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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Need help please [on hold]

An electron's speed is doubled from $0.2~c$ to $0.4~c$. By what ratio does its momentum increase ? What happens to the momentum ratio when the electron's speed is doubled again from $0.4~c$ to $0.8~c$ ...
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119 views

Plane curve transform to moving inertial system coordinates

As a non-phycisist I hope my question makes sense and is understandable. It deals with special relativity. I suppose there is a e.g. plane curve ( e.g. a circle ) given in the x-y plane of of an ...
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4answers
69 views

Can a photon have little to no energy and/or speed?

Can a photon move more slowly than the speed of light and behave 'non-relativistically,' so to speak. Perhaps another way to express my thought is: could we stop a photon from moving?
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602 views

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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1answer
51 views

Hafele-Keating revisited with a gravity clock

Most modern clocks use electromagnetic phenomena to measure time. There are perhaps some older clocks that involve gravity to some degree (hour glass, pendulum), but I believe they still have a ...
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I know light's speed in vacuum is constant, but what about its velocity?

Is the velocity of light in vacuum constant? It seems it would be different depending on whether it is coming toward you or away from you, but I just want to make sure. Does the direction of light ...
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Lorentz Invariant Integration Measure [closed]

When we canonically quantize the scalar field in QFT, we use a Lorentz invariant integration measure given by $$\widetilde{dk} \equiv \frac{d^3k}{(2\pi)^3 2\omega(\textbf{k})}.$$ How can I show that ...
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Proving the Lorentz invariance of the Lorentz invariant phase space element

I have been looking around for a satisfactory answer to prove that $$\frac{d^3\vec{p}}{2E_{\vec{p}}}$$ where $E_{\vec{p}}=+\sqrt{(|\vec{p}|c)^2+(mc^2)^2}$, is Lorentz invariant. The standard answer ...
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What can change a photon's frequency?

I found this question: Is it possible to apply force to a light particle? As it states, gravity can change the frequency of light by changing its momentum. My question regards other phenomena that ...
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1answer
49 views

Polarization vector identity in Minkowski space?

Playing around with numerical light-like momenta $p^\mu_1,p^\mu_2$ (light-like meaning ${p_1}^\mu {p_1}_\mu={p_2}^\mu {p_2}_\mu=0$) and corresponding polarization vectors ...
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How to prove $\frac{\mathrm{d}^3\vec{p}}{E}$ is Lorentz invariant? [duplicate]

To prove $\frac{\mathrm{d}^3\vec{p}}{E}$ is Lorentz invariant is to prove $$\frac{\mathrm{d}^3\vec{p}}{E} = \frac{\mathrm{d}^3\vec{p}'}{E'} \qquad(\mathrm{d}^3\vec{p} := \mathrm{d}p_x \mathrm{d}p_y ...
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61 views

Electric field energy of two parallel moving charges at relativity speeds

Assume two particles of the same charge $q$ moving in parallel trajectories on the x,y plane. The distance between them is $d$ and it's defined in the y axon. The problem is to calculate the energy of ...
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59 views

Analytical mechanics with SR

Is there an analytical mechanics with SR? Of course you can write down the Lagrangian and Hamiltonian of a free particle. What about non-free? Are there any problems? To be specific: what would the ...
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3answers
731 views

How is quantum mechanics compatible with the speed of light limit?

Consider a free electron in space. Let us suppose we measure its position to be at point A with a high degree of accuracy at time 0. If I recall my QM correctly, as time passes the wave function ...
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Can we find actual rest mass of things on Earth

Earth moves around the Sun and the Sun moves around the galaxy and the galaxy moves with unknown speed and direction. We have speed so the mass of us all altered. Can we know the real rest mass? If ...
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2answers
141 views

How do I transform onto a relativistic rotating frame of reference?

In classical mechanics, the usual formula to translate the evolution of a quantity as seen from an inertial frame of reference to a rotational frame is: $$\frac{d \textbf{A} }{dt} \vert_{Inertial} = ...
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1answer
52 views

Proof of conservation of energy with the relativistic definition of force

Professor Susskind proved conservation of energy in one of his lectures by taking the classical definition of force ($F = ma$) and by showing that its time derivative is zero. How can we do that with ...
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1answer
333 views

Theoretically if you passed the speed of light in a medium, would there be a sonic boom equivalent?

