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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Coulomb Gauge under Lorentz Boost

In the Coulomb gauge for the Maxwell potential we have $$ A^0 = 0 \\ \partial_i A^i = 0 $$ Under an infinitesimal Lorentz Transformation with parameter $\epsilon$, we have $$ A^\mu(x) \rightarrow ...
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Could we find relativistic energy in a simple way?

I asked a couple of questions on mass(-energy) increasing with speed, but there is still a very simple aspect I cannot understand, I hope you can give a simple and direct answer: The formula to find ...
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71 views

What is the Lorentz group representation for a general spin?

Setup, as I understand things so far: One way to think about where the spin of a quantum field comes from is that it is a consequence of the ways that different types of fields transform under ...
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Why is a theory Lorentz invariant if the Lagrangian is Lorentz invariant?

For if I started by trying to make the Hamiltonian Lorentz invariant, I would have failed. Indeed, the Hamiltonian is part of a covariant tensor. But how do I know that the Lagrangian is not a part of ...
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Do mechanical waves also carry momentum as well as energy? [closed]

I have read that electromagnetic waves carry momentum because they carry energy, while energy is equivalent to mass. So they carry momentum. But this explanation is in the context of special ...
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1answer
386 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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34 views

Twin Paradox when both twins are moving [duplicate]

Let's say twin scientists A and B start on Earth. Twin A moves east at speed v comparable to light, and Twin B moves west at speed v comparable to light. After some time, they reverse directions and ...
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78 views

At what speeds does time dilations start to occur?

My question is, is it possible for time dilation to occur at a speed less than that of speed of light?
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82 views

How is time dilation consistent between both observer?

There is a special variant of time dilation paradox bugs me. Imagine there are 2 small spaceships moving toward each other in constant speed. Each ship has an observer on-board. According to both ...
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Definitions: 'locality' vs 'causality'

I'm having trouble unambiguously interpreting many answers here due to the fact that the terms locality and causality are sometimes used interchangeably, while other times seem to mean very different ...
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135 views

Meaning and logic of Einstein's train thought experiment

This seems to be a recurrent topic but I wasn't able to find any satisfactory discussion about this tought experiment. I will quote the original story from Einstein's and put my doubts inside: Up ...
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24 views

Error in deriving constant acceleration relativistic distance

Bob accelerates away from Carol at proper acceleration $a$ (in light seconds per second), and Carol wants to know how far Bob has traveled when $t$ seconds pass in Bob's frame. Using ...
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Do Einstein's postulates of relativity emerge from the Minkowski spacetime metric?

Does the constancy of the speed of light for all observers naturally emerge from the Minkowski spacetime metric? Do Einstein's two postulates of relativity emerge from the Minkowski spacetime metric? ...
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Can $E=mc^2$ be derived from the Minkowski spacetime metric? $s^2=x^2+y^2+z^2-(ct)^2$?

Can $E=mc^2$ be derived from the Minkowski spacetime metric? $s^2=x^2+y^2+z^2-(ct)^2$? If so, how? Can the equivalence of mass and energy be derived from the Minkowski spacetime metric? Has someone ...
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346 views

Infinitesimal transformations for a relativistic particle

The action of a free relativistic particles can be given by $$S=\frac{1}{2}\int d\tau \left(e^{-1}(\tau)g_{\mu\nu}(X)X^\mu(\tau)X^\nu(\tau)-e(\tau)m^2\right).$$ If we then make an infinitesimal ...
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752 views

Why do we identify symmetric 2nd rank tensors with spin-2 particles in string theory?

I am going through Tong's lecture notes on String Theory and came across the following irrep decomposition (Chap 2, p.43) of the bosonic string first excited states: $$\text{traceless symmetric} ...
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4answers
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Is there an underlying physical reason why the Coriolis force is similar to the magnetic component of the Lorentz force?

