Abstract
It is difficult to articulate how we should take a realist attitude towards Bohmian mechanics because there are many versions of it. This paper aims to clarify the realist commitments of Bohmian mechanics and how we can understand it from a general scientific realist perspective. I use the box experiment, a double-slit like experiment conducted by Cardone et al. (Phys Lett A 326(1–2):1–13, 2004; Int J Mod Phys B 20(09):1107–1121, 2006), as a working example to argue that a causal realist account (in the sense of selective realism) that is applicable to Bohmian mechanics, has to be supplemented with the use of Inference to the Best Explanation. The reason is because causal realism on its own does not form a sufficient basis for realism about Bohmian mechanics. In particular, I argue that the existence of the pilot wave explains why we observe an anomalous interference effect in the experiment of Cardone et al. The conclusion to draw is that a complete realist account about Bohmian mechanics rests on explanatory considerations.
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source S1 and the detector A, which is the shortest distance photons passing through slit F1 and detected at detector A. The diagonal dash line s represents the shortest distance between the (putative) pilot wave and detector A (no photons could pass F2), which is the path the pilot wave passing through slit F2 and arriving at A. But it does not represent any physical trajectory of photons from S2, because C is situated at the place to ensure no photons from S2 go through F2 (For a more detailed description of the setup see Cardone et al. 2004). Note For permission to use Fig. 1, see the file “RightsLinkLicense(PermissionToUseFigure).”
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Notes
This is Bohm’s version of Bohmian mechanics which he proposes in 1952.
We should keep the causal version of Bohmian mechanics separate from a causal realist account of Bohmian mechanics. Scientific realism is often formulated in terms of three dimensions, the metaphysical, the semantic and the epistemic. The causal version of Bohmian mechanics refers to the metaphysical dimension of the Bohmian model, such that it introduces a force term which is derivable from the quantum potential when we rewrite the wave function in a polar form. And this force appears when we describe how the wave and particles interact, such that the wave guides and pushes particles around in the universe. On the other hand, a causal realist account purports to offer an epistemic justification on realism about Bohmian mechanics.
The anomalous interference effects of photons were also observed when using microwave and infrared laser beams. One with microwaves emitted by horn antennas, at IFAC—CNR (Ranfagni and co-workers), and the other with infrared CO2 laser beams, at INOA (Meucci and co-workers). See Cardone et al. (2006, pp. 1113–1114).
More specifically, ΔA ranged from (2.2 ± 0.4) μV to (2.3 ± 0.5) μ V, values well below the threshold energy E0,em = 4,5 μV, and the anomalous effect was observed within a distance of at most 4 cm from the sources. See Mignani et al. (2012, p. 3).
In the literature a three-dimensionalist view sometimes refers to the position of Bohmian mechanics that denies a physical realist attitude towards the wave function. This can include Belousek’s (2003) account which takes particles and the quantum forces to be ontology in the 3-D space, or primitive ontology which takes only particles as ontology. But some Bohmians such as Hubert and Romano (2018) argue for a version of Bohmian mechanics which takes the wave function as a multi-field in the 3-D space. So the contrast between primitive ontology and wave function ontology might better capture the ontological difference we need in this paper, although it might leave out Belousek’s (2003) account, compared to a division between a three-dimensionalist view and wave function ontology.
There are other ways to divide different versions of Bohmian mechanics, such as between the guidance approach and the quantum potential approach which focuses on the discussion of the quantum potential. This division places emphasis on the dynamical equations and asks whether the guiding equation (first-order) or the classical-like Hamilton-Jacob equation (second-order) is fundamental. Primitive ontology is considered as a guidance approach.
See Belousek (2003, pp. 141–143) for Belousek’s criticism of Albert’s account.
In both nomological interpretations of the wave function, their advocates argue that only the universal wave function has the nomological status, rather than effective wave functions, because the universal wave function when considered as a law encompasses all particles in the universe rather than particles in a subsystem.
One possible way to argue that realism about the wave function as a physical entity instead of a mathematical construct is through Inference to the Best Explanation, by arguing, for instance, the wave has to be a physical entity that interacts with and guides particles. And this is the best explanation for explaining some quantum phenomena, such as interference.
