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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395 views

Point charge 4-current derivation

How do I derive that the 4-current of a point charge is $$j^{\mu}(x)=ec\int_{-\infty}^{+\infty}\dot{z}^{\mu}(s)\delta(x-z(s))ds$$ where $\dot{z}^{\mu}(s)$ is the 4-velocity of the charge and $s$ is ...
2
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1answer
145 views

Lorentz invariance of the wave equation

I want to show that the 2-d wave equation is invariant under a boost, so, the starting point is the wave equation $$\frac{\partial^2\phi}{\partial x^2}=\frac{1}{c^2}\frac{\partial^2\phi}{\partial ...
3
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1answer
638 views

Fermi Walker vs. Fermi transport

A vector field $f^\mu$ is said to be Fermi-Walker transported along a curve $\gamma$ parametrized with $\tau$ if the following holds $$\frac{\mathrm{D}}{\mathrm{d}\tau}f^\mu = -(a^\mu v^\nu - a^\nu ...
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2answers
285 views

Inertial Frames of Reference - Description of an Inertial Frame of Reference

An inertial frame of reference is described as being a frame of reference in which the first law of Newton (the law of inertia) holds. This means that all events as described with respect to this ...
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1answer
94 views

Developments originating from $E=mc^2$

What kind of significant impacts have originated from $E=mc^2$. Generally, it is regarded as the most famous equation of all time. Except for nuclear energy (fission and fusion) I do not know any ...
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1answer
160 views

Tensor manipulation

Having a bit of trouble applying what I know about tensor manipulation, given, $T^{\mu \nu} = \left( g^{\mu \nu} - \frac{p^\mu n^\nu + p^\nu n^\mu}{p \cdot n} \right)$, I need to compute quantities ...
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1answer
215 views

Sign and Four Acceleration Special Relativity

If $ use $(+,-,-,-)$ sign convention then four position, four velocity become positive but four acceleration becomes negative! $x_{\mu}x^{\mu}=\tau^2c^2,$ $U_{\mu}U^{\mu}=c^2,$ ...
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1answer
46 views

How the effect travel's? [duplicate]

Let us assume that we placed lot's of ball touching each other in a hollow cylindrical tube, now if we push one ball at the end the ball at the other end move's instantly. So how do the information ...
2
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1answer
484 views

Angular velocity and the speed of light

So, accelerate a particle to just under the speed of light, then send it round a bend, technically it accelerates due to the change of direction, will its speed exceed or match $c$? Keep it simple, ...
7
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1answer
508 views

What if the binding energy becomes larger than the rest mass?

Looking at the equation for binding energy and mass defect, $$ B = m_{\text{free}} - m_{\text{bound}} \\ \Rightarrow m_{\text{bound}} = m_{\text{free}} - B, $$ my question is the following. Suppose ...
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2answers
765 views

Lorentz boost matrix for an arbitrary direction in terms of rapidity

We have derived the Lorentz boost matrix for a boost in the x-direction in class, in terms of rapidity which from Wikipedia is: Assume boost is along a direction $\hat{n}=n_x \hat{i}+n_y \hat{j}+n_z ...
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1answer
121 views

What's the relativistic energy of a moving strained spring as $k\to\infty$ [closed]

Suppose a spring with stiffness $k$, is strained by constant forces on each end. In a frame where the strained spring moves at a constant velocity, what's the total relativistic energy of the moving ...
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3answers
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Can something travel faster than light if it has always been travelling faster than light?

I know there are zillions of questions about faster than light travel, but please hear me out. According to special relativity, it is impossible to accelerate something to the speed of light. However, ...
2
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2answers
777 views

What is potential energy in special relativity?

