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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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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444 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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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 ...
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83 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
92 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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94 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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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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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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239 views

Why is the metric tensor symmetric? [duplicate]

I was reading Schutz, A First Course in General Relativity. On page 9, he argued that the metric tensor is symmetric: $$ ds^2~=~\sum_{\alpha,\beta}\eta_{\alpha\beta} ~dx^{\alpha}~dx^{\beta} $$ ...
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65 views

Invariance in Euclidean and Minkowski spaces

Consider Wick's rotation from Minkowski to Euclidean space in QFT. What is the connection between O(4) invariance in Euclidean space and Lorentz invariance in Minkowski space? If we define a quantity ...
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119 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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On the no-faster-than-light in special relativity

In the special relativity it is well established that, in the vacuum no one can ever travel faster than light, due to the relativistic velocity addition formula. Recently I saw some silly statement ...
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1answer
46 views

The norm of the vector sum of two 4-momentum vectors before and after pair production

Two photons traveling along the x-axis (in a lab frame of reference) of different frequencies are about to collide. Their 4-momentum vectors are (h$\nu_1$/c , h$\nu_1$/c , 0, 0) and (h$\nu_2$/c , ...
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Parameterisation of the equation of motion for a relativistic massive point particle

The equation of motion for a relativistic massive point particle is given by: $$\frac{dp_{\mu}}{d \tau} = 0,$$ where $p_{\mu}$ is the four-momentum defined by $p_{\mu} = m \frac{dx_{\mu}}{ds/c}$, ...
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1answer
76 views

Are moving objects producing stronger gravity fields? [duplicate]

If the strength of gravitational influence exerted by a body is derived from its mass and energy then is it true that a moving object which has some kinetic energy should also produce stronger ...
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2answers
110 views

What experience tells us that gravitational acceleration cannot vanish everywhere?

In attempt to describe the consequences of the Equivalence Principle: When there are gravitational accelerations present, as for example in the gravitational field of the earth, the space cannot be ...
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45 views

Would magnetic charge (i.e., magnetic monopoles) be Lorentz invariant if it existed?

Would magnetic charge (i.e., magnetic monopoles) be Lorentz invariant if it existed? It is clear that Maxwell's equations in themselves permit magnetic charges but what would their relativistic ...
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44 views

Does an electron beam always repel electrons outside the beam?

Having read that question: Magnetic force as a relativistic effect? And quoting from the answer: http://physics.stackexchange.com/a/143901/7743 If you want to analyze things in the electrons' ...
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1answer
33 views

Relativistic conical pendulum [closed]

I came across this problem while going through old exams of my Physics department: A pendulum with mass $m$ is swinging on the $xy$ plane at high velocity $v = 10^7\ ms^{-1}$, performing a ...
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Is the Einstein Energy-Momentum equation $E^2 = p^2c^2 + m_0^2c^4$ valid only for Free Particles?

Is the energy -momentum relation $$E^2 = p^2c^2 + m_0^2c^4$$ satisfied only by free particles or even bound particles? Does the Energy refer to total Energy(including potential) or only (kinetic ...
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Reference Needed: Time Dilation for Muons Reaching Earth's Surface

On the Hyperphysics Site we have the following page: Hyperphysics, "Muon Experiment", http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/muon.html which makes the following statement as its first ...
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40 views

Calculating time dilation

I'm writing a science fiction story where the protagonist's experience requires long intervals between events. My plan is to put him/her/it on a spaceship between events at an appreciable percentage ...
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Total cross section of particle decay

Suppose a particle A travelling along the $z$-axis and decays into particles B and C. The cross section is given by $$\frac{d\sigma}{d\cos\theta^*} = k(1+\cos\theta^*)^2$$ where $k$ is a constant ...
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154 views

Tricks for evaluating tensor contractions with Levi-Civita symbol

I am trying to evaluate the Lorentz invariant $\epsilon^{\alpha\beta\gamma\delta}F_{\alpha\beta}F_{\gamma\delta}$, where $F_{\mu\nu}$ is the electromagnetic field tensor, $$ F_{\mu\nu} = ...
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Conserved charge for boosts? [duplicate]

In (3+1) dimension Poincare group has three types of Symmetries : a) Four space-time translations b) Three spatial rotations and c) Three boosts Among them, (a) implies "conservation of ...
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Taking a 'relative' limit

I am looking at Hamiltonians for specific physical situations. I have taken a given Hamiltonian $\vec{H}(\vec{p}, \vec{x})$ and have found the following Hamiltonian equations: $$\frac{d\vec{x}}{dt} = ...
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Does reversal of one spatial direction count as a discrete Lorentz transformation?

