- Geometry of Minkowski Space-Time | Francesco Catoni | Springer
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- Introduction to special relativity and Minkowski spacetime diagrams
Geometry of Minkowski spaces.
Geometry of Minkowski Space-Time | Francesco Catoni | Springer
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Learn how we and our ad partner Google, collect and use data. Two other derivations are given which are valid in any pseudo-Euclidean space of the same type. An alternative view comes from regarding Minkowski space-time projectively as a velocity space. This is possible with Minkowski's original representation but is best seen when Minkowski space-time is regarded differentially as a special case of the metric of General Relativity. Here the space may also be considered as differential space-time in the sense of Minkowski'. It may be considered as a projective space and in this case, as a velocity space which is a Lobachevsky space with hyperboloid representation.
Projection of the hyperboloid to a disc or spherical ball gives an associated Beltrami-Klein representation of velocity space. The Cayley metric for the velocity space representation leads to relativistic addition of two velocities.
Introduction to special relativity and Minkowski spacetime diagrams
The paper emphasizes the importance of Weierstrass coordinates as they are highly appropriate to the relativity application. They also show the close relation between the hyperboloid representation and the equivalent spherical one, the hyperbolic space being then regarded as a sphere of imaginary radius which has historically been a guiding idea and one closely related to Special Relativity.
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