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A Puzzle for the Field Ontologists

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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.

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  1. I thank a referee of European Journal for Philosophy of Science for this precise expression of the puzzle.

  2. It has been argued that these fields have effective mass and charge distributions, which can be measured by protective measurements [1, 2, 15, 16].

  3. Note that the wave function of the two electrons will be still a product state during a protective interaction between them [1, 2, 15, 16].

  4. I thank a referee of European Journal for Philosophy of Science for this insightful proposal.

  5. It may be worth noting that v(x,t) does not refer to the actual velocity of particles, which is in finite. This is in notable contrast to Bohm’s theory, where v(x,t) determines the actual velocity of particles moving along continuous trajectories [20].

  6. It is also possible that the random motion of particles may affect the time evolution of the wave function and the Schrödinger equation is replaced by a revised Schrödinger equation with a stochastic evolution term describing the RDM as a stochastic process. This will lead to collapse theories (see [16, Chap. 8] for more details).

  7. Note that I omit the self-energy of an electron here, since after the divergent self-interaction is removed by renormalization, it is a small quantity compared with the supposed self-interactions analyzed in this paper.


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I am very grateful to the editors and referees of this journal for their insightful comments and helpful suggestions. This work is supported by the National Social Science Foundation of China (Grant No. 16BZX021).

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Correspondence to Shan Gao.

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Gao, S. A Puzzle for the Field Ontologists. Found Phys 50, 1541–1553 (2020).

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