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A Deflationary Account of Quantum Theory and its Implications for the Complex Numbers

Barandes, Jacob A. (2025) A Deflationary Account of Quantum Theory and its Implications for the Complex Numbers. [Preprint]

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Abstract

Why does quantum theory need the complex numbers? With a view toward answering this question, this paper argues that the usual Hilbert-space formalism is a special case of the general method of Markovian embeddings. This paper then describes the ‘indivisible interpretation’ of quantum theory, according to which a quantum system can be regarded as an ‘indivisible’ stochastic process unfolding in an old-fashioned configuration space, with wave functions and other exotic Hilbert-space ingredients demoted from having an ontological status. The complex numbers end up being necessary to ensure that the Hilbert-space formalism is indeed a Markovian embedding.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Barandes, Jacob A.jacob_barandes@harvard.edu0000-0002-3740-4418
Keywords: quantum foundations; interpretations of quantum mechanics; complex numbers; mathematical physics; Markovian laws; non-Markovian laws; stochastic processes; time-reversal; symmetries; indivisible stochastic processes; Strocchi-Heslot formalism
Subjects: General Issues > Determinism/Indeterminism
General Issues > Laws of Nature
Specific Sciences > Mathematics
Specific Sciences > Physics
Specific Sciences > Probability/Statistics
Specific Sciences > Physics > Quantum Mechanics
General Issues > Structure of Theories
Specific Sciences > Physics > Symmetries/Invariances
Depositing User: Dr. Jacob Barandes
Date Deposited: 30 Jul 2025 12:51
Last Modified: 30 Jul 2025 12:51
Item ID: 26048
Subjects: General Issues > Determinism/Indeterminism
General Issues > Laws of Nature
Specific Sciences > Mathematics
Specific Sciences > Physics
Specific Sciences > Probability/Statistics
Specific Sciences > Physics > Quantum Mechanics
General Issues > Structure of Theories
Specific Sciences > Physics > Symmetries/Invariances
Date: 28 July 2025
URI: https://philsci-archive.pitt.edu/id/eprint/26048

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