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

Abstract:Why does quantum theory need the complex numbers? With a view toward answering this question, I argue that the usual Hilbert-space formalism is a special case of the general method of Markovian embeddings. I then describe 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.

Quantum Physics (quant-ph); History and Philosophy of Physics (physics.hist-ph)

arXiv:2602.01043 [quant-ph]

(or arXiv:2602.01043v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2602.01043 Focus to learn more arXiv-issued DOI via DataCite

https://doi.org/10.1017/psa.2026.10245 Focus to learn more DOI(s) linking to related resources

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