Abstract
This paper defends wave function realism against the charge that the view is empirically incoherent because our evidence for quantum theory involves facts about objects in three-dimensional space or space-time (local beables). It also criticizes previous attempts to defend wave function realism against this charge by claiming that the wave function is capable of grounding local beables as elements of a derivative ontology.
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Notes
The ‘so-called’ in the sentence will be explained in Sect. 3.
When I talk about ‘quantum theory’ in this paper, I am using this as a convenient shorthand for all of the various precise physical theories that have the essential features required for them to count as ‘quantum’ theories. See Sect. 2 for discussion.
There is a very similar objection raised briefly in Maudlin (2010), pp. 141–142.
This will be represented by ‘\(\uppsi \)’ when we are describing the quantum state of a localized system. The quantum state of the entire universe will be represented using ‘\(\Psi \)’.
This is a representation of a system not in a three-dimensional space, but instead a 3N-dimensional one, where N is the number of objects in the system under consideration. In a configuration space representation, locations are given by a sequence of three-times-N numbers, where the first three numbers correspond to the x-, y-, and z-coordinates of the first object in the system under some coordinatization of the 3-space, the next three numbers correspond to the x-, y-, and z-coordinates of the second object, and so on with the last three numbers corresponding to the x-, y-, and z-coordinates of the Nth object in the system.
In metaphysics, fundamental representations are those that aspire to provide complete, precise, and objective descriptions of what there is. See e.g. Sider (2011).
Here I am eliding other features of the total quantum state. We will need to capture additional degrees of freedom as well corresponding to the various dynamical features (electric charges, field values, etc.) of our system. These are sometimes interpreted as corresponding to additional, internal spatial dimensions.
This should arguably be viewed only as an approximation. In relativistic quantum field theories, there cease to be determinate facts about particle number. What is the official, correct way of describing the dimensionality of this space is a serious issue that needs to be addressed by the wave function realist, but will not be discussed here. See Ney (2013).
Partly for the reasons alluded to in note 10.
It should be noted that Wallace and Timpson make this proposal in the context of defending an Everettian approach to quantum theories. Decoherence will play a different role in the context of a collapse approach to quantum mechanics.
(Monton (2006), p. 785) argues this way as well against the wave function realist.
The talk of ‘fictive’ mappings may be distracting here. What’s going on is that Maudlin is responding to an earlier paper of Albert’s (1996) in which Albert distinguishes the fundamental, real configuration space, from the illusory (hence, ‘fictive’) three-dimensional space that emerges as the result of the behavior of the wave function. Albert now holds [see his (2013)] that the emergent low-dimensional space is for its emergence no less real than the fundamental space. It is not a fiction, not illusory.
The qualification ‘wholly’ is meant to distinguish this from a case in which there are two fundamental spaces, one which is three-dimensional and one which is six-dimensional. The question we are asking is whether fundamentally there could be only one space and yet it is both three- and six-dimensional.
This is more complicated on the Everettian picture since here there are multiple, incompatible results of measurements. However also on the Everett approach, there are multiple measurers. Whether Everettian quantum mechanics in particular is able to explain how quantum theories get confirmed (and solve the measurement problem) is a topic for another day.
Things would be easy if the three dimensions of our ordinary experience were three of the many dimensions of the configuration space. Then, these dimensions would simply be there as parts of the total configuration space and there would be no problem claiming they exist. But this is not the case (see Ney 2012, pp. 538–540). No one of the individual dimensions of configuration space corresponds to any of these three dimensions in which (say) pointers are supposed to have height, width, and depth.
Whether it does this is controversial once we extend the discussion to the relativistic domain.
See (Kim (2005), pp. 108–112) for a general description of functional reduction.
Notice the ‘yet’ here. I am not arguing the wave function realist cannot in principle meet this challenge. But functionalism is likely a dead end here, as fruitful as it may be in other domains.
The situation we are considering is actually more extreme of course. Holograms of pointers are still objects in three-dimensional space.
We can easily imagine a measurement procedure that worked not by our observing the location of some pointer or other object, but instead one that depended on other features of some object, for example, the color of a lightbulb. Albert (1992, pp. 100–104) makes this point as well (though in a different context).
Even setting aside this very general point about confirmation, as Albert Solé pointed out to me, if we consider the specific kinds of laws we find in our best theories, these seem to require the passage of time to confirm them. This is most obvious when we consider laws of dynamical evolution like Schrödinger’s equation. But even in the case of laws of coexistence (such as the ideal gas law), these get tested and confirmed by someone’s making a change in the value of a variable at one time and finding a resultant change in the system at a later time.
