The special theory of relativity describes the motion and dynamics of objects moving at significant fractions of the speed of light.

learn more… | top users | synonyms (5)

6
votes
7answers
407 views

What is $c + (-c)$?

If object A is moving at velocity $v$ (normalized so that $c=1$) relative to a ground observer emits object B at velocity $w$ relative to A, the velocity of B relative to the ground observer is $$ v ...
-1
votes
1answer
59 views

If we could reach very high speeds, could we measure the velocity of the Earth this way?

If we could reach (nearly) the speed of light with spaceships, could we measure the velocity of the Earth by launching three perpendicular rockets, accelerating them, and measuring how much fuel ...
1
vote
2answers
145 views

Beginner question: timelessness of massless particles [duplicate]

I am not very familiar with the quirkiness of relativity, and I was wondering how to explain this situation. If a beam of light is shining at some object at some distance from the origin of the beam, ...
1
vote
1answer
87 views

What is the status of massless photons traveling through a medium?

Photons in vacuum have no proper time, and they are not considered as observers and not as reference frame. But what about photons travelling through matter? Their velocity is lower than light speed, ...
5
votes
1answer
433 views

Relationship between the continuity equation and the wave equation

What exactly is the relationship between the continuity equation and the wave equation? Suppose $J^\mu$ is a contravariant vector that satisfies the continuity equation $\partial_\mu J^\mu=0$. Let ...
17
votes
5answers
796 views

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 ...
64
votes
10answers
8k views

Can Maxwell's equations be derived from Coulomb's Law and Special Relativity?

As an exercise I sat down and derived the magnetic field produced by moving charges for a few contrived situations. I started out with Coulomb's Law and Special Relativity. For example, I derived the ...
2
votes
1answer
52 views

Sub-light speeds and momentum conservation law

Let's imagine a boat on a lake. Observer A is sitting on the shore. Observer B is sitting in the boat on the bow. Observer B has a ball attached to the end of a string which he holds in his hand. ...
1
vote
1answer
83 views

Effective field theory for fermion gas

Reading about fermion gas in a paper they used the following Lagrangian, which describes an effective field theory for nonrelativistic fermions (I neglect the four point interaction term). $$ L = ...
0
votes
1answer
131 views

The mass of the photon will decrease with reduced velocity?

Since photon has zero rest mass, it will has zero mass when the velocity is zero. We are now being able to slower down the photon in experiment. Is the mass of photon reduced with the decreased ...
0
votes
2answers
97 views

Discrepancy ( or Confusion ) in the mass of photon

$E$ = $mc^2$ And also $E$ = $hf$ (f - frequency) And hence Einstein said $m$ = $hf\over c^2$ And so photons have mass But later he also said $M$ = $M_0\over \sqrt {1-v^2/c^2}$ Where if we put $v ...
1
vote
1answer
101 views

Special relativity: circumventing velocity-addition formula

Two spaceships approach an observer from an equal distance and from an opposite direction with an equal speed $v$ in the observer's intertial reference frame $O$. The speed of a spaceship in the ...
12
votes
1answer
1k views

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 ...
3
votes
2answers
1k views

Gravitational Length Contraction

General Relativity predicts that a clock at rest in a gravitational field will run slower than a clock in free fall. Similarly, will a vertical ruler on the earth's surface be shorter than a ruler in ...
6
votes
3answers
278 views

$E=mc^2$ resembles kinetic energy formula?

The simplest equation expressing mass–energy equivalence is the famous $E=mc^2$ where $c$ represents the speed of light. Compare this with $E_K = \frac{1}{2}mv^2$. Since $E=mc^2$ can be applied to ...
0
votes
1answer
224 views

Maximum speed higher than the speed of light

I wanted to ask if higher speed than the speed of light will be discovered, will scientists be able to adjust the special relativity to the new situation? I read that informations transmitted faster ...
1
vote
0answers
79 views

Why don't we experience dilatations in Minkowski spacetime?

The question This question follows on from the use of projective coords for spacetime in Notation for Translation Group Generators . Under Felix Klein's Erlangen Program, Minkowski spacetime starts ...
3
votes
4answers
435 views

Is relative velocity invariant under special relativity?

