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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How does a photon experience space and time?

To an an external observer it appears that time has stopped for photon. But this relation is reflexive, so for an observer travelling with the photon it appears the universe has stopped everywhere. ...
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Is kinetic energy a relative quantity? Will it make inconsistent equations when applying it to the conservation of energy equations?

If the velocity is a relative quantity, will it make inconsistent equations when applying it to the conservation of energy equations? For example: In the train moving at $V$ relative to ground, ...
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Is there an easy way to show that $x^2-t^2=1/g^2$ for a (relativistic) body undergoing acceleration g?

A professor asked me about the (c=1) equation: $$x^2 - t^2 = 1/g^2$$ which I used in a paper. Or with $c$: $$x^2 - (ct)^2 = c^4/g^2.$$ I told him that it was the exact equation of motion for a ...
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Does a photon in vacuum have a rest frame?

Quite a few of the questions given on this site mention a photon in vacuum having a rest frame such as it having a zero mass in its rest frame. I find this contradictory since photons must travel at ...
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Is the Planck length Lorentz invariant?

The planck length is defined as $l_P = \sqrt{\frac{\hbar G}{c^3}}$. So it is a combination of the constants $c, h, G$ which I believe are all Lorentz invariants. So I think the Planck length should ...
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How realistic is the game “A slower speed of light”?

The game "A slower speed of light" from MIT claims to simulate effects of special relativity: Visual effects of special relativity gradually become apparent to the player, increasing the ...
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Why does nonlinearity in quantum mechanics lead to superluminal signaling?

I recently came across two nice papers on the foundations of quantum mechancis, Aaronson 2004 and Hardy 2001. Aaronson makes the statement, which was new to me, that nonlinearity in QM leads to ...
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Is it only the Higgs field that stops me from getting to $c$?

Is it only the higgs field that stops me from accelerating up to the speed of light or is there other restriction concerning the increase in mass? In other words if I had a Higgs field shield on my ...
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Why the vacuum polarization does not decrease the speed of light?

On one hand, in the classical electrodynamics polarization of transparent media yields in lowering the speed of light by the factor of $n=\sqrt{\epsilon_r \mu_r}$ (refractive index). On the other, in ...
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Status of experimental searches for tachyons?

Now that the dust has settled on the 2011 superluminal neutrino debacle at OPERA, I'm interested in understanding the current status of experimental searches for neutrinos. Although the OPERA claim ...
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What are the mechanics by which Time Dilation and Length Contraction occur?

What are the mechanics of time dilation and length contraction? Going beyond the mathematical equations involving light and the "speed limit of the universe", what is observed is merely a phenomenon ...
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Why and how is the speed of light in vacuum constant, i.e., independent of reference frame?

I was told that the Galilean relative velocity rule does not apply to the speed of light. No matter how fast two objects are moving, the speed of light will remain same for both of them. How and why ...
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Acceleration in special relativity

I am currently studying the motion of relativistic charged particles in electromagnetic fields. More exactly, we first derived the equation of motion in the 4-vector formalism. I was a bit confused ...
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The Four-Clock Special Relativity Conundrum

Two open-car trains approach each other at fixed velocities. Each has a radar to see how quickly the other train is approaching, but apart from that the trains have no a priori knowledge of each ...
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Would time freeze if you can 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 speed limit for anything with mass. So, if I were ...
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The definition of an inertial reference frame in Einstein's relativity

I'm reading Sean Carroll's book on general relativity, and I have a question about the definition of an inertial reference frame. In the first chapter that's dedicated to special relativity, the ...
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Fundamental invariants of the electromagnetic field

It is a standard exercise in relativistic electrodynamics to show that the electromagnetic field tensor $F_{\mu\nu}$, whose components equal the electric $E^i=cF^{i0}$ and magnetic ...
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Do particles have different spins in different frames of reference?

Let's say we have two photons, whose momentum vectors point to opposite directions. Also spin angular momentum vectors of the photons point to opposite directions. (Sum of spins is zero) Now we ...
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If two ultra-relativistic billiard balls just miss, will they still form a black hole?

This forum seems to agree that a billiard ball accellerated to ultra-relativistic speeds does not turn into a black hole. (See recent question "If a 1kg mass was accelerated close to the speed of ...
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A simple pendulum moving at a relativistic speed - how does the period change?

I've been pondering the precise mechanism of time dilation for the example of a simple pendulum in two different situations: The observer and ground are at rest in one frame of reference; the ...
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Why does the (relativistic) mass of an object increase when its speed approaches that of light?

I'm reading Nano: The Essentials by T. Pradeep and I came upon this statement in the section explaining the basics of scanning electron microscopy. However, the equation breaks down when the ...
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How do photons travel at a speed that should be impossible to attain?

If it requires infinite amount of energy to travel at the speed of light then how photon attains this speed? Its source is never infinitely sourced.
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What if photons are not the fastest particles?

Einstein originally thought that special relativity was about light and how it always travelled at the same speed. Nowadays, we think that special relativity is about the idea that there is some ...
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Why is the space-time interval squared?

The space-time interval equation is this: $$\Delta s^2=\Delta x^2+\Delta y^2+\Delta z^2-(c\Delta t)^2$$ Where, $\Delta x, \Delta y, \Delta z$ and $\Delta t$ represent the distances along various ...
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How large is the universe?

We know that the age of the universe (or, at least the time since the Big Bang) is roughly 13.75 billion years. I have heard that the size of the universe is much larger than what we can see, in other ...
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What does a frame of reference mean in terms of manifolds?

