TY - JOUR
T1 - Ensembles and experiments in classical and quantum physics
AU - Neumaier, Arnold
N1 - DOI: 10.1142/S0217979203018338
Coden: IJPBE
Affiliations: Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria
Adressen: Neumaier, A.; Institut für Mathematik; Universität Wien; Strudlhofgasse 4 A-1090 Wien, Austria; email: [email protected]
Source-File: 506Scopus.csv
Import aus Scopus: 2-s2.0-0041694229
Importdatum: 24.01.2007 11:23:27
22.10.2007: Datenanforderung 1920 (Import Sachbearbeiter)
04.01.2008: Datenanforderung 2054 (Import Sachbearbeiter)
PY - 2003
Y1 - 2003
N2 - A philosophically consistent axiomatic approach to classical and quantum mechanics is given. The approach realizes a strong formal implementation of Bohr's correspondence principle. In all instances, classical and quantum concepts are fully parallel: the same general theory has a classical realization and a quantum realization. Extending the "probability via expectation" approach of Whittle to noncommuting quantities, this paper defines quantities, ensembles, and experiments as mathematical concepts and shows how to model complementarity, uncertainty, probability, nonlocality and dynamics in these terms. The approach carries no connotation of unlimited repeatability; hence it can be applied to unique systems such as the universe. Consistent experiments provide an elegant solution to the reality problem, confirming the insistence of the orthodox Copenhagen interpretation on that there is nothing but ensembles, while avoiding its elusive reality picture. The weak law of large numbers explains the emergence of classical properties for macroscopic systems.
AB - A philosophically consistent axiomatic approach to classical and quantum mechanics is given. The approach realizes a strong formal implementation of Bohr's correspondence principle. In all instances, classical and quantum concepts are fully parallel: the same general theory has a classical realization and a quantum realization. Extending the "probability via expectation" approach of Whittle to noncommuting quantities, this paper defines quantities, ensembles, and experiments as mathematical concepts and shows how to model complementarity, uncertainty, probability, nonlocality and dynamics in these terms. The approach carries no connotation of unlimited repeatability; hence it can be applied to unique systems such as the universe. Consistent experiments provide an elegant solution to the reality problem, confirming the insistence of the orthodox Copenhagen interpretation on that there is nothing but ensembles, while avoiding its elusive reality picture. The weak law of large numbers explains the emergence of classical properties for macroscopic systems.
M3 - Review
SN - 0217-9792
VL - 17
SP - 2937
EP - 2980
JO - International Journal of Modern Physics B
JF - International Journal of Modern Physics B
IS - 16
ER -