I know that it is technically impossible to reach the speed of light in vacuum since the mass of the object traveling would reach infinity. However in a medium, would there be some sort of theoretical ...
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30 views

Entanglement and Special Relativity [on hold]

There are 2 particles entangled and move far apart to 2 measuring devices . The first measurement of either particle will collapse the wave function and set spin up and spin down on the particles. 2 ...
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1answer
48 views

Derivation of magnetic force for a charge in motion relative to a wire (M. Purcell's Electricity and Magnetism)

I have a question regarding the derivation of magnetic force in M. Purcell and David Morin's Electricity and Magnetism. In the first part, they derived the force first by assuming that a charge q is ...
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3answers
110 views

Why does a violation of locality not imply a violation of relativity?

This question is closely related to: What counts as information? Taking the specific example, again, of the EPR experiment. I think everyone agrees on the following: The act of measuring the ...
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4answers
158 views

Why is the momentum of a particle $\gamma mv$?

I am very new to relativity, and as I was going through Resnick & Halliday, I saw that momentum was no longer $mv$, rather $\gamma mv$. This was the proof: $$p = mv = m \frac{\delta x}{\delta ...
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Trying to derive compton scattering using 4-vectors [closed]

I'm trying to derive the energy of a photon after compton scattering: $$ E_\gamma' = \frac{E_\gamma}{1 + \frac{E_\gamma}{m_ec^2} (1-\cos \theta)}$$ where $E_\gamma'$ is the photon energy after ...
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Motion decomposition (Relativistic case)

When an electron moves at very close at $c$ (speed of light), is it physical to decompose the motion in two other directions (like what we do in classical case). If so, the motion in each direction ...
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Determining the range of values for separation angle (Landau problem)

I encountered a problem while reading the following exercise from the second Landau & Lifshitz volume: Determine the range value in the $L$-system for the angle between the two decay particles ...
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2answers
54 views

Can a spaceship increase velocity “infinitly” [duplicate]

This keeps me awake at night, and i can't seem to find the solution. Introduction: Suppose an observer is currently at rest, and a space ship accelerates close to the speed of light (current velocity ...
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36 views

Don't photons pass photons move away at speeds faster than light? [duplicate]

I understand there is a longstanding rule that nothing travels faster than the speed of light... but if you had two flashlight aimed at each other and turned them on inside a vacuum the photons from ...
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1answer
61 views

Calculate Time travel with Time Dilation [closed]

Does the following hold: If we have: person A moving at a speed of $0$; person B moving at a speed of $xC$ (where $C$ is speed of light, $x$ a fraction) And if time passes for $m$ ...
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Differentiating relativistic charge with respect to velocity [closed]

Given that $$Q' = \int d^{3}x \bigg[ \rho \big( \frac{vx}{c^{2}},x,y,z \big) - \frac{v}{c^{2}} j^{x} \big( \frac{vx}{c^{2}},x,y,z \big) \bigg],$$ I am trying to prove to myself that: $$\frac{dQ'}{dv} ...
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86 views

Since the Earth is moving through space, do we experience time dilation?

What I mean is, the Earth orbits around the sun at around 30km/s, while I understand that this isn't a very high velocity does time dilation still occur to say a person who is completely stationary in ...
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Travelling faster than the speed of light

Let's say I fire a bus through space at (almost) the speed of light. If I'm inside the bus (sitting on the back seat) and I run up the aisle of the bus will I in fact be traveling faster than the ...
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500 views

Exact definition of momentarily comoving reference frame (MCRF)

Consider a particle $P$ in the framework of special relativity with position $r(t)=(ct,x(t),y(t),z(t))$ respect to an inertial reference frame $\Sigma=(ct,x,y,z;O)$. I need to know if the following ...
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3answers
135 views

How is it possible for the wavelength of light to change in a medium?

