The Time Concept in Atonic and Sub-Atonic Systens - Reconciliation of the Time-Reversal-Invariance and the Macroscopic Arrow of Time

Abstract

A new conception of time is presented in the framework of the quantum generalized stochastic and infinitely divisible fields. A non-unitary evolution operator lacking the continuous group property is derived from a time-reversal-invariant field theory in Minkowski's space. It describes the arrow of time on the quantum level. By quantizing the field action integral the usual evolution operator is obtained as a particular case. Quantum processes violating the T-symmetry are possible in the present theory. It is also explained why Born's interpretation of the wave function is necessary. The Feynman path integral is obtained as the limit of a series of similar integrals with finitely additive measures. This form of the Feynman integral does not conflict on the quantum level Heisenberg's Uncertainty Principle.