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Spontaneous Localization Theories with a Particle Ontology

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Do Wave Functions Jump?

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 198))

Abstract

Spontaneous localization theory is a quantum theory proposed by GianCarlo Ghirardi, together with Alberto Rimini and Tullio Weber in 1986. However, soon it became clear to Ghirardi that his work was more than just one theory: he actually developed a framework, a family of theories in which the wavefunction jumps, but where the ontology of the theory is underdetermined. After acknowledging that the wavefunction did not provide a satisfactory ontology, he assumed that matter was described by a continuous matter density field in three-dimensional space, whose evolution is governed by a stochastic wavefunction evolution. Alternatively, Bell assumed that the wavefunction would govern a spatiotemporal event ontology, dubbed ‘flashes.’ However, not much work has been done with the perhaps most obvious possibility, namely that physical objects are made of particles. This paper has two aims. First to explain the reason why people require spontaneous localization theory to be more than just a theory about the wavefunction. This is done by showing how the problem everyone in the foundation of quantum mechanics take to be the fundamental problem of quantum mechanics, namely the measurement problem, is a red herring. Then, the paper explores the possibility of spontaneous localization theories of particles. I argue that this discussion is not a mere exercise, as spontaneous localization theories of particles may be amenable to a relativistic extension which does not require a foliation, and because in general the peculiar type of indeterminism of spontaneous localization theories may help sheding new light on the nature of the tension between quantum theory and relativity.

Forthcoming in: V. Allori, A. Bassi, D. Dürr and N. Zanghí (eds.) Do Wave Functions Jump? Perspectives on the Work of GianCarlo Ghirardi. Springer.

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Notes

  1. 1.

    See e.g. Bell [2].

  2. 2.

    See Dürr et al. [7], Allori et al. [8,9,10], Allori [11,12,13,14,15].

  3. 3.

    That is, regardless of whether some coordinates \(r_{1} , r_{2} , \ldots ,r_{N}\), where N is the number of particles thought to exist in the universe (roughly of the order of \(10^{90}\)) can be interpreted as the position of real particles or not, the wavefunction is a function of a high-dimensional variable \(q = \left( {r_{1} , r_{2} , \ldots ,r_{N} } \right)\).

  4. 4.

    Se Allori [11,12,13,14,15,16] and references therein for an exposition of these arguments.

  5. 5.

    The reason for this is unclear, and I cannot fully explore this issue in this paper. Presumably however one could say that historically the theory developed and flourished after the proposal of the Schrödinger’s equation, and so from that moment on it seemed unthinkable to not consider it as part of the theory.

  6. 6.

    However, see Sect. 4 for more on this.

  7. 7.

    See Albert [17], Ney [18, 19] and references therein for proposals to make sense of this.

  8. 8.

    See Dürr et al. [7], Goldstein and Teufel [20], Goldstein and Zanghí [21], Allori [16] for a defense of the nomological approach. Since the wavefunction is part of the axioms of quantum theory, it can be naturally regarded as a Humean law (see [22,23,24,25]). There are other ways in which someone could think of the wavefunction, broadly speaking, as nomological. One can think of the wavefunction as a property which expresses some non-material aspect of the particles [26]. Similarly, one can endorse a dispositional account where laws are understood in terms of dispositions, which in turn are described by the wave-function [27, 28]. Arguably, since dispositions can be time dependent, the objection to the nomological view that laws of nature are time independent while the wavefunction evolves in time seems less compelling here. Having said that, I think these proposals are not very promising in that they rely on the notion of properties which are notoriously a rough nut to crack. As Esfeld [24] has pointed out, there are several severe problems in trying to spell out what fundamental properties are, both in the classical and the quantum domain. On a different tone, let me notice that the objection that in theories with the wavefunction only there are two spaces involved and the relationship between these spaces is a mystery closely resembles one of the objection against Cartesian dualism: if mental states are not in three-dimensional space, how are they interacting with physical states? With this analogy in mind, one can argue that the answer of the proponents of the POA will be similar to the one of the reductive physicalist, presumably a functionalist: the wavefunction is whatever function it plays to generate the empirical data (see [15] for more on this).

