Aspects of Quantum Theory

Inge S. Helland
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Inge S. Helland: University of Oslo, Department of Mathematics

Chapter Chapter 5 in Epistemic Processes, 2018, pp 77-130 from Springer

Abstract: Abstract The basic formalism of quantum theory is reviewed and put into my setting. In particular, spin and angular momentum are considered, and also e-variables like position and momentum. For the spin/angular momentum case, the correspondence between question-and-answer pairs and unit Hilbert space vectors is proved directly. A link to statistical inference is found by proving a focused version of the likelihood principle. From this and from an assumption of rationality the Born rule is proved. A macroscopic example is proposed. Measurements and quantum statistical inference are briefly discussed. Bell’s inequality issues are considered from an epistemic point of view. The free will theorem is mentioned, and the Schrödinger equation is derived in the one-dimensional case. Several so-called paradoxes are explained from an epistemic setting. Quantum measurements when the density matrix is completely unknown are discussed from a statistical point of view. A discussion of the book so far concludes the chapter.

Date: 2018
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DOI: 10.1007/978-3-319-95068-6_5

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