I know what is rest energy $E_0=m_0 c^2$, total energy $E=\gamma E_0$, kinetic energy $E- E_0=(\gamma-1) E_0$, and momentum $p=\gamma m_0 c$. But what is potential energy in special relativity?
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2answers
503 views

Causality and Quantum Field Theory

I have a problem with proof of causality in Peskin & Schroeder, An Introduction to QFT, page 28. To avoid confusion I use three vectors notation, rewriting the Eq. (2.53) for $y=0$ as follows: ...
9
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2answers
554 views

Violation of Lorentz invariance (Lagrangian for particle)

I'm trying to get the relativistic action (or Lagrangian) for a free particle in the case of violation of Lorenz invariance. Suppose we have the modified dispersion relation: $$ ...
2
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2answers
295 views

Why is there no time dilation for frequency of a wave?

Since frequency of a wave is a function of time, then for a particular ray of the wave, why would the frequency remain the same when observed from a moving reference frame? The frequency should change ...
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2answers
364 views

Is the curvature of spacetime invariant? Could it be characterized as the ether?

I'm writing a paper for a Philosophy of Science course about GR/SR and I'm wondering if I can (1) characterize the curvature of spacetime as invariant and (2) argue that this is what Einstein referred ...
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1answer
139 views

How would time duration and space distance change when we move in the speed of light? [closed]

It is possible to figure out how time duration and space distance change when we are close to the speed of light - but I am not sure what happens to them if we travel in the speed of light.
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0answers
37 views

Why can't we accelerate to the speed of light? [duplicate]

Why can't we accelerate to the speed of light? It's just a speed and nothing else. Universe also crossed the speed of light at the time of big bang. Is this is just a interpretation or there is any ...
5
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2answers
146 views

What are the uses of proper length as a parameter?

Proper time is used to parameterize the world line of a moving particle in a way which is Lorentz invariant, which is elegant and powerful. Since space and time are usually treated on the same ...
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2answers
297 views

What is the highest speed time dilation has been tested?

What is the highest speed time dilation has been tested? How close to the Special Relativity prediction did it get?
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1answer
374 views

Life of a photon [duplicate]

I am a student of class 12th and as far as i know when anything reaches about 99.99% of the speed of light it starts traveling in time or time for it slows down so that it don't breaks the speed ...
2
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3answers
138 views

Please explain this statement about Lorentz transformations

I'm reading Sternberg's Group Theory and Physics. I have a question about chapter 1.2 Homeomorphisms. Background: A Lorentz Metric is defined as $||{\bf x}||^2=x_0^2-x_1^2-x_2^2-x_3^2$ And a ...
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2answers
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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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1answer
449 views

Faraday's Law and Galilean Invariance

In Jackson's text he says that Faraday law is actually: $$ \oint_{\partial \Sigma} \mathbf{E} \cdot \mathrm{d}\boldsymbol{\ell} = -k\iint_{\Sigma} \frac{\partial \mathbf B}{\partial t} \cdot ...
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1answer
128 views

Senior High School work on Doppler measurements

Sorry this question is really vague- as a result I'm very confused. Perhaps you can help me make sense of it. "Radar measurements: Construct a space-time diagram of the radar tracking of an asteroid ...
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1answer
292 views

Lorentz transformation problem

In the equation (1.18) they omitted the translation vector $a^\mu$, but why?
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1answer
37 views

Measuring life through radiation

Dramatic title, I know. But it's shorter than Measuring a person's effective mass through radiation and comparing it to their weighed mass and I figured this would get people's attention. I just ...
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3answers
401 views

If time slows down when you move faster, does this give you an “effective speed” different from your proper speed?

Suppose you're travelling at 0.9c toward the sun, and you tag past the Earth and start a clock. Would Lorentz contraction/time dilation cause you to get to the sun faster than (about) 9 minutes ...
3
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2answers
780 views

Metric coefficients in rotating coordinates

Let $(t,x,y,z)$ be the standard coordinates on $\mathbb{R}^4$ and consider the Minkowski metric $$ds^2 = -dt^2+dx^2+dy^2+dz^2.$$ I am trying to compute the metric coefficients under the change of ...
4
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1answer
544 views

Mass of a compressed spring

I was wondering if: The mass of a compressed spring is greater than that of an uncompressed spring The mass of a body on the surface of the Moon is greater than that on Earth according to the ...
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0answers
100 views

