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.
12,879
questions
1
vote
1
answer
83
views
Which of these sentences best describes the equivalence between mass and energy? [closed]
Which of these sentences best describes the equivalence between mass and energy?
mass is a form of energy.
mass and energy are two manifestations of the same property: mass-energy.
mass is energy ...
0
votes
0
answers
59
views
Vertex at high $s$ Mandelstam variable
Previously I asked the question Mandelstam variables high-energy limit in which it was said that the result $stu \approx -s^2 t$ for $s$ large was derived in the forward limit ($t \rightarrow 0$) and $...
-5
votes
4
answers
135
views
Is special relativity really a phenomenon or just a result of a bunch of light hitting us at once?
Apologies for using layman/vague/incorrect terms as I'm not a physicist.
We know that Proxima Centauri is located 4.25 lightyears away from Earth. Which means that any light hitting us from Proxima ...
1
vote
0
answers
87
views
How an event horizon forms from a spherically symmetric collapsing shell
I have a question about how an event horizon can form from a spherically symmetric collapsing shell. Using the following logic, I'm trying to understand what I'm missing here.
Consider a meter stick ...
3
votes
1
answer
316
views
How are $SL(2, \mathbb{C})$ and $SL(2, \mathbb{C}) \times SL(2, \mathbb{C})$ related to the Lorentz Group?
I know from Weinberg and Schwartz's book on Quantum Theory of Fields that $SL(2, \mathbb{C})$ double-cover $SO^{+}(1,3)$.
However, moving to the Lie algebra, based on the following wiki:
https://en....
0
votes
0
answers
83
views
Is this a valid experiment to measure the one-way speed of light?
Consider the following setup. Place a light source at point $A$ and three mirrors at point $B,C,D$ such that the light follows the path $ABCDA$ (refer diagram). Let the distance $AB=CD=2d$ and $BC=CD=...
2
votes
1
answer
111
views
Does electromagnetism have no free parameters?
In SI units, Maxwell's equations (in vacuo) seem to have two free "parameters" or "constants". The vacuum permittivity, however, can be eliminated by properly redefining the ...
0
votes
2
answers
135
views
What are the correct values for relativistic 3-momentum $p=mv$?
Is the value of $m$ in this formula relativistic mass or real mass? Just trying to figure out if this is the right equation for my problem.
0
votes
0
answers
32
views
Acceleration limit [duplicate]
From the theory of relativity, we know that the highest speed achievable for any massive object is the speed of light. So we can say $c$ is the speed limit is there some similar limit on maximum ...
0
votes
2
answers
97
views
How can time slow down and speed up for a particle simaltaneously?
Suppose there's a kangaroo baby in its mother's pouch and there's a light bulb 300,000 km from them. If someone turns on the bulb, both kangaroos will agree that the light bulb takes 1 s to turn on ...
1
vote
1
answer
560
views
Mandelstam variables high-energy limit
Let $s,t,u$ be the usual Mandelstam variables defined by $s = (p_1 + p_2)^2$, $t = (p_1-p_3)^2$ and $u = (p_1 - p_4)^2 = 4m^2 - t -s$. I am trying to convice myself of that $stu \approx -s^2 t$ for ...
-4
votes
2
answers
122
views
Why does this experiment not show how fast a reference frame is moving?
An observer on a train has a light pulse generator on the floor and a mirror on the ceiling. The time a light pulse takes to travel from the generator and back again can be measured. The observer ...
0
votes
1
answer
150
views
Four-divergence of the wedge product
I have maybe simple question, but I cannot find it anywhere in the internet.
When I calculate four-divergence on tensor, being wedge product, do I calculate it the way A or B?
$$
\partial_{\alpha} \, ...
1
vote
2
answers
610
views
Elastic scattering $A+B \rightarrow A+B$: How to express the scattering angle in terms of $s, t$?
There is an elastic reaction $A + B \rightarrow A + B$ and we need to express the scattering angle in terms of Mandelstam variables $s, t$.
From what I know: $s=(p_A + p_B)^2$ and $t=(p_A - p_C)^2$.
...
2
votes
0
answers
157
views
Undetermined terms in perturbative expansion of Lorentz Transformation?
I am trying to solve problem 2.1 in Schwartz, which is to derive the transformations $x \rightarrow \frac{x+vt}{\sqrt{1-v^2}}$ and $t \rightarrow \frac{t+vx}{\sqrt{1-v^2}}$ in perturbation theory. ...
19
votes
5
answers
5k
views
If our solar system and galaxy are moving why do we not see differences in speed of light depending on direction?
May be a silly and simple question, but I've been wondering if:
The speed of light is constant, and
When we're moving in the same direction (where both the emitter and the receiver move with the ...
