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 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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1answer
52 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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104 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
93 views

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
36 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
66 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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81 views

What experience tells us that gravitational acceleration cannot vanish everywhere?

In attempt to describe the consequences of the Equivalence Principle, Papapetrou in his book, said: When there are gravitational accelerations present, as for example in the gravitational field of ...
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0answers
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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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1answer
40 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
23 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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2answers
114 views

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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Relativity Mass [duplicate]

How does mass increase as velocity approaches the speed of light? Why does the (relativistic) mass of an object increase when its speed approaches that of light?
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0answers
43 views

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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1answer
37 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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37 views

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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3answers
116 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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0answers
24 views

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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31 views

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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1answer
52 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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4answers
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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
48 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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3answers
113 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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1answer
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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
59 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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2answers
60 views

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
63 views

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
66 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
36 views

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
134 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
63 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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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
49 views

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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2answers
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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 $E=mc^2$?
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1answer
39 views

Time dilation: reference frame [closed]

So I'm calculating how long it will take for half of some muons to decay for in a stationary observers frame of reference. They have a half life of 2.2 * 10^-6 and are moving at a speed of .98c ...
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2answers
108 views

Speed of light paradox [duplicate]

If I send two rockets from the Earth in opposite directions, at, say, 60% of the speed of light relative to the Earth, then relative to each other they are travelling at 120% of the speed of light. ...
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Why wouldn't any Emission Theory work?

http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/origins_pathway/#Emission Here, at the Emission theories of light, I loved the discussed theory. There seems to be a contradiction right ...
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1answer
43 views

Absoluteness of Simultaneity

I think this is a very important question because if simultaneity is absolute, then it shakes the foundation of relativity. But it was asked here a month ago, and no one answered it. Neither does ...
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1answer
67 views

Question about scalar product of 2 four-vectors [closed]

I'm looking for help to prove that $\mathbf{a\cdot b}=-ab\ cosh \ \theta$, where: $a=\sqrt{\mathbf{-a\cdot a}}$, $b=\sqrt{\mathbf{-b\cdot b}}$, and $cosh \ \theta$ is $\gamma$, for a Lorentz ...
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Klein paradox in graphene

When considering the Klein paradox in graphene Katsnelson, Novoselov and Geim introduce a potential barrier (see http://www.nature.com/nphys/journal/v2/n9/full/nphys384.html). But I cannot understand ...
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1answer
62 views

If time-like paths are geodesics, what physical principle applies to space-like intervals?

If I have a number of particles interacting with one another locally, then the center of mass of the system moves along a geodesic. Taking this further with the particles interacting via an EM field, ...
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Causality and how it fits in with relativity

I was talking to my teacher the other day about Einstein's spacetime and there's one thing he couldn't explain about the nature of Cause. I may be being stupid or just unable to comprehend, thanks for ...
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1answer
83 views

Problem understanding Lorentz invariance [duplicate]

So they usually started with "...This is obviously Lorentz invariant, because of the 4-vector character of the quantity,..., (and after a two page long derivation) another quantity is also obviously ...