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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Number of the Generators of Poincare Group

It is said that the Poincare group, $P(3,1)$ has $10$ generators. $6$ of them are the generators of the Lorentz group, $O(3,1)$ and the other $4$ generators are the generators of $4D$ translational ...
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182 views

Is time dilation real? [duplicate]

If a body with an accurate clock is moving away from A which is stationary, then the time in B would be slower than that in A. Since relative to B A would have an equal velocity time in A would be ...
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2answers
423 views

How does time dilate in a gravitational field having a relative velocity of v with the field?

Consider a Mass on earth. The time dilation on the surface of Earth is $$T' = T \sqrt{1 - \frac{2GM}{rc^2}}$$ Now if the mass is moving around the earth at velocity of v w.r.t Earth, what will be ...
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Number of Parameters of Lorentz Group

We embed the rotation group, $SO(3)$ into the Lorentz group, $O(1,3)$ : $SO(3) \hookrightarrow O(1,3)$ and then determine the six generators of Lorentz group: $J_x, J_y, J_z, K_x, K_y, K_z$ from the ...
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How to interpret Lenz's law in STR?

By the Lenz's law, when a charged particle goes through a coil it generates a magnetic field. This field generates a current in the coil, slowing down the particle. But by Special Relativity (STR), ...
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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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1answer
232 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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126 views

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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1answer
69 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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1answer
139 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
115 views

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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131 views

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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196 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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2answers
161 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
296 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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2answers
119 views

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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1answer
439 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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1answer
175 views

Adjoint representation of the Lorentz group

Is it possible to construct an adjoint representation for the Lorentz group?
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58 views

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
134 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
141 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
56 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
126 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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2answers
307 views

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
109 views

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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1answer
435 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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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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1answer
519 views

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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58 views

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
127 views

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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55 views

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
234 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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1answer
38 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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108 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
123 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 ...
2
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2answers
129 views

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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1answer
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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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1answer
168 views

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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210 views

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
117 views

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
95 views

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 ...