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

TL;DR

This paper explores why complex numbers are essential in quantum theory, proposing that the Hilbert-space formalism is a special case of Markovian embeddings and that complex numbers ensure this formalism's consistency.

Contribution

It introduces a new interpretation of quantum theory as an indivisible stochastic process and explains the necessity of complex numbers within this framework.

Findings

Hilbert-space formalism is a special case of Markovian embeddings

Complex numbers are necessary for the formalism to be Markovian

Quantum systems can be viewed as indivisible stochastic processes

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.