  9. 9.

    For more, see Allori [15].

  10. 10.

    See Egg and Esfeld [30], Esfeld and Deckert [31].

  11. 11.

    Here’s a sketch of some possible responses. To the objection that flashes are counterintuitive one could reply that a satisfactory explanation can lead us far from common sense, so sometimes getting away from commonsensical explanation may be the right thing to do. For instance, while common sense suggests that matter is continuous, atomic theory has shown us that it is not the case: atomic theory, with its in-breath and in-depth explanatory power, is a better explanation of the behavior of matter than our common sense. So, we are justified in accepting atomic theory even if it pictures a world which is distant from what we initially thought. Moreover, the reply goes, in the case of GRWf abandoning common sense for an unfamiliar ontology makes the theory more compatible with relativity, as suggested by Bell (however, see Sect. 6). Also, one could question the fact that the ontology and the explanation is really counterintuitive in a negative sense. It is true that the action of fields is continuous even if there are no flashes. However, this is a problem only if the field are intended as material, which in the POA is not necessarily the case: they could be taken to be not generated by the particles, but rather alike to nomological entities, similarly to what happens for the wavefunction in quantum theory (see Allori [14] for a discussion of this). Also, see Esfeld [32] for a defense of GRWf. To the objection that the matter density has tails which could be crossed by other objects without any visible interaction, one could arguably maintain that this is counterintuitive merely when we look at things from a classical perspective: only because classically matter which encounters other matter interacts with it, it does not mean that it has to be the case in the quantum domain. Moreover, the fact that the quantum formalism is in terms of particles does not seem to force us to interpret it as a theory of particles, as one could presumably endorse the formalism of a continuous localization theories (CSL) which does not require particles [32]. Finally nonlocality is a puzzle for all theories, not merely GRWm, so that it is unclear how serious the last objection actually is.

  12. 12.

    See Allori et al. [8, 10], Bedingham [35], Allori [15].

  13. 13.

    However, see Bohm and Hiley [36], p. 346.

  14. 14.

    Other particle theories, aside from the pilot-wave theory, are stochastic mechanics [37], and Bell-type quantum field theories [38,39,40]. In both theories the wavefunction evolves deterministically, in contrast with GRW-type particle theories. In the former the particles evolve according to a stochastic Markov process, while in the latter the evolution is also stochastic but the particles can also be created and destroyed.

  15. 15.

    For more on empirical coherence, see Barrett [41], Huggett and Wüthrich [42].

  16. 16.

    See Dürr et al. [46, 47].

  17. 17.

    For a criticism, see Barret [49] and Esfeld and Gisin [50], who argue that these theories, even if they are Lorentz invariant in terms of the overall histories of their PO, are unable to describe single events in a relativistic invariant way.

  18. 18.

    Another interesting attempt of a relativistic pilot-wave theory without a foliation has been proposed by Sutherland [52, 53], which however involves retrocausation.

  19. 19.

    Of course, if the rGRWp proposed above requires a microscopic inverse arrow of time, then this may be taken to diminish the explanatory power of the theory. However, since the theory has yet to be constructed this kind of considerations seem premature.

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Authors and Affiliations

  1. Department of Philosophy, Northern Illinois University, Dekalb, IL, USA

    Valia Allori

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Editors and Affiliations

  1. Department of Philosophy, Northern Illinois University, Naperville, IL, USA

    Valia Allori

  2. Department of Physics, University of Trieste, Trieste, Italy

    Angelo Bassi

  3. Mathematisches Institut, LMU, Munich, Germany

    Detlef Dürr

  4. Dipartimento di Fisica INFN-Sezion, Universitá di Genova, Genoa, Italy

    Nino Zanghi

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Allori, V. (2021). Spontaneous Localization Theories with a Particle Ontology. In: Allori, V., Bassi, A., Dürr, D., Zanghi, N. (eds) Do Wave Functions Jump? . Fundamental Theories of Physics, vol 198. Springer, Cham. https://doi.org/10.1007/978-3-030-46777-7_7

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