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.
11,549
questions
0
votes
0
answers
19
views
Failure of Central Limit Theorem for Juttner Distribution?
So I've heard the claim Central Limit Theorem can give the Maxwell Boltzmann distribution.
However, it fails to reproduce the Juttner distribution. Why is this so?
- 1,063
0
votes
0
answers
19
views
Rindler's criterion and definition of linearity of the Lorentz and Poincaré transformations
In Wolfgang Rindler's "Introduction to Special Relativity", 2.ed. 1991, on p.11 his derivation of the special Lorentz transformation $ x'=f(x) $ starts with the proposition that this ...
- 189
0
votes
0
answers
46
views
Understanding where equation $2.3$ comes from?
I'm trying to understand this paper (equation $2.3$ specifically):
Bini, D., Carini, P., & Jantzen, R. T. ($1995$). Relative observer kinematics in general relativity. Classical and Quantum ...
- 1,063
0
votes
0
answers
16
views
Speed of light problem [duplicate]
This question totally hypothetical and I'm aware we can't travel at speed of light but IF ....
If you were to travel at the speed of light according to Einsteins theory of relativity you would gain ...
- 1
4
votes
4
answers
243
views
Time Dilation Explanation [closed]
This might be a dumb question but I'm still going to ask it.
So basically I've been trying to learn Special Relativity through this lecture by Brian Greene, and the way he justifies time dilation is ...
- 49
0
votes
0
answers
29
views
Logistics of Recreating the Michaelson-Morley Experiment
I want to recreate the Michaelson-Morley Experiment and am wondering how technically challenging it would be. I'm not looking for it to be super precise, just good enough to provide reasonable ...
- 21
-2
votes
2
answers
70
views
Can space proper-time (SPT) diagrams as used by Lewis Epstein in Relativity Visualized be used to explain the twins paradox of special relativity?
Space proper-time (SPT) diagrams are perhaps easier for the layman to understand than Minkowski diagrams, although I don't much about them.
I have been, so far, unable to understand fully the latter, ...
0
votes
1
answer
96
views
Why using incorrect formula results in a correct formula? [duplicate]
I know that the mass of a photon is zero. However, others say no it is just the rest mass which is zero, the relativistic mass isn't, but I say that no it is also zero because the rest mass $m$ is ...
- 45
1
vote
1
answer
24
views
Can we interpret timelike, rest frame motion as velocity in the time direction? If so, does it cause charge to generate a ''$B$ field'' perp. to time?
For background: I've had courses on SR/GR from Hartle, E&M from Griffiths/Purcell, and know E/B fields are unified/transform with lorentz boost.
My question is less about 'does SR account for E/B ...
2
votes
2
answers
73
views
$t$ and $t'$ in Lorentz transformations
I don't really understand what the primed and unprimed coordinates imply in Lorentz transformations. In all of the books, they simply derive the coordinates, assuming that an inertial frame $ S$ is at ...
- 31
0
votes
0
answers
15
views
Velocity addition and Thomas precession
In Goldstein’s classical mechanics, section 7.3, there's an approximation (7.19) that I do not understand, in particular $\beta''_y=\beta'_y/\gamma $. Worse, even if I accept the approximation, it ...
- 11
2
votes
1
answer
90
views
What will happen if one used $[\phi (x), \frac{\partial L}{\partial (\partial _x\phi(x))}]=i\hbar$ to get a Quantum Field Theory?
Classical field theory does not discriminate between space and time, but canonical quantisation does. We use the relation $$[\phi (x), \frac{\partial L}{\partial (\partial _t\phi(x))}]=i\hbar$$ to get ...
- 2,929
-2
votes
1
answer
35
views
Moving spaceship problem in Special Theory of Relativity [closed]
Answer is (a).
I am thinking like this way.
According to passengers in moving spaceship, they take 1 hr to reach the Pegasus. Or we can say that as they will find themselves at rest, so the Pegasus ...
- 255
1
vote
1
answer
38
views
Lorentz transformations in Minkowski space including invariants
Let's assume the reference frame of a still observer with the 2 axes: the x-axis and time axis t. Let's say there's another observer within that frame moving with a constant velocity v with respect to ...
-3
votes
0
answers
26
views
Are there things with different physical attributes that serve exact same purpose in a system? [closed]
I’ve been puzzling about this cross-disciplinary concept for the last week.
Can you think of any two things that have different physical make up that serve the exact same purpose?
For instance, ...
2
votes
1
answer
78
views
Proof that conservation of momentum is Lorentz invariant
In classical mechanics, if
$$\frac{\mathrm d}{\mathrm d t}\sum_i m_i\vec{v_i}=0$$is true for one frame of reference, then it is easy to prove that this is true for all frames (since different frames ...
