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Questions tagged [special-relativity]

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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Minkowski diagram of two frames in rest with respect to each other

I'm starting to study Minkowski diagrams, but I can't figure out how should the axis of a $S'$ system look if it is in rest with respect to the frame $S$. I've seen that in all diagrams the origin ...
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1answer
46 views

Question about twin paradox

I just started to learned modern physic for a two weeks, and the i got some problem to understand about the resolution of twin paradox I have attached two pages of picture above that makes me ...
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1answer
42 views

What does the “$T$” superscript mean on vector?

My relativity book defines the "worldline" of a system as: \begin{equation} x(\tau)=(x^0(\tau),x^1(\tau),x^2(\tau),x^3(\tau))^T \end{equation} I often see velocities written in the same form: $U=(0,...
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3answers
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What exactly does the observer's coordinate system mean in special relativity?

This seems like a very basic question but I'm having a hard time understanding it, more precisely hard time visualizing it. Let say there is an observer, and we wish to somewhat formalize his ...
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Check that the Poincaré's transformations form a group structure

How can I answer to this question ? I know that this is a Lorentz transformation + a translation but I don't know how to start. What's the difference between group/group structure ?
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How is Inönü-wigner contraction done?

I have read that little group for the massive particles is $SO(3)$ and for the massless particles is $E(2)$ in 4 dimensions. How does one take zero mass limits for the representations and show that it ...
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2answers
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Why didn't Lorentz conclude that no object can go faster than light?

Based on Lorentz factor $\gamma = \frac{1}{\sqrt {1-\frac{v^2}{c^2}}}$ it is easy to see $v < c$ since otherwise $\gamma$ would be either undefined or a complex number, which is non-physical. Also, ...
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The energy mass equivalence relation [on hold]

I wanted to know that what is the reason we believe that the energy mass equivalence relation i.e. E = mc^2 is true? What experiments other than that on the nucleons, compels us to believe this is ...
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1answer
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What property of the speed of light $c$ is involved in the proof of the invariance of the interval in special relativity?

Here is an explanation of why the spacetime interval $c^2t^2-x^2-y^2-z^2$ is invariant under Lorentz transformation in Wikipedia. Link of the proof. I kind of understand it, but the explanation does ...
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2answers
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Which type of future represents Einstein's relativity? [on hold]

Does the universe is created at this moment and you choose a version of the options, relative to all possible choices and because of this the future is uncertain, does not exist? Or Does that the ...
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1answer
31 views

Inverse Compton scattering

Given a collision between a high energy cosmic ray proton (~$10^{20}$ eV) and a CMB photon, I want to calculate the final energy of the photon. I know to proceed, I use the following conservation of ...
2
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1answer
32 views

Muon decay in muons frame of reference, time muon expects us to record

I have already asked a question regarding this concept but it was flagged as a duplicate. I know this misconception is very common for special relativity but I haven't found a question that talks ...
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6answers
194 views

Why relativistic Lagrangian doesn't simply equal kinetic minus potential energy $L=T-V$?

As the question above, I wonder why the relativistic Lagrangian is written as: $$L=-mc² \sqrt{1-\frac{v²}{c²}} - V ~=~-\frac{mc^2}{\gamma} -V~?$$ I know that the kinetic energy of a relativistic ...
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3answers
73 views

Thermal energy turning into mass?

When you heat an object it's mass increases $E=mc^2$. What I don't understand is that this energy can be converted to mass and still be thermal energy too (object still hot). When a radioactive ...
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1answer
41 views

Relativistic effect in a current carrying wire

In many places I read that in the rest frame of a current carrying wire (electrons in motion), the spacing between the positive ions is length contracted and equal to the length contracted spacing ...
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1answer
31 views

Invariance of length [on hold]

Invariance of interval in Minkowski space under coordinate transformation was proved by the postulates of special relativity. (https://physics.stackexchange.com/a/453536/213658 .see this answer) Is ...
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1answer
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Solution to invariance equation when deriving Lorentz transformation