A notion of causality associated with Bohmian mechanics appears in the discussion of nonlocality. Since nonlocality as action at a distance is an inherent feature of Bohmian theory, one might wonder whether nonlocality is coherent with a causal realist theory. Jean Bricmont (2016) has argued that Bohmian mechanics is nonlocal (pp. 111–126; pp. 162–169). But it is important that we keep these two aspects of causality separate, as causal realism in this paper is a view that some claims about entities can be satisfied through a causal explanation or inference, while the notion of causality associated with nonlocality is that there can be a causal process between two spatially separated systems. Although there can be a claim about nonlocality that it is causally warranted, one should not confuse these two notions of causality.
Sengupta et al. have also shown that both Bohmian trajectories and the Bohmian trajectories as the quantum potential goes to zero exhibit non-crossing behavior, but classical trajectories exhibit crossing behavior (2014, p. 3).
Chakravartty’s (1998) distinction may seem familiar, since it is very much like Psillos’s distinction between essential features and idle features, where the latter only plays a role to complete the scientific story without being warranted any realist commitments. But their distinctions differ in that Chakravartty explicitly thinks that the essential features are detection properties that are causally obtained, which goes further than Psillos’ criterion to point out where the essential features originate.
Notice that unlike Hacking (1983) and Cartwright’s (1983) versions of entity realism which are independent of a particular theory, Chakravartty’s entity realism (as part of his semirealism) “explains the fact that we have continuity of reference across theory change by appealing to unchanging attributions of those detection properties which underwrite the causal interactions we exploit by means of detection” (1998, p. 400).
Chakravartty’s SR unlike in Worrall’s account, “contain substantive information about entities: namely, regarding detection properties” (1998, p. 407). Chakravartty commits only to those “mathematical equations relating detected objects, or more specifically, detection properties, as expressing causal relations between those objects” (1998, p. 401).
One should keep in mind that not all unobservable entities can fit Hacking’s criterion. This limitation of not being able to manipulate some entities is in fact quite general. As Egg points out, there might be some real entities which we will never be able to manipulate, such as events that evolutionary biology reconstructs (2014, p. 23).
Although it is tempting, it is not by default to assume that classical particles and Bohmain particles are the same. A causal account is also inadequate for telling us whether the electrons or photons in the box experiment are in fact Bohmian particles and what their nature is. For instance, Hacking’s entity realism, if it works, gets us from the fact that we can use electrons or photons to investigate other parts of nature to the claim that they exist, but this sheds no light on telling us whether classical particles and Bohmian particles are the same sort of particles, or whether electrons or photons are Bohmian particles. This is a serious defect of causal accounts, because some Bohmians, such as Goldstein et al. (2005), think Bohmian particles are conceptually different from classical particles. For instance, Goldstein et al. (2005) defend the view that Bohmian particles are just points, that is we do not distinguish electrons from muons, or electrons from photons, for instance. On the other hand, Bohmian mechanics, if one believes in the truth of this theory, offers some insight on the nature of these entities. According to Bohmian mechanics, for instance, a particle is piloted by the wave and does not follow a straight-line trajectory when there is no classical force acting on it (unlike classical particles will move in a straight-line under the same condition). Sometimes, that a particle follows such a trajectory suggests that it is a Bohmian particle. The Bohmian says more than just that particles exist; they exist as Bohmian particles.
It is often believed (according to the standard interpretation of quantum mechanics) that there are neither particles nor waves before measurement is made at the detector.
For the Bohmian, the wave function is defined in the configuration space. A configuration space is a mathematical space. And for a quantum system with N particles, the configuration space of the system is 3 N-dimensional. According to Bricmont, the configuration space of the system consists of the set of all possible positions of all the N particles, where N is arbitrary and could in principle include all the particles in the universe (2016, p. 52). According to Lewis, in Bohmian mechanics, one can understand that “the state of a quantum system at a time is specified by the distribution of wavefunction properties over the possible values of 3 N coordinates” (2004, p. 726).
If we can manipulate the wave function in the same way we manipulate the particles, which are three-dimensional objects, then we have a reason to think that the wave function is a three-dimensional object. For this possibility of the wave function as a three-dimensional entity, see Hubert and Romano (2018). But this will imply that configuration space realism is false because configuration space realism says that the wave function is in a configuration space, rather than a three-dimensional physical space.
Cardone and Mignani (2007) point out that the two lighting sources S1 and S2 emit wavepackets with very similar frequency spectra, so that photons from S1 can be carried by waves emitted by S2 (p. 4442).
According to Lipton, although there is a distinction between truth-values of the statements that make up a scientific theory (for statement realists) and the existence of entities (for entity realists), the comparison is not straightforward (1994, p. 102). He states that, “to say that a particular kind of entity exists is, after all, to make a statement, and one that is true just in case the entity does indeed exist” (Lipton 1994, p. 102).
