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Underdetermination: A Realist Interpretation of Quantum Mechanics and Bohmian Mechanics

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Abstract

It is generally believed that two rival non-relativistic quantum theories, the realist interpretation of quantum mechanics and Bohmian mechanics, are empirically equivalent. In this paper, I use these two quantum theories to show that it is possible to offer a solution to underdetermination in some local cases, by specifying what counts as relevant empirical evidence in empirical equivalence and underdetermination. I argue for a domain-sensitive approach to underdetermination. Domain sensitivity on theories’ predictions plays a role in determining whether two or more theories are empirically equivalent and underdetermined. To support my argument for the denial of the empirical equivalence between Bohmian mechanics and the realist interpretation of quantum mechanics, I argue that they are not empirically equivalent when we consider their predictions for domains outside their application, using the relativistic domain as an example.

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Notes

  1. It is possible to define empirical equivalence with respect only to currently available data. Under this definition, it is a matter of time that two currently empirically equivalent theories may turn out to be not equivalent.

  2. Bohmian mechanics accounts for all of the phenomena governed by nonrelativistic quantum mechanics, from spectral lines and scattering theory to superconductivity, the quantum Hall effect and quantum computing (Goldstein, 2017). But note that this is not sufficient to claim that BM and RI are empirically equivalent. Instead, we need a stronger claim that the two theories make the same predictions for all experiments and observable phenomena they apply to.

  3. This is what sometimes called contrastive underdetermination.

  4. Another way to understand the relevance of this kind of empirical evidence is to understand them as providing an analogous case to the Bohmian model, such that the macroscopic “walkers” help us visualize the Bohmian model.

  5. A configuration space is an abstract high-dimensional space, such that the configuration space for a quantum system with N particles is 3 N-dimensional. The configuration space of the N-particle system consists of the set of all possible positions of all the N particles, and could in principle include all the particles in the universe (Bricmont, 2016).

  6. See Maudlin (2002) for the presentation of the two postulates. But note that Maudlin (2002) does not take these two postulate to refer to a realist interpretation of quantum mechanics. In fact, we can have a realist understanding of these two statements which I discuss in Sect. 1.2.

  7. See Maudlin (2002) and Suárez (2015).

  8. The wave function is a universal wave function, not for ensemble of subsystems of the universe.

  9. This equilibrium assumption of BM is crucial to the empirical equivalence or underdetermination between BM and RI within their shared, primary domain of application.

  10. Some argue that this guidance equation is not a postulate, because it can be derived in several ways, see Dürr et al. (2013).

  11. One should note that not all Bohmians adopt this postulate, but David Bohm does. This postulate does not appear in the formulations of some other Bohmians such as, Durr, Goldstein and Zanghi. If one accepts all these five postulates, one adopts a causal version of BM, but if accepting only 1’-4’, one adopts a minimal version of BM.

  12. “It has been pointed out how these two versions of Bohmian mechanics differ minimally in ontology. This difference is indeed minimal, since neither version by itself describes how the world is ultimately furnished ontologically, but to the contrary leaves the fundamental ontological options wide open” (Suárez, 2015). For instance, the two versions haven’t said if the wave-function is a physical object.

  13. I leave multivalued logic aside and restrict to two-value logic, so a statement is either true or false.

  14. This is often referred to as the semantic dimension of scientific realism.

  15. The minimalist will not describe the relation between the wave and particles in terms of some quantum force mediating them. The minimalist can say that the wave is associated with particles, but do not commit to any other unobservables that describe their interactions or relations.

  16. According to Dürr et al. (1992), “a Bohmian universe, though deterministic, evolves in such a manner that an appearance of randomness emerges, precisely as described by the quantum formalism and given, for example, by “ρ=|ψ|2.” A crucial ingredient in our analysis of the origin of this randomness is the notion of the effective wave function of a subsystem, a notion of interest in its own right and of relevance to any discussion of quantum theory”.

