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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Volume element $\mathrm{d}^4k =\mathrm{d}k^0 \,|\mathbf{k}|^2\,\mathrm{d}|\mathbf{k}| \,\mathrm{d}(\cos\theta) \,\mathrm{d}\phi$ in Minkowski space?

Suppose we have an integral $$\int \mathrm{d}^4k \,\ f(k)$$ we want to evaluate and that we're in Minkowski space with some metric $(+,-,-,-)$. Is it true that: $$\mathrm{d}^4k = \mathrm{d}k^0\ ...
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Energy conserved… or not? Confused!

I am confused. Could someone kindly explain what's going on in this question? A particle of mass $m$ and charge $e$ moves in the $x,y-$ plane. There is a constant magnetic field $B$ that points in ...
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How Special Relativity causes magnetism

So my physics teacher assigned us an article about how special relativity causes magnetism in a wire with a current, even with the low drift velocities of electrons in a current. It seemed that the ...
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79 views

Relativistic canonical transformation

What is relativistic canonical transformation? I need every piece of information about it. Does anyone know a reference or an article about relativistic canonical transformation? For example, in ...
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2answers
2k views

Does inertia increase with speed?

I have heard that when the speed of the object increase, the mass of the object also increase. (Why does an object with higher speed gain more (relativistic) mass?) So inertia which is related to ...
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Einsteins train though experiment. What if the train is moving at the speed of light? (layman Q) [closed]

I understand einstein's train paradox. Where one man on a platform is passed by a man in a traincar, at the moment they meet a flash of light is given off in the middle of the train car. To the man on ...
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69 views

Speed of Light and Information

Einstein in his thought experiment(?) for the constancy of speed of light in vacuum in all frames reasoned , that if speed of light of vacuum isn't constant than you'll be able to perceive effect ...
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138 views

Neutrinos and Speed of light

Einstein's Special Theory of relativity postulates that the speed of light is same for all frames. Suppose a neutrino is there moving at the speed of light. Then will that neutrino also be flowing ...
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How to keep the clock of a spaceship synchronised to the clock of an observer? [duplicate]

I read that the clocks of GPS satellites seem to run slower than the clock of stationary observer, because of their speed (special relativity) and seem to run faster than the clock of stationary ...
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485 views

Why is the Dirac equation not used for calculations?

From what I understand the Dirac equation is supposed to be an improvement on the Schrödinger equation in that it is consistent with relativity theory. Yet all methods I have encountered for doing ...
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305 views

The definition of Lorentz transformation

I know that the Lorentz transformation, when two frames $\mathcal{S}$ and $\mathcal{S}'$ are in standard configuration (the axes are all parallel to their counterparts in the other inertial frame) is ...
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3answers
248 views

Mass in special relativity

I have just got a query about how this equation works if its right. We have Newtonian Physics saying $F=ma$, According to the 'Mass in special relativity' the mass changes according to $$m= ...
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Is period of rotation relative?

My question is inspired by the following answer by voix to another problem: "There is a real object with relativistic speed of surface - millisecond pulsar. The swiftest spinning pulsar currently ...
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2answers
280 views

Doubts concerning Wigner's classification

Wigner classified particles in function of the eigenvalues of $P_\mu P^\mu$ and $W_\mu W^\mu$. Then, it can be proved that for massless particles spin values can be only $\pm s_{max}$. But for a ...
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Why is this thought experiment flawed: A vast lever rotating faster than the speed of light [duplicate]

If there were a vast lever floating in free space, a rigid body with length greater than the width of a galaxy, made of a hypothetical material that could endure unlimited internal stress, and this ...
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1answer
362 views

Why does Lorentz factor not hold for relativistic mass when we apply it to photons? [duplicate]

We know that the photon itself is massless particle $m_0=0$. But we also know, that the mass of the objects does increase with their energy. And we know that under certain circumstances (gravity, ...
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3answers
768 views

Does relativistic mass have weight?

If an object was sliding on an infinitely long friction-less floor on Earth with relativistic speeds (ignoring air resistance), would it exert more vertical weight force on the floor than when it's at ...
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2answers
147 views

Limit on velocity in Minkowski Spacetime geometry

Let A be a rocket moving with velocity v. Then the slope of its worldline in a spacetime diagram is given by c/v. Since it is a slope, c/v = tan(theta) for some theta > 45 and theta < 90. Does ...
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Solving the equation of relativistic motion

How does one solve the tensor differential equation for the relativistic motion of a partilcle of charge $e$ and mass $m$, with 4-momentum $p^a$ and electromagnetic field tensor $F_{ab}$ of a constant ...
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There must be free positive charges, moving oppositely to electrons for the wire with current to stay neutral

All popular expositions (e.g. these ones) of relativistic electromagnetism claim univocally that electrons in motion become more dense due to the speed. They teach that Lorentz contraction of charges ...
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How to understand the emergent special relativity in the superfluid?

The superfluid vacuum theory was proposed to understand some features of the vacuum (aether) from the emergence point of view. Although made up of non-relativistic atoms, the low-energy excitations of ...
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248 views

Do velocity and acceleration time dilation factors add?

For a spinning space station such as in 2001, A Space Odyssey, what would be the time slowing in the perimeter of the spinning space station with respect to the center axis of the station? The ...
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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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283 views

Bound State of Only Massless Particles? Follows a Time-Like Trajectory?

Is there any way in which a bound state could consist only of massless particles? If yes, would this "atom" of massless particles travel on a light-like trajectory, or would the interaction energy ...
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3answers
202 views

Reaching the speed of light via quantum mechanical uncertainty?