Because of my mathematical background, I've been finding it hard to relate the physics-talk I've been reading, with mathematical objects. In (say special) relativity, we have a Lorentzian manifold, ...
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Essential background for QFT study

The preface to Mark Srednicki's "Quantum Field Theory" says that to be prepared for the book, one must recognize and understand the following equations: $$\frac{d\sigma}{d\Omega} = ...
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Does the speed of light vary in noninertial frames?

The speed of light is the same in all inertial frames. Does it change from a non-inertial frame to another? Can it be zero? If it is not constant in non-inertial frames, is it still bounded from ...
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What's the relationship between $SL(2,\mathbb{C})$, $SU(2)\times SU(2)$ and $SO(1,3)$?

I'm a beginner of QFT. Ref. 1 states that [...] The Lorentz group $SO(1,3)$ is then essentially $SU(2)\times SU(2)$. But how is it possible, because $SU(2)\times SU(2)$ is a compact Lie group ...
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Relativity of Simultaneity

Relativity of Simultaneity seems to be about OBSERVING two events simultaneously (please correct me if I am wrong). However, as long as the two events are separated by a distance (any distance) then ...
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How is quantum mechanics compatible with the speed of light limit?

Consider a free electron in space. Let us suppose we measure its position to be at point A with a high degree of accuracy at time 0. If I recall my QM correctly, as time passes the wave function ...
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How to understand the emergent special relativity in the superfluid?

The superfluid vacuum theory was proposed to understand some features of the vacuum (aether) from the emergence point of view. Although made up of non-relativistic atoms, the low-energy excitations of ...
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Can the CPT theorem be valid if Lorentz invariance is only spontaneously broken?

Earlier, I asked here whether one can have spontaneous breaking of the Lorentz symmetry and was shown a Lorentz invariant term that can drive the vacuum to not be Lorentz invariant. How relaxed are ...
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Does special relativity make magnetic fields irrelevant?

I've heard that special relativity makes the concept of magnetic fields irrelevant, replacing them with relativistic effects between charges moving in different velocity frames. Is this true? If so, ...
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Does the discreteness of spacetime in canonical approaches imply good bye to STR?

In all the canonical approaches to the problem of quantum gravity, (eg. loop variable) spacetime is thought to have a discrete structure. One question immediately comes naively to an outsider of this ...
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How does $E=mc^2$ put an upper limit to velocity of a body?

How does $E=mc^2$ put a upper limit to velocity of a body? I have read some articles on speed of light and they just tell me that it is the maximum velocity that can be acquired by any particle. How ...
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Einstein's special relativity beyond the speed of light

Could someone with access to this paper which claims to have new transformations between frames with relative motion faster than light which are supposedly consistent with special-relativity, say what ...
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What determines which frames are inertial frames?

I understand that you can (in principle) measure whether "free particles" (no forces) experience accelerations in order to tell whether a frame is inertial. But fundamentally, what determines which ...
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The derivation of the Belinfante-Rosenfeld tensor

It seems me that there is a "difference" (at least apparently) in how the Belinfante-Rosenfeld tensor is thought of in section 7.4 of Volume 1 of Weinberg's QFT book and in section 2.5.1 of the ...
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Deriving the action and the Lagrangian for a free point particle in Special Relativity

My question relates to Landau & Lifshitz, Classical Theory of Field, Chapter 2: Relativistic Mechanics, Paragraph 8: The principle of least action. As stated there, to determine the action ...
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Invariant spacetime - distance - Circular Motion

I understand that the closer something travels to the speed of light, that time will stretch by a factor, and distance will compress by the same factor. My question is, if something travels in a ...
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How fast can time flow? A question of time dilation

(I would describe myself as an illiterate physics enthusiast, so I hope you'll forgive me if my ignorance is borderline offensive.) If I've understood anything of the concept of time dilation, your ...
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Understanding the “$\pi$” of a rotating disk

Let us say you are in an inertial reference frame with a circular planar disk. If you take your meter measuring rods (or perhaps tape measure) you can find the diameter and circumference of the disk. ...
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In QFT, why does a vanishing commutator ensure causality?

In relativistic quantum field theories (QFT), $$[\phi(x),\phi^\dagger(y)] = 0 \;\;\mathrm{if}\;\; (x-y)^2<0$$ On the other hand, even for space-like separation $$\phi(x)\phi^\dagger(y)\ne0.$$ ...
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Motivation for preservation of spacetime volume by Lorentz transformation?

My favorite way of deriving the Lorentz transformation is to start from symmetry principles (an approach originated in Ignatowsky 1911; cf. Pal 2003), and one of my steps is to prove a lemma stating ...
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Clocks in special relativity

One book on special relativity says: Any observer at rest relative to his own timepiece will see that other clocks moving with respect to him run fast - the greater their speed, the faster they ...
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Conservation of phase space volume in Rindler space-time

Let us consider Rindler space-time, i.e. Minkowski space-time as seen by a constantly accelerating observer. My question is, does Liouville's theorem, i.e. the conservation of phase space volume in ...
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What are the consequences of relativistic angular velocities?

If I take a rod of some radius $r$ and length $L$, and I spin this rod with angular velocity $\omega$. How would the geometry of the rod appear to an observer as one converges to $c$? What are the ...
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Rotate a long bar in space and get close to (or even beyond) the speed of light $c$

Imagine a bar spinning like a helicopter propeller, At $\omega$ rad/s because the extremes of the bar goes at speed $$V = \omega * r$$ then we can reach near $c$ (speed of light) applying some ...
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How does Newtonian gravitation conflict with special relativity?

In the Wikipedia article Classical Field Theory (Gravitation), it says After Newtonian gravitation was found to be inconsistent with special relativity, . . . I don't see how Newtonian ...