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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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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Symmetrical twin paradox

Take the following gedankenexperiment in which two astronauts meet each other again and again in a perfectly symmetrical setting - a hyperspherical (3-manifold) universe in which the 3 dimensions are ...
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Are gravitomagnetic monopoles hypothesized?

My understanding is that gravitomagnetism is essentially the same relativistic effect as magnetism. If so, why is it that I've heard so much about magnetic monopoles, but never gravitomagnetic ...
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Is there an official name for “Lorentz Pairs” like energy and momentum?

In learning about relativity I've noticed that in the construction of Lorentz invariants (specifically four-vectors) two physical quantities that were previously considered distinct are instead ...
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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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What is so special about speed of light in vacuum?

I will try to be as explanatory as possible with my question. Please also note that I have done my share of googling and I am looking for simple language preferable with some example so that I can get ...
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Accelerating particles to speeds infinitesimally close to the speed of light?

I'm in a freshmen level physics class now, so I don't know much, but something I heard today intrigued me. My TA was talking about how at the research facility he worked at, they were able to ...
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Is it a postulate or a well proven fact that speed of light remains constant w.r.t any observer?

We usually heard that speed of light in vacuum $c$ remains same no matter how observer is moving? I am wondering whether is it taken as a postulate or a proven phenomenon that $c$ is constant ...
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Proving that interval preserving transformations are linear

In almost all proofs I've seen of the Lorentz transformations one starts on the assumption that the required transformations are linear. I'm wondering if there is a way to prove the linearity: Prove ...
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How would we see a near-lightspeed object emitting light?

Consider an object travelling near the speed of light relative to us (let it be a spaceship or a star), which is emitting light (consider it monochromatic resulting from a two level electronic ...
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Why isn't general relativity the obvious thing to try after special relativity?

To preface my question, I ask this as a mathematics student, so I don't have a very good sense of how physicists think. Here is the historical context I'm imagining (in particular taking into account ...
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In relativity, can/should every measurement be reduced to measuring a scalar?

Different authors seem to attach different levels of importance to keeping track of the exact tensor valences of various physical quantities. In the strict-Catholic-school-nun camp, we have Burke ...
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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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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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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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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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Thought experiment regarding an object approaching a mirror

Here's a thought experiment I came up with in class today when my mind drifted (I however highly doubt I'm the first to think about this since it is pretty rudimentary) : Let's say superman ...
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Double light speed

Let's say we have $2$ particles facing each other and traveling at speed of light Let's say I'm sitting on #$1$ particle so in my point of view #$2$ particle's speed is $c+c=2c$, double light speed? ...
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What is “special” and what is “general” in Relativity?

Initially I thought in special relativity the velocity was constant, whereas general relativity allowed treatment of accelerated frames as well. But now I have heard that SR is only valid locally?
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What problems with Electromagnetism led Einstein to the Special Theory of Relativity?

I have often heard it said that several problems in the theory of electromagnetism as described by Maxwell's equations led Einstein to his theory of Special Relativity. What exactly were these ...
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Limitations on how far one can travel in the universe

Someone once incorrectly told me that, given the speed of light is the speed limit of the universe, aliens would have to live for hundreds of years if they are to travel distances of hundreds of light ...
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Electrons faster than speed of light

While looking at some exercises in my physics textbook, I came across the following problem which I thought was quite interesting: It is possible for the electron beam in a television picture tube ...
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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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Can we find actual rest mass of things on Earth

Earth moves around the Sun and the Sun moves around the galaxy and the galaxy moves with unknown speed and direction. We have speed so the mass of us all altered. Can we know the real rest mass? If ...
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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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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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Does relativistic mass have weight?

If an object was sliding on an infinitely long friction-less floor on Earth with relativistic speeds (ignoring air resistance), would it exert more vertical weight force on the floor than when it's at ...
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Is period of rotation relative?

My question is inspired by the following answer by voix to another problem: "There is a real object with relativistic speed of surface - millisecond pulsar. The swiftest spinning pulsar currently ...
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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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Can quaternion math be used to model spacetime?

Quaternions are commonly used to model 4 dimensional systems where the quaternion consists of a real 3 dimensional vector and an imaginary scalar. So on the surface Quaternions seem well suited to ...
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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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How to explain (pedagogically) why there is 4 spacetime dimensions while we see only the 3 spatial dimesions?

I have been asked this question by a student, but I was able and in the same time incapable to give a good answer for this without equations, so do you have ideas how one can explain this in a simple ...
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Newton's Bucket

Newton's Bucket This thought experiment is originally due to Sir Isaac Newton. We have a sphere of water floating freely in an opaque box in intergalactic space, held together by surface tension and ...
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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 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 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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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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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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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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Quaternions and 4-vectors

I recently realised that quaternions could be used to write intervals or norms of vectors in special relativity: $$(t,ix,jy,kz)^2 = t^2 + (ix)^2 + (jy)^2 + (kz)^2 = t^2 - x^2 - y^2 - z^2$$ Is it ...
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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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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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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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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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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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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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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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What happens when a photon hits a mirror?

When a photon of light hits a mirror does the exact same photon of light bounce back or is it absorbed then one with the same properties emitted? If the same one is bounced back does it's velocity ...
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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 ...