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The differential and cone structures of spacetime

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Abstract

We propose to model spacetime by a differential space rather than by a differential manifold. A differential space is the pair (M, C), where M is any set, and C a family of real functions on M, satisfying certain axioms; C is called a differential structure of a corresponding differential space. This concept suitably generalizes the manifold concept. We show that C can be chosen in such a way that it contains all information about the causal structure of spacetime. This information can be read out of C with the help of only one postulate, namely that physical signals travel along piecewise smooth curves in (M, C). We effectively construct the Minkowski spacetime, with its cone structure, in this way. Some comments are made.

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Authors and Affiliations

  1. Institute of Nuclear Physics, ul. Radzikowskiego 152, 31-342, Cracow, Poland

    Piotr Multarzyński

  2. Vatican Astronomical Observatory, 00-120, Vatican City State

    Michael Heller

Authors
  1. Piotr Multarzyński
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  2. Michael Heller
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Multarzyński, P., Heller, M. The differential and cone structures of spacetime. Found Phys 20, 1005–1015 (1990). https://doi.org/10.1007/BF00738377

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  • DOI: https://doi.org/10.1007/BF00738377

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