Probabilistic time

Abstract

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 Schrödinger 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.

new references, 30 pages

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• Quantum mechanics from classical statistics
• Lattice spinor gravity
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• Universality of geometry
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Cited by in corpus (6)

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• Quantum formalism for classical statistics
• Quantum computing with classical bits
• Reparametrization Invariance and Some of the Key Properties of Physical Systems
• Fermionic quantum field theories as probabilistic cellular automata
• Quantum fermions from classical bits