QUANTUM MECHANICS WITH CHAOS: Correspondence Principle, Measurement and Complexity

The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the correspondence principle to chaotic systems. In return one should accept the modified form of quantum formalism (presented by the Schrödinger equation) which, however, does not contradict the ordinary form and the main postulates of quantum mechanics. It introduces the principle of the fundamental dynamic multivaluedness (redundance) extending the quantum paradigm to complex dynamical behaviour. Moreover, a causal solution to the well-known problems of the foundation of quantum mechanics, those of quantum indeterminacy and wave reduction, is also found using the same method. The concept of the fundamental dynamic uncertainty thus established is universal in character and provides a unified scheme of the complete description of arbitrary complex system of any origin (physics/9806002). This scheme incorporates, in particular, universal definitions of complexity, (non)integrability, and general solution, as well as the physically complete notion of probability. One obtains thus a self-consistent hierarchic picture of the world characterised by a (high) non-zero complexity and containing the intrinsic causal randomness, where the causally extended quantum mechanics can be consistently interpreted as several lowest levels of complexity (quant-ph/990215,16). This is a descriptive representation of a large work issued in the form of preprint (IMP 95-1) and now also presented as a series of e-prints (quant-ph/9511034-38) and included into a book by the same author (see the Comments field of this e-print). This presentation contains the table of contents of the full paper (the preprint), its extended abstract, and some sample parts slightly adjusted for convenience. * Address for correspondence: Post Box 115, Kiev 30, Ukraine 252030. E-mail address: [email protected]