Probabilistic time

Details Probabilistic time Probabilistic time

2010-02-12

arxiv.org/abs/1002.2593v2

Physics

High Energy Physics

High Energy Physics - Theory

extended discussion of emergence of non-commuting operators and quantum correlations 31 pages

Scientific paper

The concept of time emerges as an ordering structure in a classical statistical ensemble. Probability distributions $p_\tau(t)$ at a given time $t$ obtain by integrating out the past and future. We discuss all-time probability distributions that realize a unitary time evolution as described by rotations of the real wave function $q_\tau(t)=\pm \sqrt{p_\tau(t)}$. We establish a map to quantum physics and the Schr\"odinger equation. Suitable classical observables are mapped to quantum operators. The non-commutativity of the operator product is traced back to the incomplete statistics of the local-time subsystem. Our investigation of classical statistics is based on two-level observables that take the values one or zero. Then the wave functions can be mapped to elements of a Grassmann algebra. Quantum field theories for fermions arise naturally from our formulation of probabilistic time.

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