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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Velocity of the photon

As far as I know photon travels in a wave pattern, that means it has $x$ and $y$ axis velocity components. If photon travels along $x$ axis, then what is it's maximum $y$ axis velocity?
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107 views

Does length contraction affect travel time?

If an astronaut leaves planet $A$ for planet $B$ at speed $v$, will the time (measured by the astronaut's clock) that it takes for the astronaut to reach planet $B$ be less than the distance between ...
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60 views

Deduction of relativistic mass formula in 1+1 dimensions

I have read the explanation/calculation of relativistic momentum and relativistic mass in the Feynman lectures, see chapter 16.4 here: http://www.feynmanlectures.caltech.edu/I_16.html. (I guess this ...
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590 views

Fundamental invariants of the electromagnetic field

It is a standard exercise in relativistic electrodynamics to show that the electromagnetic field tensor $F_{\mu\nu}$, whose components equal the electric $E^i=cF^{i0}$ and magnetic ...
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73 views

Majorana equation and non-invariance of spinor representation under discrete Lorentz transformations

Here I asked about getting an equation for two-component spinor as the alternative for Dirac equation. It was found that it is called Majorana equation. It may be easily derived by using historical ...
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2answers
173 views

Peskin and Schroeder Equation 3.23

I've been trying (for a while) to prove that $S^{\mu\nu}:=\frac{i}{4}\left[\gamma^\mu,\,\gamma^\nu\right]$ is a representation of the Lorentz Lie algebra, that is, to prove that it satisfies the ...
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2answers
187 views

Twin Paradox in case of two twins that don't meet

If there are two twins. such that one of them goes on a space voyage maintaining a constant velocity, and that one never returns to earth, and the twins decide to never meet but send information about ...
2
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1answer
165 views

Proper time in Nordstrom gravity

This wikipedia article claims that there are two interpretations of Nordstrom's scalar theory of gravity: 1) A scalar field theory on flat space. The reason why an apple falls is that its mass is ...
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2answers
159 views

Speed of light, lasers and mass

Hopefully this isn't a bad question. Light travels at the speed it does and nothing else can travel that fast because things have mass, correct? Or at least correct on an elementary level. And if ...
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209 views

Unitary Lorentz transformation on quantized Dirac spinor

I am stuck again on page 59 of Peskin and Schroeder. In particular, I do not know how they get equation (3.110). Let me first give some background in the way that I understand it (but I might be ...
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225 views

Trying to rhyme Peskin and Schroeder with Weinberg

This is a follow up question of this one. In the Vol 1, Weinberg derives how a unitary operator $U(\Lambda)$ acts on one-particle states, which is given by equation (2.5.2): \begin{equation} ...
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114 views

Question about Weinberg's derivation of a one-particle states under the Poincare group

I'm reading QFT: Vol 1 by Weinberg and I have a (perhaps trivial) question about a statement he makes on page 63. I can follow him to his derivation of equation (2.5.2): \begin{equation} P^\mu ...
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1answer
148 views

Combining relativistic velocities in the same direction using Lorentz transformation matrices

It is known that when combining the Lorentz Transforms of two frames with velocities $v_{1}$ and $v_{2}$ in the same direction it is equivalent of computing a Lorentz Transform of a single frame with ...
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Infinitesimal Lorentz transformation is antisymmetric

The Minkowski metric transforms under Lorentz transformations as \begin{align*}\eta_{\rho\sigma} = \eta_{\mu\nu}\Lambda^\mu_{\ \ \ \rho} \Lambda^\nu_{\ \ \ \sigma} \end{align*} I want to show that ...
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389 views

Do photons age in a medium?

According to special relativity, time starts to slow down as we increase our speed and eventually stops once we get to the speed of light. By that logic, photons don't age in a vacuum state as, to us, ...
3
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2answers
134 views

Time Slowing Down [duplicate]

I'd like to ask a question if I may about the relativity. When travelling at the speed of light(which is impossible for particles with masses) or very close to it, would it be me, myself, seeing my ...
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5answers
574 views

Does decrease in temperature affect mass $E=mc^2$?

My understanding of Quantum physics and String Theory is very basic and I don't yet have a grasp on the maths, but in my research I have come up with a question. Does a decrease in temperature also ...
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2answers
226 views

The signature of the metric and the definition of the electromagnetic tensor

I've read the definition of the electromagnetic field tensor to be ...
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1answer
103 views

Equation for relativistic electron and two-component spinor

Recently I heard that there is some "alternate" equation for the Dirac one. It can be introduced if we refuse some properties of the theory describes the electron, which Dirac used in his original ...
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258 views

Can we show that time is orthogonal to space?

It's easy to show that the time we measure is "in a different direction" from the space directions we measure. However, it's not immediately obvious to me that these directions are orthogonal. How do ...
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2answers
197 views

Does the pilot of a rocket ship experience an asymptotic approach to the speed of light?

A question has recently come up that goes beyond my knowledge of special relativity. Suppose a pilot has his foot on the gas pedal of a rocket ship and keeps it applied to achieve a constant ...
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1answer
233 views

Peskin & Schroeder Chapter 3.1 EoM Lorentz Invariant under Lorentz Invariant Lagrangian

From Peskin & Schroeder QFT page 35: The Lagrangian formulation of field theory makes it especially easy to discuss Lorentz invariance. And equation of motion is automatically Lorentz ...
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60 views

What “time” is it for or on Voyager 1? If you could be “still” in the Universe who fast would time be? [duplicate]

I just sent this to JPL but am not putting all my eggs in one basket so thought I would try some other clever people. :-) I think about physics and space quite a lot but I'm not a maths genius so do ...
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1answer
375 views

