Quantum Dynamics and Kinematics from a Statistical Model Selected by the Principle of Locality

Abstract

Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of Local Causality. By contrast, here we shall show that the Schrödinger equation with Born's statistical interpretation of wave function and uncertainty relation can be derived from a statistical model of microscopic stochastic deviation from classical mechanics which is selected uniquely, up to a free parameter, by the principle of Local Causality. Quantization is thus argued to be physical and Planck constant acquires an interpretation as the average stochastic deviation from classical mechanics in a microscopic time scale. Unlike canonical quantization, the resulting quantum system always has a definite configuration all the time as in classical mechanics, fluctuating randomly along a continuous trajectory. The average of the relevant physical quantities over the distribution of the configuration are shown to be equal numerically to the quantum mechanical average of the corresponding Hermitian operators over a quantum state.

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

“…We have shown in Refs. [19,21] that imposing the principle of Locality of no-influence-at-a-distance singles out uniquely an exponential distribution of deviation from infinitesimal action, up to a free parameter λ which determines its average deviation as |λ/2|. We have also shown that such a statistical model leads to a 'generalized Schrödinger equation' in which the reduced Planck constant of the usual Schrödinger equation is replaced by |λ| (see Eq.…”

“…To this end, we have argued in Refs. [19,21] that imposing the principle of Locality and Macroscopic Classicality leads uniquely to a class of probability distribution given by the following exponential law:…”

“…Let us proceed to show that the above statistical model obeys the principle of Locality demanded by the theory of relativity that due to the finite maximum velocity of interaction, two subsystems spacelike separated from each other can not influence each other [19,21].…”

“…Noting the above fact, we have argued in Refs. [19,21] that the exponential law of the transition probability of Eq. (10) is the unique form of probability distribution of the deviation from infinitesimal stationary action, up to the free parameter λ which determines its average deviation as |λ|/2, that is singled out among the infinitude of possibilities by the principle of Locality and Macroscopic Classicality, mathematically represented respectively by Eqs.…”

Understanding quantum mechanics: a review and synthesis in precise language

“…Other predictions, beyond those of quantum mechanics, are being experimentally explored [272,519]. Related developments include two similar models: one based on particles, rather than fields [520], and the other deterministic, rather than stochastic [521]. Not directly related but similar approaches include one based on the interaction of a signal wave with a carrier wave [522], and another based on a retrocausal constraining of a classical field [ [342,[527][528][529][530].…”