Psillos (2009) has a more detailed discussion on why Cartwright’s entity realism is an instance of IBE by connecting it with Inference to the Best Cause.
According to Psillos, “if we think of causal inference as Inference to the Best Cause, then we are committed to the view that the inferential weight is carried by the explanatory quality of the causal explanation offered, on its own and in relation to competing alternatives” (2009, p. 8).
Nonetheless, Cartwright, Suarez and Egg face a general problem that renders their causal realist accounts dubious. According to Wüthrich, these accounts presuppose rather than infer the existence of the involved entities, “otherwise we could not have observed occurrences of the factors, we could not know to have manipulated them, or we could not have gathered statistical data about them” (2017, p. 463).
Egg’s IBTE here is what we usually call IBE.
The way that Egg defines material inference is that “what is to count as material inference needs to be defined in terms of the kinds of properties that can be ascribed to entities as a result of such inference (let us call them material properties)” (2012, p. 265).
Although Bohmian mechanics is a non-relativistic theory, it nonetheless possesses features that are relevant to relativity, such as nonlocality which is understood as action at a distance. So it is possible for one to argue that there is an inconsistency between Bohmian mechanics and the maximum limit of velocity (i.e. the speed of light). But one can also argue that there is no such inconsistency because there is no transmission of message due to this nonlocality.
Thanks to one of the referees for pointing out the empirical equivalence between primitive ontology and wave function ontology. And there is a potential worry for why the box experiment provides a reason from explanatory considerations to favor wave function ontology.
References
Albert, D. Z. (1996). Elementary quantum metaphysics. In Bohmian mechanics and quantum theory: An appraisal (pp. 277–284). Springer, Dordrecht.
Allori, V. (2018). Scientific realism and primitive ontology or: The pessimistic induction and the nature of the wave function. Lato Sensu, revue de la Société de philosophie des sciences, 5(1), 69–76.
Allori, V., & Zanghì, N. (2004). What is Bohmian mechanics. International Journal of Theoretical Physics, 43(7–8), 1743–1755.
Belousek, D. W. (2003). Formalism, ontology and methodology in Bohmian mechanics. Foundations of Science, 8(2), 109–172.
Bhogal, H., & Perry, Z. R. (2017). What the Humean should say about entanglement. Noûs, 51, 74–94.
Bricmont, J. (2016). Making sense of quantum mechanics. Cham: Springer International Publishing.
Brown, H. R., Elby, A., & Weingard, R. (1996). Cause and effect in the pilot-wave interpretation of quantum mechanics. In Bohmian mechanics and quantum theory: An appraisal (pp. 309–319). Springer, Dordrecht.
Callender, C. (2015). One world, one beable. Synthese, 192, 3153–3177.
Cardone, F., & Mignani, R. (2004). Energy and geometry: An introduction to deformed special relativity (Vol. 22). Singapore: World Scientific.
Cardone, F., & Mignani, R. (2007). The shadow of light: Challenging classical and quantum electrodynamics. International Journal of Modern Physics B, 21(26), 4437–4471.
Cardone, F., Mignani, R., Perconti, W., & Scrimaglio, R. (2004). The shadow of light: Non-Lorentzian behavior of photon systems. Physics Letters A, 326(1–2), 1–13.
Cardone, F., Mignani, R., Perconti, W., Petrucci, A., & Scrimaglio, R. (2006). The shadow of light: Lorentz invariance and complementarity principle in anomalous photon behavior. International Journal of Modern Physics B, 20(09), 1107–1121.
Cartwright, N. (1983). How the laws of physics lie. Oxford: Clarendon Press.
Chakravartty, A. (1998). Semirealism. Studies in History and Philosophy of Science, 29(3), 391–408.
Dürr, D., Goldstein, S., & Zanghi, N. (1997). Bohmian mechanics and the meaning of the wave function. experimental metaphysics–quantum mechanical studies in honor of Abner Shimony, ed. RS Cohen, M. Horne. Journal of Stachel. Boston Studies in the Philosophy of Science, Kluwer.
Dürr, D., Goldstein, S., & Zanghì, N. (2013). Quantum physics without quantum philosophy. Berlin: Springer.
Egg, M. (2012). Causal warrant for realism about particle physics. Journal for General Philosophy of Science, 43(2), 259–280.
