Probabilistic Time

Feb, 2010
22 pages
Published in:
  • Found.Phys. 42 (2012) 1384-1443
e-Print:

Citations per year

200920132017202120241320
Abstract: (arXiv)
The concept of time emerges as an ordering structure in a classical statistical ensemble. Probability distributions pτ(t)p_\tau(t) at a given time tt 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 qτ(t)=±pτ(t)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.
Note:
  • new references, 30 pages
  • Probabilistic description of time
  • Emergence of quantum mechanics
  • Local-time subsystem
  • Transfer matrix formalism for periodic probabilities
  • algebra: Grassmann
  • wave function
  • rotation
  • Schroedinger equation
  • statistics
  • unitarity