If a metre stick passes an observer at speed $v$, would all observers in any inertial frame of reference say the speed of the meter stick relative to the observer is exactly $v$? If so what is it ...
2
votes
1answer
124 views

Considering the theory of special relativity: Is torque still a vector?

Considering the theory of special relativity: Is torque still a vector? In classical mechanics it is easy: You have 3 axes and thus 3 planes. Every plane has its own torque so torque has 3 ...
1
vote
0answers
16 views

Consistency of the Speed of Light [duplicate]

My question is simple and possibly stupid, but I wanted to know hypothetically what would happen if two objects start moving away from each other at half the speed of light (0.5c). Is the observed ...
1
vote
3answers
424 views

Does the the quantum field theoretic process of particle–antiparticle annihilation break the axioms of Special Relativity?

$\textbf{Note that this diagram hasn't anything to do with the question directly.}$ After a particle and its antiparticle annihilate, their energy is converted into a force carrier particle, such ...
29
votes
5answers
3k views

What do you really see on a line of clocks as you pass by them at high speed?

According to my understanding of SR, if I travel at 0.8c relative to a line of clocks, I should see the clocks in front of me going 3 times faster than my own, and those behind me going 3 times slower ...
1
vote
1answer
114 views

Quantitative relation between two charges moving in parallel in two frames of reference

The relevant question is here. The accepted answer may have explained my question in a descriptive manner. However, I want to see how things are related quantitatively. Imagine we have two charges ...
0
votes
3answers
72 views

How should two particles accelerate to have their separation Lorentz-contract?

Suppose we have two particles with initial separation of $|x_2^\text{init}-x_1^\text{init}|=d$. At time $t=0$ they start accelerating with proper acceleration of $w$. Then position of the $i$th ...
8
votes
2answers
3k views

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 ...
5
votes
3answers
2k views

Why does light travel at the same speed when measured by a moving observer? [duplicate]

I know the hypothesis that the light speed is constant is retained by experiments. But is there any theory explaining why the light speed is constant no matter how an observer moves relative to light? ...
1
vote
2answers
132 views

Do the effects of special relativity occur instantaneously?

Imagine a second earth one lightyear away from our earth. Now imagine a bunch of scientists with a plane and some atomic clocks who are living on this second earth and who perform the Hafele-Keating ...
0
votes
2answers
705 views

What is pseudo tensor?

What is the pseudo tensor in relativity? How do we transform tensor and pseudo tensor under parity?
0
votes
1answer
53 views

Special Relativity - Reconciling 3 different frames

A Space Station S has two ships parked at it: P - PuttPutt and Q - Quick. S, P and Q synchronize their clocks. At noon P and Q take off in the same direction. P quickly accelerates to $c/4$ and Q ...
1
vote
4answers
344 views

Relativity of simultaneity example in Resnick

My question is a follow-up to this question about simultaneity. I would have posted it as a comment to the replies for that question, but I wasn't allowed to. When Resnick introduces relativity of ...
1
vote
3answers
263 views

Relativity and photon interactions

A particle's interaction (with anything it can interact with) can be thought of as it making a measurement of the physical quantity associated with the interaction, (e.g. electric field in case of the ...
2
votes
1answer
149 views

Notation for Translation Group Generators

The generators of the translation group $T(4)$ are given below: $P_0 \equiv -i \begin{pmatrix} 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 \\ 0 ...
8
votes
2answers
121 views

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 ...
9
votes
2answers
202 views

What axiomatizations exist for special relativity?

Einstein 1905 gives the following axiomatization of special relativity (Perrett and Jeffery's translation): The laws by which the states of physical systems undergo change are not affected, whether ...
3
votes
4answers
560 views

Is special relativity axiomatic?

Can special relativity be somewhat described by the following statement? If the speed of light is a universal constant, and if light can be placed in separate frames of motion, then time must be ...
34
votes
6answers
23k views

Why does GPS depend on relativity?

