The Statistical Interpretation of Quantum Mechanics

1970 ◽  
Vol 42 (4) ◽  
pp. 358-381 ◽  
Author(s):  
L. E. BALLENTINE
Keyword(s):  
Quantum Mechanics ◽  
Statistical Interpretation ◽  
Interpretation Of Quantum Mechanics

scholarly journals The Ensemble Interpretation of Quantum Mechanics and Scientific Realism

2021 ◽  
Vol 9 (1) ◽  
pp. 5-17
Author(s):  
Alexander Pechenkin ◽  
Keyword(s):  
Twentieth Century ◽  
Quantum Mechanics ◽  
Point Of View ◽  
Statistical Interpretation ◽  
Interpretation Of Quantum Mechanics ◽  
Ensemble Approach ◽  
Important Principle ◽  
The Usa ◽  
Soviet Russia ◽  
Lev Landau

The article takes under consideration three versions of the ensemble (statistical) interpretation of quantum mechanics and discusses the interconnection of these interpretations with the philosophy of science. To emphasize the specifics of the problem of interpretation of quantum mechanics in the USSR, the Marxist ideology is taken into account. The present paper continues the author’s previous analysis of ensemble interpretations which emerged in the USA and USSR in the first half of the 20th century. The author emphasizes that the ensemble approach turned out to be a dead end for the development of the interpretation of quantum mechanics in Russia. The article also argues that in Soviet Russia, the classical Copenhagen (standard) approach to quantum mechanics was used. The Copenhagen approach was developed by Lev Landau in 1919–1931 and became the basis of the Landau-Lifshitz famous course on quantum mechanics, one of the classics of twentieth-century physics literature (the first edition was published in 1947). Although Vladimir A. Fock’s approach to the interpretation of quantum mechanics differs from the standard presentation by Lev Landau and Evgeny Lifshitz, Fock put forward a very important principle that complementarity is a “firmly established law of nature”. The fundamental writings of Lev Landau, Vladimir Fock and Igor Tamm, the authors of the mid-twentieth century, did a lot to defend the standard point of view such as the popular interpretations by Landau and Lifshitz. This approach can be traced back to Landau’s early writings and to Fock’s criticism of the ensemble approach.

ENTANGLEMENT, LOCALITY, AND SEPARABILITY: A TREATISE ON DIFFERENT VIEWPOINTS

2007 ◽  
Vol 05 (01n02) ◽  
pp. 157-167 ◽  
Author(s):  
THOMAS KESSEMEIER ◽  
THOMAS KRÜGER
Keyword(s):  
Quantum Mechanics ◽  
The Other ◽  
Statistical Interpretation ◽  
Interpretation Of Quantum Mechanics ◽  
Bell’S Inequality ◽  
Other Hand ◽  
The Common ◽  
Statistical Operator ◽  
Definition Of ◽  
Non Locality

Within the framework of a statistical interpretation of quantum mechanics, entanglement (in a mathematical sense) manifests itself in the non-separability of the statistical operator ρ representing the ensemble in question. In experiments, on the other hand, entanglement can be detected, in the form of non-locality, by the violation of Bell's inequality Δ ≤ 2. How can these different viewpoints be reconciled? We first show that (non-)separability follows different laws to (non-)locality, and, moreover, it is much more difficult to characterize as long as the mostly employed operational rather than an ontic definition of separability is used. In consequence, (i) "entanglement" has two different meanings which may or may not be realized simultaneously on one and the same ensemble, and (ii) we have to disadvise the use of the common separability definition which is still employed by the majority of the physical community.

scholarly journals The Statistical Origins of Quantum Mechanics

2010 ◽  
Vol 2010 ◽  
pp. 1-18 ◽  
Author(s):  
U. Klein
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Classical Mechanics ◽  
Statistical Interpretation ◽  
Interpretation Of Quantum Mechanics ◽  
Local Conservation ◽  
Expectation Values ◽  
Strong Argument ◽  
Probability Current ◽  
The Mean

It is shown that Schrödinger's equation may be derived from three postulates. The first is a kind of statistical metamorphosis of classical mechanics, a set of two relations which are obtained from the canonical equations of particle mechanics by replacing all observables by statistical averages. The second is a local conservation law of probability with a probability current which takes the form of a gradient. The third is a principle of maximal disorder as realized by the requirement of minimal Fisher information. The rule for calculating expectation values is obtained from a fourth postulate, the requirement of energy conservation in the mean. The fact that all these basic relations of quantum theory may be derived from premises which are statistical in character is interpreted as a strong argument in favor of the statistical interpretation of quantum mechanics. The structures of quantum theory and classical statistical theories are compared, and some fundamental differences are identified.

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