Quantum mechanics from classical statistics

• Verfasst von: Wetterich, Christof [VerfasserIn]
• Titel: Quantum mechanics from classical statistics
• Verf.angabe: C. Wetterich (Institut für Theoretische Physik, Universität Heidelberg)
• E-Jahr: 2010
• Jahr: [April 2010]
• Umfang: 47 S.
• Fussnoten: Available online 4 January 2010 ; Gesehen am 29.11.2023
• Titel Quelle: Enthalten in: Annals of physics
• Ort Quelle: Amsterdam [u.a.] : Elsevier, 1957
• Jahr Quelle: 2010
• Band/Heft Quelle: 325(2010), 4 vom: Apr., Seite 852-898
• DOI: doi:10.1016/j.aop.2009.12.006
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Classical statistical description of quantum mechanics
• Sach-SW: Conditional correlations
• Sach-SW: Foundation of quantum mechanics
• K10plus-PPN: 1871613272

Abstract

Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by only a few probabilistic observables. Their expectation values define a density matrix if they obey a “purity constraint”. Then all the usual laws of quantum mechanics follow, including Heisenberg’s uncertainty relation, entanglement and a violation of Bell’s inequalities. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. Born’s rule for quantum mechanical probabilities follows from the probability concept for a classical statistical ensemble. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem. As an illustration, we discuss a classical statistical implementation of a quantum computer.