Proper time and Minkowski structure on causal graphs (Q2752490)
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scientific article; zbMATH DE number 1661038
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Proper time and Minkowski structure on causal graphs |
scientific article; zbMATH DE number 1661038 |
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Proper time and Minkowski structure on causal graphs (English)
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3 September 2002
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discrete causal structures
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sine-Gordon model
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Minkowskian spacetime
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This paper joins the recent attempt to present spacetime by discrete causal structures. The idea is to replace the Minkowskian spacetime at small scales by a simple directed graph of events, and to evaluate the proper time by the volume of the corresponding Alexandrov sets. The problems of Lorentz invariance and passing from small to large scales are analyzed in more details. The sine-Gordon theory is presented as an example of how this discrete model works.NEWLINENEWLINENEWLINEIn the mathematical background of this paper, we may remark that discreteness of spacetime is due to superadditivity of the proper time, which naturally leads to horistologies, but not to topologies [compare our papers \textit{T. Balan} in Stud. Cercet. Mat. 44, 89-107 and 267-284 (1992; Zbl 0765.53058 and Zbl 0784.53046), and ibid. 46, No. 2,121-133 (1994; Zbl 0821.46027)].
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