Car parking special-relavity puzzle

Hi I read the following puzzle from an old text book long time ago. However it doesn't provide the answer. So what is the solution? Let's suppose a car is going to park to a garage and the garage is ...
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1answer
127 views

What is movement through time? [duplicate]

In general, when I think of movement through space, I think of this: $$\frac{dx}{dt}$$ But in special relativity, we also have a concept of relative duration, which means that $t$ must have a rate ...
5
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1answer
568 views

Lorentz transformation of classical Klein–Gordon field

I'm trying to see that the invariance of the Klein–Gordon field implies that the Fourier coefficients $a(\mathbf{k})$ transform like scalars: $a'(\Lambda\mathbf{k})=a(\mathbf{k}).$ Starting from the ...
5
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2answers
853 views

Impulse from absorbing a photon? Is there an increase in rest mass?

I'm going through A P French's special relativity. In one chapter (6) the following is set up: Suppose that a stationary particle of mass $M_0$ is struck by a photon of energy $Q$, which is ...
5
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3answers
611 views

Why do clocks measure arc-length?

Apologies in advance for the long question. My understanding is that in GR, massive observers move along timelike curves $x^\mu(\lambda)$, and if an observer moves from point $x^\mu(\lambda_a)$ to ...
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3answers
341 views

Relativistic equivalent of a spring-force?

Usually what helps me understand a concept better in physics is to write a simulation of it. I've got to the point where I'm competent in the basics of special relativity, but, I can't figure out how ...
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1answer
282 views

Photons, no energy? [duplicate]

I am only 14, so I don't know much about physics, and I would appreciate help on this topic. A photon, is said to have 0 mass. However, they carry energy, as electromagnetic radiation. Albert ...
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1answer
122 views

The status / acceptance of block time?

What is the current status or acceptance of block time as it relates to Einstein's theory of relativity? Has quantum mechanics ruled it out or is it still the favored view of the world? Perhaps there ...
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4answers
1k views

The real meaning of time dilation

Is this true or false: If A and B have clocks and are traveling at relative velocity to each other, then to B it APPEARS that A's clock moving slower, but A sees his own clock moving at normal speed. ...
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1answer
233 views

Why does only one twin travel in the twin paradox?

The wikipedia page repeatedly says that the twin travelling in space is the only one which travels, and also is the only one which faces acceleration and deceleration. So it does not age, while the ...
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1answer
157 views

Special relativity, acceleration and being in two places at once (How to resolve this paradox?):

Imagine I am on Earth I have a clock which measures time $t$. When my Earth clock reads time $t$, then when I look at a moving spacecraft's clock I see the time $t'$. Let us assume time is measured ...
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2answers
525 views

If we are travelling with the speed of light, can we see what's behind us? [closed]

If we are travelling with the speed of light, can we see whats behind us(like if we are moving away from earth can we able see the earth)? And how we see the things that we are approaching with speed ...
14
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2answers
1k views

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 $$\phi(x)\phi^\dagger(y)\ne0.$$ ...
5
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3answers
182 views

How would I perceive a purple ball when traveling at relativistic speeds

I have a 'thought experiment' which I'd like to ask about. I was thinking what speed I would have to drive towards a crossing to see a red light as a green light - pretty easy, using the doppler ...
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Does Mansuripur's Paradox involve fictitious charges?

Mansuripur's Paradox involves a magnet moving at relativistic speeds in an external electric field. Additional: thanks to Retarded Potential, who found the original paper. If I understand correctly, ...
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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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4answers
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Is time dilation an illusion?

It is said that we can verify time dilation by flying a very accurate clock on a fast jet or spaceship and prove that it registers less time than the clocks on earth. However, the clocks on earth ...
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1answer
318 views

Why does 'proper length' exist as a notion?

$$\text{proper time}= \tau= \sqrt{dt^2-d\mathbf{s}^2}$$ $$\text{proper length}= L= \sqrt{-dt^2+d\mathbf{s}^2}$$ What tangible benefit is brought about by calling $i \tau$ 'proper length' (applying ...