So my physics class has just finished a long unit on optics while at the same time I've been trying to teach myself relativity. I admit my understanding is probably rudimentary, but I figured all the ...
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102 views

Paradox - Laws of physics are the same in all inertial reference frames vs Equivalence Principle (Pictures Added)

According to the equivalence principle, no experiment should exist that one can perform to determine whether one is in an accelerating elevator, or in a gravitational field. I will outline two ...
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427 views

How much fuel is required for star travel considering relativistic time dilation?

John Rennie's Q&A How long would it take me to travel to a distant star? discusses about interstellar travel taking into consideration. There was a case that discussed about constant ...
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Ηow does a current density becomes a charge density?

The transformations in special relativity of current and charge density fields are given as follows: $\bar J' = \begin{matrix} \gamma(J_x - Vρ) \\ J_y \\ J_z \end{matrix}$ $ρ' =\gamma (ρ - {V J_x ...
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Galilean relativity & the road to special relativity

Firstly, I just want to make sure that I've understood the notions of relative and absolute quantities correctly. Elementary analysis shows that position and velocity are relative quantities. Indeed, ...
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Is the fourth dimension of Minkowski Spacetime viewed as an axis? [duplicate]

In the three axes of space, I can move in a positive or negative fashion, up or down, side to side, etc. Why is this not the same for the axis of time, if it is an axis? If it's not an axis, what is ...
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1answer
120 views

Vector representations of Lorentz transformation in terms of $E$ and $p$

Hello everybody the things I understand are the transformation properties of a four vector given as $\tag{1} p^\mu = \Lambda^\mu_{\,\,\nu} p^\nu.$ and an arbitrarily boosted transformation is of the ...
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2answers
156 views

Explain the notion of light/electromagnetic waves/photons to a non-physicist

A non-physicist asked me about special relativity. My explanations naturally were based on gedankenexperiments involving light. This forced the question: "What is light? It is particles, isn't? Or is ...
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44 views

Which is the corrispondent of the Lorentz's transformation in general relativity?

The Lorentz's transformations tell us how space and time change in a flat case? There are a more general and powerfull transformation for general relativity?
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Special Relativistic approximation to GR

Some time ago I was talking to a professor in college about some of the fundamental aspects and origin of General Relativity. I was surprised to learn, in fact, that a pretty good approximation to GR ...
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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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1answer
81 views

Does the Unruh effect really describe a thermal bath?

If we consider a free (massless scalar) field $\phi$ in Minkowski space and look at it in Rindler coordinates (which correspond to what an accelerated observer sees), we find that the action of the ...
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Is distance always 0 relative to an object moving at speed of light $c$?

As I understand it, when an object is traveling at the speed of light, relative to itself all travel is instantaneous and the distance is zero. If a photon traveling from the sun was aligned with the ...
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The speed of light/EM waves in vacuum; as if there was another one in non-vacuum?

Q1: is there a speed of a photon other than in "vacuum"? Q2: isn't "speed of light in vacuum" misleading? If I understand, that light moves with speed of light until there is "something in between" ...
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66 views

The invariance vs constancy of the speed of light in vacuum

This is perhaps as much a question of semantics as of physics but it is something I have been thinking about recently and was wondering if anyone else had a perspective on this. Now, it could be that ...
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4answers
78 views

Photon Emission/Absorbsion from the Photons Perspective [duplicate]

First some assumptions. 1) Photons travel at the speed of light. 2) From the photon's reference spacetime is contracted to 0 length in the direction of photon travel. 3) From the photon's reference ...
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2answers
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Clarification on meaning of scalar in math and scalar in physics

When a mathematician says something is a scalar, say on the plane, they mean that it associates to points on the plane real numbers. When a physicist says something is a scalar, they mean that if we ...
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What would've happened if we wormhole Titan to orbit between Jupiter and Mars? [migrated]

Lets assume we humankind can not only wormhole the spacecraft, but planets and moons. So, what would've happened to Earth if we pulled Aurora to be Mars's third moon? What if we moved Titan in between ...