Abstract
In recent years there has been a robust but inconclusive debate over the existence and nature of indeterminacy in the world as described by quantum mechanics. I suggest that the inconclusive nature of the debate stems from starting from a metaphysical theory of indeterminacy. I propose instead framing the issue as a Carnapian explication project: start with the informal notion of indeterminacy used by physicists, and consider how best to make that concept precise. I defend a precisification based on von Neumann’s interpretation of quantum states, and consider the nature of the indeterminacy that results.
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Notes
- 1.
From hereon I will generally drop the word “determinately”: to say that a system has a property (lacks a property) means that it determinately has that property (determinately lacks that property).
- 2.
Torza (2021) defines indeterminacy in terms of facts rather than property possession. The definition here can be regarded as a special case of Torza’s for facts about the possession of a property; this is the only kind of fact considered in this paper.
- 3.
The nature of the necessity here is an interesting question. It is not a logical necessity that a disjunction of this form is true. Rather, the source of the necessity is the property structure of the world. Does this make it a metaphysical necessity? This question is briefly taken up in Sect. 23.5.
- 4.
Suppose a system satisfies Definition 1, and let q be the property of lacking p. Then the set {p, q} is a non-empty complete set of mutually exclusive properties, and the system fails to have each of them, hence satisfying Definition 2. Conversely, suppose a system violates Definition 1: for each property p i in {p 1, p 2, … p n}, it either has p i or lacks p i. Since there is no vector that is orthogonal to every eigenstate ϕi, the system cannot lack every property in the set. Hence it must have some property in the set, in violation of Definition 2.
- 5.
It is worth noting that the state of the molecule will not be exactly an eigenstate of being located in the tube, since it will have a very small term corresponding to tunneling through the tube. Here and in the following I assume that such small terms can be ignored, but the justification for this claim would take us too far afield; see Lewis (2016, 86).
- 6.
Classical property ascription violates von Neumann’s association of every proposition with a projection: “The particle lacks the z-spin-up property” does not correspond to a projection. This asymmetry between having a property and lacking a property may or may not be problematic, depending on whether one thinks there is a legitimate distinction here.
- 7.
- 8.
- 9.
There may be simplicity trade-offs: a classical logic is arguably simpler than a quantum logic, but Torza’s definition of indeterminacy is arguably simpler than Wilson’s. My point is just that there is no clear winner on simplicity grounds.
- 10.
One might insist that metaphysical indeterminacy is indeterminacy at the fundamental level. Then the question of whether quantum indeterminacy is metaphysical would reduce to the question of whether it is fundamental. As just mentioned, this is not a settled issue.
References
Barnes, E., & Williams, J. R. G. (2011). A theory of metaphysical indeterminacy. In K. Bennett & D. Zimmerman (Eds.), Oxford studies in metaphysics (Vol. 6, pp. 103–148). Oxford University Press.
Baym, G. (1969). Lectures on quantum mechanics. Addison-Wesley.
Bell, J. S. (1964). On the Einstein-Podolsky-Rosen paradox. Physics, 1, 195–200.
Birkhoff, G., & von Neumann, J. (1936). The logic of quantum mechanics. Annals of Mathematics, 37, 823–843.
Bokulich, A. (2014). Metaphysical indeterminacy, properties, and quantum theory. Res Philosophica, 91, 449–475.
Calosi, C., & Mariani, C. (2021). Quantum indeterminacy. Philosophy Compass, 16, e12731.
Calosi, C., & Wilson, J. (2019). Quantum metaphysical indeterminacy. Philosophical Studies, 176, 2599–2627.
Calosi, C., & Wilson, J. (2021). Quantum indeterminacy and the double-slit experiment. Philosophical Studies, 178, 3291–3317.
Carnap, R. (1950). Logical foundations of probability. University of Chicago Press.
Darby, G. (2010). Quantum mechanics and metaphysical indeterminacy. Australasian Journal of Philosophy, 88, 227–245.
Glick, D. (2017). Against quantum indeterminacy. Thought, 6, 204–213.
Healey, R. (2012). Quantum theory: A pragmatist approach. British Journal for the Philosophy of Science, 63, 729–771.
Juffmann, T., Truppe, S., Geyer, P., Major, A. G., Deachapunya, S., Ulbricht, H., & Arndt, M. (2009). Wave and particle in molecular interference lithography. Physical Review Letters, 103, 263601.
Kochen, S., & Specker, E. P. (1967). The problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics, 17, 59–87.
Leifer, M. S. (2014). Is the quantum state real? An extended review of ψ-ontology theorems. Quanta, 3, 67–155.
Lewis, P. J. (2016). Quantum ontology. Oxford University Press.
Pusey, M. F., Barrett, J., & Rudolph, T. (2012). On the reality of the quantum state. Nature Physics, 8, 475–478.
Skow, B. (2010). Deep metaphysical indeterminacy. The Philosophical Quarterly, 60, 851–858.
Spencer, Q. (2018). Racial realism I: Are biological races real? Philosophy Compass, 13, e12468.
Torza, A. (2020). Quantum metaphysical indeterminacy and worldly incompleteness. Synthese, 197, 4251–4264.
Torza, A. (2021). Quantum metametaphysics. Synthese, 199, 9809–9833.
Wilson, J. M. (2013). A determinable-based account of metaphysical indeterminacy. Inquiry, 56, 359–385.
Von Neumann, J. (1932). Mathematische Grundlagen der Quantenmechanik. Springer.
Wolff, J. (2015). Spin as a determinable. Topoi, 34, 379–386.
Acknowledgments
I would like to thank Jeff Barrett, Claudio Calosi, David Glick, Chris Hitchcock, Mahmoud Jalloh, Christian Mariani, Chip Sebens, Amie Thomasson, Alessandro Torza, Jessica Wilson, and two anonymous referees for very helpful comments on earlier drafts of this paper.
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Lewis, P.J. (2022). Explicating Quantum Indeterminacy. In: Allori, V. (eds) Quantum Mechanics and Fundamentality . Synthese Library, vol 460. Springer, Cham. https://doi.org/10.1007/978-3-030-99642-0_23
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