Understanding the time dilation calculation in Brian Cox's Doctor Who lecture

Background My son has just watched Brian Cox's fascinating "The Science of Doctor Who" lecture on space-time and was particularly intrigued by the part (at 22m:22s) where he said: Let us say that ...
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329 views

About the standard derivation of the gravitational redshift

The objective is to derive the gravitational redshift ONLY from the Einstein's equivalence principle (E.E.P.), without using the whole theory of Relativity. This is the standard "informal" derivation ...
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105 views

Principle of relativity - a second, equivalent form, using invariants

Most people state the principle of relativity like this: "The rules of physics must take the same form in all inertial frames." Question: is this an equivalent way of saying the same thing: ...
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A problem about special relativity [closed]

i can't understand it clearly, so please help me!
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903 views

Maxwell's Equations using Differential Forms

Maxwell's Equations written with usual vector calculus are $$\nabla \cdot E=\rho/\epsilon_0 \qquad \nabla \cdot B=0$$ $$\nabla\times E=-\dfrac{\partial B}{\partial t} \qquad\nabla\times ...
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(References) Study of Asymptotically Flat spacetimes

I am interested in studying the asymptotic structure of Minkowski spacetime in General Relativity. I believe most of the work in this area concerns the asymptotic structure of Minkowski space at null ...
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110 views

Space contraction: what do we see

This is my opinion about what we will see. When the pipe arrive at the bar, we will be unable to see some part of it anymore (the pipe will absorb the light emitted by the bar), even if the pipe and ...
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141 views

Neglecting second order differentials

I am currently doing some Lorentz invariance exercises considering infinitesimal Lorentz transformations, and have been told to neglect second order differentials. It's not the first time I have come ...
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65 views

Transformation of a time-dependent acceleration to another frame

How do I transform a time-dependent acceleration between to rest frames? I was given a particular problem and while I found possibilities [1] [2] for acceleration-transformations when the acceleration ...
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3answers
260 views

If space and time are equivalent, what's Spin in time dimension

This troubles me: We are talking about time and space being equivalent, but still only consider Spin in the $x$, $y$ or $z$-direction. What's Spin in time dimension? Is it distinction between ...
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1answer
420 views

Is it only the Higgs field that stops me from getting to $c$?

Is it only the higgs field that stops me from accelerating up to the speed of light or is there other restriction concerning the increase in mass? In other words if I had a Higgs field shield on my ...
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Why is the speed of light considered as a fundamental constant if its speed changes with medium resulting in refraction? [duplicate]

I know that the speed of light, the universal constant of gravitation and the Planck's constant are considered to be the three fundamental constants of the universe. But, why is speed of light ...
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1answer
64 views

Special Relativity and current in wire [duplicate]

If I am a stationary observer and the electrons are moving relative to me,then shouldn't its density increase according to special relativity and thereby create an altogether negative net charge.
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1answer
94 views

Time dilation apeears in the both frame: Where is the problem?

Let we consider time in stationary frmae t, and respect the to stationary frame moving frame time $t^ \prime $ . According to lorentz transformation, $$t^\prime= ...
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101 views

What is the linearized form of relativistic hydrodynamics?

What I'm looking for: Let $\vec{W}$ be the vector of conserved variables for a 1-dimensional, adiabatic, (special) relativistic, electrically neutral fluid. (Yes, something that simple!) I'm looking ...
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Are length contraction and time dilation physical?

Are length contraction and time dilation real physical phenomena, or are they just a measurement issue?
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1answer
120 views

A relativistic meter stick and a thin disk

I have a question like the "pole in the barn" special relativity "paradox", but I'm not sure what to make of this: Question A meter stick lies along the $x$-axis and approaches the origin, moving ...
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Is temperature a Lorentz invariant in relativity?

If an observer starts moving at relativistic speeds will he observe the temperature of objects to change as compared to their rest temperatures? Suppose the rest temperature measured is $T$ and the ...
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1answer
185 views

Time dilation and the speed of light in the twin paradox

Suppose we look at the twin paradox where the twin traveling at high speed relative to an observer on earth has a clock which counts time by sending photons of light across a distance within the ...
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2answers
166 views

What if a particle falls into the center of a central field? [closed]

Given a central field $U(r)$ satisfies $U(r) \rightarrow -\infty$ when $r \rightarrow 0$, then What if a particle falls into the center of a central field? Can you help me analysis this question in ...
3
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2answers
349 views

Spacelike and timelike photons

I know the definition of space-like and time-like intervals. How do you show that in some reaction the virtual photon(s) is spacelike/timelike? On page 191 Peskin and Schroeder, it says "since ...
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2answers
121 views

Distance travelled in spaceship Newton vs Einstein

If you get in the canonical 1G windowless spaceship and accelerate for 5 years as determined by your trusty wristwatch, then decelerate for 5 years, then decide its time to see where you are would the ...
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4answers
170 views

Could velocity be taken as fundamental instead of time?

In physics time and length are taken as fundamental in the SI system and, as it seems, in the thinking of physicists. Could one instead take velocity, with c as its unit, together with length as ...
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115 views

Non-zero charge density due to Lorentz contraction in current carrying wires

In trying to answer this question I came across the following problem. The original question relates to the idea that what looks like a magnetic field in one reference frame, ends up as an ...
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2answers
387 views

current in wire + special relativity = magnetism

Current in wire + moving charge next to wire creates magnetic force in the stationary reference frame OR electric force in the moving reference frame from special relativity due to change in charge ...
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6answers
4k views

How does velocity cause time dilation?

I've been trying to learn about the speed of light and time dilation, but I'm at an impasse. The presented facts say that if I travel around the solar system at 50% the speed of light and then come ...
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Momentum of light in medium [duplicate]

Maybe this has been asked before, but I didn't find anything about it. I am wondering about the momentum of light in media with refractive index n>1 (so to say, not in vacuum). There are two ...