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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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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What is the relativistic mass of this spinning ball? [closed]

Relativistic Mass is: $$ m_r = \frac{m}{\sqrt{1 - v^2/c^2}} $$ So Einstein says that the faster an object moves, the more mass it gains (relativistic mass). So suppose you have a spherical ball ...
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Does spacetime have a “preferred” speed/metric? [duplicate]

I read recently that spacetime has a preferred speed, c, and that all observers would agree on the speed of anything moving at c. In particular, there is nothing unique about light when talking about ...
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Einstein's first postulate implies the second?

Einstein's two postulates of special relativity are as follows, 1. The principle of relativity: The laws of physics are the same in all inertial systems. There is no way to detect absolute ...
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How to connect Einstein's Special Relativity (SR) with General Relativity (GR)?

How Einstein's SR becomes GR? $$ds^2=dr^2-c^2dt^2,$$ $$ds^2=g_{\mu\nu}dx^{\mu}dx^{\nu}.$$ When the $s$ is constant $ds^2=0$, isn't it true? How to connect Einstein's SR with GR? What is the ...
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Do GR and SR have to be considered together to determine time dilation? [duplicate]

In another related question: How to connect Einstein's Special Relativity(SR) with General Relativity(GR)? , John Rennie stated that SR is a subset (or rather can be derived from) GR, but not vice ...
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If $v_{a \dot{b}}$ transforms like a four-vector, what does $v_{a}^{\dot{b}}$ describe?

The $( \frac{1}{2}, 0)$ representation of the Lorentz group acts on left-chiral spinors $\chi_a$, the $( 0,\frac{1}{2} )$ representation on right-chiral spinors $\chi^{\dot a}$. The $( \frac{1}{2}, ...
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Recoil velocity and mass of particle after absorbing photon

I'm working a problem out of d'Inverno's "Introducing Einstein's Relativity", and I'm hitting a funny issue with my algebra. The problem states: An atom of rest mass $m_0$ is at rest in a ...
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Conservation of relativistic momentum

I'm trying to prove that momentum, $\rho = m \, v \, \gamma(v)$, is conserved in all frames of reference. I'm having problems with the following situation that I made; momentum is not conserved to ...
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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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How is the special theory of relativity observed for these types of clocks?

I'm trying to understand Special Theory of Relativity through reading Feynman's lectures. In chapter 15 Feynman gives example of clock: rod of 1m length with mirrors at the ends. Light goes from ...
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How can we travel back to time if we go with a speed $>> c$? [duplicate]

I have read "If something attains the speed more than that of light then it can travel back to time." I want to know how it happens. Also, in relativity why can nothing acquire velocity beyond ...
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Mass in special relativity?

Is the mass of a object at rest defined by $$E=mc^2$$ where $m$ is the rest mass. I.e. does the rest mass include every thing from thermal to gravitational potential energy and every other possible ...
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30 views

Proving property of lorentz transforms

I've been trying to learn relativity from Weinberg's Gravitation and Cosmology without very good knowledge of the mathematical background. I am developing it alongside, but there is one particular ...
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176 views

Confusion about proper time in special relativity

I have a problem understanding what proper time really means, well actually, it's the symmetry that confuses me... Suppose for convenience that particle A has a mean life-time of 10 seconds in its own ...
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The definition of Lorentz transformation

I know that the Lorentz transform, when two frames $\mathcal{S}$ and $\mathcal{S}'$ are in standard configuration (the axes are all parallel to their counterparts in the other inertial frame) is ...
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Why does moving near light speed keep you young? [duplicate]

As was shown in the movie Interstellar, when you go close to a black hole or move near the speed of light in space, then your clock runs slower than a clock on Earth. In the movie, Matthew ...
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Why does Energy-Momentum have a special case?

I was reading Energy-momentum, and I came across this simplified equation: $$E^2 = (mc^2)^2 + (pc)^2$$ where $m$ is the mass and $p$ is momentum of the object. That said, the equation is pretty ...
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In special relativity what is the energy of a macroscopic body?

Is the energy of a macroscopic body in special relativity still given by: $E=\gamma m c^2$? If so why do we not need to consider the motion of the individual particles that make it up? Is this because ...
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Is there a mathematical reason for the Lagrangian to be Lorentz invariant?

The Hamiltonian is the energy, which is just one component of a four-vector and therefore not Lorentz invariant. The Lagrangian is the Legendre transform of the Hamiltonian and I was wondering if ...
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What is a homogeneous and isotropic frame of reference?

I have heard that inertial frames of reference in the context of special relativity are both isotropic and homogeneous. I know what isotropic and homogeneous mean in a general context, but what do ...
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Pair production and energy conservation?

Consider the question whether a photon can decay, in the free space, into an electron and a positron - a pair production event. Such an event I don't think is possible, because both energy and ...
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Special Relativity Explanation [duplicate]

I'm in a relatively basic Physics class in university, and was reading the section in my textbook about The Principle of Relativity. It says: Einstein's Theory of Relativity ... added the ...
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The mas-energy equivalence for rest mass

It is clear that the kinetic energy can be derived as $(m-m_0)c^2$. However, why do we say that $m_0c^2$ is the rest mass energy? It seems that this mass-energy equivalence for rest mass is just a ...
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Doppler Shift when Light Travels Through Two Different Mediums

When considering the Doppler shift, the 'canonical equation' is $$f=\frac{c+vr}{c+vs}f_0$$ However, this equation seems to run into trouble in the following situation: A light source inside water is ...
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Does my explanation of relativity have any validity?

