For questions relating to Einsteins special relativity theory, the equivalence of physical laws in different inertial frames.

# Questions tagged [special-relativity]

98 questions

**21**

votes

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### 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

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### 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

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### 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…

The First StyleBender

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votes

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### 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

**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

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votes

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### 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…

Fernando Garcia Cortez

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### 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}} =…

confusedstudent

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### 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

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**4**

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**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

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votes

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### 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 K says thanks to Monica

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votes

**3**answers

### Can a manifold be reconstructed from its charts?

I'm learning special relativity and I am having a confusion on this mathematical point. Whenever any sort of motion or non motion happens in the world, it can only be perceived by the scientist in a chart (inertial frame). But, we say there exists a…

A plate of momos

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### Rigorous proof of time dilation (using only 1 spatial dimension).

$\newcommand{\set}[1]{\{#1\}}$ $\newcommand{\mc}{\mathcal}$ $\newcommand{\R}{\mathbf R}$ $\newcommand{\ST}{\mathbf S}$
Introduction
The purpose of this post is to understand the theorem of time dilation in special relativity.
Before even stating the…

caffeinemachine

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### The causal cones are convex

Taking into account the definitions of causal, temporal, spatial and luminous vectors, I want to test the following results:
Each temporal cone is convex.
The proof of this first result would be the following:
Let v, w be temporal in the same…

User090299

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**1**answer

### Killing vectors in Minkowski Metric

Firstly, I know this is a physics-related problem, and I have posted here, but the physics forum seems so much more empty then this one, so here it goes:
I was in the process to find the Killing vectors for the Minkowski Metric and I stumbbled into…

H44S

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### $SL(2,\mathbb{R})$ as a Lorentz Group $O(1,2)$

Define $$X = \bigg\{ \begin{pmatrix} x_0+x_1 & x_2 \\ x_2 & x_0-x_1 \end{pmatrix} | x_i \in \mathbb{R} \bigg\}.$$
Given $g\in SL(2,\mathbb{R})$, consider $s(g)$ which is a transformation $x \rightarrow gxg^T$ where $x\in X$.
We can view $s$ as a map…

Nugi

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