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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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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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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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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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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118 views

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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2answers
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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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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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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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79 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
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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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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 ...
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1answer
567 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
222 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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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
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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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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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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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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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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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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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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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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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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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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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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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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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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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3answers
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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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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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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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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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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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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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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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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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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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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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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 ...