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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What does a relativistically moving capacitor “look” like? [duplicate]

Suppose I have a parallel plate capacitor with a vacuum between the plates, a voltage $V$ across them and a capacitance of $C$. What will this arrangement look like to an observer in a uniformly ...
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1answer
38 views

Are 2 time intervals the same only for same speeds?

I'm only amateur in modern phsyics having read some about relativity theory and time measurements depending on relative movement. Is it true that 2 clocks measure time the same only if the relative ...
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1answer
42 views

Change in line density of electrons

We're proving that electricity and magnetism are essentially two manifestations of the same underlying phenomenon by using the toy example of a positive charge moving parallel to an infinitely long ...
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13 views

I am looking for a good primer on Special relativity [duplicate]

I am starting a course in Gravity and Quantum Field Theory this year, and I have all of the prerequisites except for a few topics in Special Relativity. I have had some SR, but only the 1-dimensional ...
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1answer
65 views

Special relativity and missing factors of $c$

I am doing problems in a textbook called 'Introduction to Classical Mechanics' by David Morin. In one of the questions it says the following: In the lab frame, two particles move with speed $v$ ...
3
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1answer
110 views

Vector fields and tensors in E&M

I'm confused by a very basic property of electric fields. The electric field is a vector field. Vectors are tensors. Wikipedia has the following statement in the article about the electromagnetic ...
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38 views

How can the clock c1 be synchronized with the clock c2?

A clock c1 is situated at a distance $L$ from an observer carrying a clock c1. How can the clock c1 be synchronized with the clock c2?
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1answer
29 views

Is there a simple explanation for the fact that the Lorentz transformation must be linear? [duplicate]

In my physics class, for deriving the Lorentz transformatuons my professor assumed that there is a linearity relatioin between the coordinates of the two systems. But why is that?? Can anyone please ...
2
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1answer
87 views

Why do we write the lengths in the following way? Question about Lorentz transformation

Yesterday we have studied the Lorentz transformation in school. So we have two frames of reference, $S$ and $S'$ . $S$ is stationary and $S'$. $S'$ has a constant velocity $v$, relative to the $S$ ...
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2answers
55 views

A confusion regarding absolute motion in SRT

Suppose i am inside a uniformly moving spaceship and I send a light beam perpendicular to the direction of motion towards the opposite wall.Since the spaceship is moving and according to special ...
3
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1answer
108 views

Doppler shift for a uniformly accelerating observer

This was given in textbook as an example. An observer on a spaceship with a four velocity $u$ is approaching from $x = +\infty$ a star at rest in the reference frame $S$ while undergoing constant ...
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1answer
49 views

Spaceship Doppler frequency

A spaceship starts falling under gravity with an acceleration $g$ as measured by an observer Barry at rest on Earth. At the instant that the ship starts to fall, an astronaut Harry at the base of the ...
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0answers
64 views

Spacetime - Fact, Hypothesis, or Working Model? [closed]

Are the concepts of spacetime an accepted fact or something less? I have a limited background in modern physics and just finished a great book by Andrew Thomas that explains in very common language ...
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1answer
115 views

Force exerted by light on a moving mirror

Consider a light with energy density E shining uniformly over a mirror. The mirror has an area A. The mirror is moving at with a velocity β. Calculate the force that the photons exert on the ...
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0answers
53 views

Four-momentum, four-velocity, energy

If given the four-momentum of any particle monitored by an observer as: p = $p^\hat{α}e_\hat{α}$ using unit vectors in observer’s reference frame and u = $e_\hat{0}$ then I get I'm just ...
2
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1answer
90 views

Maxwell's equation for non inertial observer

Applying Maxwell's equation we can prove that light will move at the speed of light for every inertial frame, is it true as well for non-inertial frames? How light moves slowly near a black hole??
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5answers
401 views

A neutrino has rest-mass and travels at (near) $c$, why isn't its mass/ energy (nearly) infinite?

If the total energy of all three types of neutrinos exceeded an average of 50 eV per neutrino, there would be so much mass in the universe that it would collapse. This limit can be circumvented ...
3
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1answer
51 views

Importance of Powers of Velocity in Classical Mechanics

Is there any general significance to calculated quantities that depend purely on general powers of the velocity of a particle/system/etc? The first power being momentum and the second being kinetic ...
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1answer
81 views

Special relativity; spaceship moving towards a planet [closed]

A spacecraft starts travelling from Earth, moving at constant speed, towards a yet-to-be-discovered planet, which is $20$ light hours away from Earth. It takes $25$ hours (according to an ...
9
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1answer
187 views

Why Lorentz group for fields and Poincaré group for particles?

Wigner treatment associates to particles the irreps of the universal covering of the Poincaré group $$\mathbb{R}(1,3)\rtimes SL(2,\mathbb{C}).$$ Why don't we consider finite dimensional ...
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1answer
85 views

Special relativity; rocket moving towards a mirror [closed]

An observer in a rocket moves toward a mirror at speed $v$ relative to the reference frame in which the mirror is stationary - call this frame $S$. A light pulse emitted by the rocket travels ...
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4answers
239 views

If a spaceship were to be able to travel at light speed, would it pass through objects undamaged? Would it damage/destroy objects?

We know, not just by scientific theory, but by practice (I have seen it with my own eyes), that an increase in velocity increases the mass of the given object proportionally. One day visiting a ...
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1answer
82 views

Why don't clocks on a train read the same time?

Two clocks are positioned at the ends of a train of length $L$ (as measured in its own frame). They are synchronized in the train frame. The train travels past you at speed $v$. It turns out ...
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142 views

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 ...
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2answers
878 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
735 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
46 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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82 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
67 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
47 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
211 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 ...
2
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1answer
96 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}) + ...
2
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0answers
103 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
101 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
80 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
46 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
202 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
61 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
175 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 ...
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2answers
93 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
207 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 ...
23
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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
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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 ...
2
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1answer
127 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 ...
4
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1answer
500 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
119 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 ...
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2answers
630 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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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 ...