I am reading A Brief History of Time by Stephen Hawking, and in it he mentions that without compensating for relativity, GPS devices would be out by miles. Why is this? (I am not sure which relativity ...
2
votes
0answers
54 views

How to show isotropy of $SU(2)$ Yang Mills stress energy tensor?

When I vary the action of the YM Lagrangian density $$L = -\frac{1}{4} F^a_{\mu \nu}F^{\mu \nu}_a + J_a^\mu A^a_\mu$$ with respect to the metric, I obtain: $$T_{\mu \nu} = \frac{-2}{\sqrt{|g|}} ...
4
votes
2answers
163 views

Why is binding energy $\Delta mc^2$?

As we know the mass-energy equivalence relation $E=mc^2$ originally came from special relativity. And the binding energy is $\Delta mc^2$. How do we know that the extra mass coming from theoretical ...
1
vote
1answer
59 views

Time difference in clocks of an accelerated frame [closed]

If we have two inertial frames $S$ and $S'$ and $S'$ is moving to the right w.r.t. $S$ with a velocity $v$. Suddenly $S$ undergoes negative acceleration (no longer being inertial) and after some time ...
1
vote
1answer
102 views

What is the speed of light from a star moving towards a observer.? [duplicate]

We can say that in vacuum speed of light is constant. But if the star is moving with a certain velocity does it add that velocity to the velocity of photons emitted out of that star?
3
votes
2answers
63 views

Why is radiation for an ultrarelativistic charge zero on axis?

I attribute it to the fact that for an ultrarelativistic charge the field is contracted and essentially there are only fields in the transverse direction and nothing longitudinally (wrt the charges ...
4
votes
1answer
256 views

Length Contraction in a Particle Accelerator

Consider $N$ particles equally spaced on a circle which are uniformly accelerated to $99\%$ the speed of light. In Newtonian mechanics, the distance between the particles would be $2\pi r/N$ (for ...
1
vote
2answers
129 views

Is the concept of rest mass correct?

Is the concept of rest mass correct? All these years, we (me, and my classmates of Undergraduate 1st Year) have been accustomed to the concept of rest-mass, and the relativistic transformation of ...
0
votes
1answer
133 views

Concerning a previous possible tachyon observation? [duplicate]

A few years ago there was a story about the Large Hadron Collider where a possible tachyon was supposedly observed. It was later shown it didn't occur yet the incident made me think. If a large ...
3
votes
1answer
210 views

Moon's orbit period as seen from a spaceship traveling at 0.8c

I am studying special relativity and I am trying to figure out the following small problem which occurred to me: An observer, the pilot of a spaceship flying to or from earth at v = 0.8c, is ...
0
votes
2answers
110 views

$F=ma$ calculation taking relativity into account?

Newton's second law of motion states that $f = ma$. However, in this equation, theoretically there could be a value of $f$ and $m$ that results in an acceleration that is enough to push an object past ...
1
vote
1answer
95 views

Verification of the Poincare Algebra

The generators of the Poincare group $P(1;3)$ are supposed to obey the following commutation relation to be verified: $$\left[ M^{\mu\nu}, P^{\rho} \right] = i \left(g^{\nu\rho} P^{\mu} - g^{\mu\rho} ...
0
votes
1answer
382 views

Showing Dirac equation's Lorentz invariance and use of unitary matrix $U$

Dirac equation is $i \hbar \gamma^\mu \partial_\mu \psi - m c \psi = 0 $ To show its Lorentz invariance, we convert spacetime into $x'$ and $t'$ from $x$ and $t$ and then $( iU^\dagger \gamma^\mu ...
2
votes
0answers
366 views

How to derive equation for probability current density in relativistic quantum mechanics [closed]

How does one derive equation for probability current density in relativistic quantum mechanics? I am asking for textbook-styled explicit derivation. No need for any other background knowledge.
2
votes
2answers
481 views

If two events separated by a spacetime interval of zero, can they both be said to be happening “now”?

Can the concept of c be validly expressed as "the rate at which an event propagates through space"? There was a television program last year featuring Prof Brian Cox. The presenter asked him "Is it ...