Abstract
Realists wanting to capture the facts of quantum entanglement in a metaphysical interpretation find themselves faced with several options: to grant some species of fundamental nonseparability, adopt holism, or (more radically) to view localized spacetime systems as ultimately reducible to a higher-dimensional entity, the quantum state or wave function. Those adopting the latter approach and hoping to view the macroscopic world as grounded in the quantum wave function face the macro-object problem. The challenge is to articulate the metaphysical relation obtaining between three-dimensional macro-objects and the wave function so that the latter may be seen in some sense as constituting the former. This paper distinguishes several strategies for doing so and defends one based on a notion of partial instantiation.
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Notes
This position is sometimes called ‘wave function monism,’ although I’ll stick with ‘wave function realism’ in what follows.
Recall that we are restricting attention to the implications of non-hidden-variable approaches to quantum mechanics. According to Bohmian mechanics, systems always possess determinate locations. Although a version of Bohmian mechanics has been proposed that rejects the fundamental existence of objects in space-time like the approach I am considering here (Albert 1996), the macro-object problem and its solutions have a very different character on such approaches. To keep this discussion relatively concise, I will not discuss Bohmian mechanics here.
Because of the symmetries of quantum particles, some would argue we should actually not think of AB and BA as corresponding to two different situations. For the purposes of this section, we will continue to work with a space in which these locations are distinguished. More will be said about this choice below in Sect. 5.
These states are empirically distinct since they entail different probabilities for measurement.
This is estimated to be 10\(^{80}\).
Another strategy for arguing for this interpretation cites its capacity to avoid fundamental non-locality (Ney forthcoming). This argument will not be discussed here.
I leave this presentation condensed because the discussion below will focus on collapse approaches. More details may be found in Bacciagaluppi (2012).
At this point, one might be skeptical that the wave function’s having low amplitude at certain points in S corresponding to conflicting macroscopic situations is enough to eliminate them. Aren’t these parts of the wave function still present? Don’t they have an effect on the state of the world? And so why are we able to ignore them in giving our account of macroscopic objects? I share this concern, but will set it aside for now.
A small note about something that may be distracting in the previous quotation. In Albert’s work, we find two points of view: first, that the three-dimensional world is an illusion, but that its appearance may be causally explained by the dynamical behavior of the wave function; second, that the three-dimensional world is genuine and that its existence may be constitutively explained by the dynamical behavior of the wave function. In his most recent work (2015), Albert unambiguously endorses the latter position (one that he has held for some time) and so that is the view I will engage with here.
Here and throughout the paper, I use ‘constitution’ as a generic metaphysical term to capture situations in which one entity or entities makes up another. As I am using it, is not intended to have any spatial or mereological implications, nor is it being restricted to a relation between entities of any particular ontological category.
I’ve tinkered with this a little bit to bring out the essential aspects of the Hamiltonian. The first term, the kinetic energy term, shows the system’s behavior is related to the masses of its constituent particles and their component velocities. The second, the potential energy term, shows the system’s behavior also depends on the distances between the individual particles.
For example, when i \(=\) 1 and j \(=\) 2, note the fact that the potential energy V in the first Hamiltonian partly depends on the value \(\hbox {x}_{\mathrm{i}}-\hbox {x}_{\mathrm{j}}\) or \(\hbox {x}_{1}-\hbox {x}_{2}\) which is simply the distance (in the x-dimension) between particles 1 and 2. In the second Hamiltonian, V depends on the value \(\hbox {x}_{(\mathrm{3i}-2)}-\hbox {x}_{(\mathrm{3j}-2)}\) or \(\hbox {x}_{1}-\hbox {x}_{4}\) where this refers to the numerical difference between the first coordinate of the center of mass of the first shadow in its three-dimensional subspace and the first coordinate of the center of mass of the second shadow in its own (different) three-dimensional subspace. This isn’t a distance; it’s merely a difference between values.
Wallace (2012) appeals to symmetries to explain three-dimensionality as well, however he does not start from a wave function realist perspective.
Note this concern could equally be raised for Albert’s proposal. Nothing logically rules out a system exhibiting behavior approximately described by multiple Hamiltonians.
See also Ney (2015).
See French and Rickles (2003) for an endorsement of this view.
It is worth pointing out that the move to this reduced state space is not completely straightforward. As Leinaas and Myrheim point out (1977, p. 5), on their way of doing this, points that correspond to two or more particles coinciding in three-dimensional location are singularities in the reduced state space.
The present discussion evades the question of the correct functional analysis altogether.
This is not a causal or grounding explanation. The appeal to symmetries plays something more like the role of a unification explanation.
Ney (2012) argues that there are no genuine three-dimensional macroscopic objects in the wave function metaphysics. Ney (2015) uses an analogy with holograms to argue that in particular just because a quantum state is such to reflect three-dimensional symmetries, this does not suffice to legitimate the existence of three-dimensional objects.
Various contemporary theorists of metaphysical fundamentality make this point that even if facts or propositions may be grounded or made true by a fundamental ontology, this does not entail that the entities these facts or propositions appear to quantify over are thereby real. See Heil (2013) for discussion of this point in the context of a truthmaking framework and Fine (2001) for discussion in the context of a metaphysical grounding framework. Contemporary metaphysicians generally reject the earlier view of Quine (1948/1953) that quantificational facts directly reflect matters of ontology.
I use ‘constitution’ in a broad sense that encompasses various more specific relations, cf. footnote 10.
This is one of the main issues explored in the 2014 volume Mereology and Location, edited by Shieva Kleinschmidt. Ned Markosian does argue in his contribution to that volume that \(\lceil \hbox {x}\) is a part of \(\hbox {y}\rceil \) be understood as (analytically) reducible to \(\lceil \hbox {x}\) is located at a subregion of the region y is located at \(\rceil \) (Markosian 2014). However, if one wants a general account of mereology that can apply to a variety of revisionary metaphysics, one ought to reject such an analysis.
Although she does not appeal to partial instantiation, this view is very much compatible with Jessica Wilson’s (2013) account of metaphysical (including quantum) indeterminacy. Wilson explicates indeterminacy in terms of a system’s possessing a determinable property while not possessing a unique determinate of that determinable (either by possessing no corresponding determinate or more than one). In the account I am offering, the locations of the N particles are indeterminate because the particles instantiate multiple determinate locations (each to a degree).
I am now talking about approximate locations since the wave function will become peaked in the form of a smooth Gaussian function around certain regions of each three-dimensional subspace. This corresponds to the high-degree-instantiation of a localized cluster of precise three-dimensional positions.
For a recent overview, see Wallace (2012).
This paper was presented at the Institut Jean Nicod, the Sorbonne, the University of Neuchâtel, and the University of California, Berkeley. I am grateful to David Albert, Claudio Calosi, Eddy Chen, Steven French, Geoffrey Lee, Kelvin McQueen, and Laura Ruetsche for critical feedback.
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Ney, A. Finding the world in the wave function: some strategies for solving the macro-object problem. Synthese 197, 4227–4249 (2020). https://doi.org/10.1007/s11229-017-1349-4
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DOI: https://doi.org/10.1007/s11229-017-1349-4