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 does this summation mean in relativity?

Equation 1.2 of 't Hooft's Introduction to General Relativity gives the Lorentz transformations: $$ (x^\mu)' = \sum\limits_{\nu = 1}^4 {L^\mu}_\nu x^\nu $$ Is this the sum of four square matrices ...
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Understanding the difference between co- and contra-variant vectors

I am looking at the 4-vector treatment of special relativity, but I have had no formal training in Tensor algebra and thus am having difficulty understanding some of the concepts which appear. One ...
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6answers
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What keeps mass from turning into energy?

I understand the energy and mass can change back and forth according to Einstein. It is fluid; it can go from one to the other. So, what keeps mass from just turning into energy? Is there some force ...
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242 views

How is Momenergy frame independent?

momenergy = mass * spacetime displacement/proper time for that displacement What I dont understand is how can the momenergy be frame independent? The unit-4 vector always points in the direction of ...
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1answer
2k views

Why does light travel at finite speed? [duplicate]

We have known for quite some time now that light travels at a finite speed of 3x10^8m/s (approx) through vacuum. But why is that? Why can't the speed be infinite? Or at least higher than the current ...
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322 views

Did the Goudsmit-Uhlenbeck analysis of spin consider relativity?

It's frequently mentioned in introductory quantum mechanics texts that Goudsmit and Uhlenbeck conjectured that the magnetic moment of an electron was due to angular momentum arising from the electron ...
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Deriving the Electromagnetic Tensor

The electromagnetic tensor is given as: \begin{equation} F_{\mu \nu} = \partial_\mu A_\nu - \partial_\nu A_\mu \end{equation} How do you derive this? And how come there is a partial derivative in ...
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122 views

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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293 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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5answers
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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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0answers
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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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4answers
487 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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0answers
138 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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3answers
136 views

How is length contraction reconciled with other objects occupying space?

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 length as the ball's diameter. ...
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2answers
110 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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1answer
213 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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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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48 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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0answers
125 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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4answers
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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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1answer
66 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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1answer
336 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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2answers
151 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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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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55 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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1answer
505 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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1answer
276 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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1answer
342 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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2answers
338 views

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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1answer
243 views

What is the theoretical upper limit on the rigidity of a material?

Take a perfectly rigid metal rod of length $2\ell$ and some uniform linear density. Place one end (‘south’) at $(0,-\ell)$ and the other (‘north’) at $(0, \ell)$. Over some reasonably short time ...
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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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2answers
179 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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158 views

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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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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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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263 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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2answers
725 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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1answer
426 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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1answer
84 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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4answers
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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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0answers
136 views

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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2answers
522 views

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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2answers
285 views

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 ...
2
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1answer
257 views

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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262 views

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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1answer
484 views

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 ...