Causal Wave Mechanics and the Advent of Complexity. II. Dynamic uncertainty in quantum systems and the correspondence principle

Abstract

The intrinsic multivaluedness of interaction process, revealed in Part I of this series of papers, is interpreted as the origin of the true dynamical (in particular, quantum) chaos. The latter is causally deduced as unceasing series of transitions, dynamically probabilistic by their origin, between the equally real, but incompatible 'realisations' (modes of interaction) of a system. The obtained set of realisations form the causally derived, intrinsically complete "space of events" providing the crucial extension of the notion of probability and the method of its first-principle calculation. The fundamental dynamic uncertainty thus revealed is specified for Hamiltonian quantum systems and applied to quantum chaos description in periodically perturbed systems. The ordinary semiclassical transition in our quantum-mechanical results leads to exact reproduction of the main features of chaotic behaviour of the system known from classical mechanics, which permits one to "re-establish" the correspondence principle for chaotic systems (inevitably lost in any their conventional, single-valued description). The causal dynamical randomness in the extended quantum mechanics is not restricted, however, to semiclassical conditions and generically occurs also in essentially quantum regimes, even though partial "quantum suppression of chaos" does exist and is specified in our description, as well as other particular types of the quantum (truly) chaotic behaviour.