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Macrocausality Implies Lorenz Group: A Physics-Related Comment On Guts's Results, Olga Kosheleva, Vladik Kreinovich
Macrocausality Implies Lorenz Group: A Physics-Related Comment On Guts's Results, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
It is known that, in the space-time of Special Relativity, causality implies Lorenz group, i.e., if we know which events can causally influence each other, then, based on this information, we can uniquely reconstruct the affine structure of space-time. When the two events are very close, quantum effects, with their probabilistic nature, make it difficult to detect causality. So, the following question naturally arises: can we uniquely reconstruct the affine structure if we only know causality for events which are sufficiently far away from each other? Several positive answers to this question were provided in a recent paper by Alexander …
Discrete Causality Implies Lorenz Group: Case Of 2-D Space-Times, Olga Kosheleva, Vladik Kreinovich
Discrete Causality Implies Lorenz Group: Case Of 2-D Space-Times, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
It is known that for Minkowski space-times of dimension larger than 2, any causality-preserving transformation is linear. It is also known that in a 2-D space-time, there are many nonlinear causality-preserving transformations. In this paper, we show that for 2-D space-times, if we restrict ourselves to discrete space-times, then linearity is retained: only linear transformation preserve causality.