Title: The Stochastic-Quantum Theorem and Quantum Gravity

Abstract: The challenges presented by quantum gravity run deeper than issues like nonrenormalizability. On the one hand, general relativity is based on physical matter evolving in a dynamical four-dimensional spacetime. On the other hand, textbook quantum theory is an instrumentalist recipe whose only predictions refer to measurement outcomes, measurement-outcome probabilities, and statistical averages of measurement outcomes over measurement-outcome probabilities. The conceptual gap between these two theories makes it difficult to see how to unify them beyond the long-wavelength limit on a static background spacetime, an approximation in which quantum (field) theory takes precedence. In particular, it is far from clear how to adapt quantum theory to the case of a truly dynamical spacetime, outside of special cases like asymptotically anti-de Sitter spacetime.

In this talk, I will present a new theorem that establishes a precise equivalence between quantum theory and a highly general class of physical stochastic processes, called generalized stochastic systems, that are defined on configuration spaces rather than on Hilbert spaces. From a foundational perspective, some of the mysterious axiomatic features of quantum theory – including Hilbert spaces over the complex numbers, linear-unitary time evolution, and the Born rule – then become the output of a theorem based on the simpler and more transparent premises of ordinary probability theory. From a somewhat more practical perspective, the stochastic-quantum theorem leads to a new formulation of quantum theory, alongside the Hilbert-space, path-integral, and phase-space formulations, and opens up the possibility of using quantum computers to simulate stochastic processes beyond the Markov approximation. The theorem may also be a hint that finding a fully stochastic generalization of general relativity could be more than merely a stepping stone toward a complete theory of quantum gravity.

This talk is based on two papers:
https://arxiv.org/abs/2309.03085
https://arxiv.org/abs/2302.10778