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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Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
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Detecting absolute motion inside a box

This is not a contradiction and I know it is impossible but still consider a thought experiment by me and point out if something is wrong. See the following picture and then the explanation follows. ...
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Consider relativity. If a stick accelerates from a stationary state, how will it look like during the acceleration?

I mean how it will be shortened in the sight of an observer in a stationary coordinate system. It seems I was not clear enough. If the stick becomes shorter, then while this is happening, the ...
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60 views

Finding the total energy in centre of mass frame

I'm working through a problem in a special relativity textbook (Woodhouse) and I'm having some difficulty. I have to show that if I have a particle of rest mass $M$, total energy $E$ colliding with a ...
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Deriving the Lorentz Transformation

I have been trying to understand a more or less geometric derivation of the Lorentz transformation, and I'm getting stuck at one spot. The wikipedia article for the Lorentz transformation for frames ...
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Deformation of light-cone

In the paper The geometry of free fall and light propagation by Ehlers and his colleagues (Gen. Relativ. Gravit. 44 no. 6, pp. 1587–1609 (2012)), when the authors introduce the differentiable ...
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What is the derivation of the speed of light $c$ that is not based on electromagnetism? [duplicate]

The "speed of light" is not just the speed of electromagnetic radiation, but of any massless particle. Therefore must not there be an expression for $c$ that is not in terms of $\mu_0$ and ...
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If you run faster than speed of light what happens with your shadow? [duplicate]

If you are running faster than the speed of light, and behind you have an a object projecting a burst of light what Happens with your shadow? If you are running slower than the light, when the light ...
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Conserved charge from conserved current associated with translational invariance

(c.f Di Francesco, 'Conformal Field Theory' P.45) Di Francesco calls the conserved charge arising from the conserved current associated with a translation invariant theory the 'four momentum'. While ...
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What is the speed of light relative to?

Consider the scenario where you measure the time it takes for light to travel to the left 10 meters and to the right 10 meters. Both measurements will take the same time, even though we are moving ...
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Is it possible to derive Lorentz transformation equation without Einstein's postulates?

Overview Einstein's proof for the Lorentz transformation is given here: From $O$'s view point, $x^2+y^2+z^2 = (ct)^2$. Form $O'$'s view point, $x'^2+y'^2+z'^2 = (ct')^2$. We find that Einstein ...
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a thought experiment in special relativity theory

We have two sets: set No.1 and set No.2 as in this picture: The observer is fixed to set No.1 . He sees set No.1 motionless and observes set No. 2 approaching with velocity 100,000 m/s. Each set ...
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What is $c + (-c)$?

If object A is moving at velocity $v$ (normalized so that $c=1$) relative to a ground observer emits object B at velocity $w$ relative to A, the velocity of B relative to the ground observer is $$ v ...
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If we could reach very high speeds, could we measure the velocity of the Earth this way?

If we could reach (nearly) the speed of light with spaceships, could we measure the velocity of the Earth by launching three perpendicular rockets, accelerating them, and measuring how much fuel ...
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How does velocity cause time dilation?

I've been trying to learn about the speed of light and time dilation, but I'm at an impasse. The presented facts say that if I travel around the solar system at 50% the speed of light and then come ...
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2answers
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Beginner question: timelessness of massless particles [duplicate]

I am not very familiar with the quirkiness of relativity, and I was wondering how to explain this situation. If a beam of light is shining at some object at some distance from the origin of the beam, ...
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1answer
37 views

What is the status of massless photons traveling through a medium?

Photons in vacuum have no proper time, and they are not considered as observers and not as reference frame. But what about photons travelling through matter? Their velocity is lower than light speed, ...
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Relationship between the continuity equation and the wave equation

What exactly is the relationship between the continuity equation and the wave equation? Suppose $J^\mu$ is a contravariant vector that satisfies the continuity equation $\partial_\mu J^\mu=0$. Let ...
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Is everything moving at c in a c unit circle

I was trying to explain special relativity to a few friends in a simple way and wound up with an analogy using a c unit circle. I was using y as travelling in time, x moving in space; move in space ...
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Are gravitomagnetic monopoles hypothesized?

My understanding is that gravitomagnetism is essentially the same relativistic effect as magnetism. If so, why is it that I've heard so much about magnetic monopoles, but never gravitomagnetic ...
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Can Maxwell's equations be derived from Coulomb's Law and Special Relativity?

As an exercise I sat down and derived the magnetic field produced by moving charges for a few contrived situations. I started out with Coulomb's Law and Special Relativity. For example, I derived the ...
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Sub-light speeds and momentum conservation law

Let's imagine a boat on a lake. Observer A is sitting on the shore. Observer B is sitting in the boat on the bow. Observer B has a ball attached to the end of a string which he holds in his hand. ...
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Graphene and relativistic dynamics

Is it possible to rewrite the Lorentz-transformations (for quantum particles) in terms of effective mass m* known from condensed matter physics? "From pencil lead to relativistic quantum physics" "A ...
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Effective field theory for fermion gas

Reading about fermion gas in a paper they used the following Lagrangian, which describes an effective field theory for nonrelativistic fermions (I neglect the four point interaction term). $$ L = ...
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1answer
50 views

The mass of the photon will decrease with reduced velocity?

