期刊
FOUNDATIONS OF PHYSICS
卷 42, 期 11, 页码 1384-1443出版社
SPRINGER
DOI: 10.1007/s10701-012-9675-3
关键词
Probabilistic description of time; Emergence of quantum mechanics; Local-time subsystem; Transfer matrix formalism for periodic probabilities
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 . We establish a map to quantum physics and the Schrodinger 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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