Abstract
The violation of Bell’s inequality has shown that quantum theory and relativity are in tension: reality is nonlocal. Nonetheless, many have argued that GRW-type theories are to be preferred to pilot-wave theories as they are more compatible with relativity: while relativistic pilot-wave theories require a preferred slicing of space-time, foliation-free relativistic GRW-type theories have been proposed. In this paper I discuss various meanings of ‘relativistic invariance,’ and I show how GRW-type theories, while being more relativistic in one sense, are less relativistic in another. If so, the initial claim that GRW-type theories have a greater compatibility with relativity is unwarranted: both type of theories violate relativity, one way or another.
Similar content being viewed by others
Notes
For sake of precision, however, notice that the theory originally proposed by Bohm (1952) is arguably not the same theory as the one developed by Dürr, Goldstein and Zanghí (1992), and now known as Bohmian mechanics. In fact, both are theories of particles; however, in Bohm’s theory is a first-order theory in which the wavefunction is considered a real physical field in space, and there is a quantum potential, while nothing of the sort is present in Bohmian mechanics (see Dürr et al. for a comparison). Nonetheless, it is common practice among physicists interested in foundations and philosophers of physics to use the locutions ‘Bohmian mechanics’ and ‘de Broglie-Bohm pilot-wave theory’ interchangeably (see e.g., Bricmont 2016b, Norsen 2016). In the following, I will not consider Bohm’s theory.
Also in this case, it has been argued that Everett did not endorse a many-worlds interpretation of his formulation of quantum mechanics (see Barrett and Byrne 2012). Nonetheless, it seems common practice among philosophers of physics and physicists to understand ‘Everettian mechanics’ to denote the many-worlds theory.
For other attempts, see Bassi and Ghirardi (2020) and references therein.
See, e.g., Goldstein et al. (2011), Vaidman (2016). However, see also Norsen (2016). For an explicitly nonlocal many-worlds theory within the primitive ontology framework see Allori et al. (2014). In addition, let me notice that, if one takes Bell’s theorem as a general argument for nonlocality, every theory will have to be nonlocal, including the many-worlds theory.
Among these theories one also finds the so-called modal interpretation. Since it has been argued (e.g., Myrvold 2002a) that they suffer from the same difficulties as the pilot-wave theory, in this paper I will only discuss the latter because it is simpler. For additional discussion on the modal interpretation and its compatibility with relativity, see also Myrvold (2009, 2021).
Goldstein (2017) and references therein.
See, e.g., Allori et al. (2008).
Allori et al. (2008).
Nelson (1985). Otherwise, in Bell-type quantum field theory, a stochastic evolution of the particles allows for creation and annihilation (see Bell 1986, Dürr et al. 2004; 2005; nonetheless, one could arguably describe particle creations and annihilations even with a deterministic dynamics, see Colin 2003, Colin and Struyve 2007; see also Nikolić 2010; for discussion, see also Oldofredi 2020).
There are two new constants of nature, the localization accuracy \(d={10}^{-7}\) m, and the localization frequency \(f={10}^{-16} {s}^{-1}\), so that microscopic systems localize on average every hundred million years, while macroscopic systems every \({10}^{-7}\) seconds. There is a more general class of GRW-like theories, namely theories in which the wavefunction spontaneously collapses, which goes under the name of CSL, continuous spontaneous localization, which is an extension of the GRW logic (see Bassi and Ghirardi 2020). I will include these theories under the label ‘GRW-type theories.’
Bell (1987).
The matter density function has been introduced in Benatti et al. (1995). It is considered as a possible primitive ontology explicitly in Allori et al. (2008).
Notice that a stochastically evolving primitive ontology (a ‘stochastic primitive ontology’) has been combined with a deterministically evolving wavefunction (a ‘deterministic wavefunction’), like in Sf, stochastic mechanics or certain Bell-type quantum field theories. Also, a ‘stochastic primitive ontology’ has been paired with a stochastically evolving wavefunction (a ‘stochastic wavefunction’), as for instance in all GRW-type theories. Instead, a deterministically evolving primitive ontology (a ‘deterministic primitive ontology’) has only been successfully combined with a deterministically evolving wavefunction (a ‘deterministic wavefunction’), as in the original de Broglie-Bohm pilot-wave theory.
In this reconstruction I follow Goldstein et al. (2011), Maudlin (2011), Norsen (2016), Bricmont (2016a). I assume that this reconstruction is correct, as my main goal in this paper is to show that, even granting that Bell has shown that reality is nonlocal, it is still problematical to think that GRW theories are more compatible with relativity than the pilot-wave theory. Indeed, most people who argue that GRW theories are more compatible with relativity than pilot-wave theories accept this reconstruction.
Einstein, Podolsky and Rosen (1935). See also Eisntein (1948).
Think for instance about the objections to Newton’s theory of gravitation. Newton agreed it was a problem and replied that his theory was incomplete, and that a future, better, theory should make this action at a distance go away (see Norsen 2011).
This is due to the relativity of simultaneity: since two spacelike separated observers, namely observers such that a signal connecting them would have to propagate faster than light, will disagree on the temporal ordering of events, to avoid causal chains to go backwards one requires physical influences to travel slower than the speed of light.
When Alice measures spin up in one direction, Bob will measure spin down in that direction.
It is interesting to notice, as emphasized by Norsen (2011), that EPR’s conclusion that quantum theory is incomplete is similar in spirit to Newton’s reply to the objection that his theory requires action at a distance (see footnote 21).
Bell (1990).
For more on Bell’s notion of local causality and on local beables, see Norsen (2011).
However, see Allori (2021) for a distinction.
