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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Would time freeze if you could travel at the speed of light?

I read with interest about Einstein's Theory of Relativity and his proposition about the speed of light being the universal speed limit. So, if I were to travel in a spacecraft at (practically) the ...
4
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1answer
574 views

Light-cone coordinates

The light-cone coordinates are defined as $$x^{\pm} ~=~\frac{x^0 \pm x^3}{\sqrt{2}}.$$ Then in the light cone coordinates the position 4-vector becomes: $(x^+, x^-, x^1, x^2)$ . Zwiebach, in his A ...
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2answers
224 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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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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1answer
213 views

Fate of largest scale structures?

In $\Lambda\mathrm{CDM}$, structures form "bottom up" with larger structures forming later. Structures are generally speaking supported by the velocity dispersion of their constituent objects (e.g. ...
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1answer
60 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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1answer
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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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5answers
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High speed and low speed photons

Looking at the discovery of the neutron, and I came across this page: http://www-outreach.phy.cam.ac.uk/camphy/neutron/neutron3_1.htm The animation on the left, talks about low energy photons and ...
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1answer
40 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 , ...
3
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1answer
71 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
35 views

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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2answers
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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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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 ...
0
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1answer
41 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
27 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 ...
2
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0answers
44 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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0answers
38 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
109 views

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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0answers
25 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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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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2answers
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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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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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2answers
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Where does the Lorentz boost for a Dirac spinor come from?

I have read, that if you have a Dirac spinor \begin{equation} \psi = \begin{pmatrix} \phi_R\\ \phi_L \end{pmatrix} \end{equation} that you can apply a Lorentz boost along the $z$-direction with ...
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1answer
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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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1answer
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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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1answer
115 views

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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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 ...
3
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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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2answers
64 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
71 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
41 views

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 ...
9
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2answers
896 views

Do tachyons move faster than light?

I am trying to understand whether or not tachyons travel faster than light. The linked Wikipedia page shows some seemingly contradictory statements, and they are confusing. For instance, the first ...
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2answers
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How do I actually calculate the Lorentz transformation of a field strength tensor

Say now I have an arbitrary field strength tensor $F$, and I want to boost it according to a Lorentz transformation matrix $(\Lambda)$ The transformation is given by $$ F^{'\mu \nu} = ...
7
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3answers
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what is the kinematics of a particle with complex mass?

particles with real-mass have time-like kinematics ($ds^2 > 0$). particles with zero-mass have light-like kinematics ($ds^2 = 0$). particles with imaginary-mass have space-like kinematics ($ds^2 < ...
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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 ...
4
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1answer
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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 ...
6
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3answers
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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 ...
4
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1answer
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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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0answers
35 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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6answers
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Minkowski Metric Signature

When I learned about the Minkowski Space and it's coordinates, it was explained such that the metric turns out to be $$ ds^{2} = -(cdx^{0})^{2} +(dx^{1})^{2} + (dx^{2})^{2} + (dx^{3})^{2} $$ where $ ...
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2answers
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No length contraction in thought experiment with co-moving measuring stick

Suppose a person standing on a platform were to observe and measure the length of a train passing by. Instead of the usual approach involving a clock and knowing the speed of the train, the person ...
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0answers
38 views

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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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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2answers
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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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3answers
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Doppler shift and special relativity

I have been listening to an audio course on Special Relativity. In the course the teacher repeatedly says that the "laws of physics are equally valid for all uniformly moving frames of reference". ...
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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 $E=mc^2$?