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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Conservation of phase space volume in Rindler space-time

Let us consider Rindler space-time, i.e. Minkowski space-time as seen by a constantly accelerating observer. My question is, does Liouville's theorem, i.e. the conservation of phase space volume in ...
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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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98 views

Can a simulated Universe simulate Special Relativity

I know there are theories (or postulates) that hold that our Universe could be a simulation. I was wondering, if Special Relativity states that two events which are not causally linked can be judged ...
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138 views

Representations of the Poincare group

Which type of states carry the irreducible unitary representations of the Poincare group? Multi-particle states or Single-particle states?
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Unitary representations of the diffeomorphism group in curved spacetime

In (special) relativistic quantum mechanics there is a standard argument that says that the (rigged) Hilbert space of states $H$ should be equipped with a projective unitary representation $U$ of the ...
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Phase space volume and relativity

Much of statistical mechanics is derived from Liouville's theorem, which can be stated as "the phase space volume occupied by an ensemble of isolated systems is conserved over time." (I'm mostly ...
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What happened to the idea of tachyonic or other superluminal neutrinos?

While hunting around for information about the recent OPERA measurement that hints at superluminal neutrinos, I discovered that this idea was actually considered back in the 1980s. Wikipedia lists as ...
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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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4answers
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Newtonian physics vs Special relativity - what is the most “relative”?

This might be a question purely of words and the meaning of them but isn't Newtonian physics more "relative" than Einstein's Special relativity? Newtonian physics predicts that laws of momentum & ...
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Break speed of light with infinite mass

I've heard that a spacecraft could never exceed the speed of light because it's (relativistic) mass quickly approaches infinity and therefore there could never create a big enough rocket to propel it ...
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128 views

Is basic quantum mechanics mathematically as robust a theory as special relativity?

This question is specifically about the robustness of mathematical models. Special relativity can be derived from very basic principles. Assuming that space is homogeneous and isotropic and that ...
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Einstein's Postulates: Simultaneity

Okay, I still don't get the solution (which I will lay out) to the following problem: Suppose that A', B', and C' are at rest in frame S', which moves with respect to S at speed v in the positive ...
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2answers
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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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1answer
60 views

Relativistic fomulae for energy and momentum?

I know that the relativistic formulae for energy and momentum are: $E = \gamma mc^2$ and $\textbf{p} = \gamma m\textbf{v}$; Can we derive these formulae? If yes, where from?
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Two observers moving opposite to each other will see each other movin 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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2answers
157 views

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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0answers
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How to find the speed of free tachyon after emission the light?

Let's have the model in which free tachyon emits the light. We have $$ E = E_{1} + E_{\omega}, \quad \mathbf p = \mathbf p_{1} + \frac{E_{\omega}}{c}\mathbf n , \quad cos(\mathbf p_{1} , \mathbf n ) = ...
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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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203 views

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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Rigorous definition of frame of reference

I'm looking for a mathematical definition of frame of reference. Most of the textbooks I have seen take it for granted and they just refer to some set of spacetime coordinates. A more mathematical ...
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81 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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There must be free positive charges, moving oppositely to electrons for the wire with current to stay neutral

All popular expositions (e.g. these ones) of relativistic electromagnetism claim univocally that electrons in motion become more dense due to the speed. They teach that Lorentz contraction of charges ...
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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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195 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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466 views

What is Relativistic Navier-Stokes Equation Through Einstein Notation?

Navier-Stokes equation is non-relativistic, what is relativistic Navier-Stokes equation through Einstein notation?
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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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How does the solar sailing concept work?

Wikipedia describes solar sailing as a form of spacecraft propulsion using a combination of light and high speed ejected gasses from a star to push large ultra-thin mirrors to high speeds. I ...
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481 views

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
190 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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16answers
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Is it possible for information to be transmitted faster than light by using a rigid pole?

Is it possible for information (like 1 and 0s) to be transmitted faster than light? For instance, take a rigid pole of several AU in length. Now say you have a person on each end, and one of them ...
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2answers
379 views

How do Doppler Effect and Time Dilation differ?

Above, I have drawn a diagram showing Doppler Effect (here we are using space-time but in a non-relativistic sense. Time and distance are the same for A and B). Edit: I am adding a relativistic ...
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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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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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How to understand the emergent special relativity in the superfluid?

The superfluid vacuum theory was proposed to understand some features of the vacuum (aether) from the emergence point of view. Although made up of non-relativistic atoms, the low-energy excitations of ...
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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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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
60 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
121 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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Must the action be a Lorentz scalar?

Page 580, Chapter 12 in Jackson's 3rd edition text carries the statement: From the first postulate of special relativity the action integral must be a Lorentz scalar because the equations of ...
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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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168 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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113 views

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
130 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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349 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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102 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
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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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Nothing can travel faster than the speed of light. In what frame of reference? [duplicate]

Since frames of reference are arbitrary, I can define a frame of reference that moves backwards with a speed greater than $c$, then any static object in that frame of reference is already traveling ...
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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 ...