Abstract
This paper argues for a broadly dispositionalist approach to the ontology of Bohmian mechanics (BM). It first distinguishes the ‘minimal’ and the ‘causal’ versions of Bohm’s theory, and then briefly reviews some of the claims advanced on behalf of the ‘causal’ version by its proponents. A number of ontological or interpretive accounts of the wave function in BM are then addressed in detail, including (i) configuration space, (ii) multi-field, (iii) nomological, and (iv) dispositional approaches. The main objection to each account is reviewed, namely (i) the ‘problem of perception’, (ii) the ‘problem of communication’, (iii) the ‘problem of temporal laws’, and (iv) the ‘problem of under-determination’. It is then shown that a version of dispositionalism overcomes the under-determination problem while providing neat solutions to the other three problems. A pragmatic argument is thus furnished for the use of dispositions in the interpretation of the theory more generally. The paper ends in a more speculative note by suggesting ways in which a dispositionalist interpretation of the wave function is in addition able to shed light upon some of the claims of the proponents of the causal version of BM.
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Notes
Other, that is, than the very minimal assumption that whatever particles exist must have determinate positions and velocities, i.e. that there are trajectories. But there are no assumptions, for instance, regarding what a particle consists in, what the background space of motion may be, whether the trajectories inhabit 3-dimensional or a higher dimensional configuration space and, of course, whether there are additional entities over and above the particles.
Thus only pragmatic reasons may lead us to embrace one or another combination of version and ontology—there can be no logical compulsion—and some of these pragmatic reasons are rehearsed later on in this paper in arguing for a particular such combination.
This is obviously not to say that the ‘minimal’ version is local, but the non-locality takes the form of non-supervenience there [see Esfeld et al. (2014, p. 79ff.), for a discussion].
The proponents of the ‘minimal’ interpretation of course also emphasize the strong differences with classical mechanical concepts (see e.g. Dürr et al. 1996, p. 25ff.), but this is to be expected in their case.
The idea that BM is not itself an ‘interpretation’ of quantum mechanics, but a theory of its own—and one open to a plurality of interpretations just like orthodox quantum mechanics, or Newtonian classical mechanics—goes back at least to Fine (1996).
Albert (1996, p. 277).
Belot (2012) helpfully divides realistic interpretations of the wavefunction in general—including in BM into three kinds: (i) object, (ii) law and (iii) property interpretations, depending on whether they take the wavefunction to be the description of a real object, a genuine law, or an actual property. In my terms, both configuration space and multifield realism are interpretations of kind (i), the nomological approach is an interpretation of type (ii) and dispositionalism is of type (iii).
Belot (2012) here defers to Forrest (1988, Ch. 5), which gives a general account of the equivalent of multi-fields but for dispositional properties or propensities! I come back to the issue in the main text, but for now one gets the idea: There is always a way to define a truncated version of the wavefunction for each particle regardless of whether the properties of the particles are interpreted to be dispositional or categorical.
Finally, also note that the same problem of communication would affect a version of configuration space realism where only the universal wavefunction is reified, but not the universal particle. On such views, there is a real wavefunction in 3N space, which effectively fixes the particle positions of each particle in 3D space—with the same difficulty to explain how the interaction occurs. (Belot 2012, p. 77).
I suppose that the wavefunction could also be taken to represent a law describing the motion of the world particle in configuration space; but this combination of nomological and configuration space realism would seem to inherit the disadvantages of both types of realism while acquiring none of their relative advantages. And, at any rate, this is not how the proponents of the nomological interpretation read it—see Durr et al. (1997), or Goldstein and Zanghi (2013).
Or, more precisely, one that does not make it subservient to the conjunction of the Schrödinger and Guidance equations.
These problems are related to the fact that the effective wavefunction is not exactly as above, which is rather a representation of a ‘conditional wave function’ that does not obey Schrödinger’s equation (Dürr et al. 1996, p. 39), but I gloss over them since I regard the problem of time-indexicality to be the more acute one anyway.
At any rate, this is certainly how we understand dynamical laws—such as Newton’s laws and the Schrödinger equation. So much seems uncontroversial, and it is enough to make the point in the main text above, but it may be objected that there are also physical laws which do not have this dynamical character—perhaps purely geometrical laws that describe the internal constitution of solids. And perhaps the wavefunction understood as a law has this different character. However, it seems to me that the same problem reappears here too—even if the laws don’t prescribe the temporal evolution of the objects in their domain, it is nonetheless bizarre to think that they themselves are time-indexed or time-dependent things.
