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

• URL: http://arxiv.org/abs/2602.01043v1
• Date: Sun, 01 Feb 2026 06:04:07 GMT
• Title: A Deflationary Account of Quantum Theory and its Implications for the Complex Numbers
• Authors: Jacob A. Barandes,
• Abstract summary: This paper argues that the usual Hilbert-space formalism is a special case of the general method of Markovian embeddings.<n>The complex numbers end up being necessary to ensure that the Hilbert-space formalism is indeed a Markovian embedding.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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