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 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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1answer
76 views

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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2answers
83 views

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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1answer
169 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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3answers
210 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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1answer
117 views

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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1answer
95 views

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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2answers
151 views

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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2answers
112 views

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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4answers
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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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4answers
93 views

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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3answers
693 views

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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1answer
103 views

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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2answers
85 views

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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2answers
274 views

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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2answers
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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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2answers
154 views

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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4answers
335 views

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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2answers
240 views

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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0answers
33 views

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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1answer
130 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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2answers
117 views

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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1answer
92 views

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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3answers
917 views

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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4answers
122 views

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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1answer
92 views

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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3answers
342 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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1answer
87 views

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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2answers
126 views

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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1answer
140 views

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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1answer
236 views

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
450 views

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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1answer
109 views

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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4answers
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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
156 views

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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1answer
76 views

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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1answer
39 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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1answer
119 views

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 ...
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1answer
177 views

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 ...
2
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1answer
285 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
569 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
190 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
145 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
43 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
178 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
72 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
126 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
57 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
158 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
267 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 ...