This may indicate that the correct construal of ‘nomological’ in this approach is Humean—in the sense that the wavefunction is meant to be a law in the Hume-Lewis best system sense of law, as a description of regularity over the course of the actual world history that best summarizes space-time coincidences (see Esfeld et al. 2014, pp. 780ff.) for some suggestions in this regard). But the possibility of undermining futures is a problem for the Humean analysis of laws too, and a law that would correct itself in the future would be just as counterintuitive from this point of view.
I will for the sake of argument assume that position is not a dispositional but a categorical property. The dispositionalist interpretation of BM would of course be further strengthened if position turned out to be a dispositional property as well (for some suggestions to the effect see Clifton and Pagonis 1995). The argument above shows that even if position is categorical, the interpretation of other properties as dispositional already serves to solve many of the problems reviewed so far in establishing the ontology of the theory.
One can also read the multifield approach dispositionally and, in fact, this is what Forrest (1988, Ch. 5) does in introducing it as a ‘propensity multifield’. This would amount, in terms of the proposal advanced in the main text above, to defining a velocity field in 3d space for each particle, for every given wavefunction for the corresponding n-particle system as defined in 3-n configuration space. I don’t see any substantial difference between this proposal—if read dispositionally in this way—and my own proposal above other than the nature of the position property itself (which, on the multifield approach would presumably be necessarily dispositional too).
In other words, I use the terms “locality” and “separability” roughly in the sense of Howard (1989). Under this aception, locality requires separability but not viceversa. In a typical EPR experiment, for example, one can have separable particle states in both wings, but non-local connections; or one can postulate one non-separable state (or even particle), but not both. The standard understanding of separability of states is as supervenience (Teller 1989) and this fits in well with Esfeld et al.’s emphasis upon the failure of Humean supervenience.
In Moliere (1673, Act III, Third interlude): “Quare Opium facit dormire: ... Quia est in eo Virtus dormitiva”.
It must be noted that there are accounts, such as Albert’s (2000) where the initial probability distributions represent objective chances already, which get as it were transferred to later chances by the dynamics. On this account there is determinism in the dynamical evolution of chances, yet stochastic or chancy determination of outcomes. The view is nonetheless controversial, and a full application to propensities must await a new paper.
In other words I now want to reserve the term “propensity” for an essentially and irreducibly objective probabilistic disposition. See Solé (2013, p. 375) for an accurate disquisition of this point in connection with my previous defence of selective propensities for BM in Suárez (2007), for which I am grateful.
In the festschrift for Max Born (Einstein 1953), where does not explicitly address BM, which had at the time just appeared in press, but more generally any realist theory about particles’ positions. He may have had in mind De Broglie’s pilot wave theory in particular.
Sometimes the word ‘dynamics’ is taken to implicitly refer to forces, as in “Newtonian dynamics” and to carry the corresponding causal connotations. More generally, however, it can be employed as in the text above to refer to any second-order derivative function of the position—and to the framework that articulates the properties that are operative at that level. Hence I am not employing the term in its most committed sense as requiring the existence of independent forces acting causally upon the particles’ velocities. Rather GPE is legitimately dynamical merely on account of its formal second order character.
References
Albert, D. (1996). Elementary quantum metaphysics. In J. T. Cushing, A. Fine, & S. Goldstein (Eds.), Bohmian mechanics and quantum theory: An appraisal (pp. 277–284). Dordrecht: Kluwer Academic Publishing.
Albert, D. (2000). Time and chance. Cambridge: Harvard University Press.
Albert, D. (2013). Wave function realism. In A. Ney & D. Albert (Eds.), The wavefunction: Essays on the metaphysics of quantum mechanics (pp. 52–57). Oxford: Oxford University Press.
Allori, V., Goldstein, S., Tumulka, R., & Zanghi, N. (2008). On the common structure of Bohmian mechanics and the Ghirardi–Rimini–Weber theory. British Journal for Philosophy of Science, 59, 353–389.
Belot, G. (2012). Quantum states for primitive ontologists. European Journal for Philosophy of Science, 2, 67–83.
Belousek, D. W. (2003). Formalism, ontology and methodology in Bohmian mechanics. Foundations of Science, 8, 109–172.
Bohm, D. (1952). A suggested interpretation of quantum theory in terms of “hidden variables” I and II”. Physical Review, 85, 166–193.
Bohm, D. (1987). Hidden variables and the implicate order. In B. Hiley & F. D. Peat (Eds.), Quantum implications: Essays in honour of David Bohm (pp. 33–45). London: Routledge.
