Questions tagged [special-relativity]
The special-relativity tag has no usage guidance.
15 questions
0
votes
0
answers
68
views
A reference for this statement (representations of universal central extensions)
Let $G$ be a connected Lie group with universal cover $\tilde{G}$. I would really appreciate if someone could give me a reference for the proof of the following fact:
"Every projective unitary ...
- 287
1
vote
1
answer
91
views
The stabilizer of a point in the connected Lorentz group
$\DeclareMathOperator\SO{SO}$For $n\geq 2$, the $n$-dimensional connected Lorentz group is defined as $$\SO(n-1,1)^{\uparrow}=\{f\in M_n (\mathbb{R}):f^T\eta f=\eta, \det (f)=1,f^0_0>0\}$$ where $$...
- 287
1
vote
0
answers
103
views
"Classifying" causally closed sets in Minkowski space
Let $M = \mathbb R^{D+1}$ be Minkowski space. Recall that the causal complement of a set $A \subseteq M$ is the set $A^\perp \subseteq M$ where $p \in A^\perp$ there is no timelike path between $p$ ...
- 64k
4
votes
1
answer
403
views
How are spatial coordinate systems in physics defined?
Grothendieck once asked "What is a meter?" (https://golem.ph.utexas.edu/category/2006/08/letter_from_grothendieck.html). This innocent sounding question, made me to think about how ...
- 3,064
3
votes
2
answers
186
views
Variational principle for relativistic gas dynamics
I know quite a lot of Variational principles (VP) yielding systems of classical mechanics. By a VP, I mean something like
$$\delta{\cal L}[U]=0$$
where ${\cal L}$ is a functional and the field belongs ...
- 52.3k
3
votes
1
answer
723
views
Is there a feature mapping for this kernel $k(x,y) = (\frac{\min(x,y)}{\max(x,y)})^2$?
In the following paper:
https://perso.crans.org/besson/publis/mva-2016/MVA_2015-16__Kernel_Methods__Homework__Besson_Clement_Zerbib.en.pdf
problem 2, Kernel 9. it is shown that $K(x,y) = \frac{\min(x,...
- 3,064
3
votes
1
answer
68
views
Determine a sign of the limitation of a certain integral
I can't determine a sign of an integral written below and it has hit a dead end.
My setting is rather special.
Let $a\in(0,1)$ be a given constant and $(x_{\varepsilon},y_{\varepsilon})\in[0,a)\times[...
- 201
8
votes
0
answers
356
views
Noncommutative geometry and line length
I would like to understand, in some formal sense, the relation between the Dirac operator and the line length introduced by Connes in noncommutative geometry. If $D$ is the Dirac operator, he sets $ds ...
- 1,687
2
votes
1
answer
417
views
Euler characteristic of Cauchy surface in Lorentz manifold
Are there any known topological restrictions on what kinds of manifolds can form the Cauchy hypersurface of a Lorentzian manifold? I'm particularly interested about restrictions on Euler ...
- 379
1
vote
1
answer
264
views
manifolds whose charts are maps to Minkowski space
I'm doing a project involving tilings of Minkowski space. For instance in 2d I have rectangular tiles determined by a spacelike line segment: the rectangle is the region caused by the line segment. ...
- 379
12
votes
1
answer
775
views
Would a closed universe with special relativity violate causality? Does the universe have to be simply connected?
This question may be more appropriate for physics.stackexchange.com, but it would be helpful to get feedback from experts in Minkowski geometry.
The classic twin paradox is a false thought experiment ...
- 3,359
18
votes
2
answers
2k
views
How does hyperbolicity of space time affect our lives?
My main research has been in hyperbolic geometry and geometric group theory. I always thought that the only real "application" of my work was that the universe is a 3-manifold.
But recently I found ...
- 3,359
14
votes
4
answers
2k
views
Why are isometries of Minkowski space necessarily linear?
The Mazur-Ulam theorem says that any surjective isometry of normed vector spaces is affine. This argument doesn't seem to apply to Minkowski space (of special relativity) since the metric is ...
- 233
2
votes
1
answer
764
views
Retarded coordinates on (flat) spacetime
Hi,
I'm trying to construct some coordinates on Minkowski spacetime based on a world line, $C$, ($\dot{C}\cdot\dot{C}=-1$) and forward light cone. I want the "time" coordinate of a point, $p$, to be ...
- 516
15
votes
3
answers
2k
views
Relativistic Cellular Automata
Cellular automata provide interesting models of physics: Google Scholar gives more than 25,000 results when searching for "cellular automata" physics.
Google Scholar still gives more than 2,...
- 9,720