Klein, Ulf (2019) From probabilistic mechanics to quantum theory. Quantum Studies: Mathematics and Foundations.

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Abstract
We show that quantum theory (QT) is a substructure of classical probabilistic physics. The central quantity of the classical theory is Hamilton's function, which determines
canonical equations, a corresponding flow, and a Liouville equation for a probability density. We extend this theory in two respects: (1) The same structure is defined for arbitrary observables. Thus we have all of the above
entities generated not only by Hamilton's function but by every observable. (2) We introduce for each observable a
phase space function representing the classical action. This is a redundant quantity in a classical context but indispensable for the transition to QT. The basic equations of the resulting theory take a ``quantumlike'' form, which allows for a simple derivation of QT by means of a projection to configuration space reported previously [Quantum Stud.:Math. Found.(2018) 5:219227]. We obtain the most important relations of QT, namely the form of operators, Schr\"odinger's equation, eigenvalue equations, commutation relations, expectation values, and Born's rule. Implications for the interpretation of QT are discussed, as well as an alternative projection method allowing for a derivation of spin.
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Item Type:  Published Article or Volume  

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Keywords:  quantumclassical relation, ensemble theory, quantization, derivation of quantum theory  
Subjects:  General Issues > Determinism/Indeterminism General Issues > History of Philosophy of Science Specific Sciences > Probability/Statistics Specific Sciences > Physics > Quantum Mechanics General Issues > Reductionism/Holism 

Depositing User:  Dr. Ulf Klein  
Date Deposited:  07 Nov 2019 02:01  
Last Modified:  07 Nov 2019 02:01  
Item ID:  16609  
Journal or Publication Title:  Quantum Studies: Mathematics and Foundations  
Publisher:  Springer  
DOI or Unique Handle:  https://doi.org/10.1007/s4050901900201w  
Subjects:  General Issues > Determinism/Indeterminism General Issues > History of Philosophy of Science Specific Sciences > Probability/Statistics Specific Sciences > Physics > Quantum Mechanics General Issues > Reductionism/Holism 

Date:  August 2019  
URI:  https://philsciarchive.pitt.edu/id/eprint/16609 
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