  17. Denying the equilibrium assumption does not commit to a different theory other than BM, but a particular version of BM. One can remain as a Bohmian even if she adopts a nonequilibrium assumption if she takes this assumption to be auxiliary rather than essential. Although adopting a nonequilibrium postulate will lead to different predictions as the usual BM and RI, this move does not abandon some leading principles of BM, such as that dynamical evolution is deterministic, there are hidden variables, etc.

  18. One possible reason why we do not see quantum non-equilibrium today is that there is relaxation from non-equilibrium to quantum equilibrium: if some non-equilibrium distributions existed in the past, they are quickly driven dynamically to quantum equilibrium (Colin, 2012).

  19. Although experimentally non-equilibrium states have not yet been created, according to Colin (2012), there have been simulations of the evolution of non-equilibrium distributions for two-dimensional systems (e.g. the two-dimensional Dirac oscillator and the Dirac particle in a two-dimensional spherical step potential).

  20. According to Colin and Valentini (2014), “it has been shown that non-Born rule distributions in pilot-wave theory can give rise to a wealth of new phenomena. These include non-local signalling—which suggests that the theory contains an underlying preferred foliation of space–time—and ‘sub-quantum’ measurements that violate the uncertainty principle and other standard quantum constraints. On this view, quantum physics is a special equilibrium case of a much wider non-equilibrium physics”.

  21. Acuña (2021) makes a similar point to Cushing (1995). According to Acuña (2021), “In quantum tunneling experiments, all theories can predict an average dwelling time within the barrier. Unlike other quantum theories, though, in Bohmian mechanics the concept of trajectory is well-defined. Thus, the tunneling time of reflected particles and the tunneling time of transmitted particles (which averaged over give the dwelling time) can be discerned and calculated”(Acuña, 2021; Cushing, 1995).

  22. See also Leavens and Aers (1993), Leavens (1996), McKinnon and Leavens (1995), and Muga and Leavens (2000) for more discussion on the calculation of arrival times.

  23. Also see Belousek (2003) for another causal version of BM which commits to the reality of the quantum potential, but not the wave function.

  24. The idea of domain separation can also be found in the literature of effective theories. An effective theory does not purport to give a complete account of the reality but only concerns its domain of application.

  25. In fact, Maudlin (2002) puts the point more assertively. According to Maudlin (2002), non-locality is unavoidable in any theory which recovers the predictions of quantum theory.

  26. Redhead also explains how to account for the statistical correlations in entanglement experiments, see Redhead (1983, 1986).

  27. Although Shimony (1990) argues that a violation of outcome independence can co-exist peacefully with special relativity, it does not imply that “there is nothing problematic” and we should try to clarify this kind of quantum nonlocality. Also, Peacock (1998) argues that “most or all of the standard arguments in favour of peaceful coexistence can be seen to be more or less question-begging”.

  28. In fact, there are attempts to detect the existence of the pilot wave from empirical testing, such as Cardone et al. (2004) and Petrucci (2019).

References

  • Acuña, P. (2021). Charting the landscape of interpretation, theory rivalry, and underdetermination in quantum mechanics. Synthese, 198(2), 1711–1740.

  • Acuña, P., & Dieks, D. (2014). Another look at empirical equivalence and underdetermination of theory choice. European Journal for Philosophy of Science, 4(2), 153–180.

    Article  Google Scholar 

  • Aharonov, Y., Oppenheim, J., Popescu, S., Reznik, B., & Unruh, W. G. (1998). Measurement of time of arrival in quantum mechanics. Physical Review A, 57(6), 4130.

    Article  Google Scholar 

  • Allori, V., & Zanghì, N. (2004). What is Bohmian mechanics. International Journal of Theoretical Physics, 43(7–8), 1743–1755.

    Article  Google Scholar 

  • Belousek, D. W. (2003). Formalism, ontology and methodology in Bohmian mechanics. Foundations of Science, 8(2), 109–172.

    Article  Google Scholar 

  • Belousek, D. W. (2005). Underdetermination, realism, and theory appraisal: An epistemological reflection on quantum mechanics. Foundations of Physics, 35(4), 669–695.

