Metric on a statistical space-time

  • Authors:

  • Jacques Calmet;Xavier Calmet

  • Affiliations:

  • Institute for Algorithms and Cognitive Systems, University of Karlsruhe, Karlsruhe, Germany;University of North Carolina at Chapel Hill, Chapel Hill, NC

  • Venue:
  • ISTASC'04 Proceedings of the 4th WSEAS International Conference on Systems Theory and Scientific Computation
  • Year:
  • 2004

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Abstract

We introduce a concept of distance for a space-time where the notion of point is replaced by the notion of physical states e.g. probability distributions. We apply ideas of information theory and compute the Fisher information matrix on such a space-time. This matrix is the metric on that manifold. We apply these ideas to a simple model and show that the Lorentzian metric can be obtained if we assumed that the probability distributions describing space-time fluctuations have complex values. Such complex probability distributions appear in non-Hermitian quantum mechanics.