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

**Abstract**

In this paper, I introduce an intrinsic account of the quantum state. This 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 independent of the usual arbitrary conventions in the wave function representation, and (3) it explains why the quantum state has its amplitude and phase degrees of freedom.
Consequently, this account extends Hartry Field’s program outlined in Science Without Numbers (1980), responds to David Malament’s long-standing impossibility conjecture (1982), and establishes an important first step towards a genuinely intrinsic and nominalistic account of quantum mechanics. I will also compare the present account to Mark Balaguer’s (1996) nominalization of quantum mechanics and discuss how it might bear on the debate about “wave function realism.” In closing, I will suggest some possible ways to extend this account to accommodate spinorial degrees of freedom and a variable number of particles (e.g. for particle creation and annihilation).
Along the way, I axiomatize the quantum phase structure as what I shall call a “periodic difference structure” and prove a representation theorem as well as a uniqueness theorem. These formal results could prove fruitful for further investigation into the metaphysics of phase and theoretical structure.

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Archival date: 2017-12-13

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References found in this work BETA

Mereology.Varzi, Achille C.

The Wave Function: Essays in the Metaphysics of Quantum Mechanics.Ney, Alyssa & Albert, David Z. (eds.)

Science Without Numbers.Field, Hartry

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Citations of this work BETA

Time's Arrow in a Quantum Universe: On the Status of Statistical Mechanical Probabilities.Chen, Eddy Keming

Quantum Mechanics in a Time-Asymmetric Universe: On the Nature of the Initial Quantum State.Chen, Eddy Keming

Hartry Field. Science Without Numbers: A Defense of Nominalism 2nd Ed. [REVIEW]Hellman, Geoffrey & Leng, Mary

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