Deterministic model equations of motion for quantum mechanics and some new modes of quantum behaviour

Abstract

In this paper we propose a deterministic basis for quantum mechanics and give equations of motion (derivable from an action principle) which describe deterministic trajectories in an extended space that the quantum events are assumed to follow. By applying the laws of classical probability, namely the conservation of probability along the deterministic trajectories, we derive a probability description which is found to be a generalization of the Schrödinger description with built-in probability interpretation. The generalized description admits of an infinite number of wave functions following coupled set of Schrö dinger-like equations while the total probability is given by the sum of the modulus squared of all these wave functions, one of which is identified as the Schrödinger function. If all the functions other than the Schrödinger wave function be neglected the Schrödinger description is retrieved. It is thus concluded that the classical probability not only embrances probability in quantum mechanics but allows other new modes for its propagation. We thus predict new modes of quantum behaviour and we discuss two situations and propose experiments where these modes could be looked for. Finally, our theory also provides an identification for the quantum of action, ħ .