A transformation $\Lambda$ is a Lorentz transformation if it satisfies $\Lambda^T g \Lambda = g$, for the flat metric $g = \left( \begin{array}{cccc} 1 &&& \\ & -1 &&& \\ ...
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55 views

Is gravitation time dilation simply c/v?

Recently, I've been very interested in forms of time dilation. I'm relatively new to relativity, so I apologize for any stupid mistake I may make. I was messing with the equation for gravitational ...
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Why the speed of light in vacuum is same in all inertial reference frames? [duplicate]

If Cathy’s velocity toward Bill and away from Amy is v = 0.9c, Cathy finds, by making measurements in her reference frame, that the light from Bill approaches her at speed c, not at c + v = 1.9c. ...
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1answer
56 views

Derivation of length contraction from lorentz transforms

i have struggled to understand how length contraction is derived. My lecture book says: length in frame S is defined as $L=x(b)-x(a)$ and in S' as: $L'=x'(b)-x'(a)$ transforming $x'(b)$ and $x'(a)$ ...
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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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Why $c$ is $3$ x $10^8$ times faster than a $1$ $m/sec$ car? [duplicate]

The value of of a dimensional constant like $c$ is often regarded as unimportant since it can be arbitrarily changed to any desired value by changing our units. For example, $c$=$3$x$10^8$ in $m/sec$, ...
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Does it make sense to model the Universe from an outside perspective? [closed]

I was reading some questions and answers about black holes and whether matter can actually pass through the apparent horizon, in particular this one: How can anything ever fall into a black hole as ...
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1answer
60 views

Order of index in Lorentz transform

I am reading Schwartz's "QFT and the standard model". On pg 13 he gives the Lorentz transform of a rotation around the x-axis: $ \left( \begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 ...
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Does special relativity happen in reverse when you freeze?

As you travel faster and faster you experience time at a slower rate, so if you travel slower and slower you should experience it at a faster rate right? My thinking is that even if you are ...
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1answer
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How fast do you have to be traveling in order to travel one light year in one year due to relativistic effects?

My apologies if my understanding is incorrect, but I believe that as you approach relativistic speeds you experience time dilation as compared to an outside observer. So taking into account this ...
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1answer
74 views

Do particles have spin because there exist spinor representations for the Lorentz group?

I am reading Peskin and Schroeder's An introduction to field theory. They first describe the spinor representation of the Lorentz group, and then they mention the fact that different particles have ...
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3answers
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Is simultaneity in SR only a pedagogical tool?

In a very recent post here I recently learned that simultaneity has no meaning in general relativity; I can accept the answer and explanation that was given for that question. But then Harry Johnston ...
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1answer
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How to combine Lorentz factors when boosting twice?

The problem came up when I was trying to solve the classical problem of a wire with current due to which a charged particle experiences a force. This force should depend only on the lorentz factor ...
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1answer
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Multiparticle Mandlestam Variables Extension

So in 4D we have three Mandlestam variables for a 4-particle scattering process. This corresponds to $p_i^\mu$ giving us 16 degrees of freedom. Momentum conservation reduces this by 4, and we have 4 ...
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2answers
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How to determine which object is moving relativistically?

Apologies in advance if I've overlooked some obvious point. In relativity, I know that there is no way to know if Object A or Object B is moving relative to the other. Each would see themselves as ...
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1answer
146 views

Are we traveling through time at the speed of light? [duplicate]

In the image below the y axis represents time and x represent velocity. Point D represents velocity c, point E represents 1 second per stationary observers second. What this chart is showing is as you ...
4
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1answer
77 views

Invariant equations of motion under Lorentz transformations

My question regards the statement that an equation of motion may be invariant under a Lorentz transformation I just finished watching the Stanford University special relativity lectures on special ...
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36 views

Electron's Frame Aharonov-Bohm Effect

In the electron's inertial frame the solenoid moves past it in the Aharonov-Bohm Effect. That means the electron sees a time varying vector potential which, by: $\vec{E}$ = ...
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Relativistically what is the difference between internal and rest mass energy of a body?

Relativistically what is the difference between internal energy and rest mass energy of a body? Could you please explain both philosphically and mathematically?
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Stopping a Body (travelling at the speed of light) [closed]

While, I read that if a body accelerates to the speed of light would have an infinite mass and therefore, infinite energy would be required to maintain the speed. A question popped up in my mind: ...
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1answer
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Is there a name for the linear quantity corresponding to the (quadratic) “interval $\Delta s^2$”?

Recently it has been affirmed here (again) that the quantity called "interval (also 'spacetime interval' or 'invariant interval')" is referring to two (in general distinct) events as arguments, such ...
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Do photons have/contribute to mass?

Do electrons gain mass by absorbing photons during excitation and releasing them by returning to the ground state? Do photons have mass in the form of energy by $E=mc^2$?