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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Whether $m$ in $E=mc^{2}$ and $F=ma$ are both relativistic mass?

I know that $m$ in $E=mc^{2}$ is the relativistic mass, but can $m$ in $F=ma$ can also be relativistic? If the answer is yes, then can you tell me whether this equation is valid $E=\frac{F}{a}c^{2}$? ...
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Maxwell's Equations using Differential Forms

Maxwell's Equations written with usual vector calculus are $$\nabla \cdot E=\rho/\epsilon_0 \qquad \nabla \cdot B=0$$ $$\nabla\times E=-\dfrac{\partial B}{\partial t} \qquad\nabla\times ...
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“Relativistic Baseball”

On Randall Munroe’s new blog “what if”, he answers the question: “What would happen if you tried to hit a baseball pitched at 90% the speed of light?” http://what-if.xkcd.com/1/ He concludes: ...
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Special relativity and electromagnets

This Veritasium video explains how electromagnets can be explained by special relativity, and how the magnetic field surrounding a current-carrying wire can also be viewed as an electric field, if ...
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Is the commutation of all possible operators sufficient to identify a spacelike interval?

It has been claimed (e.g. here) and apparently already been established, that the interval $x - y$ being (called) "spacelike" implies that $\bigl[\hat O (x),\, \hat O' (y)\bigr]=0$ for any two (not ...
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current in wire + special relativity = magnetism

Current in wire + moving charge next to wire creates magnetic force in the stationary reference frame OR electric force in the moving reference frame from special relativity due to change in charge ...
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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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Relativistic centripetal force

The thought randomly occurred to me that a circular particle accelerator would have to exert a lot of force in order to maintain the curvature of the trajectory. Many accelerators move particles at ...
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Is there a rest frame for the Higgs boson?

If there is a non-zero expectation value for the Higgs boson even in "vacuum", since the Higgs boson has a mass unlike photons, then I would expect it to have a rest frame. So why doesn't a non-zero ...
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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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Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation?

In Physical Review Letters, there was a paper recently published: Masud Mansuripur, Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation, Phys. ...
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Can a black hole form due to Lorentz contraction? [duplicate]

Possible Duplicate: If a 1kg mass was accelerated close to the speed of light would it turn into a black hole? Imagine, a rod of length L is moving with velocity approaching the speed of ...
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How do we measure the range of distant objects despite relativistic effects?

When we observe astronomical objects like distant galaxies there are several complicating factors for estimating the distance: Relativistic speed result in length contraction Relativistic speed ...
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Is “Causality” the equivalent of a claim that the future is predictable based on the present and the past?

In classical (Newtonian) mechanics, every observer had the same past and the same future and if you had perfect knowledge about the current state of all particles in the universe, you could ...
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What's wrong with this QFT thought experiment?

In quantum field theory, the propagator $D(x-y)$ doesn't vanish for space-like separation. In Zee's book, he claims that this means a particle can leak out of the light-cone. Feynman also gives this ...
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Relativistic center of mass

Recently I realized the concept of center of mass makes sense in special relativity. Maybe it's explained in the textbooks, but I missed it. However, there's a puzzle regarding the zero mass case ...
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Why do we identify symmetric 2nd rank tensors with spin-2 particles in string theory?

I am going through Tong's lecture notes on String Theory and came across the following irrep decomposition (Chap 2, p.43) of the bosonic string first excited states: $$\text{traceless symmetric} ...
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Is proper time a vector?

Proper time is identical with the spacetime interval of a timelike movement. A spacetime interval is the dot product of two vectors and thus a scalar. Proper time however is always pointing exactly ...
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What's the difference between space and time?

I'm having a hard time understanding how changing space means changing time. In books I've read people are saying "space and time" or "space-time" but never explain what the difference is between the ...
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Time Dilation - How does it know which Frame of Reference to age slower?

Okay, I'm asking a question similar to this one here: Time Dilation - what happens when you bring the observers back together?. Specifically, I am curious about a specific angle on the second part of ...
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Can one create mass from energy?

Due to $ E =m c^2 $, one can convert mass to energy. A classic example would be matter/anti-matter annihilation to produce energy (photons, etc.). Can one do the reverse? So could one do something to ...
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Are Classical Field Theory and Quantum Mechanics of a single particle (nonrelativistic or “classical”) limits of Quantum Field Theory?

Recently I talked about QFT with another physicist and mentioned that the Quantum Field Theory of a fermion is a quantisation of its one-particle quantum mechanical theory. He denied this and ...
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How to prove that proper orthochronous Lorentz transformations form a group?

Proper orthochronous Loentz transform are Lorentz transforms that satisfy the conditions (sign convention of Minkowskian metric $+---$) $$\det \Lambda=+1, \qquad \Lambda^0{}_0 \geq +1.$$ How to prove ...
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If a neutrino has a rest frame, why can't a photon have a rest frame as well?

Concerning Rest Frame Wikipedia states: For example, in the rest frame of a neutrino particle travelling from the Crab Nebula supernova to Earth the supernova occurred in the 11th Century AD ...
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How does wind speed affect the velocity of light?

As you know, there is a maximum speed things can go called $c$, the "speed of light." Light in a vacuum goes $c$. Light in the atmosphere, however, goes a little less than $c$. My question is: what ...
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How do I develop an intuitive model of spacetime?

