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

Why does quantum theory need the complex numbers? With a view toward answering this question, this article argues that the usual Hilbert-space formalism is a special case of the general method of Markovian embeddings. This article 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.