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 proper acceleration is $du/dt$ and not $du/d\tau$?

Wikipedia says: In relativity theory, proper acceleration[1] is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object. and says: In the ...
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Does the general topology of Minkowski space-time change under a Lorentz transformation?

Does the general topology of Minkowski space-time change under a Lorentz transformation? Open balls in $\mathbb{R}^{4}$ (with the standard topology) are not invariant under Lorentz transformations. ...
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Does entanglement not immediately contradict the theory of special relativity?

Does entanglement not immediately contradict the theory of special relativity? Why are people still so convinced nothing can travel faster than light when we are perfectly aware of something that ...
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Do all massless particles (e.g. photon, graviton, gluon) necessarily have the same speed $c$?

I suppose there was a discussion already on speed-of-gravity-and-speed-of-light. But I silly wonder whether all the massless mediators of four fundamental forces, i.e. Graviton: $g_{\mu\nu}$ ...
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Relative Motion

I read the following: http://www.feynmanlectures.caltech.edu/I_15.html#Ch15-S4 "Now let us see what happens to the moving clock. Before the man took it aboard, he agreed that it was a nice, ...
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Bound State of Only Massless Particles? Follows a Time-Like Trajectory?

Is there any way in which a bound state could consist only of massless particles? If yes, would this "atom" of massless particles travel on a light-like trajectory, or would the interaction energy ...
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Velocity Time Dilation

In Wikipedia article about time dilation, it says: "Hafele and Keating, in 1971, flew caesium atomic clocks east and west around the Earth in commercial airliners...the moving clocks were expected ...
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Generators of Poincare Groups

How can I determine the generators of the Poincare Group, $P(1,3)$ explicitly? Here $P(1,3)$ means a matrix Lie group.
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What is a Lorentz boost and how to calculate it?

I know very little special relativity. I never leaned it properly, but every time I read someone saying: "if you boost in the x-direction, you get such and such" my mind goes blank! I tried ...
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Does magnetic propagation follow the speed of light?

Does magnetic propagation follow the speed of light? E.g. if you had some magnet of incredible strength and attached an iron wire that is one light year long to it, would the other end of the iron ...
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Infinitesimal Lorentz transformation is antisymmetric

The Minkowski metric transforms under Lorentz transformations as \begin{align*}\eta_{\rho\sigma} = \eta_{\mu\nu}\Lambda^\mu_{\ \ \ \rho} \Lambda^\nu_{\ \ \ \sigma} \end{align*} I want to show that ...
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Do we move at the speed of light relative to light?

My understanding of relativity isn't very sophisticated, but it seems to me that relative to a photon moving at the speed of light, we are moving at the speed of light. Is this the case?
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Why is the Dirac equation not used for calculations?

From what I understand the Dirac equation is supposed to be an improvement on the Schrödinger equation in that it is consistent with relativity theory. Yet all methods I have encountered for doing ...
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Would travelling at relativistic speeds have any impact on human biology?

If a person was sitting on a craft that has accelerated to near light speed speed from Earth (e.g. 99.999% of light speed) would there be any impact on his or her human biology due to relativistic ...
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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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Lorentz transformation of the Spinor Field

I'm reading chapter 3 of Peskin and Schroeder and am stuck on page 43 of P&S. They have defined the Lorentz generators in the spinor representation as: \begin{equation} S^{\mu \nu} = ...
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The notion called aether

I am trying to learn relativity theory and going through an introductory text on special relativity. I stumbled on the Michelson-Morley experiment. The book claims (accounts) that the result of this ...
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Darwin term and Zitterbewegung

I've noticed that in the discussion of the fine structure of Hydrogen atom standard QM texts claim that the Darwin term, which corrects energy of $\ell=0$ (or $s$-) states only, is related to the ...
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Frequency of cosmic microwave background

Some people refer to cosmic microwave background's (CMB) frame of reference as an absolute one. If I understand correctly, we can measure 'absolute' velocity in this frame by using the Doppler effect. ...
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How can photons interact with anything?

I read photons do not age because they move at the speed of light. So when a photon interacts with my eyes, aren't they apart in space-time by the difference of the time in the frame of reference of ...
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How is the speed of light constant in all directions for all observers?

Please imagine the following thought-experiment: Order of Events: Pulse - A single pulse of light is emitted from the light towards the mirror Reflect - The pulse hits the mirror and is ...
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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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Help Me Gain an Intuitive Understanding of Lorentz Contraction

I'm having a hard time getting an intuitive understanding of Lorentz Contraction. I understand what it is by definition but I don't 'get it.' I'm not a physicist, just an amateur, so sorry if this ...
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Why does Minkowski space provide an accurate description of flat spacetime?

What is the chain of reasoning (beginning, of course, from observations about the universe) that leads one to predict that Minkowski space provides an accurate description of space-time in the ...
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Meaning of spin

I'm pretty astounded that I did not hear about this sooner, but in my course on QFT our professor told us that the concept of spin can be used to mean three things: Mechanical spin (apparently a ...
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The Dual Cloud Chamber Paradox

2012-04-07 Addendum: The Dual Cloud Chamber Paradox Two 10m diameter spheres $A$ and $B$ of very cold, thin gas have average atomic separations of 1nm. Their atoms are neutral, but ionize easily and ...
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Is there a relativistic generalization of the Maxwell-Boltzmann velocity distribution?