Requiring that the spacetime interval (1 spatial dimension) between the origin and an event $(t,\, x)$ stays constant under a transformation between reference frames: $$c^2t^2-x^2= c^2t'^2- x'^2$$ we ...
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Probably very easy exercise - Lorentz transformation [on hold]

Sorry to bother you with such questions but I just got so confused that I feel like I don't understand anything anymore... Could you please let me know if I got it right? The exercise is: "A train ...
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0answers
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Special Relativity synchronous [on hold]

Please, help answer my question about Special Relativity and synchronous. I needed to frame it with a diagram, so I prepared the question at this link Thank you: http://www.faceandwall.com/synchronous ...
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0answers
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Parametric Equation of a space like two sheeted hyperboloid in 2+1 dimensional spacetime in terms of $u$, and $v$ given this coordinate system in

For the space like two sheeted hyperboloid the way the coordinate for points on the two sheeted hyperboloid are defined is The equations $u=0$, and $v=0$ both describe geodesics. that are ...
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3answers
91 views

Is magnetic force relativistic effect or intrinsic property?

In this video, they explain that magnetic force is an effect of electric force due to special relativity. https://www.youtube.com/watch?v=1TKSfAkWWN0 But then, the same authors explain in this video ...
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0answers
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It seems to be a disproof for time dilation, according to a proof [duplicate]

Let's say the light Ray is emitted in an angle relative to the floor of spacecraft, in which the motion of light Ray relative to earth is a line perpendicular to the horizon. Then the proof in the ...
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1answer
39 views

What are some of the reasons for raising/lowering indices of a tensor?

In Dirac's paper: Classical theory of radiating electrons, he decides to raise and lower the indices on the same object multiple times: \begin{align*} \frac{\partial{A_{\mu}}}{\partial{x_{\mu}}} &...
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2answers
79 views

Can time dilation show who's moving?

Imagine a person going in a spacecraft moving away from the Earth, when he return from his journey he notice the time has passed slowly than for the habitants on the Earth. Noting this, we can ...
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1answer
49 views

Special relativity and time dilation

Im studying Relativity and there is something that my mind really cant proccess right now. That would be the Deformation of time on heavily gravitational bodies. For an example lets take the movie ...
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0answers
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Why do EM waves not require a medium to travel trough? [duplicate]

Why do EM waves not require a medium to travel trough? I'm not able the understand the topic, unless i understand why they don't require a medium.
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0answers
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Transformation of $4-$velocity

Notation: a greek index indicates four labels; spacetime coordinates $\mu = (0,1,2,3)$. A latin index indicates three labels; spatial coordinates $i = (1,2,3)$. $$* * *$$ A quantity, to be ...
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1answer
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Energy-momentum relation in SR and GR

There is the famous energy-momentum relation $$E^2 - p^2 c^2 = m^2 c^4.$$ I thought it is always valid. "Always" means it is valid in general, so in GR and SR. It is something like an elemantary ...
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1answer
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Does the Vector Potential Coil and Transformer Violate Special Relativity?

"Vector Potential Coil and Transformer" by M. Diabo et al reports the induction of voltage by a time varying curl free vector potential. A refinement reported in "Vector-Potential Coil and ...
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0answers
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Symmetry between frames of reference in special relativity giving different sets of times for an event [duplicate]

If there is a space ship travelling at 0.8c, such that gamma is 5/3, relative to earth. If that space ship has to travel to say Sirius, which is 8.8 light years away. I know that relative to an ...
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4answers
286 views
+150

Weyl spinor representations and the Lorentz group

I'm currently trying to read up on the Lorentz-group and it's representations. I've found a couple of posts here on stack-exchange that I find helpful and confusing at the same time, so I would be ...
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Killing vectors corresponding to the Lorentz transformations

I have a problem with one thing. Let's consider the Lorentz group and the vicinity of the unit matrix. For each $\hat{L}$ from such vicinity one can prove that there exists only one matrix $\hat{\...
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0answers
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Invariance of measure under Lorentz transformations without the four dimensional expression

Ticciati's book Quantum Field Theory for Mathematicians states that the invariance of the measure $$\int\frac{\text{d}^3\vec{k}}{2\sqrt{\left\|\vec{k}\right\|^2+\mu^2}}$$ can be shown by direct ...
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0answers
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Relativistic vs. non-relativistic Error

I want to clarify a concept for myself. Is it correct to use the following formula for finding the error in measured relativistic momentum and non-relativistic momentum: $$\frac {\gamma mv-mv}{\gamma ...
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2answers
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Can the world line of a particle be successively differentiated to any order to always give a four-vector?

