Quantum mechanics from classical statistics
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 valu...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article (Journal) |
| Language: | English |
| Published: |
[April 2010]
|
| In: |
Annals of physics
Year: 2010, Volume: 325, Issue: 4, Pages: 852-898 |
| DOI: | 10.1016/j.aop.2009.12.006 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.aop.2009.12.006 Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S0003491609002462 
|
| Author Notes: | C. Wetterich (Institut für Theoretische Physik, Universität Heidelberg) |
| Summary: | 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. |
|---|---|
| Item Description: | Available online 4 January 2010 Gesehen am 29.11.2023 |
| Physical Description: | Online Resource |
| DOI: | 10.1016/j.aop.2009.12.006 |