No-signaling non-unitary modification of quantum dynamics within a deterministic model of quantization

Abstract

We have developed in the previous works a statistical model of quantum fluctuation based on a chaotic deviation from infinitesimal stationary action which is constrained by the principle of Locality to have a unique exponential distribution up to a parameter that determines its average. The unitary Schr\"odinger time evolution with Born's statistical interpretation of wave function is recovered as a specific case when the average deviation from infinitesimal stationary action is given by $\hbar/2$ for all the time. This naturally suggests a possible generalization of the quantum dynamics and statistics by allowing the average deviation fluctuates effectively randomly around $\hbar/2$ with a finite yet very small width and a finite time scale. We shall show that averaging over such fluctuation will lead to a non-unitary average-energy-conserving time evolution providing an intrinsic mechanism of decoherence in energy basis in macroscopic regime. A possible cosmological origin of the fluctuation is suggested. Coherence and decoherence are thus explained as two features of the same statistical model corresponding to microscopic and macroscopic regimes, respectively. Moreover, noting that measurement-interaction can be treated in equal footing as the other types of interaction, the objective locality of the model is argued to imply no-signaling between a pair of arbitrarily separated experiments.