dorsal/arxiv
View SchemaQuantum Causality, Stochastics, Trajectories and Information
| Authors | V. P. Belavkin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0208087 |
| URL | https://arxiv.org/abs/quant-ph/0208087 |
| DOI | 10.1088/0034-4885/65/3/201 |
| Journal | Rept.Prog.Phys. 65 (2002) 353-420 |
Abstract
A history of the discovery of quantum mechanics and paradoxes of its interpretation is reconsidered from the modern point of view of quantum stochastics and information. It is argued that in the orthodox quantum mechanics there is no place for quantum phenomenology such as events. The development of quantum measurement theory, initiated by von Neumann, and Bell's conceptual critics of hidden variable theories indicated a possibility for resolution of this crisis. This can be done by divorcing the algebra of the dynamical generators and an extended algebra of the potential (quantum) and the actual (classical) observables. The latter, called beables, form the center of the algebra of all observables, as the only visible (macroscopic) observables must be compatible with any hidden (microscopic) observable. It is shown that within this approach quantum causality can be rehabilitated within event enhanced quantum mechanics (eventum mechanics) in the form of a superselection rule for compatibility of the consistent histories with the statistically predictable future. The application of this rule in the form of the nondemolition principle leads to the statistical inference of the von Neumann projection postulate, and also to the more general quantum information dynamics for instantaneous events, spontaneous localizations (i.e. quantum jumps), and state diffusions (i.e. continuous trajectories). This gives a dynamical solution, in the form of a Dirac boundary value problem and reduced filtering equations, of the notorious decoherence and measurement problems which was tackled unsuccessfully by many famous mathematicians and physicists starting with von Neumann, Schroedinger and Bohr.
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"abstract": "A history of the discovery of quantum mechanics and paradoxes of its\ninterpretation is reconsidered from the modern point of view of quantum\nstochastics and information. It is argued that in the orthodox quantum\nmechanics there is no place for quantum phenomenology such as events. The\ndevelopment of quantum measurement theory, initiated by von Neumann, and Bell\u0027s\nconceptual critics of hidden variable theories indicated a possibility for\nresolution of this crisis. This can be done by divorcing the algebra of the\ndynamical generators and an extended algebra of the potential (quantum) and the\nactual (classical) observables. The latter, called beables, form the center of\nthe algebra of all observables, as the only visible (macroscopic) observables\nmust be compatible with any hidden (microscopic) observable.\n It is shown that within this approach quantum causality can be rehabilitated\nwithin event enhanced quantum mechanics (eventum mechanics) in the form of a\nsuperselection rule for compatibility of the consistent histories with the\nstatistically predictable future. The application of this rule in the form of\nthe nondemolition principle leads to the statistical inference of the von\nNeumann projection postulate, and also to the more general quantum information\ndynamics for instantaneous events, spontaneous localizations (i.e. quantum\njumps), and state diffusions (i.e. continuous trajectories). This gives a\ndynamical solution, in the form of a Dirac boundary value problem and reduced\nfiltering equations, of the notorious decoherence and measurement problems\nwhich was tackled unsuccessfully by many famous mathematicians and physicists\nstarting with von Neumann, Schroedinger and Bohr.",
"arxiv_id": "quant-ph/0208087",
"authors": [
"V. P. Belavkin"
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"doi": "10.1088/0034-4885/65/3/201",
"journal_ref": "Rept.Prog.Phys. 65 (2002) 353-420",
"title": "Quantum Causality, Stochastics, Trajectories and Information",
"url": "https://arxiv.org/abs/quant-ph/0208087"
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