Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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.

1
vote
2answers
141 views

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 ...
2
votes
2answers
222 views

Heisenberg uncertainty and Lorentz contraction

Consider a particle in a frame moving with speed $v$ relative to the lab frame. By Lorentz contraction, the width of the wavefunction will be smaller in the lab frame, resulting in smaller $\Delta x$. ...
2
votes
1answer
29 views

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 ...
-5
votes
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 ...
3
votes
3answers
80 views

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 ...
0
votes
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,...
47
votes
2answers
7k views

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, ...
0
votes
0answers
26 views

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 ?
1
vote
1answer
150 views

Do SR Postulates Require the Interval to be Invariant?

Let's define the interval as $I=\eta_{\mu\nu}dx^\mu dx^\nu$ where $\eta_{\mu\nu}$ is defined to be a frame invariant diagonal matrix whose diagonal elements are $-1,+1,+1,+1$ . By definition, $\eta_{\...
1
vote
0answers
32 views

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 ...
1
vote
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 ...
1
vote
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 ...
-6
votes
0answers
40 views

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 ...
8
votes
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 ...
1
vote
1answer
35 views

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 ...
-1
votes
2answers
59 views

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 ...
2
votes
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 ...
5
votes
1answer
390 views
+50

Frames of reference of Maxwell's Equations

The Maxwell's Equations are one of the most famous sets of equations physics have ever known. But just as different sets of equations are applicable to different frames of reference, where are Maxwell'...
4
votes
4answers
242 views

Paradox in special relativity involving capacitor

In Laboratory-reference frame (LRF) A horizontally moving (with constant speed) flat capacitor would have a different size of plates therefore resulting in different capacity $C'$, namely: $$ C' = \...
1
vote
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 ...
2
votes
3answers
104 views

Are pseudospinors valid or useful?

We all know that in addition to scalars and vectors, there are pseudoscalars and pseudovectors, which have an additional sign flip under parity. These are useful and necessary when constructing ...
0
votes
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 ...
3
votes
1answer
131 views

Identifying Lorentz Covariant Equations

Statement: $\phi , A^{\mu}, T^{\mu \nu}$ are a Lorentz scalar, vector, and tensor. Which of the following equations are Lorentz covariant. a. $\phi = A_{0}$ b. $\phi = A^{\mu}A_{\mu}$ c. $\phi = ...
2
votes
1answer
34 views

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 ...
6
votes
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 ...
1
vote
1answer
157 views

Special Relativity pothole paradox

Consider a man who is 1 metre in width and is running (at relativistic speeds) towards a pothole in the ground which is also 1 meter in width. In the reference frame of the man it appears as though ...
0
votes
0answers
41 views

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 ...
-3
votes
0answers
17 views

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 ...
2
votes
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 ...
5
votes
2answers
225 views

Does STR imply that time dilation is effected by an orientation of clocks?

Many texts about STR time dilation use as an example thought experiment with 2 mirror photon clock. The conclusion of this experiment is: In a frame moving relative to the clock, they will appear to ...
0
votes
0answers
12 views

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 ...
4
votes
1answer
91 views

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 ...
2
votes
1answer
153 views

Simulation of relativistic probe passing through an external solar system

I recently read about the Breakthrough Initiative to launch "StarShot", a nano-probe that is designed to travel to Alpha Centauri at $0.2c$. One of the challenges to be solved involves the precise ...
3
votes
1answer
158 views

Clock on a pendulum

If a clock is swinging on a pendulum (assume it's on some massive object with gravity) what happens when that system is moving at relativistic speeds? To an inertial observer, on the back-swing (i.e. ...
1
vote
0answers
53 views

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 ...
0
votes
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 ...
0
votes
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}}} &...
0
votes
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 ...
1
vote
2answers
159 views

Definition of a tensor

I think a tensor of rank $m$ on an $n$-dimensional space $V$ is a multilinear map $T : V^n \to \mathbb{R}$. For example a tensor of rank $3$ is a multilinear map $T:V^3 \to \mathbb{R}$. If $\{\textbf{...
-6
votes
0answers
51 views

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 ...
0
votes
1answer
75 views

Proving a general formula for the boost transformation of the electromagnetic field

In inertial frame $\mathcal{O}$, a region of space-time is filled with constant electric field $\vec{E}$ and magnetic field $\vec{B}$. Another inertial frame $\mathcal{O}'$ has 3-veclocity $\vec{V}$ ...
16
votes
5answers
46k views

Why don't electromagnetic waves require a medium?

As I understand it, electromagnetic waves have two components which are the result of each other, i.e., when a moving electric charge creates a changing magnetic field at point X then a changing ...
-1
votes
0answers
28 views

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.
0
votes
1answer
157 views

What is the definition of contravariant dual field tensor?

This is p.205 of Ta-pei cheng book. The dual field tensor is defined in $(10.52)$ in terms of the covariant tensor. Then I think the definition of contravariant dual field tensor is just reversing the ...
3
votes
1answer
158 views

Fermi's understanding of the Doppler effect

I am now reading the classic paper by Dicke, The Effect of Collisions upon the Doppler Width of Spectral Lines At the very beginning of the paper, Dicke said ''Quantum mechanically, the Doppler ...
0
votes
1answer
50 views

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 ...
0
votes
0answers
38 views

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 ...
0
votes
2answers
173 views

Special relativity thought experiment

I'm trying to build some intuition to some basic concepts in Special Relativity. The following is a thought experiment from one of my lectures. Here are the statements: (1) According to Alice, her ...
0
votes
1answer
407 views

How can I prove that the following Lagrangian is Lorentz-invariant iff the axionic field is a pseudoscalar?

My professor has given me the following action stating that $a(x)$ is an axionic field and told us in class that for this action to be Lorentz invariant the field must be a pseudoscalar. $$ S = -\int ...
-1
votes
0answers
15 views

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 ...