I am your nightmare poster - a layman trying to learn special relativity. (I'm also a refugee from stackoverflow.com: trust me, it's only going to get worse). Apologies in advance if my question is ...
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Why is pseudorapidity defined as $-\log \tan \theta/2$

Why the log? Is it there to make the growth of the function slower? As this is a common experimental observable, it doesn't seem reasonable to take the range from $[0,\infty)$ to $(-\infty,\infty)$ ...
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Boosts are non-unitary!

The boost transformations are not unitary unlike rotations, the boost generators are not Hermitian. When this induces transformations in the Hilbert space, will those transformation be unitary? I ...
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Is acceleration relative?

A while back in my Dynamics & Relativity lectures my lecturer mentioned that an object need not be accelerating relative to anything - he said it makes sense for an object to just be accelerating. ...
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Einstein's Gedanken Experiment that lead to the Special Theory of Relativity

Once, I read that Einstein founded the special relativity theory by imagining how an observer moves at the speed of light. How does this thought experiment work? How to reach from this imagination to ...
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Is Einstein's Special Relativity completely inclusive of Newton's 3 laws of motion?

Relativity has always been explained to me (in books I've read, etc) as a superset of newton's laws - that is; it encapsulates all of Newton's mechanics in addition to other effects (observer effect, ...
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Has relativity of simultaneity been directly observed?

I know that thought experiment about trains when a flash of light in the middle reaches the both end simultaneously for a passenger but different times for the bystander. So were there (non-thought) ...
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What is Relativistic Navier-Stokes Equation Through Einstein Notation?

Navier-Stokes equation is non-relativistic, what is relativistic Navier-Stokes equation through Einstein notation?
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Representations of the Poincare group

Which type of states carry the irreducible unitary representations of the Poincare group? Multi-particle states or Single-particle states?
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The equivalent electric field of a magnetic field

I know that Lorentz force for a charge $q$, with velocity $\vec{v}$ in magnetic field $\vec{B}$ is given by $$\vec{F} =q \vec{v} \times \vec{B}$$ but there will exist a frame of reference where ...
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Spin-Statistics Theorem (SST)

Please can you help me understand the Spin-Statistics Theorem (SST)? How can I prove it from a QFT point of view? How rigorous one can get? Pauli's proof is in the case of non-interacting fields, how ...
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Why Negative Energy States are Bad

The argument is often given that the early attempts of constructing a relativistic theory of quantum mechanics must not have gotten everything right because they led to the necessity of negative ...
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What are the linear maps which preserve the time-like cone?

I'm looking at the set of time-like vectors: $\mathcal{T}_+ = \{ x \in \mathbb{R}^4 \mbox{ s.t. } x^T \eta x \geq 0 \:, x^0\geq 0\} $, where $\eta = \mbox{diag}(1, -1, -1, -1)$. I want to be able to ...
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Is the total cross section a Lorentz Invariant?

In Peskin and Schroeder's book (P&S), on the botton of page 106, the authors say that the total cross section transforms as its only non-invariant factor, namely: $$ {1 \over E_{A} E_{B} |v_A - ...
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Can we show that time is orthogonal to space?

It's easy to show that the time we measure is "in a different direction" from the space directions we measure. However, it's not immediately obvious to me that these directions are orthogonal. How do ...
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Special relativity and massless particles

I encountered an assertion that a massless particle moves with fundamental speed c, and this is the consequence of special relativity. Some authors (such as L. Okun) like to prove this assertion with ...
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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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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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Transformation of angles in special relativity

My question is about the problem below Depicted are two space ships (the USS Voyager and the USS Enterprise), each with velocity $v=c/2$ relative to the space station (Babylon 5). At the exact ...
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Horizon and Unruh radiation for a finite period of acceleration

It's a well known fact that an observer that accelerates at a constant rate from $-c$ at past infinity to $+c$ at future infinity sees a horizon in flat Minkowski spacetime. This is easy to see from a ...
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What is the formula for the relativistic ellipse?

If an astronomer moves at relativistic speed, the stars and constellations are distorted. He sees the stars towards which he is moving blue shifted, while the ones he's moving away from are red ...
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What if the binding energy becomes larger than the rest mass?

Looking at the equation for binding energy and mass defect, $$ B = m_{\text{free}} - m_{\text{bound}} \\ \Rightarrow m_{\text{bound}} = m_{\text{free}} - B, $$ my question is the following. Suppose ...
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What's the purpose of the arbitary additive constants in Einstein's Inertia of Energy Paper?

In Einstein's paper: Does the Inertia of a Body Depend upon its Energy content? he introduces arbitary additive constants whose purpose I'm confused about. The paper has a frame $(x,y,z)$ where a ...
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Can a spinor be defined as any quantity which transforms linearly under Lorentz transformations?

Recently I’ve come across a few papers from China (e.g. Xiang-Yao Wu et al., arXiv:1212.4028v1 14 Dec 2012) that make the following statement: ...any quantity which transforms linearly under ...
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Do velocity and acceleration time dilation factors add?

For a spinning space station such as in 2001, A Space Odyssey, what would be the time slowing in the perimeter of the spinning space station with respect to the center axis of the station? The ...