1
vote
2
answers
96
views
Why does the mass-energy associated with nuclear potentials obey $m = \gamma m_0$?
Here is a thought experiment that has me confused.
Imagine a particle, the nonexiston. If possible, ignore quantum mechanics and let the nonexiston be a classical particle with spooky action at a ...
1
vote
2
answers
2k
views
Generators of Lorentz transformations
In Chapter 3 of Peskin and Schroeder's Introduction to Quantum Field Theory they write
For the rotation group, one can work out the commutation relations by writing the generators as differential ...
-1
votes
2
answers
278
views
Why is light speed constant even in respect of a moving body? [duplicate]
My teacher told that speed of light is constant. The speed of moving object appears 0 when seen by another moving object( of same speed as that of first) but she told that light speed is constant ...
1
vote
2
answers
101
views
Would somebody feel a magnetic field if they are travelling at the same velocity as a charge?
I am little bit curious about how magnetic fields are being generated when a charge moves.
I want to check if somebody travelling along with a charged particle, would that person experience a magnetic ...
2
votes
1
answer
148
views
Is $E=mc^2$ relevant while accelerating a book across a table?
I'm having a difficult time making the connection between the Newtonian conception of mass and that proposed by special relativity and particle physics. From a Newtonian perspective, mass is that ...
11
votes
3
answers
2k
views
Observing light from a falling elevator
Today in my physics class, my teacher said that if one would point a laser into a falling elevator (acceleration because of a gravitational field), an observer inside the elevator would see the light ...
2
votes
1
answer
194
views
Ultrarelativistic limit for neutrinos: Why is this approximation working?
In this section of the Wikipedia article on neutrino oscillations, a neutrino mass eigenstate $\left|\nu_i\right>$ is written as
$$\left|\nu_i(t)\right> = e^{-i(E_it-\vec p_i\cdot\vec{x})} \left|...
2
votes
2
answers
323
views
Proof for impossibility of FTL Signals
Is there is formal proof for the fact that signals must always travel at a speed less than the speed of light in a vacuum?
I understand that special relativity dictates that for massive particles to ...
0
votes
2
answers
74
views
How to interpret Lorentz transform in Special Relativity when the time axis position for different objects are not horizontally even? [closed]
I have a question regarding a spacetime animation I am contructing, please. The animation is as follows. Einstein stands on the train station while Curie stands on board a train. At time 0, they are ...
3
votes
3
answers
350
views
Why proper time is a measure of space?
Recently I've been trying to learn General and Special Relativity by myself. There is an specific thing I do not understand perfectly, proper time in the metric of the space-time.
Take the case of an ...
1
vote
1
answer
230
views
Imaginary Lorentz factor in special relativity [duplicate]
This thing is making me confuse, what is mean by imaginary Lorentz factor in Physics? What is the physical meaning of imaginary?
0
votes
2
answers
144
views
How to implement length contraction in special relativity
I am trying to construct a special relativity animated simulation, and am unclear about some aspects, please.
The animation is as follows:
From the simulation coordinate system's point of view, ...
1
vote
1
answer
55
views
What is the correct way to use Lorentz transform for special relativity in this situation?
I am trying to construct a Lorentz transform special relativity animated simulation, and am unclear about some aspects, please.
The simulation is as follows:
At time=0, the person at the center [0,0,...
1
vote
1
answer
280
views
How to determine sub and superscript for divergence theorem in Minkowski Space?
Suppose we are given a type $(0,2)$ tensor $T_{\mu\nu}$ in a Minkowski space with $(-,+,+,+)$ signature. Consider a closed 3-dimensional hypersurface $\partial \Omega$ which encloses a volume $\Omega$ ...
3
votes
1
answer
137
views
Why does the direction of the plane's velocity matter in the Hafele and Keating Experiment to verify gravitational time dilation?
I found this confusing because a plane's velocity is defined relative to the ground. So, no matter what the plane's direction is, the relative speed of the clocks (hence the Lorentz factor) on the ...
-5
votes
1
answer
108
views
These guys occur but why? [closed]
We all know that if we consider the assumption of Einstein that is no material object can travel faster than light to be true then two effects that are
Length Contraction And Time Dilation
seem to be ...
-1
votes
1
answer
92
views
How many quanta can travel at light speed relative to each other simultaneously? [duplicate]
How many quanta can travel at light speed relative to each other simultaneously?
I know the concept of being "simultaneous" breaks down at a distance so let's assume for the sake of ...
8
votes
2
answers
383
views
Do wavefunctions shrink under Lorentz boosts?
