Bonn 2020 – scientific programme

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AGPhil: Arbeitsgruppe Philosophie der Physik

AGPhil 6: Quantum Theory I

AGPhil 6.3: Talk

Wednesday, April 1, 2020, 17:45–18:15, H-HS III

Why wavefunction realists should be Hilbert-space fundamentalists — •David Schroeren — Philosophy Department, 1879 Hall, Princeton University, Princeton, NJ 08544, USA

I argue that wavefunction realists should endorse Hilbert-space fundamentalism: the thesis that the Hilbert space of abstract ‘kets’ characterizes a fundamental physical space in its own right. I proceed as follows. For a system with spin, the wavefunction-realist physical field is mathematically characterized by an element of the form ψ(x)⊗ |ϕ⟩, where |ϕ⟩ is a ket in a spin Hilbert space H spanned by basis elements |j,m⟩ for −j ≤ m ≤ j. The goal is to show that wavefunction realists should be fundamentalists about Hilbert spaces H as linear spaces rather than as projective spaces that consist of rays. My argument proceeds from two observations: first, that the actual world is such that its quantum properties are characterized in terms of projective representations of symmetry groups rather than linear ones; and second, that the nature of projective representations of SO(3) entails that spin is half-integer-valued, rather than integer-valued. I then argue both that we can and should regard this as a physical explanation of the fact that spin is half-integer valued. Subsequently, I argue that the relevant explanation is contrastive: if the world had been such that its physical properties are characterized by linear representations of symmetry groups rather than projective ones, then spin would be integer-valued. Finally, I argue that this contrastive explanation implies fundamentalism about spin Hilbert spaces as linear spaces.