Suppose you accelerate a body to very near the speed of light $c$ where $v = c - \epsilon$. Although this would take an enormous energy, is it possible the last arbitrarily small velocity needed -- ...
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168 views

Difference between vector and pseudo-scalar

In physics, a pseudo-scalar is a quantity that behaves like a scalar, except that it changes sign under a parity inversion such as improper rotations while a true scalar does not. Can someone show me ...
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Einstein’s Thought Experiment of a Stationary Box and a Photon

1) First of all, let us consider a particle of light, also known as a photon. One of the interesting properties of photons is that they have momentum and yet have no mass. This was established in ...
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How do we measure the range of distant objects despite relativistic effects?

When we observe astronomical objects like distant galaxies there are several complicating factors for estimating the distance: Relativistic speed result in length contraction Relativistic speed ...
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Is there a relativity-compatible thermodynamics?

I am just wondering that laws in thermodynamics are not Lorentz invariant, it only involves the $T^{00}$ component. Tolman gave a formalism in his book. For example, the first law is replaced by the ...
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Are gravitational time dilation and the time dilation in special relativity independent?

There are two kinds of time dilation: One because the other clock moves fast relative to me (special relativity). Another one because the other clock is in a stronger gravitational field (general ...
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What is the Andromeda Paradox?

I have been studying causality (specifically why there is no such thing as a simultaneous instant of time across all observers) recently and I keep hearing references to the Andromeda paradox. Can ...
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Relativistic origin of magnetic field

There is an explanation in the Wikipedia. Unfortunately the article is quite verbose and doesn't clearly explain why both positive and negative charges vary density even if only one is moving. It is ...
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592 views

Relativistic charge density in a closed loop

When charges of conductance are at rest, there is an average distance between them. The relativistic origin of magnetic field says that distances between electrons shrink when they are set into a ...
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What is Relativistic Navier-Stokes Equation Through Einstein Notation?

Navier-Stokes equation is non-relativistic, what is relativistic Navier-Stokes equation through Einstein notation?
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Relativistic Computation?

Is it possible to employ relativity to develop computational technology? Here is a really basic example: Build a Computer and Feed it the Problem (say the problem is projected to take 10 years to ...
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Live feed from a Rocket traveling near the speed of light?

Okay, odd question popped up in my physics class today. If a rocket ship is traveling at .99c for 1 year, and is streaming a video at 30 frames/sec to earth, how would the earth feed be affected? ...
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260 views

Doppler shift of radio signals to an accelerating observer

Suppose a man leaves from Earth to a star which is 1000 light years away. He accelerates to a velocity such that the entire trip lasts a year, from the reference frame of the rocket. Now lets pretend ...
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Stuff can't go at the speed of light - in relation to what? [duplicate]

We all know that stuff can't go faster than the speed of light - it's length becomes negative and all kinds of weird stuff happens. However, this is in relation to what? If two objects, each moving ...
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297 views

What is the exact mechanism by which time dilates?

What is the exact mechanism by which time dilates for a fast moving object? Can the time dilation be explained by any theory other than relativity?
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Rate of spontaneous tachyon emission

It's not possible for an electron to emit or absorb a photon without the presence of a third particle such as an atomic nucleus; without the third particle, it's impossible for such a process to ...
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108 views

Faraday tensor, antisymmetric electromagnetic tensor

I want to write $F^{\mu \nu}F_{\mu \nu}$ in terms of $F_{\mu \nu}F^{\mu \nu}$. How to do it?
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Relativity Problem with Three Reference Frames

I'm having trouble with the understanding on this last problem from my homework set. Two cars playing demolition derby are moving towards each other with constant velocity, as measured by Marvin, ...
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Cancelling special & general relativistic effects

We know that for a GPS we need to make a correction for both general and special relativity: general relativity predicts that clocks go slower in a higher gravitational field (the clock aboard a GPS ...
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Faraday tensor, antisymmetric rank two

$F^{\mu \mathcal{V}}$ is defined in http://www.lecture-notes.co.uk/susskind/special-relativity/lecture-7/relativistic-lorentz-force/ How to show that $F^{\mu \mathcal{V}}$$F_{\mu \mathcal{V}}$, is ...
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4answers
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What is the process that gives mass to free relativitic particles?

When a free particle move in space with a known momentum and energy then what is the physical process that gives mass to that free (relativistic) particle? What is role does the Higgs field in that ...
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Does an accelerating spaceship move backwards due to length contraction?

Let's assume I have a spaceship in front of me let's say at 1000000km distance. Now let's assume I have also a stationary wall just behind the spaceship at 999999km. Initially the spaceship's speed is ...
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If there's a light ray and it's turned to a new location by a certain angle

Imagine that there's a light ray, with source at point A, and it's directed towards point B (which is very far from point A) and it continues for a huge distance. How will an observer at point B ...
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Relativistic Doppler effect derivation

This is about a step in a derivation of the expression for the relativistic Doppler effect. Consider a source receding from an observer at a velocity $v$ along the line joining the two. Light is ...
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Proton-proton collisions

I have a question about proton-proton collisions at the LHC. Firstly, the 4-momentum $p^\mu=(E/c,\vec{p})$ can be represented as $p^\mu =(m_T \cosh \Psi, p_T \cos \phi , p_T \sin \phi, m_T c \sinh ...
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$\frac{dt}{d\tau}=\gamma$ in special relativity

I hope this is not too silly a question: We often see $$\frac{dt}{d\tau}=\gamma=\frac{1}{\sqrt{1-v^2}},$$ taking $c=1$. Problem: I don't understand why... In the Minkowski metric, using the ...