Causal Wave Mechanics and the Advent of Complexity. III. Universal structure of complexity

Details Causal Wave Mechanics and the Advent of Complexity. III. Universal structure of complexity Causal Wave Mechanics and the Advent of Complexity. III. Universal structure of complexity

1995-11-23

arxiv.org/abs/quant-ph/9511036v2

Physics

Quantum Physics

29 pages, PostScript 3.0 from an MS Word file; material is included into the author's book "Universal Concept of Complexity by

Scientific paper

The universal dynamic uncertainty, discovered in Parts I and II of this series of papers for the case of Hamiltonian quantum systems, is further specified to reveal the hierarchical structure of levels of dynamically redundant 'realisations' which takes the form of the intrinsically probabilistic 'fundamental dynamical fractal' of a problem and determines fractal character of the observed quantities. This intrinsic fractality is obtained as a natural, causally derived property of dynamic behaviour of a system with interaction and the corresponding complete solution. Every branch of the fundamental dynamical fractal of a problem, as well as the probability of its emergence, can be obtained within the extended nonperturbative analysis of the main dynamic equation (Schroedinger equation in our case), contrary to basically restricted imitations of fractality within the canonical, single-valued approach. The results of the dynamical chaos analysis in Hamiltonian quantum systems, Parts I-III, are then subjected to discussion and generalisation. The physical origins of the dynamic uncertainty are analysed from various points of view. The basic consequences, involving essential extension of the conventional, unitary (= single-valued) quantum mechanics, are summarised. Finally, we emphasize the universal character of the emerging notions of dynamic multivaluedness (or redundance), causal randomness (or dynamic uncertainty), first-principle probability, (non)integrability, general solution, and physical complexity applicable to real dynamical systems of any kind.

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