What is Quantum Mechanics? A Minimal Formulation

Foundations of Physics 48 (3):295-332 (2018)

Abstract
This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the presentation is the so-called “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 all-important phenomenon of quantum incompatibility. Two fundamental theorems of Hilbert space, the Kochen–Specker–Bell theorem and Gleason’s theorem, then lead inevitably to the well-known 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.
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DOI 10.1007/s10701-018-0145-4
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References found in this work BETA

Quantum Probabilities as Degrees of Belief.Jeffrey Bub - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):232-254.
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A Reconstruction of Quantum Mechanics.Simon Kochen - 2015 - Foundations of Physics 45 (5):557-590.
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Citations of this work BETA

Relational Quantum Mechanics and Probability.M. Trassinelli - 2018 - Foundations of Physics 48 (9):1092-1111.

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