    Article  Google Scholar 

  • Boström, K. J. (2015). Is Bohmian Mechanics an empirically adequate theory?. arXiv preprint arXiv:1503.00201.

  • Bricmont, J. (2016). Making sense of quantum mechanics. Springer International Publishing.

    Book  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Colin, S. (2012). Relaxation to quantum equilibrium for Dirac fermions in the de Broglie–Bohm pilot-wave theory. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 468(2140), 1116–1135.

  • Colin, S., & Valentini, A. (2014). Instability of quantum equilibrium in Bohm's dynamics. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences (Vol. 470, No. 2171, p. 20140288). The Royal Society.

  • Cushing, J. T. (1994). Quantum mechanics: Historical contingency and the Copenhagen hegemony. University of Chicago Press.

    Google Scholar 

  • Cushing, J. (1995). Quantum tunneling times: A crucial test for the causal program. Foundations of Physics, 25, 269–280.

    Article  Google Scholar 

  • Das, S., & Dürr, D. (2019). Arrival time distributions of spin-1/2 particles. Scientific Reports, 9, 2242.

    Article  Google Scholar 

  • Dürr, D., Goldstein, S., & Zanghi, N. (1992). Quantum equilibrium and the origin of absolute uncertainty. Journal of Statistical Physics, 67, 843–907.

    Article  Google Scholar 

  • Dürr, D., Goldstein, S., & Zanghì, N. (1995). Bohmian mechanics and the meaning of the wave function. arXiv preprint quant-ph/9512031.

  • Dürr, D., Goldstein, S., & Zanghì, N. (2013). Quantum physics without quantum philosophy. Springer.

    Book  Google Scholar 

  • Dürr, D., Goldstein, S., Norsen, T., Struyve, W., & Zanghì, N. (2014). Can Bohmian mechanics be made relativistic? Proceedings of the Royal Society a: Mathematical, Physical and Engineering Sciences, 470(2162), 20130699.

    Article  Google Scholar 

  • Gisin, N. (2018). Why Bohmian mechanics? One-and two-time position measurements, Bell inequalities, philosophy, and physics. Entropy, 20(2), 105.

    Article  Google Scholar 

  • Glennan, S. (2017). The new mechanical philosophy. Oxford University Press.

    Book  Google Scholar 

  • Goldstein, S. (2010). Bohmian mechanics and quantum information. Foundations of Physics, 40(4), 335–355.

    Article  Google Scholar 

  • Goldstein, S. (2017). Bohmian mechanics. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Summer 2017 Edition). https://plato.stanford.edu/entries/qm-bohm/. Accessed 23 April 2018.

  • Goldstein, S., & Tumulka, R. (2003). Opposite arrows of time can reconcile relativity and nonlocality. Classical and Quantum Gravity, 20(3), 557.

    Article  Google Scholar 

  • Hacking, I. (1983). Representing and intervening: Introductory topics in the philosophy of natural science. Cambridge UP.

    Book  Google Scholar 

  • Healey, R. (1997). Nonlocality and the Aharonov-Bohm effect. Philosophy of Science, 64(1), 18–41.

    Article  Google Scholar 

  • Kitcher, P. (1993). The advancement of Science. Oxford University.

    Google Scholar 

  • Kocsis, S., Braverman, B., Ravets, S., Stevens, M. J., Mirin, R. P., Shalm, L. K., & Steinberg, A. M. (2011). Observing the average trajectories of single photons in a two-slit interferometer. Science, 332(6034), 1170–1173.

    Article  Google Scholar 

  • Psillos, S. (1996). Scientific realism and the’pessimistic induction’. Philosophy of Science, 63, S306–S314.

    Article  Google Scholar 

  • Lakatos, I. (1976). Falsification and the methodology of scientific research programmes. In Can theories be refuted? (pp. 205–259). Dordrecht: Springer.

  • Laudan, L., & Leplin, J. (1991). Empirical equivalence and underdetermination. The Journal of Philosophy, 88(9), 449–472.

