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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whats the rate of energy increase required for constant acceleration between 0.0c and 0.99c?

I was wondering how much energy would be required to accelerate 1000kg to 0.99c at 1G. What I don't understand is what the rate of increase of energy is required as velocity increases. I was looking ...
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Why is travelling around the speed of light a problem?

I don't fully understand what would happen if we could travel at the speed of light. But I saw somewhere here that it would mean events happen out of order. But why is this a problem. It is said that ...
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Why $x=-ct$ line in a spacetime diagram?

I can understand why the $x=ct$ line is needed as follows: If $c \Delta t \geq \Delta x$ then the event can be causally related to your current position, so the event could not appear in reverse ...
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Why is the Mixed Faraday Tensor a matrix in the algebra so(1,3)?

The mixed Faraday tensor $F^\mu{}_\nu$ explicitly in natural units is: ...
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Is this a Lorentz-scalar? How do I tell?

I'm struggling to identify whether a scalar is a Lorentz-scalar. E.g: $$\partial_i A^i \quad i \in {1,2,3}.$$ How do I determine if this is a Lorentz-scalar or not? If got the same problem with ...
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Massless particle that have momentum not equal to 0

I saw some problems in special relativity that use conservation of total energy and momentum and the conclusions are spectacular. My problem is the following: how can a massless particle like neutrino ...
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How can we show that the speed of light is really constant in all reference frames?

I had a debate with a friend who cannot believe that the speed of light is constant. He said something like: so what if in the Michelson-experiment the moving apparatus simply added a constant ...
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Why does the Michelson-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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Why does the equivalence principle not violate special relativity?

If the equivalence principle asserts that there is no way to determine whether our reference frame is accelerating or is being acted upon by gravity (i.e. the laws of physics are the same in both ...
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Time slowed by gravity

If time moves more slowly on Earth (due to our proximity to a gravitational body) than for someone orbiting Earth in a spaceship, yet the opposite occurs in the frequently cited "twin paradox" of the ...
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Poincare invariant Lagrangians

The Lagrangian density of a Poincare invariant theory should not depend explicitly on the space-time coordinates. Does this mean $$ \partial_\mu \mathcal{L}=0~? $$ If this is the case doesn't the ...
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Is the Speed of Light an universal spacetime constant, the velocity of electromagnetic waves, or of photons?

This question has been touched tangentially by What's a better phrase than "speed of light" for the universal spacetime speed constant? and Could light travel more slowly than the ...
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Would a craft travelling increasingly close to the speed of light appear to be decelerating?

I've been pondering the implications of time dilation. Is it right to assume that if a craft was travelling at a speed very close to the speed of light (>= 0.9999c for example), that to an external ...
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Proof that 4-potential exists from Gauss-Faraday field equation

This is a problem concerning covariant formulation of electromagnetism. Given $$\partial_{[\alpha} F_{\beta\gamma]}~=~ 0 $$ how does one prove that $F$ can be obtained from a 4-potential $A$ such ...
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Why do we use the complexification of the Lorentz group?

I do understand why we are using the double cover, but why exactly do we make the transition to complex Lorentz transformations? Where and why are they needed? To be precise: The double cover of ...
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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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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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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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Understanding the time dilation calculation in Brian Cox's Doctor Who lecture

Background My son has just watched Brian Cox's fascinating "The Science of Doctor Who" lecture on space-time and was particularly intrigued by the part (at 22m:22s) where he said: Let us say that ...
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Proper time for an accelerating object

As far as I have read so far, proper time is the time measured on the clock of an inertial frame moving uniformly with respect to another inertial frame. The concept and the mathematical expression ...
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Distinguish between Past and Future

When writing the metric in Minkowski space, how can we distinguish between the past and the future? I understand the answer after drawing the light cone but I want to know how we get that by just ...
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Proper Time for Deceleration in Special Relativity

As stated here: http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html A rocket which accelerates to some point, then decelerates back to 0 over the same distance will measure a proper time ...
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What is the interpretation of the Chern-Simons electromagnetic spin density?

Hans de Vries (who happens to be a no-longer-active physics.SE user) has an online book (referenced below) in which ch. 6 is a presentation of an object he calls the Chern-Simons current, ...
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Light in Different Reference Frames

I think I'm just confused, but for some reason I thought that light moving straight in one frame would have to move in the same direction in another frame. I know there are photons-but because I have ...
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Can acceleration feel like constant gravity for indefinitely long?

So here's the setup: I'm in a spaceship, without windows as always, and the ship is accelerating upwards at a constant rate of $1\,\text{g}$. So inside the spaceship it feels like I'm being pulled ...
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Proper times of two observers in a three-torus

Consider two observer in a tree-torus space of size $L$. Observer $A$ is at rest, while observer $B$ moves in the $x$-direction with constant velocity $v$. $A$ and $B$ began at the same event, and ...
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Terminology for opposite null lines

Is there a name for two null lines that lie on the opposite sides of the null cone? Each line can be obtained from the other by reflection in the axis of the null cone (the time-axis). In terms of ...
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Using Einstein's Relativity: Who is younger?

