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arXiv 1202.6578math-phgr-qcmath.MPphysics.hist-ph
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作为不变等价关系的同时性

Simultaneity as an Invariant Equivalence Relation

Marco Mamone-Capria

备注：
Some corrections, mostly of misprints. Keywords: special relativity, simultaneity, invariant equivalence relations, Malament's theorem
发表信息：
Found. Phys. 42: 1365-83, 2012
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摘要：

本文讨论了经典物理学和相对论物理学中的群不变等价关系的概念。全面检查牛顿，伽利略和庞加莱不变等价关系在$\R^4$，它提供了替代的证明，补充和偶尔更正的结果在文献中，包括Malament定理和它的一些变种。有人认为，作为一个不变的等价关系的解释的一致性，虽然有趣的本身，并没有削减在狭义相对论的一致性的约定性的辩论。

英文摘要：

This paper deals with the concept of simultaneity in classical and relativistic physics as construed in terms of group-invariant equivalence relations. A full examination of Newton, Galilei and Poincaré invariant equivalence relations in $\R^4$ is presented, which provides alternative proofs, additions and occasionally corrections of results in the literature, including Malament's theorem and some of its variants. It is argued that the interpretation of simultaneity as an invariant equivalence relation, although interesting for its own sake, does not cut in the debate concerning the conventionality of simultaneity in special relativity.

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