I've been trying to explain relativity to myself by developing a model based upon small finite changes along one dimension. For me, as a computer programmer, this model works well as an explanation ...
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The Relativity of Simultaneity and its Impact on “Seeing” Events

Will the rocket really see the supernova L first for sure? The position of the rocket is not specific. We just know that it is at the left of the galaxy. We know that R will explode first in the ...
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Why does time dilation cause you to age slower? And is time considered relative to the observer?

I understand that the higher your velocity the slower light will move. But how does time itself slow down while you are moving faster?
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Can I fix a point in Minkowski space to give it a vector space structure?

I looked up the term Minkowski space on Wikipedia. It said There is an alternative definition of Minkowski space as an affine space which views Minkowski space as a homogenous space of the ...
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Is Minkowski space usually a vector space or an affine space?

When I visited Wikipedia's page on Minkowski space, it seemed to offer two definitions. The first defined Minkowski space a vector space. Then, in a later section, it says The section above ...
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Why is special relativity so special? [duplicate]

The title says it really. Why is special relativity so special? I'm just curious as to how and why the term 'special' came to describe the theory of relativity where gravitational forces are ...
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Is a non-accelerating object far from a gravity source moving at the speed of light through time?

I'm trying to understand the Minkowski spacetime better. If an object is not undergoing acceleration, and is far from any large mass, does it travel maximally "fast" through time? Can we calculate a ...
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Successive measurment of incompatible variables on an entangled state

Suppose I have 2 particles in an entangled state with opposite spins far away from each other, both stationary with respect to the lab. At time t=0 I measure the spin of both particles in the x ...
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Muon decay why proper length in the earth frame?

Consider the two diagrams below (ignore the velocities), Consider the situation in the right hand picture where we have a rod connected to the earth. Let us now say that the muon is created at the ...
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Thought experiment regarding an object approaching a mirror

Here's a thought experiment I came up with in class today when my mind drifted (I however highly doubt I'm the first to think about this since it is pretty rudimentary) : Let's say superman ...
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1answer
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Time difference between two moving inertial frames of reference [closed]

This is a question I am trying to solve: Let S and S' be two inertial frames of reference and S' is moving relative to S at a velocity of 0.6c. When x = x' = 0, t = t' = 0. At t = 2 x 10-7 s, an ...
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Photon energies after neutral pion decay

I am trying to find the photon energies of the decay $\pi_0 \rightarrow \gamma\gamma$ and their dependence on the pion energy $E_{\pi}$, its initial velocity $\beta$ and the scattering angle between ...
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The cap on massive particles's speed is below the speed of light due to Planck length?

This answer http://worldbuilding.stackexchange.com/a/8525/1991 claims that no particle can accelerate further after its de Broglie wavelength becomes Planck length. Given that speed at this point is ...
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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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Two particle collision - excited particle emits photon absorbed by the other particle

Part (a) Doing everything in the lab frame: 4-vector before collision: $(Mc,0)$ Let $E$ be energy of photon emitted, p be momentum of de-excited particle. 4-vector after collision: ...
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Why does the Michleson-Morley experiment only contradict the aether?

This question is related to Validity of Maxwell's equations with no aether or relativity? (so please read this first). In this question, the answers seem to suggest that getting rid of the aether ...
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Special relativity and the electromagnetic field tensor [closed]

Ok, I've got an exam for general relativity in the next week and I'm working through a (special) relativity problem at the moment and I just cant seem to get the solution indicated at all and was ...
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Possible Answer To The Double-Slit Experiment [closed]

I think I might have figured the double-slit experiment out. I am not going to explain it here, Google it if you don't know it. If I am wrong please tell me why: Matter are relative to observers ...
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why do x Schwarzschild radii equal time dilation effects of speed of light going y times faster than an object^2?

let me walk you through the math. First you start with the gravitational time dilation formula where: $$ T_1=T\sqrt{1-\frac{2GM}{rc^2}} $$ and rather than entering $r$ for the radius we replace $r$ ...
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Why does the speed of light totally prevent instantaneous information exchange?

Based on the classical light-cone approach it's easy to see you can't transmit information faster than $c$ but why does the speed of light (as far as I know) treat information transmission in this way ...
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How does a frame of reference work in relativity? [duplicate]

I am struggling to understand what frame of reference means in relativity. Imagine the twin scenario. Twin A is at rest, while twin B travels somewhere and back at near the speed of light. If one ...
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What is the relativistic calculation of travel time to Proxima Centauri?

It has already been asked here how fast a probe would have to travel to reach Alpha Centauri within 60 years. NASA has done some research into a probe that would take 100 years to make the trip. But ...
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3 inertial frames compared in STR

Suppose an event is observed in 3 inertial frames K, K' and K''. The coordinates in K are $(x,t)$ in K' are $(x',t')$ in K'' are $(x'',t'')$. The K' and K'' coordinates are then Lorentz-transformed to ...
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Michelson-Morley experiment revisited under the light of special relativity

Taking into account the composition of speeds in special relativity, lets suppose that a Michelson-Morley interferometer is moving at a speed of $\vec{v}$: the speed of Earth relative to the local ...