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Quantum Mechanics and 3 N -Dimensional Space

I maintain that quantum mechanics is fundamentally about a system of N particles evolving in three-dimensional space, not the wave function evolving in 3N-dimensional space. 1. What is quantum mechanics fundamentally about? I believe that quantum mechanics is fundamentally about particles – quantum mechanics describes the behavior of systems of particles evolving in three-dimensional space (or, if you prefer, four-dimensional space-time). (At least, that’s what I would say for non-relativistic quantum mechanics – for the relativistic case, I’d say that quantum mechanics is fundamentally about fields, existing in four-dimensional space-time. The ontological issue I’m interested in is fundamentally the same in the relativistic and non-relativistic cases, so I’ll stick with the non-relativistic case for simplicity.) Some physicists and philosophers disagree with my claim that quantum mechanics is fundamentally about particles – they would hold that quantum mechanics is fundamentally about the wave function, construed as a really existing field evolving in a 3N-dimensional space (where N is the number of particles standardly thought to exist in three-dimensional space). I don’t believe in the wave function, and the point of this paper is to convince you that you shouldn’t believe in it either. Now, of course I think that the wave function is a useful mathematical tool; it is useful to describe systems as having quantum states, represented by wave functions. But as a matter of ontology, the wave function doesn’t exist – or at least, the wave function is no more real than the numbers (like 2, or B) that go into the equations used to describe quantum systems. The wave function is, at best, an abstract entity – and if you’re a nominalist about abstract entities like I am, then you should be happy to say that the wave function doesn’t exist. I’ll start by spelling out in a bit more detail my preferred picture of what quantum