I couldn't help but notice that the expression for the magnetic component of the Lorentz force, $$\mathbf F = q\,\mathbf v \times \mathbf B\,,$$ is very similar in its mathematical form to the ...
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27 views

Synchronization of clocks

I have read the book "Introduction to special relativity " by Robert Resnick In the book I have found that "If the distance between the clocks is L, one observer will see the other clock lag his by ...
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1answer
67 views

Plane Wave Solutions of the Dirac Equation

I'm trying to understand the plane wave solutions of the Dirac Equation. But I'm still a newbie on indices notation and contravariant and covariant objects. What I don't understand is how to get: ...
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Were Michelson-Morley results a surprise?

How unexpected were the Michelson-Morley experiment results? Did physicists have theoretical reasons to predict that the speed of light would result to be invariant?
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178 views

What's the max speed a man-made satellite can travel in space before its circuitry stopped working?

Assume it could withstand extreme temperatures in either direction. I'm mainly curious what would happen to its circuits as it approached the speed of light.
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59 views

Radiative equilibrium of a relativistic black body

A black body in empty space in the CMB rest frame should (discounting starlight) come to an equilibrium temperature of around 2.7 K. However, if the body is moving relative to the CMB frame, one side ...
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1answer
66 views

Force, Mass, Motion? $E = mc^2$

Does any object needs force to move? If 'yes', does the matter needs mass to form a force? These questions arises from me because $E = mc^2$ and $F = ma$ does not relate and one does not agrees with ...
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How to express in terms of spacetime intervals the average speed of one participant having moved between two suitable others

Given a flat region of spacetime as set $\mathcal S$ of events together with values of spacetime intervals (up to a common non-zero constant) for each pair of events, $s^2 : \mathcal S \times \mathcal ...
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3answers
313 views

Why does the Michelson-Morley experiment only contradict the aether?

This question is related to Validity of Maxwell's equations with no aether or relativity? (so please read this first). In this question, the answers seem to suggest that getting rid of the aether ...
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85 views

Why is the speed of light being invariant and finite in all inertial reference frames?

I understand the basics of Lorentz transformation and Riemann Geometry but I still cannot understand why the speed of light is the same in all inertial references. Has anyone ever researched about ...
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Planes of Simultaneity on Minkowski diagrams

As seen from a "stationary" reference frame, Why do lines of simultaneity for fast-moving observers run parallel to distance axis instead of perpendicular to the time axis. Obviously, in a regular t ...
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What's the problem with light traveling at speed higher than $c$?

I'm trying to understand how Einstein concluded that time is relative based on thought experiments such as a torch attached to the end of a rocket. Based on answers to questions like this one, this ...
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3answers
212 views

How can we prove charge invariance under Lorentz Transformation?

We have gravitational force between two massive particles and we have electromagnetic force between two charged particles. When special relativity suggests that mass is not an invariant quantity why ...
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1answer
50 views

Behaviour of Dirac Bilinears

Dirac bilinears transform in the Lorentz indices as, $\bar{\psi}\psi$ scalar $\bar{\psi}\gamma^\mu\psi$ vector $\bar{\psi}\sigma^{\mu\nu}\psi$ 2nd rank (antisymmetric) tensor ...
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1answer
61 views

How time and speed of light are related? [closed]

I want to know how speed and light and time are related? How will motion with highspeed effect time? I am not a physics student. I want an answer which is free of mathematical relations. I want an ...
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1answer
16 views

How to express in terms of spacetime intervals whether two participants in a flat region were at rest to each other

Given a flat region of spacetime as set $\mathcal S$ of events together with values of spacetime intervals (up to a common non-zero constant) for each pair of events, $s^2 : \mathcal S \times \mathcal ...
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4answers
117 views

Tensor calculus in special relativity

We say that any function $f(t,x,y,z)$ is a tensor of rank {0 0} because it takes no vectors or one-forms in order to give a real number. But couldn't we have just written the same function as ...
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1answer
67 views

Dot product in index notation [closed]

This is a question about a small exercise I am trying to do in order to check if I am correct. Such type of quantities can appear in propagators in QFT. Since I am not an index expert I need some ...
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1answer
75 views

Different definitions of the parity transformation for the Dirac spinors

There are two definitions of the parity transformation acting on the Dirac spinors: $\Psi_P = \eta \gamma^0 \Psi$ with $\eta = i$ ($P^2=-1$ as in Srednicki) and $\eta=1$ ($P^2=+1$ as in Peskin & ...
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1answer
70 views

Relativistic acceleration of a rocket?