    Article  Google Scholar 

  • Leavens, C., & Aers, G. (1993). Bohmian trajectories and the tunneling time problem. In R. Wiesendanger & J. Güntherodt (Eds.), Scanning tunneling microscopy III (pp. 105–140). Springer.

    Chapter  Google Scholar 

  • Leavens, C. (1996). The ‘tunneling time problem’ for electrons. In J. Cushing, A. Fine, & S. Goldstein (Eds.), Bohmian mechanics and quantum theory: An appraisal (pp. 11–130). Springer.

    Google Scholar 

  • Lewis, P. J. (2016). Quantum ontology: A guide to the metaphysics of quantum mechanics. Oxford University Press.

    Book  Google Scholar 

  • Maudlin, Tim. (2002). Quantum non-locality and relativity: metaphysical intimations of Modern Physics. Blackwell.

    Book  Google Scholar 

  • McKinnon, W. R., & Leavens, C. R. (1995). Distribution of delay times and transmission times in Bohm’s causal interpretation of quantum mechanics. Physical Review A, 51, 2748–2757.

    Article  Google Scholar 

  • Muga, J. G., & Leavens, C. R. (2000). Arrival time in quantum mechanics. Physics Reports, 338, 353–438.

    Article  Google Scholar 

  • Nikolić, H. (2005). Relativistic quantum mechanics and the Bohmian interpretation. Foundations of Physics Letters, 18(6), 549–561.

    Article  Google Scholar 

  • Peacock, K. A. (1998). On the edge of a paradigm shift: Quantum nonlocality and the breakdown of peaceful coexistence. International Studies in the Philosophy of Science, 12(2), 129–150.

    Article  Google Scholar 

  • Petrucci, A. (2019). Lorentz violation and quantum mechanics. In Journal of Physics: Conference Series (Vol. 1251, No. 1, p. 012040). IOP Publishing.

  • Redhead, M. (1983). Nonlocality and peaceful coexistence. In Space, Time and Causality (pp. 151–189). Springer.

  • Redhead, M. L. (1986). Relativity and quantum mechanics—conflict or peaceful coexistence? Annals of the New York Academy of Sciences, 480(1), 14–20.

    Article  Google Scholar 

  • Riggs, P. J. (2009). Quantum causality: conceptual issues in the causal theory of quantum mechanics (Vol. 23). Springer Science & Business Media.

  • Rivat, S. (2021). Effective theories and infinite idealizations: A challenge for scientific realism. Synthese, 198(12), 12107–12136.

  • Shimony, A. (1984), “Controllable and uncontrollable non-locality”, In: S. Kamefuchi et al. (eds), Foundations of Quantum Mechanics in Light of the New Technology, Tokyo: Physical Society of Japan, pp. 225–230. Reprinted in Shimony (1993), pp. 130–139.

  • Shimony, Abner. (1986). Events and processes in the quantum world. In R. Penrose & C. J. Isham (Eds.), Quantum concepts in space and time (pp. 182–203). Oxford University Press.

    Google Scholar 

  • Shimony, A. (1989). Search for a worldview which can accommodate our knowledge of microphysics. Philosophical Consequences of Quantum Theory, 25–37.

  • Shimony, A. (1990). An exposition of Bell’s theorem. In Sixty-two years of uncertainty (pp. 33–43). Boston, MA: Springer.

  • Suárez, M. (2015). Bohmian dispositions. Synthese, 192(10), 3203–3228.

  • Valentini, A. (2002). Subquantum information and computation. Pramana, 59(2), 269–277.

    Article  Google Scholar 

  • Van Fraassen, B. C. (1991). Quantum mechanics: An empiricist view. Oxford University Press.

    Google Scholar 

  • Worrall, J. (2011). Underdetermination, realism and empirical equivalence. Synthese, 180(2), 157–172.

    Article  Google Scholar 

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    Chunling Yan

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Yan, C. Underdetermination: A Realist Interpretation of Quantum Mechanics and Bohmian Mechanics. Found Sci 28, 529–550 (2023). https://doi.org/10.1007/s10699-022-09839-z

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