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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Does a muon detector on Earth's surface correctly measure the mean lifetime of a muon?

Just a simple question. Does a muon detector on Earth's surface correctly measure the mean lifetime of a muon? I would think the answer is no because most muons detected are created about 15 km above ...
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223 views

Why light can't go faster then 300 000 km/s? What prevents it? [duplicate]

Why can't the speed of light be faster then approx 300 000 km/s? What prevents it?
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What is the energy required to create mass of m at a height of h above the Earth?

What is the energy required to create mass of m at a height of h above the Earth? Is it $E= m c ^2$ or $E = mc ^ 2 + mgh$ ? Let's reverse the process also. If you convert mass $m$ at $h = 0$ to ...
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A vertical variation of modern versions of Michelson-Morley

For almost a year now, I have been in the uncomfortable position of having an idea. However, there is one nice thing about this idea. It makes a concrete, exact and relatively easy to test physical ...
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66 views

Is observation a component of the Lorentz transformation?

For a while I've been trying to write a simple geometric derivation of the Lorentz transformation, based only on the second postulate. Although I'm able to successfully derive the Lorentz ...
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104 views

Understanding the operation of Thomas precession

How can we physically understand the operation of Thomas Precession? This modifies the effective energy of coupling between the spin and the orbital angular momentum of the electron by an extra factor ...
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1answer
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Is this a valid proof that the four-current is conserved?

The four-current of a particle moving along a worldine $X^\nu(s)$ is defined as $$j^\mu(x^\nu) = ec \int u^\mu(s)\, \delta^4(x^\nu - X^\nu(s)) \, ds$$ So here's my proof that this is conserved: ...
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Light & Observer moving perpendicular to each other

Light is the yellow arrow. Observer is the black arrow. Observer is moving at a constant speed of v, w.r.t to a Galilean frame of reference. Now from the point of view of the observer (O), how ...
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194 views

Why is light speed the limit? [duplicate]

Why is the light speed a limit? Why can't anything go faster than light? Not even a single atom?
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150 views

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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1answer
161 views

Does time dilation correct for the Doppler effect?

Knowing that a body in motion experiences time dilation, "also" knowing when two objects travel at a great speed away from one an other, both observers experience the others clock as moving slower ...
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Difficulty in understading a part of the book “A Brief History of Time”?

Sorry if the question is not upto the standard of the site but i really can't understand what the following para says. I am reading the book "A Brief History of Time" by Stephen Hawking and in the ...
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395 views

Boosts are non-unitary!

The boost transformations are not unitary unlike rotations, the boost generators are not Hermitian. When this induces transformations in the Hilbert space, will those transformation be unitary? I ...
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145 views

Adjoint representation of the Lorentz group

Is it possible to construct an adjoint representation for the Lorentz group?
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When do wave function collapse in this case?

In relativity, an event A can occur before another event B in one frame while A may occur after event B in another. In quantum mechanics, we may measure the spin of two entangled electrons: If you ...
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1answer
131 views

Has QFT successfully mediated between QM and Special Relativity?

I understand that QFT is the theoretical framework for combining QM and Special Relativity, but as I understand it, though even without proof or experimental confirmations; has QFT managed to "behind ...
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1answer
134 views

Original formula of Einstein time dilation

The formula of time dilation at constant speed v is known. The formula $T_0'= T /\gamma$ where gamma is the Lorentz factor. I would be interested, as Einstein's original formula was. I've checked ...
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1answer
49 views

Relativity of simultaneity and cause-effect

Relativity says that two events simultaneous in one reference frame might not be simultaneous in another reference frame. Can we extend this idea a little and say that the order of two events might be ...
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1answer
117 views

$\tau$ pair production question

There's a question on my homework about the process $e^{-} e^{+} \rightarrow \tau^{+} \tau^{-}$. Specifically, it is claimed that the minimum energy required of the colliding positron and electron ...
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What changes occur while an atom approches the speed of light?

My knowledge of atomic dynamics is a little superficial. But to my understanding an electron travels an orbital path around a nucleus of an atom. "correct?" So let's say that if a hydrogen atom were ...
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1answer
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Calculate time dilation with Lorentz transformation [duplicate]

It is possible to calculate the time dilation with Lorentz transformation? So with the equation $$t'=\gamma(t-\frac{x v}{c^2}) \tag{1}$$ in which $\gamma$ is the Lorentz-Factor? In an exercise I have ...
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230 views

Lorentz transformation for electric and magnetic fields

How do derive the following transformation rule (J.D. Jackson third Edition 11.10) for electric and magnetic field? $$\vec E' = \gamma \left( \vec E + \vec \beta \times \vec B\right) - ...
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301 views

Twin Paradox, calculating spacetime intervals from both perspectives

I've very recently started to try to understand special relativity. I'm want to get a decent understanding of the twin paradox. I'll post what I've done so far and highlight what's gone wrong for me. ...
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Can the apparent velocity of an approaching spacecraft be faster than light?

Consider watching an alien space ship at Alpha Centauri (at 4.5 light years away) through a telescope from earth. This space ship turns towards us, and starts travelling toward us at what appears to ...
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Generators of Poincare Groups

How can I determine the generators of the Poincare Group, $P(1,3)$ explicitly? Here $P(1,3)$ means a matrix Lie group.
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Does the speed of light in different mediums affect the lorentz transformation?

