How to Teach Quantum Mechanics

I distinguish between two conceptually different kinds of physical space: a space of ordinary material bodies, which is the space of points at which I could imaginably place (say) the tip of my finger, or the center of a billiard-ball, and a space of elementary physical determinables, which is the smallest space of points such that stipulating what is happening at each one of those points, at every time, amounts to an exhaustive physical history of the universe. In all classical physical theories, these two spaces happen to coincide – and what we mean by calling a theory “classical”, and all we mean by calling a theory “classical”, is (I will argue) precisely that these two spaces coincide. But once the distinction between these two spaces in on the table, it becomes clear that there is no logical or conceptual reason why they must coincide – and it turns out (and this is the main topic of the present paper) that a very simple way of pulling them apart from one another gives us quantum mechanics