Suppose I have a relativistic wavefunction for some massive particle, defined by Dirac equation. Suppose the particle is free from interactions.
Let us suppose that the probability density takes the ...
0
votes
2
answers
104
views
Relativistic motion in particle accelerator
This question is attempting to simulate the process of a circular particle accelerator. We are given a constant electric field $E$ along the angular direction and a varying magnetic field $B$ along ...
4
votes
2
answers
133
views
Could a non-photon massless particle travel at a speed other than $c$? [duplicate]
The speed of light is given as $c=\frac{1}{\sqrt{ε_0μ_0}}$ which is in terms of the electric and magnetic constants.
Hypothetically, another massless particle could exist which does not interact with ...
2
votes
2
answers
190
views
Global conservation + Lorentz invariance = local conservation?
On the page 83 of "Quantum Field Theory Lectures of Sidney Coleman", Coleman showed an interesting example:
It seems that global conservation law and local conservation law can be related. ...
0
votes
1
answer
535
views
$\mathfrak so(1,3)$ generators hermitian or antihermitian?
In Schwartz "Quantum field theory and the standard model" pag 160, the generators of the rotation are Hermitian, while the generators of boosts are anti-Hermitian, as an example:
$ J_1 = \...
-5
votes
1
answer
206
views
Is This Why the Speed of Light is Universally Invariant?
Please could you tell me if the following is an original thought or whether this is already understood. I ask because I am undertaking a piece of writing on the nature of spacetime. What I discuss ...
1
vote
1
answer
106
views
Vacuum Cherenkov Radiation
Hi I was reading this paper (Pair Creation Constrains Superluminal Neutrino Propagation) for an assignment and I came across the following question:
in the article, it is said that if we assume that ...
0
votes
2
answers
95
views
Does increase in relativistic mass with speed violate principle of relativity?
From special relativity we know that,
$$ m = \frac{m_0}{\sqrt {1-\frac {v^2}{c^2}}} $$
where,
$m$, $m_{0}$ and $v$ are the relativistic mass, rest mass of the object and speed relative to the observer ...
1
vote
0
answers
76
views
Born-Infeld equation with a coefficient: which phenomena it describes?
Let us consider the well known Born-Infeld equation
$$-{\rm div}\left(\frac{\nabla u}{\sqrt{1-\frac{1}{b^2}|\nabla u|^2}}\right) =g(u).$$
It appears quite naturally in several fields such as ...
0
votes
0
answers
65
views
Definition of acceleration and inertial frames of reference
Sorry for my math lacks, I hope you'll be patient even if this question will probably not be clear.
How can we define acceleration in special relativity (and in Newtonian mechanics were we apply ...
-1
votes
3
answers
296
views
Couldnt we "race" light to determine its one-way speed?
From my (basic) understanding the biggest problem of measuring the speed of light is clock synchronization. But I question why this is necessary. To be more specific, what if, instead of measuring ...
-1
votes
4
answers
161
views
Can special relativity contain general relativity?
I realized that considering merely an upper limit for speed per se can hint at gravity(more precisely black holes).
Very naively with Newtonian mechanics, one can derive the following formula for ...
-1
votes
2
answers
212
views
Is the speed of light in is uniform non-vacuum medium constant for all observers? [duplicate]
I am running at $5 \text{ ms}^{-1}$ and holding a torch pointing in the direction of motion. This torch has a large block of glass attached to the end. Would a stationary observer see the light as ...
1
vote
1
answer
463
views
Does potential 4-momentum exist or not?
I've heard that
"First, unlike energy, momentum cannot be stored. There's no such thing as potential momentum. Potential energy exists because energy isn't about moving, it's about doing."
...
-2
votes
1
answer
66
views
What to make out of this.....? [closed]
Let's set up an experiment first.
Suppose there is a body of rest mass $m$ at rest in an observers inertial frame and it is accelerated to almost $c$ (speed of light) at constant acceleration $a$ with ...
2
votes
1
answer
50
views
How to call the "constant factor $K$" in Gourgoulhon's definition of "ideal clocks"? And: May distinct ideal clocks have unequal values $K$?
Éric Gourgoulhon, "Special Relativity in General Frames: From Particles to Astrophysics" (2013), presents in sect. 2.3.2 (page 33) definitions of the notions "clock" and "...
2
votes
2
answers
245
views
Is $\mathfrak sl(2,\Bbb C)_\Bbb R \cong \mathfrak so(1,3)_\Bbb R$?
That is: is $\mathfrak sl(2,\Bbb C)$ isomorphic to $\mathfrak so(1,3)$ when both are considered as real algebra?
I am using the following six generators for $\mathfrak sl(2,\Bbb C)_\Bbb R$, as by ...