Suppose we have a person A and a person B. Person B travels very close to speed of light and never returns. He's constant in speed. Then, we can say two things: B is younger than A. A is younger ...
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What would an observer see if he/she flew toward a clock at relativistic speeds?

If an observer approaches a clock at a significant fraction of the speed of light, would they see the clock's hands moving at a faster or slower than usual rate? I figure there are two competing ...
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A video conference between earth and a space shuttle

I have just started looking into special relativity and I have come up with an intriguing gedanke, as Einstein himself called such theoretical thought experiments. Imagine a space shuttle traveling ...
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How much energy can be extracted from hydrogen?

http://en.wikipedia.org/wiki/B-L says that the difference between baryon number and lepton number is conserved. Ordinary hydrogen has one of each, but turning it into helium releases only the binding ...
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How is 4-current a 4-vector?

I am looking at Jackson sec 11.9, where he states that the $\rho,\bf{J}$ form the 4-current $$J^\alpha=(c\rho,\bf{J})$$ Jackson says this is from the invariant of the 4-divergence $\partial^\alpha ...
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Particle here at a given time, in another galaxy a second later… Really?

I read "The Quantum Universe (Cox & Forshaw)" that a particle can be measured at a given position at a given time, and in another galaxy one second later. The probability of such event may be ...
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Is acceleration relative in relativity?

Suppose a box A is moving relative to a Box B, then by time dilation equation if I take 1 sec passed for an observer in A then for an observer in B will be little longer. Now if I suppose that the box ...
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Why can the spin of a relativistic particle not be orthogonal to its momentum?

I have read that the 3-momentum of a relativistic particle cannot be orthogonal to its spin 3-vector. When thinking about how the spin vector transforms when the particle approaches light speed, it ...
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Is the energy per degree of freedom $\frac{1}{2}kT$ in relativistic systems?

The equipartition theorem says that the mean energy per degree of freedom is $\frac{1}{2} kT$. Is this result relativistically correct?
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Where does the Lorentz boost for a Dirac spinor come from?

I have read, that if you have a Dirac spinor \begin{equation} \psi = \begin{pmatrix} \phi_R\\ \phi_L \end{pmatrix} \end{equation} that you can apply a Lorentz boost along the $z$-direction with ...
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Does time really differs drastically?

As I heard/read time moves slower and slower for me as I speed up, but does it change drastically? Our current formulas say, If I go at a speed very close to light's, time almost stops. I've seen ...
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In QFT, why do fermions have to anticommute in order to insure causality?

I have seen this question and I believe I understand the answer to it. However, AFAIK, only for bosons the causality condition is a vanishing commutator. For fermions we expect the anticommutator ...
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Is sound relative when travelling fast?

If I was listening to music through my headphones and travelling close to the speed of light and time is slowing down around me , would the music slow down as well?
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Is speed of light invariant in different inertial frame?

Don't get angry at me. I believe in special relativity just as any scientist would. But reading this article http://arxiv.org/abs/0708.2687 I realize that actually I haven't done any experiments on ...
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Is Michelson-Morley experiment an axiom?

Sorry for my ignorance, but does the result of Michelson-Morley experiment have some explanation? Is there some reason why light speed in vacuum is maximum or we just find it by experiments?
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Deriving formula for time dilation

Last week in class we derived the formula for time dilation using light clocks and got $$t=\gamma t_0\quad \gamma=\left(1+\left(\frac vc\right)^2\right)^{-1/2}$$ So far so good. However, after class I ...
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Why is the Faraday Tensor derived from the Lorentz force?

If we start from the Lorentz force, $$\textbf{F}=q\textbf{E} +q\textbf{v}\times\textbf{B}$$ and use the four velocity u$^{\mu}$ and the four momentum p$^{\nu}$, then we get to ...
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Is speed of light ( Sun-to-Earth ) related to the movement speed of solar system?

The speed of light has been measured to be 299 792 458 m/s. Now, the Solar System is traveling at an average speed of 828,000 km/h (230 000 m/s). Summing up the numbers we get close to 300 000 000 m/s ...
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Velocity measurement in relativistic perspectives

I understand the precepts of relativistic time dilation, but I'm looking to nail down the local perception of velocity in each frame. My question is threefold: Given two observers $A$ (rest frame) ...
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Relativity on a moving train

I've been given the following scenario: Observer $B$ is in the center of a train carriage which is moving at velocity $v$ with respect to an observer $A$. Two light signals are emitted from ...
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Theoretical Upper Bound on Processor Speed?

Barring aside considerations such as heat dissipation, capacitance, etc... (aka any sort of technological issue) what is the fastest speed of a processor? I am told that at distances of 1 planck ...
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Special Relativity moving in space

Given that time is 'just another' dimension and people get hung up on the fact that we cannot go back and forth in time like the other dimensions. Is there any proof that the corner of 8th Avenue and ...
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How can the Lorentz transformation cause two objects' masses to both increase?

Suppose there are two people A and B. A is standing on the earth and B is on a rocket in space. Now B passes by the earth at a speed of 0.9c and A sees him. According to A, B's mass would have ...