I'm trying to solve a physics brain-teaser and getting nowhere fast. My knowledge of special relativity is very basic. In the problem a rocket is flying linearly at relativistic speeds (say ...
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2answers
66 views

How does SUSY avoid to create non-Lorentz interactions?

A three-legs fermion interaction or boson absorbing a fermion are things we do not see in QFT because the corresponding terms in the Lagrangian are not Lorentz invariant. But in susy, naively, such ...
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Gradient of $ct'$ axis in spacetime diagrams

This is either an unimportant piece of information or it's meant to be obvious, but I can't find anywhere what the gradient of the $ct'$ axis in a spacetime diagram should be. I know that the $ct'=1$ ...
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1answer
28 views

Multiple Objects at Constant Speed

Imagine 1 million objects travelling in space, at a constant speed, along an imaginary line. They don't deviate from that line for the sake of this argument. Now, object 1 has a velocity of $v_{1}=1$ ...
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796 views

Orthochronous Lorentz transformations are time-preserving and $SL(2,\mathbb{R})$

Let's consider the pseudosphere/hyperboloid in $\mathbb{R}^{1,2}$ given by $$x^2+y^2-z^2=-R^2.$$ We know that the Lorentz group $$O(1,2)=\{ A \in Mat(3,\mathbb{R}): A^tGA=G \},$$ where ...
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1answer
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How does time dilation occur due to velocity and gravity [duplicate]

I am trying to understand and clarify the way time dilation occurs due to general and special relativity and for which reason. In the case where an object is approaching a planet in free-fall how does ...
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1answer
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Status of experimental searches for tachyons?

Now that the dust has settled on the 2011 superluminal neutrino debacle at OPERA, I'm interested in understanding the current status of experimental searches for neutrinos. Although the OPERA claim ...
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3answers
156 views

Why did Einstein took speed of light unit or constant in his equation of relativity?

We can find that no object can have speed more than light from Einstein's equation of relativity because if anything have speed more than light then we get -ve value within square root. But why did ...
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How to find kinetic energy given relativistic linear momentum?

The relativistic energy of a particle is given by the expression \begin{equation} E^2 = m^2c^4 + p^2c^2 \end{equation} The rest energy is $E_{0}=mc^2$ and the momentum is $p=mc$. In the rest frame, ...
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1answer
2k views

How do I derive the Lorentz contraction from the invariant interval?

Reviewing some basic special relativity, and I stumbled upon this problem: From the definition of the proper time: $$c^2d\tau^2=c^2dt^2-dx^2$$ I was able to derive the time dilation formula by using ...
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3answers
72 views

Mass and frequency of photons [duplicate]

Light is affected by gravity which means light has got mass. Quantum theory tells us that light consists of discrete quanta of energy, which we call photons. These photons have a rest mass of zero (as ...
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Can special relativity be derived from the invariance of the interval?

As far as I know, the classical approach to special relativity is to take Einstein's postulates as the starting point of the logical sequence, then to derive the Lorentz transformations from them, and ...
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1answer
81 views

What gauge field can be constructed from Lorentz symmetry?

You can take a global symmetry and promote it to a local gauge symmetry by introducing an appropriate gauge field and upgrading the partial derivative to a covariant derivative. The photon field ...
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2answers
375 views

How to achieve speeds faster than light? [duplicate]

So, I heard that all speed is relative. And that nothing can travel faster than light. Then I guess it is OK for a spaceship to leave Earth at 0.6c constant speed. And what if an other spaceship were ...
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6answers
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If I run along the aisle of a bus traveling at (almost) the speed of light, can I travel faster than the speed of light?

Let's say I fire a bus through space at (almost) the speed of light in vacuum. If I'm inside the bus (sitting on the back seat) and I run up the aisle of the bus toward the front, does that mean I'm ...