal distance decreases, from 10m ...
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Resolution of the EPR paradox using relativity of simultaneity

A simple explanation for photon entanglement experiments Example: Quantum teleportation La Palma-Teneriffa in 2012 (distance 143 km) - Photons were entangled in such a way that when measuring ...
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3answers
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Does a moving object curve space-time as its velocity increases?

We always hear how gravity bends space-time; why shouldn't velocity? Consider a spaceship traveling through space at a reasonable fraction of the speed of light. If this spaceship, according to ...
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Resolution of the EPR paradox using special relativity

Please refer to the question "Resolution of the EPR paradox using relativity of simultaneity" I hope that this question will be clearer. EPR photon experiments are a paradox for scientists. Can ...
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114 views

Mass in terms of special relativity

According to special relativity mass doesnt add up like we think it does. That is, a system of 2 protons might not necessarily have a system mass of 2*(mass of one proton). If the protons are ...
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1answer
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Who popularized $E=mc^2$?

When asking a layman for a mathematical or physical equation you will almost certainly get the answer "$E$ equals $m$ $c$ squared". In fact, $E=mc^2$ is something like a symbol of physics in popular ...
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Because position is relative, is it possible to see a star orbiting a planet? [duplicate]

Position is relative, as it depends on the reference frame. We usually visualize the sun at the center of the solar system. BUT, we can also visualize the Earth at the center of the solar system, ...
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36 views

A condition for relative gas

Consider an ideal gas in a box. we know (no matter what, right?) that each massive particle's energy holds $E^2=c^2p^2+m^2c^4$ . how come that the condition for that gas to be relativistic is ...
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Dirac adjoint of a matrix

The Dirac adjoint for Dirac spinors is defined as, $$ \bar{u} = u^{\dagger} \gamma^{0} \, . $$ However I have come across this, $$ \overline{\gamma^{\mu}} = \gamma^{\mu} \, , \tag{1} $$ (where ...