A Puzzle for the Field Ontologists
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A Puzzle for the Field Ontologists Shan Gao1 Received: 2 August 2020 / Accepted: 3 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract It has been widely thought that the wave function describes a real, physical field in a realist interpretation of quantum mechanics. In this paper, I present a new analysis of the field ontology for the wave function. First, I argue that the non-existence of self-interactions for a quantum system such as an electron poses a puzzle for the field ontologists. If the wave function represents a physical field, then it seems odd that there are (electromagnetic and gravitational) interactions between the fields of two electrons but no interactions between two parts of the field of an electron. Next, I argue that the three solutions a field ontologist may provide are not fully satisfactory. Finally, I propose a solution of this puzzle that leads to a particle ontological interpretation of the wave function. Keywords Quantum mechanics · Wave function · Field ontology · Self-interactions · Particle ontology
1 Introduction The field ontology for the wave function has been a popular position among philosophers of physics [32]. For example, in Bohm’s theory, the wave function may be regarded as either a real, physical field in a fundamental high-dimensional space ([11, p. 128], [3–5]), or a multi-field in three-dimensional space ([14, Chap. 5], [12, 21]). The former is usually called wave function realism. There are also other similar field ontologies of quantum mechanics. For example, in Everett’s theory, spacetime state realism has been proposed ([36, 35, Chap. 8], [34]). According to this view, the fundamental ontology of quantum mechanics consists of a state-valued field evolving in four-dimensional spacetime. Besides, in collapse theories, the mass density ontology is a popular view [7, 8, 17–19]. According to this view, “what the theory
* Shan Gao [email protected] 1
Research Center for Philosophy of Science and Technology, Shanxi University, Taiyuan 030006, People’s Republic of China
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Foundations of Physics
is about, what is real ‘out there’ at a given space point x, is just a field, i.e. a variable m(x, t) given by the expectation value of the mass density operator M(x) at x.” [17]. There have been obections to the field ontologies of quantum mechanics, such as the objections to wave function realism ([24, 25, 26, 27, 28, 29, 30, 16, Chap. 7], [13]), the objections to spacetime state realism ([9, Chap. 3], [10, 22, 33]), and the objections to the mass density ontology [31]. In this paper, I will present a new analysis of the field ontology for the wave function. First, I will argue that the nonexistence of self-interactions for a quantum system such as an electron poses a puzzle for the field ontologists. If the wave function represents a physical field, then it seems odd that there are (electromagnetic and gravitational) interactions between the fields of two electrons but no interactions between two parts
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