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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Speed of Light and Special Relativity

If light is travelling vertically upwards and I am travelling horizontally and perpendicular to light, the velocity of light in the vertical direction will get reduced. How does this happen? How does ...
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187 views

Rigorous definition of frame of reference

I'm looking for a mathematical definition of frame of reference. Most of the textbooks I have seen take it for granted and they just refer to some set of spacetime coordinates. A more mathematical ...
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250 views

What does 99.9% speed of light mean when there is no absolute velocity?

So when people say: 'I am approaching the speed of light, and to get to 100% light I would need infinite energy' they are essentially saying that this situation is impossible? I read this in ...
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Possible values of energies and impulses of virtual photon emitted by real electron

I need to find the possible values of energies and impulses of virtual photon emitted by real electron. I don't understand how to compute it (look to the text below). Let's introduce the free ...
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192 views

Speed of light travel

I have just started special theory of relativity. The limiting speed known as speed of light fascinated me most. I asked my teacher: Consider two massless objects moving in the same direction at ...
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84 views

Quantum Eraser under Lorentz Boost

Suppose I am conducting the Quantum Eraser experiment. The results of this experiment are easy to understand with the traditional quantum mechanical interpretation of a pair of entangled photons. ...
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Lenght contraction question

Say I have a ball at 0.999999% the speed of light going past the Sun toward Earth. Now from the ball's reference frame, the distance between Earth and Sun is the same lenght as the ball's diameter. My ...
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72 views

Speed of light and relativity [duplicate]

Suppose there are two observers $A$ & $B$ both are in motion, now $A$ sees $B$ is moving with speed $'u'$. A says that another object $'d'$ is moving with speed $c+u$ w.r.t. A in the same ...
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94 views

Lorentz Transformations

I am trying to understand Lorentz Transformations in SR. I have some doubts. 1) In the derivation for Lorentz Transformations, why do we assume that Galilean Transformations hold true when an ...
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42 views

Allowed transformations in General Relativity [duplicate]

So in Special Relativity we have: $$ \Lambda \eta \Lambda^T=\eta $$ Is there an analagous formula for the metric in General Relativity?
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32 views

Relativistic aberration - half-sky radius

With relativistic aberration, a sky full of stars gets concentrated in the direction of motion. As a rough measure of the degree of concentration, one could use the radius of a small circle, centered ...
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63 views

Relativistic Black Hole? [duplicate]

So recently, looking at high energy particles through the lens of General and Special Relativity has peaked my interest. One thing I was considering, using the electron as the first example, is as ...
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Do all massless particles (e.g. photon, graviton, gluon) necessarily have the same speed $c$?

I suppose there was a discussion already on speed-of-gravity-and-speed-of-light. But I silly wonder whether all the massless mediators of four fundamental forces, i.e. Graviton: $g_{\mu\nu}$ ...
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40 views

How is the universe is experienced at light speed? [duplicate]

When moving faster, we experience time dilation and space contraction. We often state that a photon does not travel through time, i.e. if it where capable of observation, it would not experience time. ...
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116 views

Faster than light possibility? [duplicate]

According to general relativity, speed is relative, so for example if you are running at 20 km/h and a car passes you at 30 km/h, the runner is actually moving at 50 km/h relative to the car. Now ...
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90 views

Relationship between mass preserving four-fources and proper acceleration

Background I studied Rindler's book on Relativity. Relevant information from this book is available on-line here: http://www.scholarpedia.org/article/Special_relativity:_mechanics Given that we ...
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139 views

Definition of Lorentz transformations as transformations of the universe?

Following Arnold's [1] definition of the universe as an affine space $ A ^4$ with the group $\mathbb R ^4$ acting on it, we may define a galilean transformation as an affine map $g:A^4 \to A^4$ which ...
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46 views

Space as a function of time? [duplicate]

So - a little bit of background. Obviously from Einstein's equations it's shown that energy can be converted to matter and vice versa; in essence, energy and matter are different manifestations of the ...
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132 views

Lorentz boost matrix in terms of four-velocity

As I understand it, the value of a 4-vector $x$ in another reference frame ($x'$) with the same orientation can be derived using the Lorentz boost matrix $\bf{\lambda}$ by $x'=\lambda x$. More ...
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Clocks tick steadily, so why is there no photon time? [duplicate]

Consider a photon bouncing left and right between two mirrors in a photon clock. Seen from inside the clock, the photon bounces at a constant frequency. Time ticks regularly. No matter whether the ...
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78 views

Nuclear fission or fusion occurring at or near the speed of light

Suppose a device or object were traveling at or near the speed of light, and fission or fusion occurred while in this state of motion, creating an enormous blast, what would occur? Would this cause an ...
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110 views

What is the significance of Einsteins postulate on speed of light?

Einstein postulated that the speed of light in free space is the same for all observers, regardless of their motion relative to the light source, where we may think of an observer as an imaginary ...
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Proving invariance of $ds^2$ from the invariance of the speed of light

I've started today the book of Landau and Lifshitz Vol.2: The Classical Theory of Fields $\S 2$. They start from the invariance of the speed of light, express it as the fact that $$c^2(\Delta ...
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What is the theoretical upper limit on the rigidity of a material?

Take a perfectly rigid metal rod of length $\ell$ and some uniform linear density. Place one end at $(0,0)$ and the other at $(0, \ell)$. Over some reasonably short time interval $t$, perhaps on the ...
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307 views

Did Einstein know about Michelson-Morley experiment?

