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

Chen, Eddy Keming (2017) An Intrinsic Theory of Quantum Mechanics: Progress in Field's Nominalistic Program, Part I. [Preprint]

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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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Item Type: Preprint
Creators:
CreatorsEmailORCID
Chen, Eddy Kemingeddy.chen@rutgers.edu
Keywords: quantum mechanics, wave function, phase structure, mathematical nominalism, intrinsic physical theory, indispensability argument, mathematical platonism, metaphysics of science.
Subjects: Specific Sciences > Mathematics > Applicability
Specific Sciences > Mathematics > Explanation
Specific Sciences > Mathematics > Ontology
General Issues > Scientific Metaphysics
Specific Sciences > Physics > Quantum Mechanics
General Issues > Structure of Theories
Specific Sciences > Physics > Symmetries/Invariances
Depositing User: Keming Chen
Date Deposited: 31 May 2017 16:01
Last Modified: 31 May 2017 16:01
Item ID: 13083
Subjects: Specific Sciences > Mathematics > Applicability
Specific Sciences > Mathematics > Explanation
Specific Sciences > Mathematics > Ontology
General Issues > Scientific Metaphysics
Specific Sciences > Physics > Quantum Mechanics
General Issues > Structure of Theories
Specific Sciences > Physics > Symmetries/Invariances
Date: 31 May 2017
URI: http://philsci-archive.pitt.edu/id/eprint/13083

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