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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Proving invariance of $ds^2$ from the invariance of the speed of light

I've started today the book of Landau and Lifshitz Vol.2: The Classical Theory of Fields $\S 2$. They start from the invariance of the speed of light, express it as the fact that $$c^2(\Delta ...
3
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0answers
117 views

What is the theoretical upper limit on the rigidity of a material?

Take a perfectly rigid metal rod of length $\ell$ and some uniform linear density. Place one end at $(0,0)$ and the other at $(0, \ell)$. Over some reasonably short time interval $t$, perhaps on the ...
4
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2answers
426 views

Did Einstein know about Michelson-Morley experiment?

The second postulate of special relativity deals with constancy of light in inertial reference frames. But, how did Einstein came to this conclusion? Did he knew about the Michelson-Morley experiment? ...
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2answers
145 views

Showing the Poincare invariance of a term

I know that this is a simple question! But I would like to know the details. How we can show that the term $$A_\mu(x)\dot{x}^\mu$$ is global and local Poincare invariant? Where $A_\mu(x)$ is ...
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0answers
85 views

At near light speeds, are small objects in your path a problem?

A mental exercise: A space ship is accelerating toward me from far away. As it approaches me, I can observe its acceleration. This high speed ship keeps accelerating faster toward the speed of light. ...
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3answers
158 views

Question on energy mass conversion

I have a question regarding the energy-mass conversion. Well, when a particle starts moving with a speed comparable to that of light, its (relativistic) mass increases that means some matter is ...
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1answer
43 views

Su­per­lu­mi­nal in­ter­ac­tions

The fact that photons emitted from an electric-dipole active atom cannot be spatially localized better than to the near-field zone of the atom is seen as the origin of genuine superluminality. ...
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3answers
243 views

Relativity and photon interactions

A particle's interaction (with anything it can interact with) can be thought of as it making a measurement of the physical quantity associated with the interaction, (e.g. electric field in case of the ...
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2answers
195 views

Will Earth clock be slower than aeroplane clock when viewed from another planet?

I know that a clock placed on an aeroplane will have slowed with respect to a clock placed on earth because the more our velocities are, compared to the speed of light, the more the time slows down. ...
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1answer
155 views

What really happens with Time Dilation? [duplicate]

I know if you move your time moves slower than someone who is stationary, by Lorentz's transformation. However, I don't get how this happens. What does it mean when time moves slower? How does it ...
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1answer
61 views

Muons Internal Clocks and Time Dilation? [closed]

I don't get how time dilation affects the half-life of muons? Time is just a tool that is used by humans how does that affect the internal clocks of elementary particles?
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1answer
77 views

Gravitational field of a particle in SR

According to special relativity, what is the gravitational field due to a particle moving with a constant velocity v? Would it be correct to assume that the particle has a stronger gravitational field ...
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3answers
141 views

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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1answer
168 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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0answers
63 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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3answers
617 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 ...
2
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0answers
75 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 ...
2
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2answers
184 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
189 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
169 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
160 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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0answers
220 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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1answer
234 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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1answer
116 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
150 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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2answers
530 views

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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2answers
393 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
137 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 ...
3
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5answers
623 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 ...
3
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2answers
241 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
107 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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2answers
266 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 ...
2
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2answers
200 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
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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
398 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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2answers
342 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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106 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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56 views

A problem about special relativity [closed]

i can't understand it clearly, so please help me!
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3answers
2k 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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111 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 ...
3
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1answer
150 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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67 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 ...
4
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3answers
261 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 ...
13
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1answer
423 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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4answers
305 views

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 ...
2
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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.
0
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1answer
96 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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1answer
106 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 ...