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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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
264 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
145 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
270 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
198 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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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
111 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
109 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 ...
3
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3answers
727 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
121 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
85 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
242 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
83 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
97 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
131 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
209 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
313 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
99 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
124 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
153 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
37 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
104 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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148 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
195 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
423 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
176 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
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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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41 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 ...
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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
71 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
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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
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
126 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
235 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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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
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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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0answers
56 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
232 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
78 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
86 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
143 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
87 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
166 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
105 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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59 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
108 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
207 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 ...