We know that the Lorentz transformation is derived using the speed of light in vacuum. But if we were to use it in water, would it change since the speed of light in water should also remain constant ...
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1answer
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A problem with a basic thought experiment in Special Relativity

This is for a class on special relativity I am to give to some school children. Moe is moving at 0.9c. At the instant he passed Joe he emits a flash of light. One microsecond later, Joe(at rest) ...
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do relativistic velocities change the apparent entropy content of the moving object?

Imagine a box of hot gas. It has a certain (large) amount of entropy, which we can relate to the amount of information needed to completely specify the position and velocity of every gas particle in ...
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Breaking the simultaneity

I have expressed my self in a detailed way. I've labeled the points to which I want an answer. I have doubt in the Einstein's rail experiments which he mentioned in his book. In this experiment ...
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Confusion about the (relativistic) mass of objects [duplicate]

According to Einstein's theory the (relativistic) mass of objects depend on speed. Then in an inertial reference frame 2 observers moving at 2 different velocities will calculate different masses for ...
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1answer
222 views

Can a spinor be defined as any quantity which transforms linearly under Lorentz transformations?

Recently I’ve come across a few papers from China (e.g. Xiang-Yao Wu et al., arXiv:1212.4028v1 14 Dec 2012) that make the following statement: ...any quantity which transforms linearly under ...
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37 views

What are the constituents of communicated time differences between moving objects?

In "The Elegant Universe," two individuals, George and Gracie, are noted to be moving relative to one another in space and wearing clocks. They sync their clocks upon passing each other. Each observes ...
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103 views

Twin Paradox - different approaches

What was the difference between Langevin's approach to the twin paradox and Max Von Laue's? I don't understand how Langevin tried to use the idea of absolute acceleration to explain the distinction in ...
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1answer
109 views

Noether Charge For Scalar Fields Under Lorentz Transformations

The conserved charge associated with the Lorentz transfomation of a scalar field is given by $Q^{\alpha\beta}=\int d^3x\frac{1}{2}(x^\alpha T^{0\beta}-x^\beta T^{0\alpha})$. The quantities $Q^{ij}$ is ...
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Does the time for communication between moving objects solely account for each object to perceive the other object's clock to more slowly tick? [duplicate]

In "The Elegant Universe," two individuals, George and Gracie, are noted to be moving relative to one another in space and wearing clocks. They sync their clocks upon passing each other. Each observes ...
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2answers
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A question about relativistic spin operator

The question comes from Ryder's Quantum Field Theory, 2nd edition. The author was looking for relativistic spin operator. It was concluded that it cannot be $J^2:=\mathrm{J} \cdot \mathrm{J}$, where ...
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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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Is time travel different from time dilation?

I just wanted to know whether time dilation is different from time travel or not. Personally I believe both are different. If they are the same things I just wanted to know why. According to me time ...
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Photons and proper time

Why is there no proper time without inertial frame? In question n°95054 I learned that there is no proper time zero and no proper distance zero for photons because they are no inertial frames. That ...
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Does the velocity of a light source influence the light

I have only just finished High school physics so my understanding is still fairly simple but I'm having trouble with this question. Imagine you are in space traveling at a relativistic speed with a ...
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1answer
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Space-Time Continuum [duplicate]

In special relativity it is said that " Time and space cannot be defined separately from one another. Rather space and time are interwoven into a single continuum known as spacetime. " What is the ...
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1answer
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Are covariant components of 4-gradient of scalar product made of contravariant components of vector?

Trying to find normal to hypersurface $p^ip_i=m^2c^2$, I take gradient of corresponding function $F=p^ip_i-m^2c^2$. What I get is: $$n_i=\frac{\partial F}{\partial p^i}=\frac{\partial}{\partial ...
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What does it mean to divide space and time?

Goldstein's mechanics book, on the chapter on relativistic mechanics says that "We cannot assume that all observers make the same division into time and space in the same way." What does it mean to ...
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Relativistic space travel?

If one travels in a spaceship at speed V, the time elapsed for the traveller relative to an observer on earth is dilated by, $$ t' = t(1 - v^2/c^2)^{1/2} $$ Does this mean that a space traveller, ...
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Time dilation formula and example

What is the time dilation formula by constant velocity? Is the right formula $$t'=t\times \sqrt{1-v^2/c^2}$$ or is it $$t'=\frac{t}{\sqrt{1-v^2/c^2}}$$ ? And can someone show me a computational ...
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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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Idea of Covering Group

$SU(2)$ is the covering group of $SO(3)$. What does it mean and does it have a physical consequence? I heard that this fact is related to the description of bosons and fermions. But how does it ...
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1answer
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Does action really have to be Lorentz-invariant in SR?

From Landau & Lifshitz The Classical Theory Of Fields it is said: To determine the action integral for a free material particle (a particle not under the influence of any external force), we ...
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If one is travelling at a significant fraction of $c$, will the length of the trip be shortened?

Assuming two stars are 1 light year apart and a traveler is travelling at 0.75 of $c$, from the point of view of the traveler what would be the observed time en route? Also, if a vehicle is constantly ...
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Why does a Lorentz scalar field transform as $U^{-1}(\Lambda)\phi(x)U(\Lambda) = \phi(\Lambda^{-1}x)$?

This problem is from Srednicki page 19. Why $U^{-1}(\Lambda)\phi(x)U(\Lambda) = \phi(\Lambda^{-1}x)$? Can anyone derive this? $\phi$ is a scalar and $\Lambda$ Lorentz transformation.