Popper’s theory of corroboration of theories by data also requires a temporal ordering. Those theories that are corroborated are those that have survived attempts to refute them (1934/2002).
I wish to thank David Baker, Shamik Dasgupta, Laurie Paul, Albert Solé, audiences at the Tucson Metaphysics Workshop, Manchester University, the University of North Carolina at Chapel Hill, the University of Oslo, and especially the referees for this journal for helping me to sharpen the views developed here.
References
Albert, D. Z. (1992). Quantum mechanics and experience. Cambridge: Harvard University Press.
Albert, D. Z. (1996). Elementary quantum metaphysics. In J. T. Cushing, A. Fine, & S. Goldstein (Eds.), Bohmian mechanics and quantum theory: An appraisal. Dordrecht: Kluwer.
Albert, D. Z. (2013). Wave function realism. In A. Ney & D. Albert (Eds.), The wave function: Essays on the metaphysics of quantum mechanics. Oxford: Oxford University Press.
Allori, V., Goldstein, S., Zanghì, N., & Tumulka, R. (2008). On the common structure of Bohmian mechanics and the Ghirardi–Rimini–Weber theory. British Journal for the Philosophy of Science, 59, 353–389.
Barrett, J. (2001). The quantum mechanics of minds and worlds. Oxford: Oxford University Press.
Bell, J. S. (1987). Speakable and unspeakable in quantum mechanics. Cambridge: Cambridge University Press.
Dürr, D., Goldstein, S., & Zanghì, N. (1992). And the origin of absolute uncertainty. Journal of Statistical Physics, 67, 1–75.
Healey, R. (2002). Can physics coherently deny the reality of time? Royal Institute of Philosophy Supplement, 5, 293.
Ismael, J. manuscript. What entanglement might be telling us.
Kim, J. (2005). Physicalism, or something near enough. Princeton: Princeton University Press.
Maudlin, T. (2007). Completeness, supervenience and ontology. Journal of Physics A, 40, 3151.
Maudlin, T. (2010). Can the world be only wavefunction? In S. Saunders, J. Barrett, A. Kent, & D. Wallace (Eds.), Many worlds? Everett, quantum theory, and reality. Oxford: Oxford University Press.
Monton, B. (2006). Quantum mechanics and 3N-Dimensional space. Philosophy of Science, 73, 778–789.
Myrvold, W. (forthcoming). What is a wave function? Synthese.
Ney, A. (2012). The status of our ordinary three dimensions in a quantum universe. Noûs, 46(3), 525–560.
Ney, A. (2013). Introduction. In A. Ney & D. Albert (Eds.), The wave function: Essays on the metaphysics of quantum mechanics. Oxford: Oxford University Press.
Ney, A., & Phillips, K. (2013). Does an adequate physical theory demand a primitive ontology? Philosophy of Science, 80(3), 454–474.
North, J. (2013). The structure of the quantum world. In A. Ney & D. Albert (Eds.), The wave function: Essays on the metaphysics of quantum mechanics. Oxford: Oxford University Press.
Popper, K. 1934/2002. The logic of scientific discovery. London: Routledge.
Sider, T. (2011). Writing the book of the world. Oxford: Oxford University Press.
Vaidman, L. (2014). Many-worlds interpretation of quantum mechanics. In Stanford encyclopedia of philosophy (Spring 2014 Edition). E. N. Zalta (Ed.) URL = http://plato.stanford.edu/archives/spr2014/entries/qm-manyworlds/
Wallace, D. (2004). Protecting cognitive science from quantum theory. Behavioral and Brain Sciences, 27(5), 636–637.
Wallace, D. (2010). Decoherence and ontology. In S. Saunders, J. Barrett, A. Kent, & D. Wallace (Eds.), Many worlds? Everett, quantum theory, and reality. Oxford: Oxford University Press.
Wallace, D. (2012). The emergent multiverse. Oxford: Oxford University Press.
Wallace, D., & Timpson, C. J. (2010). Spacetime state realism I. British Journal for the Philosophy of Science, 61, 697–727.
Zurek, W. (1991). Decoherence and the transition from quantum to classical. Physics Today, 44, 36–44.
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Ney, A. Fundamental physical ontologies and the constraint of empirical coherence: a defense of wave function realism. Synthese 192, 3105–3124 (2015). https://doi.org/10.1007/s11229-014-0633-9
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DOI: https://doi.org/10.1007/s11229-014-0633-9