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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Time dilation all messed up!

Okay! There is a problem with my logic and i cannot seem to point out where. There's a rocket ship travelling at close-to-c speed v without any acceleration (hypothetically), and there is an observer ...
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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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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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Do tachyons move faster than light?

I am trying to understand whether or not tachyons travel faster than light. The linked Wikipedia page shows some seemingly contradictory statements, and they are confusing. For instance, the first ...
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Center-of-mass frame for massless particles

Given a scattering event where a photon and electron go in and a photon and electron come out, what is the center of mass frame? I'd say, since the photon has no mass, it's the rest frame of the ...
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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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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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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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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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How can time be relative?

I don't understand how time can be relative to different observers, and I think my confusion is around how I understand what time is. I have always been told (and thought) that time is basically a ...
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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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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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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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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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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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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 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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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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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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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 is the speed of light relative to?

Consider the scenario where you measure the time it takes for light to travel to the left 10 meters and to the right 10 meters. Both measurements will take the same time, even though we are moving ...
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Where's the energy in a boosted capacitor?

Suppose I look at a parallel plate capacitor in its rest frame and calculate the electrostatic energy, $E$. Next, I look at the same capacitor in a primed frame boosted in the direction perpendicular ...
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Do particles with exactly zero energy exist?

In my understanding, in Newtonian mechanics if something has no mass it cannot be said to "exist" since it cannot possibly have energy or momentum and thus cannot participate in interactions or be ...
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Is there a strong force analog to magnetic fields?

In special relativity, magnetism can be re-interpreted as an aspect of how electric charges interact when viewed from different inertial frames. Color charge is more complex than electric charge, but ...
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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 is the difference between the properties of Electron spin and Photon polarization/helicity?

What is the difference between a photon's polarization/helicity and an electrons spin half? I know that the photon is spin 1 but isn't its polarization analogous to spin half? This question stems ...
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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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Validity of Maxwell's equations with no aether or relativity?

In From Paradox to Reality: Our Basic Concepts of the Physical World by Fritz Rohrlich page 55 it states that [...] just doing away with the ether would not have resolved all problems. The ...
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Why collide a moving particle with a particle at rest, rather than two moving particles?

I was just reading some lecture notes about relativistic and quantum mechanics, and in the later part of this page the author demonstrates that any relativistic particle collision in the "lab" ...
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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 was Albert Einstein's proof for $E=mc^2$?

Most people know the famous equation: $$E=mc^2$$ What were his steps of thinking for this equation that helped us discover so much about our world?
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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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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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Charge conjugation in Dirac equation

According to Dirac equation we can write, \begin{equation} \left(i\gamma^\mu( \partial_\mu +ie A_\mu)- m \right)\psi(x,t) = 0 \end{equation} We seek an equation where $e\rightarrow -e $ and which ...
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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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Proving invariance of $ds^2$ from the invariance of the speed of light

I've started today the book of Landau and Lifshitz Vol.2: The Classical Theory of Fields $\S 2$. They start from the invariance of the speed of light, express it as the fact that $$c^2(\Delta ...
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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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How Special Relativity causes magnetism

So my physics teacher assigned us an article about how special relativity causes magnetism in a wire with a current, even with the low drift velocities of electrons in a current. It seemed that the ...
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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's wrong with this application of Thomas Precession to circular motion velocity measurements?

If you happen to have the Third Edition of Classical Electrodynamics by John David Jackson, turn to section 11.8, as that's where I'm getting all this from. If not, you should still be able to follow ...
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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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What happens if light/particles exceeded the speed of light for a particular medium

While the speed of light in vacuum is a universal constant ($c$), the speed at which light propagates in other materials/mediums may be less than $c$. This is obviously suggested by the fact that ...
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Minkowski spacetime: Is there a signature (+,+,+,+)?

In history there was an attempt to reach (+, +, +, +) by replacing "ct" with "ict", still employed today in form of the "Wick rotation". Wick rotation supposes that time is imaginary. I wonder if ...
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Minkowski Metric Signature

When I learned about the Minkowski Space and it's coordinates, it was explained such that the metric turns out to be $$ ds^{2} = -(cdx^{0})^{2} +(dx^{1})^{2} + (dx^{2})^{2} + (dx^{3})^{2} $$ where $ ...
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Potential energy in $E_f^2=(mc^2)^2+(pc)^2$?

Let's consider $$E_f^2=(mc^2)^2+(pc)^2$$ where the $mc^2$ is the rest energy due to the rest mass -- in Finnish "lepomassa". $$ \sqrt{(mc^2)^2+(pc)^2} - mc^2~=~(\gamma-1)mc^2$$ is the kinetic ...
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Lay explanation of the special theory of relativity? [closed]

What is Einstein's theory of Special relativity, in terms a lay person can follow?
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What happens when relativistic effects stop?

I'm currently learning special relativity in high school and we only primarily deal with what happens when an object is moving at constant relativistic speeds. But what if the object slowed back down ...
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Is Minkowski space usually a vector space or an affine space?

When I visited Wikipedia's page on Minkowski space, it seemed to offer two definitions. The first defined Minkowski space a vector space. Then, in a later section, it says The section above ...
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How to derive addition of velocities without the Lorentz transformation?

Lorentz contraction and time dilatation can be deduced without Lorentz transformation. Can you deduce also the theorem of addition of velocities $$w~=~\dfrac{u+v}{1+uv/c^2}$$ without Lorentz ...
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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 ...