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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Handedness of Reference Frames?

I am developing a new derivation of the Lorentz transformation which I think and hope is more attractive to students than those I have seen in currently available texts. I am carefully defining and ...
8
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2answers
865 views

What does it mean when physical theories are inconsistent?

I am hoping that someone can explain in layman terms why Newtonian mechanics and Maxwell's equations are inconsistent. Wikipedia says that this inconsistency is what led to the development of ...
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9answers
724 views

Why does Energy-Momentum have a special case?

I was reading Energy-momentum, and I came across this simplified equation: $$E^2 = (mc^2)^2 + (pc)^2$$ where $m$ is the mass and $p$ is momentum of the object. That said, the equation is pretty ...
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0answers
45 views

Undefined result of relativistic velocity addition formula [duplicate]

Isn't it impossible to estimate the velocity of framework through relativistic velocity addition formula when the event moves at speed of the light? $$u=\frac{v-v'}{1-vv'/c^2}$$ if $v=v'=c$ ...
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0answers
81 views

Energy of moving capacitor

On the following link were a discussion about energy in capacitor moving parallel to its field: Where's the energy in a boosted capacitor? My question is what happen if capacitor is moving ...
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1answer
65 views

Timelike curves in Special Relativity

I have a question that probably might sound silly to most of you. We know that a natural Lorentz-invariant parametrization of a timelike curve is provided by: $$\tau$$ the Lorentz-invariant proper ...
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1answer
46 views

Why a hole in the Dirac sea can be seen as having opposite energy?

In the Dirac's old attempt of relativistic quantum mechanics, a hole in the $E'$ level of the Dirac sea was interpreted as a particle of opposite charge and positive energy. I do get why it can be ...
2
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4answers
187 views

Poincare invariant Lagrangians

The Lagrangian density of a Poincare invariant theory should not depend explicitly on the space-time coordinates. Does this mean $$ \partial_\mu \mathcal{L}=0~? $$ If this is the case doesn't the ...
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1answer
87 views

Is it okay to Wick rotate to give the negative of the Euclidean metric? Also, could we make the space-like coordinates imaginary instead?

There are 2 parts to my question: 1) Say we choose the metric signature to be (-+++), as in the Wikipedia page. Then the invariant interval in Minkowski space is written: $ds^{2} = -(dt^{2}) + ...
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0answers
78 views

Show: Lorentz-invariance of solution of Klein-Gordon equation [closed]

Assume $\psi$ is a solution of the Klein-Gordon equation (KGE). Let $\Lambda$ be a Lorentz transformation. Show: $\phi = \psi(\Lambda^{-1} \cdot )$ is also a solution of the KGE. I try to ...
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1answer
62 views

How fast must Nadia travel so that she is the same biological age as her twin upon returning to Earth? [closed]

Two twins, Nadia and Aidan, decide to have an adventure when they turn 21. Aidan chooses to travel to a distant star 10 light years away at a speed of 0.8c. Nadia decides to travel to a closer ...
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1answer
77 views

Electromagnetism in flat space

I want to get a deeper understanding of how Electric and Magnetic fields transform under Lorentz transformation. That is how to start from gauge transformation of Electric and Magnetic fields $$E= ...
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0answers
43 views

Relation involving the Lorentz transformation and the inverse of its transpose

The relation I was referring to in the title is $${\Lambda_a}^b= \eta_{ac} {L^c}_d \eta^{db}$$ where ${\Lambda_a}^b$ is the inverse transpose of $L$, the Lorentz transformation. I was wondering ...
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4answers
186 views

Nature of Fields in QFT

I'm not exactly an expert in quantum physics, but this seems to be a simple question, and I can't find an answer anywhere! There are specific types of fields used in physics: scalar fields (i.e. as ...
2
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1answer
58 views

First variation of the action in relativistic notation - Landau & Lifshitz “Classical theory of fields”

In Landau & Lifshitz's book, Classical theory of fields, the action for a free particle is defined as: $$\tag{8.1} S= \int ^b _a {-mc \ \text d s}=0,$$ where $$\text d s=c\,\text d ...
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2answers
156 views

