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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Non-symmetric Lorentz Matrix

I was working out a relatively simple problem, where one has three inertial systems $S_1$, $S_2$ and $S_3$. $S_2$ moves with a velocity $v$ relative to $S_1$ along it's $x$-axis, while $S_3$ moves ...
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Are events in this experiment simultaneous if observed in platform's frame?

In some contexts e.g. on Wikipedia it is defined as a matter of happening . In others(e.g. as defined by Einstein in his book "Relativity the special and general theory") it is defined as a matter of ...
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Why is causality preserved in special relativity?

PART 1: I was reading the article Relativity of simultaneity Wikipedia. I couldn't understand this line: "if the two events are causally connected ("event A causes event B"), the causal order is ...
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What would happen if some signal could move faster than light?

The two postulates of STR doesn't say that any signal cannot move faster than light. It also doesn't assert that any signal except light cannot have velocity equals to that of light. So at the very ...
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Two observers moving opposite to each other will see each other moving at speeds greater than light? [duplicate]

I read this question at another forum but the thread was already closed. Here's the description: Two observers A and B are both moving at a velocity of 0.9 times the speed of light with respect to a ...
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Relativistic Doppler effect on gamma rays

I'm trying to solve the following problem : An electron-positron pair annihilates, creating two photons. At what speed must an observer move along the line of the photons in order that the ...
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Does our current notion of velocity/acceleration (based on calculus) require absolute time?

When people explain special relativity, they say that a velocity in one frame leads to time dilation in that frame relative to a stationary frame. When we say something like ...
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Question about relative speeds on a different “scales of perception”

I was kind of puzzled yesterday when thinking about this. If we observe an object moving away from us with 10m/s we would say the object is moving away from us really slowly But if we (humans, ...
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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$\tau$ 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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Twin paradox on a cosmic scale

I am referring to yet another version as the classical twin paradox. In my version the moving apart of the twins is entirely induced by space expansion between them and they move apart each other at ...
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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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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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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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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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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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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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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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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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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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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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Twin paradox with two intertial frames in general relativity

I assume the twin paradox from special relativity is well known. I wish to focus on the apparent symmetry of the problem: both observer seems to move away from each other, and then come back. Yet, the ...