For questions relating to Einsteins special relativity theory, the equivalence of physical laws in different inertial frames.
Questions tagged [special-relativity]
138 questions
25
votes
1 answer
Minkowski plane vs. hyperbolic plane
As a physics student, I have studied some elements about hyperbolic geometry in many different contexts.
In linear algebra, I was told that equipping $\mathbb{R}^2$ with a non-degenerate symmetric bilinear form gives us a space isometric to the…
TeicDaun
- 313
15
votes
6 answers
Sum of two velocities is smaller than the speed of light
Using the Lorentz transformation from special relativity, we get that the sum of two velocities can be expressed as
$$u=\frac{u'+v}{1+\frac{u'v}{c^2}}.$$
Given that $|u'|,|v| \le c$, I want to prove that $|u| \le c$, ie. that the velocity never…
user258521
- 1,059
14
votes
2 answers
An unzipping problem
Imagine a continuous one-dimensional line, which is duplicated exactly once. Duplication starts at random spacetime points. Once a point is duplicated, it starts a double duplication wave moving in either direction at constant speed $v$ (similar to…
sam wolfe
- 3,465
11
votes
1 answer
Is the exponential map to the indefinite special orthogonal groups $SO^+(p,q)$ surjective?
Is the exponential map to the identity component of the special indefinite orthogonal groups
$$ \mathrm{exp} \colon \mathfrak{so}(p,q) \to SO^+(p,q)$$
surjective?
Friedrich
- 891
7
votes
0 answers
Why are the fundamental and anti-fundamental representation in $SL(2,\mathbb{C})$ not equivalent?
I am currently learning symmetries/group theory and I learnt that the fundamental representation and the anti-fundamental representation of $SL(2,\mathbb{C})$ are not equivalent. This means that no similarity transformation can map one of them to…
6
votes
2 answers
Is Minkowski space locally Euclidean?
The Minkowski spacetime $\mathbb{R}^{1,3}$ is said to be a manifold (isomorphic to $SO^{1,3}$. But according to the definition of a manifold it should be locally euclidean. However, this seems to be wrong, in general relativity your pseudo…
user23238
6
votes
1 answer
How is the Lorentz group, $\text{O}(1,3)$, defined using set theoretic notation?
Context
I am studying special relativity. I am trying to understand how to define the group elements of the Lorentz group, $\text{O}(1,3)$. I understand from [1] that the Lorentz group is has (at least 3) subgroups. These are $\text{O}^+(1,3)$,…
Michael Levy
- 1,194
5
votes
2 answers
How to prove that all Minkowski spacetime isometries (transformations in Poincare group) are compositions of translation and Lorentz Transformations?
It is said in wikipedia that Minkowski spacetime isometries, i.e. the transformation that preserves
$$
(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2-(t_1-t_2)^2
$$
between points, can be represented as $\mathbb{R}^{1,3}\rtimes O(1,3)$, meaning that it…
Mr. Egg
- 754
5
votes
2 answers
Is there a closed form for the recurrence $V_{n+1}={V_n+\Delta V\over 1+{V_n\cdot \Delta V/C^2}}$, for constants $\Delta V$ and $C$?
I was wondering if the following recurrence formula has a closed form:
$$V_{n+1}={V_n+\Delta V\over 1+{V_n\cdot \Delta V\over C^2}}$$
where $\Delta V$ and $C$ are positive constants, $V_n$ is the velocity of the $n$-the inertial frame and the…
Mostafa Ayaz
- 33,056
4
votes
4 answers
What is the conceptual idea behind raising and lowering indices?
I've been watching Eigenchris' playlists on Tensors for beginners and Tensor calculus. His videos really clear up a lot of concepts. In the last video of the Tensor for beginners series, he talks about the motivation behind raising and lowering…
f_garcia
- 197
4
votes
0 answers
Spinors and Klein-Gordon Equation
I'm currently working through Chapter 13 of Wald's General Relativity and spinors are being a little illusive to me. The question is pretty much: Using the Klein-Gordon equation in the form: $$\partial_{A'_{1}A}\phi^{A_{1}...A_{n}} =…
4
votes
1 answer
I wanted to know of book suggestions that can help me overcome my fear of indices
I want to go deeper into General Relativity and Tensor Analysis. However, manipulating the indices always seems to overwhelm me. I wanted to know if there is a good book that covers up that and also lists all the important results related to index…
Infinity540
- 437
4
votes
0 answers
Rocket to a ray of light
$A$ and $B$ are two stationary points on a line $30,000,000$ km apart.
A light flashes at $B$, and at that precise moment a rocket takes off at $A$ at $180,000$ km/second.
The rocket is considered stationary relative to itself, and thus Point $B$ is…
Leibel
- 41
4
votes
1 answer
Series $\sum_{n=1}^{\infty} \left[K_0\left(\sqrt{[n\beta-it]^2+s^2 }\right)+K_0\left(\sqrt{[n\beta+it]^2+s^2}\right)\right]$
Let $\beta > 0$ and $t, s \in \mathbb{R}$. Furthermore, suppose that $-t^2 + s^2 > 0$. Define the following function:
$$
F( \beta, t, s )\ : = \ \sum_{n=1}^{\infty} \left[K_0\left(\sqrt{[n\beta-it]^2+s^2…
QuantumEyedea
- 2,815
4
votes
1 answer
Relativistic particle annihilation- getting wrong answer
While preparing for my exams, I found the following question on a past paper for which I am getting a different answer to what the question says I should be getting, I can't see where I am going wrong or whether what I have is equivalent to the…
Hadi Khan
- 1,138