The variation of the Lagrangian density under an infinitesimal Lorentz transformation

I'm trying to introduce myself to QFT following these lectures by David Tong. I've started with lecture 1 (Classical Field Theory) and I'm trying to prove that under an infinitesimal Lorentz ...
0
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2answers
86 views

Time dilation confusion

I'm just starting to learn about special relativity, and I'm a little bit confused about something. Take the example of an observer in $S$ on the ground observing a train move at constant velocity $v$ ...
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1answer
67 views

Rotational symmetry in integration

Can someone please tell me why $$4\int d^4x \, x^\mu x^\nu ~=~\int d^4x \, g^{\mu\nu}x^2 $$ by some rotational symmetry argument?
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1answer
79 views

Navigating a Time Machine

Notes: The background for this question is working out details of a sci-fi story. Answers to the effect of "time travel isn't possible" or "FTL isn't possible" are therefore not helpful. I'm looking ...
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1answer
150 views

Time Dilation Problem [closed]

I'm having some trouble using the time dilation formula. Say an astronaut leaves Earth for 10 years, at 0.85c. How much time has passed according to an observer on Earth? I tried using the ...
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6answers
6k views

Should I abandon my thought experiment about time?

I'm trying to think about special relativity without "spoiling" it by looking up the answer; I hope someone can offer some insight - or at least tell me I'm wrong. Suppose I have an ordinary clock ...
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2answers
85 views

Is the energy of momentum stored physically? [closed]

While an object is moving, relativity will say it weighs more, especially so as it approaches light speed. The increase in energy is then easily sensed as an increase in mass (Almost as a rock in ...
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1answer
121 views

In QFT, why do fermions have to anticommute in order to insure causality?

I have seen this question and I believe I understand the answer to it. However, AFAIK, only for bosons the causality condition is a vanishing commutator. For fermions we expect the anticommutator ...
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1answer
482 views

What happens if someone travelling just under the speed of light makes a telephone call?

Apart from the possibility that radio transmission will not work, what would happen if someone travelling fast enough relative to another individual to experience significant time dilation made a ...
2
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1answer
115 views

How can one always be standing still when compared to the speed of light?

I was thinking if I built a device with 7 clocks, synchronized to each other, one in the middle, one up, down, left, right, behind and in front of me, say 1 meter away, and I fired a laser from the ...
4
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2answers
578 views

Is special relativity a special case of general relativity, qualitatively?

Since Einstein name his theory Special Relativity and General Relativity, there should be some expected relationship between them, particularly "Special Relativity" being a special case of the more ...
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3answers
97 views

Lightspeed (invariance) measurement methods

I would like to know, how measurements of the speed of light are conducted these days, especially in the context of the invariance of $c$. Do all the methods involve mirrors to redirect the photons ...
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5answers
389 views

Special Relativity, 2nd Postulate — Why? [duplicate]

As a lowly physics undergrad who has been chewing on this 2nd postulate of special relativity for a year or more, I simply can't wrap my head around reasons why it is true or how Einstein might have ...
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2answers
43 views

Special Relativity Question: Doppler shift

Imagine an observer watching a moving rocket carrying on it both, a light source and a clock. If on the rocket the clock is synchronized with the frequency of the light being emitted then will not a ...
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0answers
61 views

Spin in relativity

Mass and spin of the particle are used in classification of elementary particles. The mass is defined to be a Lorentz invariant quantity. On the other hand, the spin is a spacelike 4-vector and cannot ...
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1answer
78 views

Do photons change velocity instantaneously?

Any object traveling at c is observed as traveling at c in all reference frames. When a photon travels through a vacuum at c, all reference frames observe it traveling at c. When a photon passes ...
2
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2answers
165 views

A whole lot of doubts on Lorentz representation

Can someone tell me in layman's language how the $(1/2,1/2)$ represents a vector field and $(0,1/2)$ or $(1/2,0)$ represents spinors and $(0,0)$ represents scalar field. Please don't be pedantic on ...
4
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1answer
101 views

Thought experiment: Tethered galaxies - to the extreme

If two rocks were tied together with a tight, absurdly long, non-elastic rope, and placed on planets at either end of Earth's observable universe - or beyond - What would happen? Is the structural ...
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1answer
64 views

4-vector velocity to Newtonian?

