What is Quantum Mechanics? A Minimal Formulation
Abstract
This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, selfcontained, clear, unambiguous and of course correct manner. The bulk of the presentation is the socalled "microscopic theory", applicable to any closed system S of arbitrary size N, using concepts referring to S alone, without resort to external apparatus or external agents. An example of a similar minimal microscopic theory is the standard formulation of classical mechanics, which serves as the template for a minimal quantum theory. The only substantive assumption required is the replacement of the classical Euclidean phase space by Hilbert space in the quantum case, with the attendant allimportant phenomenon of quantum incompatibility. Two fundamental theorems of Hilbert space, the KochenSpeckerBell theorem and Gleason's theorem, then lead inevitably to the wellknown Born probability rule. For both classical and quantum mechanics, questions of physical implementation and experimental verification of the predictions of the theories are the domain of the macroscopic theory, which is argued to be a special case or application of the more general microscopic theory.
 Publication:

Foundations of Physics
 Pub Date:
 March 2018
 DOI:
 10.1007/s1070101801454
 arXiv:
 arXiv:1711.04209
 Bibcode:
 2018FoPh...48..295F
 Keywords:

 Quantum mechanics;
 Hilbert space;
 Quantum incompatibility;
 Physics  History and Philosophy of Physics;
 Quantum Physics
 EPrint:
 26 pages