An Intrinsic Theory of Quantum Mechanics: Progress in Field’s Nominalistic Program, Part I

In this paper, I introduce an intrinsic account of the universal wave function. My account contains three desirable features that the standard platonistic account lacks: (1) it does not refer to any abstract mathematical objects such as complex numbers, (2) it is free from the usual arbitrary conventions in the wave function representation, and (3) it explains why the wave function has its amplitude and phase degrees of freedom. Consequently, my account extends Hartry Field’s program outlined in Science Without Numbers (1980), partially responds to David Malament’s impossibility conjecture (1982), and establishes an important step towards a genuinely intrinsic and nominalistic account of quantum mechanics. Next, I compare and contrast the present account with Mark Balaguer’s nominalistic theory (1996). I then show that my account provides a new perspective on the debate about “wave function realism,” an increasingly popular view in metaphysics of quantum mechanics developed and defended by David Albert (1996), Barry Loewer (1996), Alyssa Ney (2012), and Jill North (2013). In closing, I suggest some future research programs for extending this account to more advanced quantum theories. Along the way, I axiomatize the quantum phase structure and prove a representation theorem and a uniqueness theorem. These results could be relevant for future studies about the metaphysics of quantum mechanics and theoretical structure.