The Maxwell-Boltzmann velocity distribution in 3D space is $$ f(v)dv = 4\pi \left(\frac{m}{2\pi k_B T}\right)^{3/2} v^2 \exp\left(-\frac{m v^2}{2k_B T}\right)dv$$ It gives the probability for a ...
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Calculate the electric field of a moving infinite magnet, without boosting

Consider a rectangular slab of permanently magnetized material. The slab's dimensions are $L_x$, $L_y$, and $L_z$, and the slab is uniformly magnetized in the $\hat{x}$-direction. The slab is not ...
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Number of the Generators of Poincare Group

It is said that the Poincare group, $P(3,1)$ has $10$ generators. $6$ of them are the generators of the Lorentz group, $O(3,1)$ and the other $4$ generators are the generators of $4D$ translational ...
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Peskin & Schroeder Chapter 3.1 EoM Lorentz Invariant under Lorentz Invariant Lagrangian

From Peskin & Schroeder QFT page 35: The Lagrangian formulation of field theory makes it especially easy to discuss Lorentz invariance. And equation of motion is automatically Lorentz ...
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Relativity and Current in Wire

If an observer is stationary relative to a current-carrying wire in which electrons are moving, why does the observer measure the density of moving electrons to be the same as the density of electrons ...
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Proof for $p=\gamma_Pmu$

As I'm reading about Relativistic Momentum, my book states the following: $$p=m \frac{\Delta x}{\Delta t}=m\frac{\Delta x}{\sqrt{(1-u^2/c^2)}\Delta t}=\frac{mu}{\sqrt{1-u^2/c^2}}=\gamma_Pmu$$ ...
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Entanglement and relativity

Two observers A and B measure a quantum entangled state and obtain correlated results, even if their separation is space-like (each is out of the light cone of the other). A possible interpretation is ...
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Why absoluteness of time implies galilean transformations?

In Landau course, vol.1 Mechanics, one finds the statement: ...the absoluteness of time necessarily implies that the ordinary law of composition of velocities is applicable to all phenomena. I ...
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Can we write the electromagnetic potential covariantly in terms of the four-current?

In the Lorenz gauge, we have a beautiful relation between the four-current and the four-potential: $$\Box A^{\alpha} = \mu_0 J^{\alpha}$$ To get $A$ in terms of $J$, however, we have to use a ...
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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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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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Why is the stress-energy tensor symmetric?

The relativistic stress-energy tensor $T$ is important in both special and general relativity. Why is it symmetric, with $T_{\mu\nu}=T_{\nu\mu}$? As a secondary question, how does this relate to the ...
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Open problems in special relativity, and non-inertial motion in flat-spacetime, or things that have been discovered recently

What classical open problems are there in special relativity, including questions about non-inertial motion in flat-spacetime, but excluding questions about quantum theories. Answers can include ...
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Does quantum mechanics allow faster than light (FTL) travel?

Let's suppose I initially have a particle with a nice and narrow wave function[1] (I will leave these unnormed): $$e^{-\frac{x^2}{a}}$$ where $a$ is some small number (to make it narrow). Let's also ...
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Causality and Quantum Field Theory

I have a problem with proof of causality in Peskin & Schroeder, An Introduction to QFT, page 28. To avoid confusion I use three vectors notation, rewriting the Eq. (2.53) for $y=0$ as follows: ...
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Is there any uncertainty between mass and proper length or time?

I was trying to naively draw a parallel between special relativity and the Heisenberg uncertainty principle. I try to understand uncertainty principle as a consequence of 4-position and 4-momentum ...
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relativistic spaceship, CMB radiation and thermodynamics

Scenario: a spaceship is travelling at a high fraction of $c$. The interstellar gas and CMB radiation has blueshifted significantly and we are facing a possible melting of the front radiation shield! ...
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Is time dilation an illusion?

It is said that we can verify time dilation by flying a very accurate clock on a fast jet or spaceship and prove that it registers less time than the clocks on earth. However, the clocks on earth ...
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A question abou $E=pc$ for massless particles

Since photon has no (rest)mass and $$E^2=(pc)^2+(mc^2)^2$$ we derive that $E=pc$ for particle with no (rest)mass. However, if we transform the non-relativistic formula for kinetic energy ...
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Does the reaction force appear without delay?

According to Newton's law of action-reaction, there is a reaction force for the action force. He did not say when the reaction appears, whether immediately or with a delay. Could you tell me the ...
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twistor-spacetime correspondence

Could someone explain the correspondence between lines in twistor space and minkowski space-time points? a basic derivation would suffice
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Would it be possible to develop special relativity without knowing about light?

My understanding of special relativity is that it is fundamentally based on the constancy of the speed of electromagnetic radiation - that this speed is a physical law (or derivable from physical laws ...
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What distinguishes time from space in Quantum Field Theory?

Consider the following expression for a general QFT action: $$ S ~=~ \int_0^t\mathrm dt~L ~=~\int_0^t\mathrm dt\int_\mathbb {R^3}\mathrm d^3x~\mathcal L ~=~\int\mathrm d^4x~\mathcal L.$$ Here we ...
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Does Light Experience Length Contraction?

Lorentz length contractions states that the length of any moving object gets divided by the Lorentz factor equal to the Lorentz factor for that object (always $\geq 1$), equal to $$ ...