Metric on a Statistical Space-Time

Details Metric on a Statistical Space-Time Metric on a Statistical Space-Time

2004-03-22

arxiv.org/abs/math-ph/0403043v1

Transactions on Circuits and Systems, 10(3), pp. 2267-2271, 2004.

Physics

Mathematical Physics

7 pages

Scientific paper

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.

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