Since photon has zero rest mass, it will has zero mass when the velocity is zero. We are now being able to slower down the photon in experiment. Is the mass of photon reduced with the decreased ...
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Discrepancy ( or Confusion ) in the mass of photon

$E$ = $mc^2$ And also $E$ = $hf$ (f - frequency) And hence Einstein said $m$ = $hf\over c^2$ And so photons have mass But later he also said $M$ = $M_0\over \sqrt {1-v^2/c^2}$ Where if we put $v ...
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Special relativity: circumventing velocity-addition formula

Two spaceships approach an observer from an equal distance and from an opposite direction with an equal speed $v$ in the observer's intertial reference frame $O$. The speed of a spaceship in the ...
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A question about special relativity theory

We have two sets: set No.1 and set No.2 as in this picture: The observer is fixed to set No.1 . He sees set No.1 motionless and observes set No. 2 approaching with velocity 100,000 m/s. Each set ...
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Confusion about proper time

A spacecraft flies away from earth with a speed of 4.8 million meter per second relative to the earth, and then returns at the same speed. The spacecraft carries a clock that has been synchronised ...
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1answer
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Why magnetic field lines and force are not orthogonal with magnets?

The below explanation why magnetism exists is superb in this video. The explanation about magnets is also great in this video. A magnet has atoms with unpaired electrons forming mini magnets. The ...
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Electron distribution around atom when moving

I do not have much experience on this but if an atom has some electrons around nucleus and the atom itself it is moving at some speed does that affect the distribution of electrons around? I am ...
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What is the difference between the properties of Electron spin and Photon polarization/helicity?

What is the difference between a photon's polarization/helicity and an electrons spin half? I know that the photon is spin 1 but isn't its polarization analogous to spin half? This question stems ...
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$E=mc^2$ resembles kinetic energy formula?

The simplest equation expressing mass–energy equivalence is the famous $E=mc^2$ where $c$ represents the speed of light. Compare this with $E_K = \frac{1}{2}mv^2$. Since $E=mc^2$ can be applied to ...
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Can Minkowski spacetime be redefined as a non-flat riemannian manifold?

Minkowski space time is defined in terms of a flat pseudo-Riemannian manifold. I have wondered if it can be redefined as Riamannian manifold and in the case what type of curvature would there appear. ...
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Maximum speed higher than the speed of light

I wanted to ask if higher speed than the speed of light will be discovered, will scientists be able to adjust the special relativity to the new situation? I read that informations transmitted faster ...
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Why don't we experience dilatations in Minkowski spacetime?

The question This question follows on from the use of projective coords for spacetime in Notation for Translation Group Generators . Under Felix Klein's Erlangen Program, Minkowski spacetime starts ...
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Is relative velocity invariant under special relativity?

If a metre stick passes an observer at speed $v$, would all observers in any inertial frame of reference say the speed of the meter stick relative to the observer is exactly $v$? If so what is it ...
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Considering the theory of special relativity: Is torque still a vector?

Considering the theory of special relativity: Is torque still a vector? In classical mechanics it is easy: You have 3 axes and thus 3 planes. Every plane has its own torque so torque has 3 ...
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Minkowski spacetime: Is there a signature (+,+,+,+)?

In history there was an attempt to reach (+, +, +, +) by replacing "ct" with "ict", still employed today in form of the "Wick rotation". Wick rotation supposes that time is imaginary. I wonder if ...
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Consistency of the Speed of Light [duplicate]

My question is simple and possibly stupid, but I wanted to know hypothetically what would happen if two objects start moving away from each other at half the speed of light (0.5c). Is the observed ...
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Does the the quantum field theoretic process of particle–antiparticle annihilation break the axioms of Special Relativity?

$\textbf{Note that this diagram hasn't anything to do with the question directly.}$ After a particle and its antiparticle annihilate, their energy is converted into a force carrier particle, such ...
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How would an electron bunch/beam look different in the rest and lab frames?

With respect to special relativity, I was wondering how the spatial dimensions would differ between the rest and LAB frame of an electron beam. System: Electron bunch/beam traveling in linear motion. ...
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What do you really see on a line of clocks as you pass by them at high speed?

According to my understanding of SR, if I travel at 0.8c relative to a line of clocks, I should see the clocks in front of me going 3 times faster than my own, and those behind me going 3 times slower ...
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Quantitative relation between two charges moving in parallel in two frames of reference

The relevant question is here. The accepted answer may have explained my question in a descriptive manner. However, I want to see how things are related quantitatively. Imagine we have two charges ...
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Can a relativistic quantum particle be completely confined into a finite hole?

If we write the Klein-Gordon equation in this form \begin{equation*} c^2 \hbar^2 \nabla^2 \Psi = \hbar^2 \ddot{\Psi} + 2i\hbar (U - mc^2) \dot{\Psi} + U (2mc^2 - U) \Psi \end{equation*} we have a ...
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Can the equivalence principle be shown to follow from special relativity?

Einstein showed in various papers that the energy content of a body was a measure of its inertial mass. If you increase the kinetic energy of a system while keeping the center of energy at rest, its ...
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Local EPR-experiments with photons in vacuum?

The principle of non-locality states "that an object is influenced directly only by its immediate surroundings." (Wikipedia) When two entangled particles are measured in an EPR experiment, we ...
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Special relativity paradox and gravitation/acceleration equivalence

One of the features of the black hole complementarity is the following : According to an external observer, the infinite time dilation at the horizon itself makes it appear as if it takes an ...
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Macroscopic Bose condensate in Special Relativity

I remember from an experiment about the Josephson effect the state of each of the super conductors is fully described by a phase factor. From there I assume that is true for any Bose-Einstein ...
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How should two particles accelerate to have their separation Lorentz-contract?

Suppose we have two particles with initial separation of $|x_2^\text{init}-x_1^\text{init}|=d$. At time $t=0$ they start accelerating with proper acceleration of $w$. Then position of the $i$th ...