Taking Quantum States as Objective Possibilities Seriously

There is a common ``back-of-the-mind idea'', prompted by phenomena such as quantum contextuality and quantum non-locality, that quantum states represent ``mere possibilities'' in some vague sense. Yet, this idea reflects itself neither in the quantum formalism nor in the way we use it. In this talk, I explore what it entails to take this idea seriously.

I begin by showing that already axiomatic probability fails to formally distinguish between possibilities and facts, even though it is conceptually a unit measure over possibilities. I propose an axiomatic enrichment which introduces the distinction into Kolmogorov's axiomatization, and explore an analogous mathematical modification of the standard quantum formalism in which Hilbert Space elements are no longer states of physical systems but objective possibilities, each linked to a set of facts we can observe if the possibility is actualized. This modification, which I call the Heisenberg Interpretation, is not testable within quantum mechanics itself, but because it erects a mathematically well-defined boundary between quantum and classical physics, and general relativity in particular, it can be tested by checking for the existence of the boundary via proposed experiments like the BMV effect or by measuring the gravity field of an ultra high energy laser. Finally, I argue that objective possibilities are an overlooked conceptual ingredient critical to all of physics.