Starting with the world line of a particle given by $x^{\mu}$, this can be successively differentiated with the particle's proper time $\tau$ to give the four-velocity from the four-position, four-...
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3answers
56 views

Is it possible to slow down the speed of light in a vaccum? [duplicate]

Is it possible to slow down the speed of light in a vaccum?
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0answers
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Four-brackets (Hodges, Momentum Twistors)

I use the reference from Andrew Hodges, available at https://arxiv.org/abs/0905.1473. I am having trouble understanding his use of the four-bracket. I refer to equation 6 and equation 9, where he ...
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1answer
30 views

Orientation of moving time clocks

Let's assume there's a high speed spaceship moving right relative to us, and it's carrying two light clocks. One of them is set up so that the bouncing light pulse is oriented horizontally, and in the ...
3
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1answer
60 views

Weinberg's Coleman-Mandula theorem proof sufficient condition for isomorphism?

In Weinberg's QFT Volume 3 book on Supersymmetry, he presents his own proof of the Coleman-Mandula theorem. As part of the proof, he proves that the only possible internal symmetry generators must ...
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2answers
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Wigner Rotation of static E & M fields is dizzying

I am looking for a formula to describe the set of inertial frames in which an electromagnetic field with non-parallel, non-perpendicular, and non-zero $E$ and $B$ transform to an electromagnetic field ...
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1answer
79 views

Energy can be created

Consider a device which converts kinetic energy into electrical energy ( just like piezoelectric generator). Now I install this on two trains of very high mass approaching each other (moving in ...
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1answer
87 views

The curious case of parallel $E$ and $B$ fields and inertial frames

In a comment to this Physics SE question, @MichaelSeifert stated, For the more general case, IIRC there's always a frame in which $\vec{E}$ and $\vec{B}$ are parallel when $\vec{E}\cdot \vec{B}\...
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2answers
75 views

Length Contraction Scenario

Suppose a space ship is traveling from star A to star B at some significant fraction of the speed of light. In the frame of the ship, the distance A to B is less than the distance in A and B's rest ...
2
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1answer
74 views

Quantum teleportation with moving Alice and Bob

I have questions regarding quantum teleportation, which keep confusing me. Suppose Alice and Bob are in the same inertial frame K, and at time t (in K) Alice teleports a quantum state to Bob. What I ...
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3answers
225 views

What is Cherenkov radiation? [duplicate]

What is Cherenkov radiation? I came across this concept when I was learning SR. Why can't particles moving at speed of excess of speed of light in the medium. Why it does not violate the limitation ...
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5answers
154 views

Is Relativity of simultaneity just a flaw in perception?

So I went through a couple of different books on special relativity ( including Einstein's own book) and I just can't seem to accept relativity of simultaneity as a real thing. I'll explain my ...
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0answers
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Trouble understanding time dilation [duplicate]

I am new to relativity, so I am sorry if this question is stupid. I've been having some trouble understanding time dilation. My problem comprises of a spaceship moving at a very high speed relative to ...
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3answers
2k views

Why is a particle non-relativistic when its kinetic energy is small compared to its rest energy?

For example, nucleons in nucleus are in motion with kinetic energies of 10 MeV. Their rest energies are about 1000 MeV. Kinetic energy of nucleons is small compared to rest energy. They are hence ...
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1answer
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Does the density of a stick change according to special theory of relativity? Provided the stick is moving at nearly the speed of light? [closed]

The equation in the image made me think of the density case in special theory of relativity !