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 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 ...
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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 ...
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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|}} ...
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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 ...
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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 \} $, where $\eta = \mbox{diag}(1, -1, -1, -1)$. I want to be able to characterize ...
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1answer
32 views

Time difference in clocks of an accelerated frame [on hold]

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 ...
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1answer
60 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?
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F-mu-nu notation [on hold]

This is a really simple question that I cannot find an answer to, strangely enough. What do these (similar) notations stand for: $F^{\mu\nu}$ $F_{\mu}^{\nu}$ $F^{a\mu\nu}$ etc etc.
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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 ...
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2answers
148 views

A question about special relativity theory

We have two sets: set No.1 and set No.2 as in this picture: The observer is fixed to set No.1 . He sees set No.1 motionless and observes set No. 2 approaching with velocity 100,000 m/s. Each set ...
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Moving coil contradiction of Faraday Induction

In Faraday's Induction Experiment, the e.m.f. induced in the induction coil becomes zero when the relative velocity of the coil and the magnet becomes zero. But one can also argue from a stationary ...
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2answers
71 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 ...
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3answers
447 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? ...
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2answers
68 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 ...
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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 ...
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1answer
58 views

Can speed be defined in the complex plane?

This question cropped up while I was playing with the equation for time dilation. If I set the speed to be $i$ (imaginary unit) the answer from the equation still makes sense, but does that matter if ...
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1answer
62 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 ...
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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.
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1answer
59 views

Bug riding on a ball moving at almost the speed of light [closed]

A ball with a bug on it is thrown at almost the speed of light. The bug looks back and observes the thrower throwing the ball. In the context of special relativity, what is the weight and the height ...
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1answer
52 views

Definition of causality relation

It seems to me that special relativity has a weird definition of the causality relation. In that theory, the only thing that matters is the space-time distance between events. But I don't think this ...
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2answers
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Length contraction and simultaneous length measurements

I am just working through an argument from Halliday Resnick to derive the Lorentz contraction (see quote below). Some paragraphs before this, the authors note that: If the rod is moving, ...
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1answer
130 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 ...
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2answers
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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 ...
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71 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} ...
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1answer
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Massless particles and the speed of light - New? Theories of existence [closed]

"The best understanding we have is that it [light] is a disturbance in the electromagnetic fields of charged bodies." http://einstein.stanford.edu/content/relativity/q212.html This is a link to the ...
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108 views

How does it seem to be that space/time always equals c?

Given the way objects move, they seem to be going all the same "velocity" so to speak, that velocity being the speed of light. Except, velocity is displacement/time, so if something goes faster, the ...
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Derivation of force law in special relativity

I've seen force defined in special relativity as the rate of change of 4-momentum $$ {\bf{F}} = \frac{d {\bf{p}}}{dt} $$ Can anyone comment on the following derivation of that relation? Take one ...
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4answers
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How much could one slow down aging using existing spacecraft?

Imagine that I board a spacecraft and head away from the Earth at top speed until I've aged twenty years, then I turn around and come back. How much younger will I be than the unexciting folk who hung ...
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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 ...
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5answers
349 views

Why Light and Observers have different laws of physics [closed]

Special relativity states: The speed of light in a vacuum is always $c$, regardless of the velocity of the observer. The laws of physics are the same for all observers in uniform motion. These two ...
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Twice the speed of light [duplicate]

If you were able to ride along a photon and a second photon passed you in the opposite direction, would what you observe be twice the speed of light? And would that change what you would see of the ...
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Metric tensor in special and general relativity

I'm having trouble understanding the metric tensor in general relativity. What I've understood so far has come from my course lecture notes used in conjunction with "The Road to Reality" by Roger ...
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Frame dragging — is there a “non-tiny” example?