Bohm, D., & Hiley, B. (1993). The undivided universe: An ontological interpretation of quantum theory. London: Routledge.
Clifton, R., & Pagonis, C. (1995). Unremarkable contextualism: Dispositions in Bohm’s theory. Foundations of Physics, 25(2), 281–296.
Durr, D., Goldstein, S., & Zanghi, N. (1997). Bohmian mechanics and the meaning of the wave function. In R. S. Cohen, M. Horne, & J. Stachel (Eds.), Experimental metaphysics: Quantum mechanical studies for Abner Shimony (pp. 25–38). Berlin: Springer.
Durr, D., Goldstein, S., & Zanghi, N. (1996). Bohmian mechanics as the foundation of quantum mechanics. In J. T. Cushing, A. Fine, & S. Goldstein (Eds.), Bohmian mechanics and quantum theory: An appraisal (pp. 21–44). Dordrecht: Kluwer Academic Publishing.
Einstein, A. (1953). Elementare Überlegungen zur Interpretation der Grundlagen der Quanten-Mechanik. Scientific Papers Presented to Max Born (pp. 33–40). Oliver and Boyd: Edinburgh.
Esfeld, M., Lazarovici, D., Hubert, M., & Dürr, D. (2014). The ontology of Bohmian mechanics. British Journal for the Philosophy of Science, 65, 773–796.
Fine, A. (1996). On the interpretation of Bohmian mechanics. In J. T. Cushing, A. Fine, & S. Goldstein (Eds.), Bohmian mechanics and quantum theory: An appraisal (pp. 231–250). Dordrecht: Kluwer Academic Publishing.
Forrest, P. (1988). Quantum metaphysics. Oxford: Blackwell.
Goldstein, S., & Zanghi, N. (2013). Reality and the role of the wave function in quantum theory. In A. Ney & D. Albert (Eds.), The wavefunction: Essays on the metaphysics of quantum mechanics (pp. 91–109). Oxford: Oxford University Press.
Hiley, B., & Peat, F. D. (Eds.). (1987). Quantum implications: Essays in honour of David Bohm. London: Routledge.
Holland, P. (1993). The quantum theory of motion. Cambridge: Cambridge University Press.
Howard, D. (1989). Holism, separability and the metaphysical implications of the Bell experiments. In P. Cushing & E. McMullin (Eds.), Philosophical consequences of quantum mechanics (pp. 224–253). Notre Dame University Press.
Lewis, D. K. (1986). Philosophical Papers (Vol. 2). Oxford: Oxford University Press.
Moliere (1673). Le Malade Imaginaire: Commedie en Trois Act.
Monton, B. (2013). Against 3N-dimensional space. In A. Ney & D. Albert (Eds.), The wavefunction: Essays on the metaphysics of quantum mechanics (pp. 154–167). Oxford: Oxford University Press.
Ney, A., & Albert, D. (2013). The wavefunction: Essays on the metaphysics of quantum mechanics. Oxford: Oxford University Press.
Solé, A. (2013). Bohmian mechanics without wave function ontology. Studies in History and Philosophy of Modern Physics, 44, 365–378.
Suárez, M. (2004). Quantum selections, propensities and the problem of measurement. British Journal for the Philosophy of Science, 55(2), 219–255.
Suárez, M. (2007). Quantum propensities. Studies in History and Philosophy of Modern Physics, 38, 418–438.
Teller, P. (1989). Relativity, relational holism and the Bell inequalities. In P. Cushing & E. McMullin (Eds.), Philosophical consequences of quantum mechanics (pp. 208–223). Notre Dame University Press.
Acknowledgments
A previous version of this paper was delivered at the I Barcelona Workshop on SpaceTime and the Wavefunction in April 2013. I am very grateful to the organizers for the opportunity to present my work on Bohmian mechanics, as well as all the participants, particularly Tim Maudlin and Albert Solé, for very helpful and constructive discussions. I also thank the Editors of the special volume for their patience and for their suggestions. Many thanks also to four anonymous referees of Synthése for very helpful comments and endorsements. Financial support is acknowledged from the Spanish Government (DGICT, Ministerio de Economía y Competitividad, projects FFI2011-29834-C03-01 and FFI2014-57064-P) and the European Commission under the Marie Curie programme (FP7-PEOPLE-2012-IEF, project number 329430).
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Suárez, M. Bohmian dispositions. Synthese 192, 3203–3228 (2015). https://doi.org/10.1007/s11229-015-0741-1
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DOI: https://doi.org/10.1007/s11229-015-0741-1