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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Translational and Rotational Energy in Special Relativity

In non-relativistic classical mechanics: $$\tag{1} \begin{eqnarray} \text{KE}&=&\frac{1}{2}\sum_i m_i v_i^2=\frac{1}{2}\sum_i m_i (\vec{v}_{cm}+\vec{v}_{i,rel})^2 \\ ...
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2answers
144 views

Paradox Regarding Time Dilation at the Speed of Light

Consider the following scenario: On earth, I pulse a laser focused at a far away mirror such that the time it takes for the light to reflect off the mirror and arrive back at me is at least a few ...
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What speed should have an alone planet to have a habitable zone due to relic radiation?

What speed should have an alone planet to have a habitable zone due to relic radiation, without any star involvement? How much time the planet will be able to remain in the habitable zone before the ...
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110 views

Spacetime and uncertainty principle

I only have limited knowledge of relativity and quantumphysics but as far as I know, the uncertainty principle relates the uncertainty of space and momentum of a particle. Einstein however, explained ...
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2answers
255 views

Why can't matter pass the speed of the light? [closed]

I have the following questions. Why can't matter pass the speed of the light? What happens to an object when it comes close to the speed of the light? What makes the object unable to surpass this ...
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2answers
153 views

Increase in Mass with Velocity [duplicate]

I just had a confusion. Does the mass of the body actually increase when it is moving with a certain velocity? Or does it only look like the mass has increase to another observer. How can the actual ...
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1answer
90 views

Physical meaning of the Rindler hyperbola vertex and the Rindler lines

Two questions regarding the Rindler diagram: 1) Does the vertex of a given hyperbola in the diagram have physical meaning? I know it is the inverse of the constant proper acceleration ($\alpha$) ...
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2answers
369 views

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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83 views

Time-Independent Gravitational Equation?

Is it possible to calculate gravitational induced position change without requiring the use of time (and therefore, acceleration) anywhere in the equation? If such an equation were to be discovered, ...
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95 views

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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Action-reaction principle in special relativity

Consider a relativistic train of weight $W_t$ in its rest frame. Force transformation equations say that in the planet's frame its weight is reduced to $W_p=\frac{W}{\gamma}$. My question is: what is ...
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1answer
107 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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375 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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1answer
77 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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1answer
446 views

Deriving the Electromagnetic Tensor

The electromagnetic tensor is given as: How do you derive this? And how come there is a partial derivative in front of $A_\mu$? Do you multiply the derivatives or what?
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1answer
99 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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4answers
427 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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59 views

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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3answers
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Is temperature a Lorentz invariant in relativity?

If an observer starts moving at relativistic speeds will he observe the temperature of objects to change as compared to their rest temperatures? Suppose the rest temperature measured is $T$ and the ...
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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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2answers
71 views

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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How is the speed of light constant in all directions for all observers?

Please imagine the following thought-experiment: Order of Events: Pulse - A single pulse of light is emitted from the light towards the mirror Reflect - The pulse hits the mirror and is ...
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2answers
329 views

About the standard derivation of the gravitational redshift

The objective is to derive the gravitational redshift ONLY from the Einstein's equivalence principle (E.E.P.), without using the whole theory of Relativity. This is the standard "informal" derivation ...
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2answers
75 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
117 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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9answers
991 views

Is causality a formalised concept in physics?

I have never seen a “causality operator” in physics. When people invoke the informal concept of causality aren’t they really talking about consistency (perhaps in a temporal context)? For example, if ...
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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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5answers
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A list of inconveniences between quantum mechanics and (general) relativity?

It is well known that quantum mechanics and (general) relativity do not fit well. I am wondering whether it is possible to make a list of contradictions or problems between them? E.g. relativity ...
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180 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
33 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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1answer
420 views

Is it only the Higgs field that stops me from getting to $c$?

Is it only the higgs field that stops me from accelerating up to the speed of light or is there other restriction concerning the increase in mass? In other words if I had a Higgs field shield on my ...
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67 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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3answers
279 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
44 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
151 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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Proving that interval preserving transformations are linear

In almost all proofs I've seen of the Lorentz transformations one starts on the assumption that the required transformations are linear. I'm wondering if there is a way to prove the linearity: Prove ...
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2answers
95 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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1answer
144 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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1answer
191 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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47 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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54 views

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
99 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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2answers
144 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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203 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
146 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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1answer
103 views

Equation for relativistic electron and two-component spinor

Recently I heard that there is some "alternate" equation for the Dirac one. It can be introduced if we refuse some properties of the theory describes the electron, which Dirac used in his original ...
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114 views

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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82 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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1answer
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What do subatomic particles look like for a 'speed of light - observer'?

Let's say that an observer is moving with the speed of light relatively to an atom that he wants to look into. He has equipment that precise that he can observe the atom and what is inside. From ...
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5answers
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Is it possible to transfer classical bits of information faster than light speed?

Is there any known, verifiable way to transfer classical information faster than light, using quantum entanglement or other phenomenon? Does quantum teleportation, or other known phenomenon, allow ...