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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Light travels in a medium

According to Snell's law : $${n_1 \over n_2} = {v_2 \over v_1}$$ $v_2 = v_1 n_1 / n_2$ Assuming that $n_1$ is vacuum , we will find the following equation: $$v = c / n$$ (We may find the same ...
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Do you encounter more photons (per unit time) when moving forwards at a constant velocity?

Let's say you have rain hitting you evenly on all sides (not very realistic, I know). If you were to move forwards at a constant speed, there would be more droplets of rain hitting you per second on ...
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Is the energy per degree of freedom $\frac{1}{2}kT$ in relativistic systems?

The equipartition theorem says that the mean energy per degree of freedom is $\frac{1}{2} kT$. Is this result relativistically correct?
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How does the idea of a scalar potential for a 3-vector field generalize to Minkowski space?

How does the idea of a scalar potential for a 3-vector field generalize to Minkowski space? As I guess, I thought one way would be to generalize 3-force to 4-force and replace the 3-gradient with the ...
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Which one to learn first: Special or general relativity? [closed]

I am extremely interested in self-learning Einstein's theory of relativity, but I don't know where to start. Can I make general relativity my starting point, and later look at special relativity as ...
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how to prove that two angles made by unprimed axes are same in minkowski diagram

I am reading special theory of relativity by resnick.In supplemntory topic A it is given that two inertial reference frame s and s' where s' is moving relative to s with uniform velocity.The diagram ...
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Using relative velocity between two frames and the time elapsed between events in one frame to find the time elapsed/event separation in the other [closed]

Q from text: A second transporternaut is beamed to a much more remote galaxy that is moving away form Earth at .87c. This time, too, she stays in the remote galaxy for one year as measured by clocks ...
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Universe without a fixed universal speed limit

What would a universe without a fixed universal speed limit (like $c$ in the actual universe) look like? Would it be paradoxical? Would time travel into the past become possible?
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Special relativity: where does this naive calculation go wrong?

Inspired by the recent question, "If all motion is relative, how does light have a finite speed?", I tried to work out a little calculation. Where does it go wrong? My friend Buzz is traveling in a ...
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Relative Velocity Problem: Light? [duplicate]

Assume 2 rockets coming towards each other at each other at 99% of speed of light, and so as they pass each other the relative velocity between 2 rockets would be 198% of Speed of Light and so what ...
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108 views

Twin paradox caused by gravitational difference in space

I am not a physicist, but have always been curious about the twin paradox. So, here is my question. There are two twins in space - Twin A and Twin B (both stationary). They are apart from each other ...
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Difference between locality and causality?

I ask this question as the two seem to be very closely related and are sometimes taken to be one and the same (in the notion of microcausality in QFT), which has left me confused as to what meaning of ...
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How do I sum up speed though space and time to obtain c (in terms of units)?

I'm still learning SR and only recently I could scratch the surface of such beautiful, complex and deep topic. This post here was really enlightening, and even though it is somewhat basic, it helped ...
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Sum according to a function - composition of velocities

An observation more than a question. Take any function $f$ (additional hypotheses may follow) and evaluate it on any two points $x_1, x_2\in\mathcal{D}_f$. Define then the sum of these two points as ...
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Vector product in a 4-dimensional Minkowski spacetime

I'm studying relativity and I lost track of interpretation along the mathematical formalism. What does vector product mean as an event? I mean, how must one interpret the result of the vector product ...
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231 views

Why do we consider Lagrangian densities in QFT?

My question is: Why do we consider Lagrangian densities in QFT (as opposed to Lagrangians as in classical mechanics)? Is it simply because of the following? We wish the theories to be Lorentz ...
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Exact meaning of locality and its implications on the formulation of a QFT

As far as I understand it, locality in physics is the statement that interactions can only occur between physical objects if the spacetime interval separating them is null or time-like. Thus, if the ...
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If all motion is relative, how does light have a finite speed?

I've often heard that Einstein shattered the notion of absolute motion (i.e. all things move relative to one another) and that he established the speed of light as being absolute. That sounds ...
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Commutation relations in QFT and the principle of locality

My question is, given two space-time points $x^{\mu}$ and $y^{\mu}$, if the events that occur at these points are simultaneous, i.e. $x^{0}=y^{0}$, are the two events necessarily space-like separated? ...
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The relation between mass and speed

Massless particles (or luxons) have no (rest) mass ($m = 0$) and a speed equal to the speed of light ($v = c$). Massive particles (or bradyons) have mass ($m > 0$) and a speed lower than the speed ...
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Simple Harmonic Motion in Special Relativity

I was trying to see what results I would get if I were to incorporate relativistic corrections into the case of a harmonic oscillator in one dimension. I thought that if the maximum velocity of the ...
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Is it possible for the light (photons) to turns into normal electromagnetic signal?

I want a theoretical opinion about this question: The relativistic Doppler Shift equation for the light is $$\frac{f_s}{f_o}=\sqrt{\frac{1+\beta}{1-\beta}}$$ where $\beta=v/c$ is the velocity of the ...
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On the Lorentz Group representation [closed]

I am going through the notes on QFT by Srednicki (which is certainly a worth reading on the subject, and can be found online, see http://web.physics.ucsb.edu/~mark/qft.html). When describing ...
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Is it true that whenever any non rigid body moves, there must be a delay between the ends? [duplicate]

Very sorry if this is still considered a duplicate to this, but unfortunately the answer to this question cannot address this because mine is a nonrigid body and involve biological locomotion concepts ...
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Two apparent contradictions in SR involving time dilation and length contraction

So I've encountered the site "Alternative Physics" – a website proposing "alternative" theories to theories in modern physics. Of course, the site claims that both SR and GR are wrong. To show "why" ...
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Question on time dilation [duplicate]

When i studied physics we had this example where someone climbes into a rocked flyes into space comes back the time that passes for him one year time on earth 86 years. I think most know what thinking ...
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Is this an inertial frame of reference in relativistic context?

What I've learned from our special relativity lectures is that an inertial frame of reference in relativity is one that experiences no gravitational forces. Also, it is a frame where if a particle is ...
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Lorentz transformation of Gamma matrices $\gamma^{\mu}$

From my understanding, gamma matrices transforms under Lorentz transformation $\Lambda$ as \begin{equation} \gamma^{\mu} \rightarrow S[\Lambda]\gamma^{\mu}S[\Lambda]^{-1} = ...
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Energy and momentum of a relativistic electron

The question is to find the magnitude, $p$ of the electron's momentum in the unit of MeV/$c$, given that the kinetic energy of the electron is 2.53 MeV. The answer provided by the book says, ...
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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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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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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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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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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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Entanglement and Special Relativity [closed]

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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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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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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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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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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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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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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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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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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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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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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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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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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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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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 ...