The four-vector condition for a particle free of forces is: $\frac{du}{dτ} = 0$ and the equivalence of this to the statement of newton's first law follows from the expression for four-velocity: ...
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1answer
65 views

Relativistic Conservation laws [closed]

Conservation of Relativistic mass and thus energy is easily proven by considering an inelastic collision of two bodies while invoking the conservation of momentum. As such the momentum law appears ...
2
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2answers
86 views

Is negative mass for a bound system of two particles forbidden?

Is there any theorem that forbids the bound system of two massive particles to have negative mass?
2
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1answer
60 views

Doppler Shift when Light Travels Through Two Different Mediums

When considering the Doppler shift, the 'canonical equation' is $$f=\frac{c+vr}{c+vs}f_0$$ However, this equation seems to run into trouble in the following situation: A light source inside water is ...
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1answer
111 views

Minkowski spacetime vs Euclidian space

Two questions marked in bold: What is the magnitude of a Minkowski spacetime four velocity? I'm deducing that it is c for all observers, but I'd like it confirmed. In Euclidian space, a velocity ...
3
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2answers
117 views

Refractive index of dielectric in different frames of reference

The setup A transparent isotropic dielectric medium moving in the negative $x'$ direction at speed $v$ in frame $S'$ is stationary in frame $S$, where it has refractive index $n$. In other words, ...
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3answers
108 views

Coulomb's Law- Why the Coulomb's law is valid only for point and static charges?

Why the coulomb's law is valid only for point and static charges? Is there is any definite reason?
2
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1answer
513 views

Dark matter a medium for light propagation

Is dark matter a candidate to fill void left by luminiferous ether as a medium for light travel?
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4answers
3k views

Why is there a controversy on whether mass increases with speed?

Some people say that mass increases with speed, some people say that the mass of an object is independent of its speed. I understand how some (though not many) things in physics are a matter of ...
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5answers
1k views

What problems with Electromagnetism led Einstein to the Special Theory of Relativity?

I have often heard it said that several problems in the theory of electromagnetism as described by Maxwell's equations led Einstein to his theory of Special Relativity. What exactly were these ...
2
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0answers
57 views

Question about Origins in Galilean transformation

I'm just learning about relativity, and every equation I see for a galilean transformation of frame $S'$ (moving with uniform velocity in the $x$-direction with respect to frame $S$) is $x'=x-vt$, ...
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1answer
178 views

How do you go from quantum electrodynamics to Maxwell's equations?

I've read and heard that quantum electrodynamics is more fundamental than maxwells equations. How do you go from quantum electrodynamics to Maxwell's equations?
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2answers
560 views

Energy & Mass of a Photon [duplicate]

$$\text{Please read the whole question before answering}$$ Before I ask my question, I would like to say that "Yes, I do know a photon has no mass." I was helping someone here on P.SE with the ...
2
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1answer
103 views

Approaching speed of light: why do objects appear further away in front of me?

A Slower Speed of Light is a video game created by the MIT Game Lab which allows users to experience what it would be like if the speed of light was closer to normal walking/running speeds and thus ...
9
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1answer
188 views

How is the Photoelectric Effect affected by Blue-Shifting

I was thinking about the Photoelectric Effect and Blue-Shifting when I came up with a thought experiment that I couldn't think of an answer for. The thought experiment is as follows: A metal plate is ...
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2answers
106 views

Inertial frames

I'm just starting my study of relativity, and I have a rough understanding of the connection between inertial frames, newton's laws, and galilean transformations, but I'd probably benefit more if ...
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2answers
208 views

A curious case of Relativistic Velocity Addition [duplicate]

The relativistic velocity addition formula is $$u = \frac{v+u'}{1+ \frac{vu'}{c^2}}$$ Where $u$ = velocity of projectile seen by rest observer "A" $v$ = velocity of moving observer "B" as seen by ...