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
1answer
61 views

Geometric derivation of Lorentz boosts

In two dimensions a very nice parametrization of the rotation group is obtained by the following line of arguments: The group of rotations is connected and compact. Therefore the exponential is ...
0
votes
1answer
43 views

Proving the linearity of the transformations between inertial frames without assuming differentiability

All the references that I could find on the proof of the linearity of the transformations assume that the map that connects the coordinates between two inertial frames is at least once differentiable. ...
0
votes
0answers
45 views

Is this calculus on the Lorentz factor right?

Can the following process be justified? The Lorentz factor is given by $$\gamma (V^i)=\left(1-\frac{V^2}{c^2}\right)^{-1/2}$$ where $V^2=\sum_{i=1,2,3}{V^iV^i}$ So, the partial derivative of the ...
0
votes
0answers
44 views

Zero order Tensor

One of the definition of tensor is that it should be invariant under transformation. Thus a tensor of order zero is a scalar should be invariant under transformation. For a tensor component $v^{\mu}$ ...
4
votes
4answers
111 views

Is Lorentz transform a tensor?

I am confused whether Lorentz transform is a tensor or not, since it is a linear transform. If yes how can I verify that?
0
votes
0answers
37 views

What does Lorentz index structure say about a full-fledged correlator?

I have a probably dumb question. Consider the following position space correlation function in a YM-theory (with or without matter fields): $$f_{\mu_1\cdots \mu_n}^{a_1\cdots a_n}(x_1,\ldots,x_n)=\...
0
votes
2answers
29 views

Energy to bring in rotation a “special” material sphere

Let's suppose that we have an ideal homogeneous sphere of mass and finite radius that rotates around a peripheral axis passing through one of its extreme points and that the only point diametrically ...
0
votes
1answer
67 views

Mass-energy equivalence - old notation

Einstein originally gave the formula as $$M = \mu + \frac{E_0}{c^2}.\tag{17}$$ In which $\mu$ was the mass of the system. Today, we more commonly get taught that the energy is in relation to the ...
1
vote
3answers
106 views

Maxwell's equations without special relativity

If Maxwell's equations were around long before special relativity, and yet they don't make sense without special relativity (like if you think of a moving charge next to an electrically neutral wire ...
1
vote
2answers
65 views

Now when we can measure gravitational field, how does the principle of equivalence hold true?

LIGO measured gravitational field waves. The whole thought experiment of Einstein, leading to ‘principle of equivalence’, assumes that there is no way to know inside the rocket that whether its ...
0
votes
2answers
65 views

Relativity and Momentum of photons

I read somewhere that as the speed of a particle approaches c, its mass tends to infinity. Light is composed of particles (photons). If that is the case, then why don't we feel an enormous weight ...
0
votes
0answers
59 views

Does absolute motion/stillness exist?

I am not a physicist :) I (think I) understand the idea that motion can be relative in the sense that, I'm standing still inside a moving train in regards to the moving train itself, but I'm moving ...
-2
votes
1answer
61 views

Muons - how are we even able to detect them? [closed]

muons have a very small half life comparable to 2.5 μs or so. But we know that it has to cover a very large distance from upper atmospheric layers to reach the particle detectors installed at earth's ...
0
votes
2answers
46 views

Is simultaneity of events relative or just our observation of it?

I have already read this post about Relativity of Simultaneity but it doesn't seem to answer my question or it confuses me even more. Please feel free to close this if I am mistaken. I (think I) ...
1
vote
0answers
24 views

How can one define a covariant rate of change of rest mass for an extended body?

For a point mass I can define a covariant rate of change of its rest mass as $\frac{d}{d\tau}m_0$ where $\tau$ is the proper time. How can I also define a covariant rate of change of rest mass for an ...
6
votes
3answers
102 views

How is rest mass $m_0$ in $E=m_0c^2$ related to mass $m$ in $F=ma$?

A particle at rest has energy given by $$E=m_0c^2$$ where $m_0$ is defined as its rest mass. So rest mass is essentially a measurement of a particle's intrinsic amount of potential energy. How is ...
6
votes
4answers
92 views

When is the value of spacetime interval $ds$ negative?

The spacetime interval in special relativity, $ds$, is defined as $$ ds^2=c^2dt^2-dx^2-dy^2-dz^2 $$ with the $(+,-,-,-)$ Minkowski sign convention. The value of $ds^2$ can be positive, zero, or ...
0
votes
2answers
99 views

Twin paradox problem from a perverse perspective

Reformulation of the problem I want to study twin paradox but considering that the reference frame of the twin that travels to Alpha Centauri has no velocity. Instead of considering that the twin who ...
0
votes
1answer
60 views

What is the role of Lorentz transform on flat spacetime in GR?

The chart before and after a Lorentz transform are both valid description of the same history of flat spacetime right? If so, is this just the same as going from one chart to another chart via the ...
2
votes
1answer
53 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 ...
-6
votes
1answer
76 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 ...
0
votes
1answer
48 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,...
3
votes
3answers
111 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
0answers
31 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 ?
3
votes
0answers
47 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 ...
50
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, ...
1
vote
1answer
39 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
vote
1answer
50 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
votes
1answer
38 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 ...
8
votes
6answers
233 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
3answers
86 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 ...
1
vote
1answer
49 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 ...
0
votes
1answer
36 views

Invariance of length [closed]

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 ...
2
votes
1answer
42 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 ...
2
votes
3answers
105 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 ...
0
votes
1answer
49 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
2answers
89 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
55 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
1answer
112 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 ...
4
votes
1answer
100 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 ...
0
votes
1answer
63 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 ...
6
votes
4answers
343 views

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 ...
0
votes
0answers
30 views

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{\...
0
votes
0answers
44 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
48 views

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-...
0
votes
3answers
57 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?
1
vote
0answers
19 views

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 ...
0
votes
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
votes
1answer
65 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 ...
2
votes
2answers
353 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 ...