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Quantum Foundations
A Deflationary Account of Quantum Theory and its Implications for the Complex Numbers
arXiv
Authors: Jacob A. Barandes
Year
2026
Paper ID
3015
Status
Preprint
Abstract Read
~2 min
Abstract Words
96
Citations
N/A
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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- This paper contributes to the Quantum Foundations research area in the Quantum Articles archive.
- It adds a 2026 reference point for readers tracking recent quantum research.
- Why does quantum theory need the complex numbers?
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