The wave function in quantum mechanics presents an interesting challenge to
our understanding of the physical world. In this paper, I show that the wave
function can be understood as four intrinsic relations on physical space. My
account has three desirable features that the standard account lacks: (1) it
does not refer to any abstract mathematical objects, (2) it is free from the
usual arbitrary conventions, and (3) it explains why the wave function has its
gauge degrees of freedom, something that are usually put into the theory by
hand. Hence, this account has implications for debates in philosophy of
mathematics and philosophy of science. First, by removing references to
mathematical objects, it provides a framework for nominalizing quantum
mechanics. Second, by excising superfluous structure such as overall phase, it
reveals the intrinsic structure postulated by quantum mechanics. Moreover, it
also removes a major obstacle to "wave function realism.
