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 in relation to Acceleration

What I am looking for is a layman's explanation on the equations required to work out Time Dilation at high speeds including acceleration and deceleration of velocity. Or I would greatly appreciate it ...
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669 views

Integration by parts to derive relativistic kinetic energy

I have come across a weird integration during derivation of relativistic kinetic energy. Our professor states that i can get RHS out of LHS using integration by parts: $$ \int\limits_0^x \! ...
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124 views

How big is an inertial frame?

How big is an inertial frame? Consider a huge rod which is rotating about a fixed point in a plane, its length is 1 light year. Thus light from its end closer to the fixed point to the end farther ...
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243 views

How does the solar sailing concept work?

Wikipedia describes solar sailing as a form of spacecraft propulsion using a combination of light and high speed ejected gasses from a star to push large ultra-thin mirrors to high speeds. I ...
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236 views

Will observers moving on a sphere experience time dilation?

A single source of light exists at a fixed point in space relative to two observers. The two observers move on the surface of a shell with a fixed radius with the light source at its centre. They move ...
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2answers
149 views

Sign convention for basic Dirac equation

The dirac equation;$$(i\gamma^\mu\partial_{\mu} - m)\psi=0 $$ is just; $$(i\gamma^{0}\partial_{0} - i\gamma^{i}\partial_{i} - m)\psi=0 $$ in a (+,---) metric right?
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121 views

Where to read about Minkowski space [duplicate]

When I learned Special Relativity, it was taught in terms of basic linear algebra, without any mention of the Minkowski space, proper time as integration on the metric, etc. However, when I am trying ...
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236 views

Relativistic kinematics of particle decay

Suppose a particle decays to three other particles. The masses of all particles are assumed to be known and we work in the rest frame of the parent particle. So there are 12 parameters for this ...
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468 views

Generating artificial gravity by using rotation

If I want to design for futuristic space stations and I want to use rotation to produce artificial gravity. One of such designs consists of a giant ring that is rotated about its centre. If it were ...
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1answer
59 views

Wavefront emitted by bodies at traveling near the velocity of light

I studied that no body can travel with the velocity of light. But, assuming that when a body moves nearly velocity of light, will it obey length contraction law of Einstein or will it emit the same ...
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1answer
196 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 ...
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1answer
112 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 ...
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337 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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209 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
85 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
121 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
172 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
45 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
292 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, ...
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375 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
474 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
114 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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600 views

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, ...
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2answers
405 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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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: ...
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477 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: $$ ...
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2answers
197 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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289 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
110 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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30 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 ...
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2answers
122 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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178 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
246 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 ...
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120 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
946 views

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
216 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
106 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
227 views

Lorentz transformation problem

In the equation (1.18) they omitted the translation vector $a^\mu$, but why?
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32 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
270 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 ...
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2answers
395 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 ...
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1answer
261 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
87 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
72 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 ...
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1answer
341 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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1answer
434 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 ...
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3answers
424 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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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
166 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
111 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 ...