The second postulate of special relativity deals with constancy of light in inertial reference frames. But, how did Einstein came to this conclusion? Did he knew about the Michelson-Morley experiment? ...
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141 views

Showing the Poincare invariance of a term

I know that this is a simple question! But I would like to know the details. How we can show that the term $$A_\mu(x)\dot{x}^\mu$$ is global and local Poincare invariant? Where $A_\mu(x)$ is ...
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At near light speeds, are small objects in your path a problem?

A mental exercise: A space ship is accelerating toward me from far away. As it approaches me, I can observe its acceleration. This high speed ship keeps accelerating faster toward the speed of light. ...
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107 views

Question on energy mass conversion

I have a question regarding the energy-mass conversion. Well, when a particle starts moving with a speed comparable to that of light, its (relativistic) mass increases that means some matter is ...
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42 views

Su­per­lu­mi­nal in­ter­ac­tions

The fact that photons emitted from an electric-dipole active atom cannot be spatially localized better than to the near-field zone of the atom is seen as the origin of genuine superluminality. ...
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118 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 ...
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138 views

Will Earth clock be slower than aeroplane clock when viewed from another planet?

I know that a clock placed on an aeroplane will have slowed with respect to a clock placed on earth because the more our velocities are, compared to the speed of light, the more the time slows down. ...
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124 views

What really happens with Time Dilation? [duplicate]

I know if you move your time moves slower than someone who is stationary, by Lorentz's transformation. However, I don't get how this happens. What does it mean when time moves slower? How does it ...
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52 views

Muons Internal Clocks and Time Dilation? [closed]

I don't get how time dilation affects the half-life of muons? Time is just a tool that is used by humans how does that affect the internal clocks of elementary particles?
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Gravitational field of a particle in SR

According to special relativity, what is the gravitational field due to a particle moving with a constant velocity v? Would it be correct to assume that the particle has a stronger gravitational field ...
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Velocity of the photon

As far as I know photon travels in a wave pattern, that means it has $x$ and $y$ axis velocity components. If photon travels along $x$ axis, then what is it's maximum $y$ axis velocity?
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Does length contraction affect travel time?

If an astronaut leaves planet $A$ for planet $B$ at speed $v$, will the time (measured by the astronaut's clock) that it takes for the astronaut to reach planet $B$ be less than the distance between ...
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57 views

Deduction of relativistic mass formula in 1+1 dimensions

I have read the explanation/calculation of relativistic momentum and relativistic mass in the Feynman lectures, see chapter 16.4 here: http://www.feynmanlectures.caltech.edu/I_16.html. (I guess this ...
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Fundamental invariants of the electromagnetic field

It is a standard exercise in relativistic electrodynamics to show that the electromagnetic field tensor $F_{\mu\nu}$, whose components equal the electric $E^i=cF^{i0}$ and magnetic ...
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Majorana equation and non-invariance of spinor representation under discrete Lorentz transformations

Here I asked about getting an equation for two-component spinor as the alternative for Dirac equation. It was found that it is called Majorana equation. It may be easily derived by using historical ...
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Peskin and Schroeder Equation 3.23

I've been trying (for a while) to prove that $S^{\mu\nu}:=\frac{i}{4}\left[\gamma^\mu,\,\gamma^\nu\right]$ is a representation of the Lorentz Lie algebra, that is, to prove that it satisfies the ...
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Twin Paradox in case of two twins that don't meet

If there are two twins. such that one of them goes on a space voyage maintaining a constant velocity, and that one never returns to earth, and the twins decide to never meet but send information about ...
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Proper time in Nordstrom gravity

This wikipedia article claims that there are two interpretations of Nordstrom's scalar theory of gravity: 1) A scalar field theory on flat space. The reason why an apple falls is that its mass is ...
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Speed of light, lasers and mass

Hopefully this isn't a bad question. Light travels at the speed it does and nothing else can travel that fast because things have mass, correct? Or at least correct on an elementary level. And if ...
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Unitary Lorentz transformation on quantized Dirac spinor

I am stuck again on page 59 of Peskin and Schroeder. In particular, I do not know how they get equation (3.110). Let me first give some background in the way that I understand it (but I might be ...
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193 views

Trying to rhyme Peskin and Schroeder with Weinberg

This is a follow up question of this one. In the Vol 1, Weinberg derives how a unitary operator $U(\Lambda)$ acts on one-particle states, which is given by equation (2.5.2): \begin{equation} ...
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100 views

Question about Weinberg's derivation of a one-particle states under the Poincare group

I'm reading QFT: Vol 1 by Weinberg and I have a (perhaps trivial) question about a statement he makes on page 63. I can follow him to his derivation of equation (2.5.2): \begin{equation} P^\mu ...
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131 views

Combining relativistic velocities in the same direction using Lorentz transformation matrices

It is known that when combining the Lorentz Transforms of two frames with velocities $v_{1}$ and $v_{2}$ in the same direction it is equivalent of computing a Lorentz Transform of a single frame with ...
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Infinitesimal Lorentz transformation is antisymmetric

The Minkowski metric transforms under Lorentz transformations as \begin{align*}\eta_{\rho\sigma} = \eta_{\mu\nu}\Lambda^\mu_{\ \ \ \rho} \Lambda^\nu_{\ \ \ \sigma} \end{align*} I want to show that ...
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Do photons age in a medium?

According to special relativity, time starts to slow down as we increase our speed and eventually stops once we get to the speed of light. By that logic, photons don't age in a vacuum state as, to us, ...
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Time Slowing Down [duplicate]

I'd like to ask a question if I may about the relativity. When travelling at the speed of light(which is impossible for particles with masses) or very close to it, would it be me, myself, seeing my ...