- 1,286
-5
votes
0
answers
33
views
Try this method to calculate the speed of light [duplicate]
The speed of light as we know by today is 299,792,458m\s. But that is a two-way speed of light. Light first striking a mirror and then reflected back. No one has actually ever measured a one-way speed ...
1
vote
0
answers
26
views
Prove that Majorana mass term is Lorentz invariance
I have a homework to prove that using one kind of chirality, let's say left-handed, we can construct a mass term. The argument is to show that this term $\psi^TCP_L\psi$ is satisfy the dimensionality ...
- 11
3
votes
6
answers
861
views
Mass definition
One definition of mass is 'a measure of the quantity of matter in an object at rest relative to the observer'. What do 'at rest' and 'relative to the observer' mean here? I know it has to do with mass ...
-3
votes
0
answers
28
views
How to know if one-way speed of light is different from other? [duplicate]
I'll be using Veritasium's idea of Mars and Earth, so if you know, you know.
We start by measuring the time it will take light to travel from Earth to Mars and for that we will use the simple formula, ...
0
votes
0
answers
102
views
+100
How do quantum probabilities transform under Lorentz transformations?
I think I get how scattering probabilities transform under Lorentz transforms. Once the interaction phase is over, the final probabilities become time independent. Hence, every observer could describe ...
- 2,929
-1
votes
3
answers
88
views
Does the notion of an universal clock really contradict special relativity? [closed]
Special relativity says that different observers qualify two events as simultaneous based on their velocities. But isn't that a statement about information they can measure rather than about reality? ...
- 198
-3
votes
0
answers
72
views
Is the speed of light accurate? [duplicate]
Speed of Light
As we know by today that the speed of light is exactly 299,792,458m\s.
French physicist Hippolyte Fizeau is credited with making the first ...
-3
votes
0
answers
86
views
Lorentz transformations (Maths) vs "reality" (Phyiscs) [closed]
Let (O) be the place of emission of a light signal (event) and (M) a point moving in a rectilinear motion (observer) uniform with a speed $\vec{u}$ and which is at time $ t=\frac{||\vec{OM}||}{c}=r$ ...
- 471
2
votes
1
answer
60
views
Proof that a Lorentz-invariant scalar function can only depend on scalar products
If we have a Lorentz-invariant scalar function $f$ of a single four-vector $x^{\mu}$ we can show that $f$ can only depend on $x^2$ (see Argument of a scalar function to be invariant under Lorentz ...
- 886
-1
votes
0
answers
65
views
What is the relativistic velocity composition law? [closed]
In Galilean relativity we have the following relative velocity composition law:
$$ \vec v_{DE} + \vec v_{EF} = \vec v_{DF} $$
Where the relative velocity between $i$ and $j$ for any $i$ and $j$ is ...
- 1,063
1
vote
3
answers
133
views
Confused about tensor notations of how vector and covectors act on each other
I'm learning/playing around with tensors and somehow got this contradiction,
suppose $\{v_i\}$ and $\{w_i\}$ are basis for a vector space $V$ and $\{ v^i \}$ and $\{w^i\}$ are basis for the dual space ...
- 23
2
votes
1
answer
97
views
Clarification on clock synchronization passage from Kleppner and Kolenkow
I have a question about the following passage from An Introduction to Mechanics by Kleppner and Kolenkow. The passage reads as follows:
The Newtonian procedure would work if the speed of light were ...
1
vote
1
answer
58
views
What is the average recessional velocity of an object in the universe?
I’m trying to get a better grasp on cosmological horizons and have a question regarding recessional velocity. In particular:
What is the average recessional velocity of a cosmological object (...
- 500
0
votes
2
answers
47
views
The Same Origin Requirement of Reference Frames
Currently learning special relativity:
My understanding is that Lorentz Transformations are the motions of Minkowski space that preserve the spacetime interval - and the same origin point.
That is two ...
- 201
-2
votes
1
answer
52
views
Will light be travelling faster than the speed of light? [duplicate]
If a photon is emitted from a light source travelling with some velocity, then surely the photon emitted in the direction of travel would have a velocity equal to the speed of light plus the velocity ...
0
votes
0
answers
44
views
Lorentz transformations in relativity [closed]
I'm trying to solve a particular problem given in Introduction to Special Relativity by R. Resnick, which goes like this:
Two observers in the S frame, $A$ and $B$, are separated by a distance of 60 ...
- 31
1
vote
1
answer
54
views
Is there only one convention to define the electromagnetic field tensor?
I know that the electromagnetic field tensor depends on which metric is used. For example wikipedia uses the $(+---)$ sign convention, but in the Griffiths we have the $(-+++)$ sign convention.
That's ...
