Abstract The intended purpose of this paper is to revive interest in stochastic mechanics among physicists, mathematicians, and philosophers. Edward Nelson, the principal advocate for it, lost faith in his theory mainly because of the difference between the multitime autocorrelation expectations of quantum mechanics and those of stochastic mechanics. In particular, he showed that although quantum mechanics decouples the dynamics of quantum systems which are separated by a large distance, stochastic mechanics does not. Some authors have argued that with collapse of the wave function incorporated into stochastic mechanics this deficiency can be mitigated. In this paper we show a way to avoid collapse of the wave function altogether and still get the equivalence of stochastic mechanics and quantum mechanics for multitime products, and to achieve dynamic separability. This is achieved by using generalized stochastic mechanics where the diffusion constant is an arbitrary constant, and by choosing a particular imaginary value for the diffusion constant. This value is chosen to reproduce the Heisenberg commutation rules for the non-commuting operators of the stochastic process by a technique that was introduced some years ago. It turns out that this implies that the stochastic process is happening in complex space, and with a relativistic generalization in mind, it implies motion in complex spacetime. The purpose of this paper is to prove that this procedure resolves the multitime dilemma facing stochastic mechanics. Other related topics discussed include Wallstrom's insight that the wave function is not necessarily single-valued; the general objection to Hidden Variables from various no-go theorems, including Bell tests; the interpretation of complex spacetime; the role of non-Markovian processes; The possible origin of quantum mechanics from chaos theory; and why complex spacetime is an interesting possibility that might underlie quantum physics.
Mark Davidson (Fri,) studied this question.