Jacob Barandes: Why We Shouldn't Believe in Hilbert Spaces Anymore 

Oxford Philosophy of Physics Seminar, Trinity Term 2021
3 June: Jacob Barandes (Harvard)
www.jacobbaran...
Title: Why We Shouldn't Believe in Hilbert Spaces Anymore, and the Case for Platonic Quantum Theory
Abstract: In this talk, I will argue that the historical focus on Hilbert spaces and their ingredients, from wave functions to Hamiltonians, has obscured the right way to think about interpreting quantum theory. Along these lines, I will explain why instead of attempting to reify Hilbert-space pictures, it may be better to regard them as analogous to gauge formulations of classical field theories. I will then argue that giving up on Hilbert-space pictures as fundamental ingredients of reality does not mean losing our grip on finding ontologies for quantum systems. To the contrary, I will present the case for a new interpretive program - the Platonic interpretation - that starts with ontological posits from the beginning and builds up the mathematical formalism from there. As I will show, Platonic quantum theory is a conservative approach that separates the ontic ingredients of quantum theory from its epistemic-statistical-nomic ingredients while also validating many of the ways that we traditionally talk about the theory, in addition to shedding new light on the measurement problem.
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