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Causality for Nonlocal Phenomena

Annales Henri Poincaré volume 18, pages 3049–3096 (2017)Cite this article

Abstract

Drawing from the theory of optimal transport we propose a rigorous notion of a causal relation for Borel probability measures on a given spacetime. To prepare the ground, we explore the borderland between Lorentzian geometry, topology and measure theory. We provide various characterisations of the proposed causal relation, which turn out to be equivalent if the underlying spacetime has a sufficiently robust causal structure. We also present the notion of the ‘Lorentz–Wasserstein distance’ and study its basic properties. Finally, we outline the possible applications of the developed formalism in both classical and quantum physics.

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Author information

Affiliations

  1. Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, ul. prof. Stanisława Łojasiewicza 11, 30-348, Kraków, Poland

    Michał Eckstein

  2. Copernicus Center for Interdisciplinary Studies, ul. Szczepańska 1/5, 31-011, Kraków, Poland

    Michał Eckstein & Tomasz Miller

  3. Faculty of Mathematics and Information Science, Warsaw University of Technology, ul. Koszykowa 75, 00-662, Warsaw, Poland

    Tomasz Miller

Authors
  1. Michał Eckstein
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  2. Tomasz Miller
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Correspondence to Michał Eckstein.

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Communicated by James A. Isenberg.

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Eckstein, M., Miller, T. Causality for Nonlocal Phenomena. Ann. Henri Poincaré 18, 3049–3096 (2017). https://doi.org/10.1007/s00023-017-0566-1

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  • DOI: https://doi.org/10.1007/s00023-017-0566-1