Jacob Barandes (Harvard)

On the one hand, scientists across disciplines act as though various kinds of phenomena physically occur, perhaps according to probabilistic laws. 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 pictures makes it difficult to see how to reconcile them. In this talk, I will present a new theorem that establishes a precise equivalence between quantum theory and a highly general class of 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 features of quantum theory – including Hilbert spaces over the complex numbers, linear-unitary time evolution, the Born rule, interference, and noncommutativity – 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, potentially opens up new methods for using quantum computers to simulate stochastic processes beyond the Markov approximation, and may have implications for how we think about quantum gravity.