Now. As I understand it, in fact, the earth (10^25 kg) creates a very small, very tiny, frame dragging effect. Indeed, we have measured this using satellite experiments. So, the Earth (10^25 kg) ...
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Special relativity allows arbitrarily low travel times between two locations [duplicate]

I wish I had a good way of illustrating this, but anyway, doesn't the following travel strategy allow you to get anywhere in arbitrarily little time? You're at rest at the origin of space-time, and ...
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1answer
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Two related questions about double-slit experiments moving at a relativistic speed

I was wondering as how would appear the interference pattern of a double-slit experiment moving at a relativistic speed v, 1) in the case of light and, 2) in the case wave matter (i.e. electrons for ...
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Do the laws of physics that apply to all observers also apply to a non-observer? [closed]

The Timelessness of a photon https://www.youtube.com/watch?v=5ELA3ReWQJY An observer's laws of physics are time based. "When you're traveling at the speed of light, time does not exist" - Neil ...
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63 views

Gravitational atraction of fast object [duplicate]

Let's imagine a asteroid that travels with 0.99999999999999999c. (I know it's impossible). Anyway... Relativistic mass of such object would be almost equal to earth's stationary mass. Now let's ...
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1answer
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Twins Paradox Paradox

I've recently has special-relativity explained to be in a rather elegant way. All objects travel at the speed of light in space time. Thus, when you travel faster through the three dimensions of ...
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1answer
55 views

Relatvity of Promise [closed]

Suppose there are two observers moving at a speed c/2 w.r.t. each other. Now they won't agree on simultaneity of space separated events. Now they decide to host a race between two racers, with common ...
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1answer
92 views

Does physics recognize the particle of light separately from the wave of light? [closed]

To frame this question, we need to assume that time freezes when traveling at the speed of light. This is theoretically congruent with Einstein's theory of relativity and the theory of time dilation, ...
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Does time move slower at the equator?

While answering the question GPS Satellite - Special Relativity it occurred to me that time would run more slowly at the equator than at the North Pole, because the surface of the Earth is moving at ...
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Twin Paradox speed of light

Twin Paradox Can anyone clarify and or correct the following for me? A space ship is flying at speed v equal to 0.8 times the speed of light. Within the ship are three stations, a transmitter at ...
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GPS Satellite - Special Relativity

I'm going through an old relativity assignment, and I've been asked to calculate the time dilation for a satellite which orbits the earth in 12 hours at 26000km from the surface, and travels at a ...
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1answer
27 views

Action of the Poincare Group on a Scalar Function

Let $F(x^\mu)$ is a scalar function; i.e. $F(x^\mu): \mathbb{R}^{1,3} \rightarrow \mathbb{R}$. How the Poincare Group $P(1,3)$ will act on it; i.e., by which formula I can calculate it for a specific ...
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Dilemma in race between muon and light

I have a dilemma concerning my understanding of Special Relativity. Maybe I am understanding or calculating something wrong and would hear so. The problem is based on muons created in the upper ...
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Is the Speed of Light an universal spacetime constant, the velocity of electromagnetic waves, or of photons?

This question has been touched tangentially by What's a better phrase than "speed of light" for the universal spacetime speed constant? and Could light travel more slowly than the ...
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Why do we say that light travels at a speed? [duplicate]

According to Einstein's theory of relativity, the more speed something has the slower that time passes for it; and presumably when traveling at the speed of light, time stops entirely. So this means ...
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7answers
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Relativity of Simultaniety

In the first figure, A and B are two equidistant points from the observer O in S. In the second figure (reference frame S') the corresponding points are A'and B' such that A'O'=O'B', where O' is the ...
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Repulsion and attraction of electric currents

Now, I understand that when a an electron travels, it creates a magnetic field. If you put two wires with current traveling in the same direction they repel, and current traveling in opposite ...
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Why does Coulomb's law not hold for fast moving charges?

We all remember calculating the electric force of interaction between a stationary nucleus and a revolving electron using Coulomb's law. The electron in this case is moving. Here's what I think about ...