Egg, M. (2014). Scientific realism in particle physics: A causal approach (Vol. 29). Berlin: Walter de Gruyter GmbH & Co KG.
Esfeld, M. (2013). Ontic structural realism and the interpretation of quantum mechanics. European Journal for Philosophy of Science, 3(1), 19–32.
Esfeld, M. (2014). Quantum humeanism, or: Physicalism without properties. Philosophical Quarterly, 64, 453–470.
Esfeld, M., Hubert, M., Lazarovici, D., & Dürr, D. (2014). The ontology of Bohmian mechanics. The British Journal for the Philosophy of Science, 65(4), 773–796.
Goldstein, S., Taylor, J., Tumulka, R., & Zanghı, N. (2005). Are all particles real? Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 36(1), 103–112.
Hacking, I. (1983). Representing and intervening: Introductory topics in the philosophy of natural science. Cambridge: Cambridge UP.
Heitmann, W., & Nimtz, G. (1994). On causality proofs of superluminal barrier traversal of frequency band limited wave packets. Physics Letters A, 196(3–4), 154–158.
Holland, P. R. (1993). The quantum theory of motion. Cambridge: Cambridge University Press.
Hubert, M., & Romano, D. (2018). The wave-function as a multi-field. European Journal for Philosophy of Science, 8(3), 521–537.
Lewis, P. J. (2016). Quantum ontology: A guide to the metaphysics of quantum mechanics. Oxford: Oxford University Press.
Lipton, P. (1993). Is the best good enough? Proceedings of the Aristotelian Society, 93, 89–104.
Lipton, P. (1994). Truth, existence, and the best explanation. In A. A. Derksen (Ed.), The scientific realism of Rom Harré. Tilburg University Press.
Lipton, P. (2004). Inference to the best explanation. London: Routledge.
Mignani, R., Petrucci, A., & Cardone, F. (2012, May). Possible experimental evidence for violation of standard electrodynamics de broglie pilot wave and spacetime deformation. In 2012 symposium on photonics and optoelectronics (pp. 1–8). IEEE.
Miller, E. (2014). Quantum entanglement, Bohmian mechanics, and Humean supervenience. Australasian Journal of Philosophy, 92, 567–583.
Musgrave, A. (1988). The ultimate argument for scientific realism. In R. Nola (Ed.), Relativism and realism in science (pp. 229–252). Dordrecht: Kluwer.
Nimtz, G., Enders, A., & Spieker, H. (1994). Photonic tunneling times. Journal de Physique I, 4(4), 565–570.
Norsen, T. (2010). The theory of (exclusively) local beables. Foundations of Physics, 40(12), 1858–1884.
Psillos, S. (2007). The fine structure of inference to the best explanation. Philosophy and Phenomenological Research, 74(2), 441–448.
Psillos, S. (2009). Cartwright’s realist toil: From entities to capacities. In Knowing the structure of nature (pp. 99–122). Palgrave Macmillan, London.
Ranfagni, A., Fabeni, P., Pazzi, G. P., & Mugnai, D. (1993). Anomalous pulse delay in microwave propagation: A plausible connection to the tunneling time. Physical Review E, 48(2), 1453.
Sengupta, S., Khatua, M., & Chattaraj, P. K. (2014). Bohmian trajectory from the “classical” Schrödinger equation. Chaos: An Interdisciplinary Journal of Nonlinear Science, 24(4), 043123.
Solé, A. (2013). Bohmian mechanics without wave function ontology. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 44(4), 365–378.
Suárez, M. (2008). Experimental realism reconsidered: How inference to the most likely cause might be sound. In Nancy Cartwright's philosophy of science (pp. 149–175). Routledge.
Suárez, M. (2015). Bohmian dispositions. Synthese, 192(10), 3203–3228.
van Fraassen, B. C. (1989). Laws and symmetry. Oxford: Clarendon.
Williams, P. (2019). Scientific realism made effective. The British Journal for the Philosophy of Science, 70(1), 209–237.
Worrall, J. (1989). Structural realism: The best of both worlds? Dialectica, 43, 99–124.
Wüthrich, A. (2017). The Higgs discovery as a diagnostic causal inference. Synthese, 194(2), 461–476.
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Yan, C. Bohmian Mechanics: Realism and the “Box” Experiment. Found Sci 26, 429–451 (2021). https://doi.org/10.1007/s10699-020-09661-5
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DOI: https://doi.org/10.1007/s10699-020-09661-5