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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Special Theory of relativity on electromagnetic waves

Since time slows down and length contracts, when we travel almost at speed of light, if the speed of light (or EM waves) remains same and the wavelength of light remains same, do we measure the ...
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Is there any experimental evidence to support the Terrell rotation?

The Shapiro delay was predicted in 1964 and observed by 1966, and is now a tool used to measure the mass of distant binary pulsars. The Terrell-Penrose rotation was published in 1959, but I can find ...
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358 views

What if a faster-than-light particle is found?

What will be the consequence (severe ones) on laws of physics if a particle that travels faster than light is discovered? I am looking for a more general answer so that a high school student would be ...
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Meaning of spin

I'm pretty astounded that I did not hear about this sooner, but in my course on QFT our professor told us that the concept of spin can be used to mean three things: Mechanical spin (apparently a ...
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Lorentz invariance of the action for free relativistic particle

I tried to check the Lorentz invariance of the standard special relativity action for free particle directly: ($c=1$) $$ S=\int L dt=-m\int\sqrt{1-v^{2}}dt $$ Lorentz boost: $$ ...
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358 views

Difference between proper and comoving frames

I'm reading this book "Introduction to Quantum Fields in Classical Backgrounds" by Mukhanov & Winitzki, and there in the chapter 8 "The Unruh Effect" they introduce 3 reference frames. Laboratory ...
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Clarification regarding Special Relativity

Empty the universe of all matter. Place the Earth in that universe sitting in an inertial frame. Take a pair of twins. One twin gets into a space ship and takes off from Earth (t=a). He ...
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81 views

Minimum $E$ of $p\bar{p}$-collision for $q\bar{q}$ pair with mass $m_q$

I am currently working out the energy required to create a particle anti-particle pair from a collision of a proton travelling along the x-direction with an anti-proton which is at rest. The particle ...
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About the theory of relativity

Why is speed of light constant in every non inertial frame of reference? Is there any theoretical explanation behind this postulate Since we cannot completely depend upon the experimental results?
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Understanding bending light beam perpendicular to motion

I'm just reading a book about gravity. An example it gives is a spaceship accelerating. A beam of light travelling at right angles to the direction of movement of the spaceship enters it via a small ...
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166 views

Bondi's k factor

Consider two observers, travelling away from each other, after meeting (at which time they sync their clocks). $O$ sends a photon towards $O'$ at times $t$, received by $O'$ at time $t'=kt$, where we ...
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Why does the inertial mass of an object rise when a force is exerted on it in a particle accelerator? [closed]

A particle in a cyclotron requires more and more force to maintain the same acceleration as it accelerates.
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169 views

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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677 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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3answers
249 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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238 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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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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1answer
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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237 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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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
198 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
113 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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339 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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211 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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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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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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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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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 ...
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1answer
298 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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376 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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478 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
115 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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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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415 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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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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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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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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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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181 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
252 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
121 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 ...
14
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2answers
957 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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218 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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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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Lorentz transformation problem

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