dorsal/arxiv
View SchemaCausal Wave Mechanics and the Advent of Complexity. I. Dynamic multivaluedness
| Authors | Andrei P. Kirilyuk |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9511034 |
| URL | https://arxiv.org/abs/quant-ph/9511034 |
| Journal | Ann. Fond. Louis de Broglie 21 (1996) 455-480 |
Abstract
Two major deviations from causality in the existing formulations of quantum mechanics, related respectively to quantum chaos and indeterminate wave reduction, are eliminated within the new, universal concept of dynamic complexity. The analysis involves a new paradigm for description of a system with interaction, the principle of dynamic multivaluedness (redundance), and the ensuing concept of the fundamental dynamic uncertainty. It is shown that both the wave reduction and truly unpredictable (chaotic) behaviour in quantum systems can be completely and causally understood as a higher sublevel of the same dynamic complexity that provides the causally complete picture of the unified wave-particle duality and relativity at its lowest level (quant-ph/9902015,16). The presentation is divided into five parts. The first three parts deal with intrinsic randomness in Hamiltonian (isolated) quantum systems as the basic case of dynamical chaos. In the last two parts a causal solution to the problem of quantum indeterminacy and wave reduction is proposed. Part I introduces the method of effective dynamical functions as a generalisation of the optical potential formalism. The method provides a legal transformation of the Schroedinger equation revealing the hidden multivaluedness of interaction process, i. e. its self-consistent, dynamical splitting into many equally real, but mutually incompatible branches, called 'realisations'. Each realisation incorporates the usual "complete" set of eigenfunctions and eigenvalues for the entire problem. The method is presented in detail for the Hamiltonian system with periodic (not small) perturbation, both in its time-independent and time-dependent versions.
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"abstract": "Two major deviations from causality in the existing formulations of quantum\nmechanics, related respectively to quantum chaos and indeterminate wave\nreduction, are eliminated within the new, universal concept of dynamic\ncomplexity. The analysis involves a new paradigm for description of a system\nwith interaction, the principle of dynamic multivaluedness (redundance), and\nthe ensuing concept of the fundamental dynamic uncertainty. It is shown that\nboth the wave reduction and truly unpredictable (chaotic) behaviour in quantum\nsystems can be completely and causally understood as a higher sublevel of the\nsame dynamic complexity that provides the causally complete picture of the\nunified wave-particle duality and relativity at its lowest level\n(quant-ph/9902015,16). The presentation is divided into five parts. The first\nthree parts deal with intrinsic randomness in Hamiltonian (isolated) quantum\nsystems as the basic case of dynamical chaos. In the last two parts a causal\nsolution to the problem of quantum indeterminacy and wave reduction is\nproposed. Part I introduces the method of effective dynamical functions as a\ngeneralisation of the optical potential formalism. The method provides a legal\ntransformation of the Schroedinger equation revealing the hidden\nmultivaluedness of interaction process, i. e. its self-consistent, dynamical\nsplitting into many equally real, but mutually incompatible branches, called\n\u0027realisations\u0027. Each realisation incorporates the usual \"complete\" set of\neigenfunctions and eigenvalues for the entire problem. The method is presented\nin detail for the Hamiltonian system with periodic (not small) perturbation,\nboth in its time-independent and time-dependent versions.",
"arxiv_id": "quant-ph/9511034",
"authors": [
"Andrei P. Kirilyuk"
],
"categories": [
"quant-ph",
"chao-dyn",
"nlin.CD"
],
"journal_ref": "Ann. Fond. Louis de Broglie 21 (1996) 455-480",
"title": "Causal Wave Mechanics and the Advent of Complexity. I. Dynamic multivaluedness",
"url": "https://arxiv.org/abs/quant-ph/9511034"
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