The introduction by Dirac of a new aether model based on a stochastic covariant distribution of subquantum motions (corresponding to a "vacuum state" alive with fluctuations and randomness) is discussed with respect to the present experimental and theoretical discussion of nontocatity in EPR situations.
It is shown (1) that one can deduce the de Broglie waves as real collective Markov processes on the top of Dirac's aether; (2) that the quantum potential associated with this aether's modification, by the presence of EPR photon pairs, yields a relativistic causal action at a distance which interprets the superluminal correlations recently established by Aspect et aL; (3) that the existence of theEinstein-de Broglie photon model (deduced from Dirac's aether) implies experimental predictions which conflict with the Copenhagen interpretation in certain specific testable interference experiments.
We analyze the time-dependent solutions of the pseudo-differential Lévy-Schrödinger wave equation in the free case, and we compare them with the associated Lévy processes. We list the principal laws used to describe the time evolutions of both the Lévy process densities, and the Lévy-Schrödinger wave packets. To have self-adjoint generators and unitary evolutions we will consider only absolutely continuous, infinitely divisible Lévy noises with laws symmetric under change of sign of the independent variable. We then show several examples of the characteristic behavior of the Lévy-Schrödinger wave packets, and in particular of the bi-modality arising in their evolutions: a feature at variance with the typical diffusive uni-modality of both the Lévy process densities, and the usual Schrödinger wave functions.
We study the non stationary solutions of Fokker-Planck equations associated to either stationary or non stationary quantum states. In particular we discuss the stationary states of quantum systems with singular velocity fields. We introduce a technique that allows arbitrary evolutions ruled by these equations to account for controlled quantum transitions. As a first signficant application we present a detailed treatment of the transition probabilities and of the controlling time-dependent potentials associated to the transitions between the stationary, the coherent, and the squeezed states of the harmonic oscillator.
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