Eddy Keming Chen
University of California, San Diego
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. (For a more recent version of this paper, please see "The Intrinsic Structure of Quantum Mechanics" available on PhilPapers.)
Keywords quantum mechanics  wave function  mathematical nominalism  indispensability argument  Field's program  intrinsic structure
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References found in this work BETA

Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Mereology.Achille C. Varzi - 2016 - Stanford Encyclopedia of Philosophy.

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Citations of this work BETA

Quantum Mechanics in a Time-Asymmetric Universe: On the Nature of the Initial Quantum State.Eddy Keming Chen - 2021 - British Journal for the Philosophy of Science 72 (4):1155–1183.
The Wave-Function as a Multi-Field.Mario Hubert & Davide Romano - 2018 - European Journal for Philosophy of Science 8 (3):521-537.

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