- 560
1
vote
1
answer
69
views
How can I calculate length contraction using hyperbolic functions?
In the image below, the pink line on the $x$ axis is the length contracted measurement correspondent to the $x'$ measurement in the primed reference system. This length (let's call it $l$) equals $x'/...
- 409
-1
votes
0
answers
88
views
Creating The Sun [duplicate]
I am a high school student and just came to know about Einstein famous formula for relativity
$$
E = mc^2
$$
I was wondering if somehow I was able to throw a considerably heavy object with a speed ...
- 71
1
vote
0
answers
57
views
Ruling out dependence of y and z coordinates in Lorentz transformation
Let us assume that motion is in the $x$ direction, axes of both coordinate systems are aligned and their origins meet at $t=t'=0$. The most general relation between $x$ and $x'$ then becomes (ruling ...
-5
votes
2
answers
101
views
Invariance of lightspeed [closed]
Is there experimental evidence (not proof by mathematical deduction based on special relativity) of the invariance of light speed in two different frames of reference? For example, is it possible to ...
- 87
0
votes
0
answers
35
views
Is there also relativistic length contraction caused by gravitational Lorentz transformation?
When objects move at relativistic speeds, their length as observed from outside gets scaled inversely proportional to the Lorentz factor in direction of the velocity: https://en.wikipedia.org/wiki/...
0
votes
2
answers
85
views
How do I calculate the mass of a moving proton?
When a proton moves it's no longer its rest mass, it now has more mass because of the Kinetic Energy. So if we're to find the new protons mass if it was moving at some speed, how would we find it? ...
- 29
0
votes
1
answer
68
views
Why is it difficult to make the Juttner distribution account for anisotropies?
Wiki states
While the classic Maxwell-Juttner distribution generalizes for the
case of special relativity, it fails to consider the anisotropic
description.
What are the challenges when one tries to ...
- 1,063
0
votes
0
answers
31
views
Name of "coordinate representation" of spacetime symmetries
I would like to know the name of the following "natural" representation for symmetry groups that can be realized as spacetime symmetries. The easiest example is for instance the translations ...
- 1,962
-1
votes
2
answers
50
views
Does atomic time slow down at faster speeds? [duplicate]
Continuing with my questioning regarding two different "times", (but hopefully within the scope inquiry this time), if two asteroids are in an orbit around the solar system, one at 10,000kph ...
- 817
1
vote
0
answers
39
views
Derivation of the transformation law for spinors
I'm reading the book Quantum Field Theory: An Integrated Approach by Eduardo Fradkin, and I got stuck where the transformation law for spinors
$$
\psi'(x') = S(\Lambda) \psi(x)
$$
is derived.
In ...
- 515
1
vote
1
answer
48
views
How can we derive the four-wavevector from first principles?
Context
From [1], I understand that, "The four-wavevector is a wave four-vector that is defined, in Minkowski coordinates, as
$$\mathbf{K}^\mu = \left(\frac{\omega}{c}, \mathbf{k}\right).\tag{1}"$...
- 240
1
vote
5
answers
119
views
Twin Paradox: Fewer Seconds or Shorter Seconds?
In Einstein's Twin Paradox thought experiment, the travel time is shorter for the traveling brother than for the stationary brother.
Since the SI unit of time in physics is the second, is the travel ...
- 520
1
vote
2
answers
117
views
How important is the concept of rapidity in relativity?
After studying the concept of rapidity and the associated formulation of special relativity in terms of hyperbolic trigonometric functions of rapidity, I've come to understand the elegance of this ...
- 409
9
votes
3
answers
1k
views
What does an area represent in a spacetime diagram?
If I have a spacetime diagram with $t$ on the vertical axis and $x$ on the horizontal axis, does calculating an area in this diagram have any physical significance?
The reason I ask is because I'm ...
- 409
1
vote
1
answer
51
views
How can you calculate how long life will last with a regular run in terms of special relativity?
Imagine, John run everyday 10 km with speed 12 km/h towards the east along the equator. If he had not run, he would have died at 70 from the point of view of a motionless observer. How long will John ...
- 113
1
vote
0
answers
39
views
On the Feynman's proof of Lorentz transformations
In this video he explains Feynman way of deriving the Lorentz transformations.
First he considers the invariance,
$$ x^{2}-(ct)^{2}=(x')^{2}-(ct')^{2}$$
He then invokes a bit of complex analysis by ...
- 420
8
votes
3
answers
439
views
If the speed of light is the maximum speed anything can travel, and temperature describes vibration or motion, is there a maximum temperature? [duplicate]
Apologies for everything. This is my first question.
Basically the title. If the speed of light is the maximum speed anything can travel, and temperature describes vibration or motion, is there a ...
- 89