Quantum Mechanics and 3N- 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. Introduction. 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 nonrelativistic 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 nonrelativistic 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 (such as 2 or p) that