Spontaneous Decoherence as a Result of a Random Course of Time

A possibility of spontaneous, not environment-induced, decoherence is considered. A hypothesis on a random course of time is proposed. According to the hypothesis a 'microscopic'time is a random process with independent increments in the 'macroscopic', averaged, time. A scale of the random process is defined by a scale time constant. If the scale constant tends to zero, then the course of time becomes not random but deterministic. It is demonstrated that the random course of time destroys phase relations between oscillations and, therefore, stationary states lose their coherence. Modifications of quantum and classical dynamics for random time are considered. All main principles of quantum or classical theory hold in these modifications. The modifications consist of averaging of physical quantities with respect to random microscopical time and going over to macroscopical time. Modified equations of a system evolution in the macroscopical time are irreversible and entropy of an isolated system increases. When the macroscopical time increases, nondiagonal elements of an averaged density matrix in the energy representation tend to zero. Thus, the hypothesis of a random course of time introduces irreversibility into systems dynamics (in macroscopic time) without violating of the main principles of classical or quantum mechanics. Experiments for checking the possibility of spontaneous decoherence and for evaluating of the scale constant are discussed. The stimulus for the considering of the spontaneous decoherence is the intention to explain the transformation of a pure state to a mix in quantum measurement and my hope to overcome difficulties (underlined by N.S.Krylov) of co-ordinating of micromechanics with randomness. I hope that the spontaneous decoherence can provide a basis for statistical physics principles. It is possible that randomness of time is a trace on the classical space-time imprinting by space-time foam.