Notice, in passing, that this requirement seems to rule out the many-worlds theory: since it is only about the evolution of the wavefunction, it does not have any local beables.
Aspect et al. (1982).
For discussions of Bell’s proof in general, see e.g., the contributions to Gao and Bell (2016).
Bell (1987).
For more on retrocausality in quantum mechanics, see e.g., Freidman (2019) and references therein.
At some point, this is what Bell seemed to have argued, at least according to Norsen (2011).
Bell (1987).
Some have also maintained that there is the additional problem that a relativistic quantum theory needs to be a field theory (Malament 1996; see also Myrvold 2021). I will not consider this difficulty in this paper because, as I will be evident in the text, the point I wish to make arises independently of this issue.
See Leinert et al. (2020), and references therein.
Notice that this type of theories is nonlocal regardless of the ontological status of the wavefunction. Nonlocality is particularly explicit if one thinks of the wavefunction as a field in configuration space (see e.g., Albert 2015, Ney 2020), or as a part of the structure of the law of interaction among of the particles (Goldstein and Zanghì 2013, Allori 2020b). It is less explicit if one considers the wavefunction to be a multi-filed in three-dimensional space (Forrest 1988; Belot 2012, Hubert and Romano 2017), or tentatively eliminated (Norsen 2015) but the nonlocality of the interaction is still there.
Berndl et al. (1996), Dürr et al. (1999).
See also Maudlin (1996).
Technically, the worry is that one could make anything relativistic invariant (or invariant with respect to any transformation) by adding suitable structure. Take a non-Lorenz invariant theory with primitive ontology \(P\) and law \(L\). That means that the ‘trajectories’ of \(P\) (i.e., their worldlines), when transformed according to the Lorentz group, are no longer solutions (that is, they are no longer possible states of affairs of the world). However, we can always add something to the primitive ontology, so that \(P?=(P,X)\), in such a way that by stipulation the new law \(L?\) would transform solutions into solutions under the Lorentz group. Such theory would be Lorentz invariant, but not genuinely so (see Bell 1987, Berndl et al. 1996).
Dürr et al. (2013).
Tumulka (2007).
This is because the flashes are constructed here in generations, and the distribution of a flash depends upon which of the other flashes belong to the same or the previous generation.
Other relativistic pilot-wave theories have been proposed, but are not viable, as they have no equivariant measure and therefore they have predictions which are inconsistent with quantum mechanics. They all use the multi-time formalism and Lorentz invariant equations for the wavefunction. For instance, in one proposal (Berndl et al. 1996; Dewdney and Horton 2001; Nikolić 2005) a current vector defined by the wavefunction generates spatiotemporal paths parametrized by a common parameter. Moreover, another proposal is Lorentz invariant without a foliation, as it uses the light-cone structure as simultaneity structure (Goldstein and Tumulka 2001, Tumulka 2007) but it has a backward microscopic arrow of time (a theories defined on the past light-cone would have been local). This theory does not describe interactions and has no equivariant measure. However, it constitutes an example on how one can use the spacetime structure to achieve nonlocality, by allowing for retrocausality.
This can be seen as the non-relativistic shadow of Lorentz invariance, because it is equivalent to assuming that absolute simultaneity plays no role in the theory: if it would, then the two times in two distant systems could not be shifted independently.
See also Maudlin (2011).
Some other attempts to relativistic GRW-type theories have been proposed which do not use the multi-time wavefunction but still have a Lorentz invariant stochastic evolution (see for instance, Bedingham 2011, Pearle 2015). This is of no consequence for the main conclusion of this paper, as I will show in Sect. 6, because the stochasticity of the evolution of the wavefunction, regardless of how this stochasticity is implemented, is the relevant ingredient.
For completeness, let me mention other proposals for relativistic spontaneous collapse theories. Some early proposals are found in Pearle (1990); Ghirardi, Grassi and Pearle (1990) but have been recognized to be problematical (see Bassi and Ghirardi 2020). Dowker and Henson (2004) construct a spontaneous collapse theory which is very similar to rGRWm, but it is defined on a lattice spacetime. It is a theory with a primitive ontology of field values at the lattice sites, and it is Lorentz invariant in the ‘correct lattice sense.’ Dove and Squires (1995) extend a previous proposal by Hellwig and Kraus (1970) developed in the context of ordinary quantum theory to a flash GRW theory. In this model, the wavefunction collapses along the past light-cone of the spacetime point at which a measurement takes place. However, the theory involves retrocausation, as explained in Tumulka (2009). Also, they only propose a Lorentz-invariant collapse rule for the wavefunction given the flashes, but no distribution law for the flashes. For more discussion on these theories, see Ghirardi and Bassi (2020), Tumulka (2006a,b, 2007).
Norsen (2010a).
It seems important to notice that the situation may be made less severe in this respect by considering the wavefunction as a multi-field in three-dimensional space, or not as part of the ontology of matter (for instance, one could consider the wavefunction part of the law of these theories). Similarly, Rovelli’s relational interpretation (1996) or Bub and Pitowsky information-theoretic account of quantum theory (2010), seem to be in a better position in this respect (even if by considering the wavefunction as epistemic they run into other problems, see e.g. Norsen 2016). Nonetheless, in addition to the ontology being local, one would also have to face the fact that the interaction is nonlocal, and this is what Bell has shown. Therefore, the advantage of these formulations seems minimal in this respect.
Norsen, p.c.
That is, no ‘spooky action at a distance’ (Einstein, Born 1971).
This idea has been criticized by Maudlin (2011).
Dürr et al. (2013).
A remark on the meaning of ‘foliation-free theory.’ This terminology should be taken to mean that there is no preferred foliation with a dynamical role. That is, the dynamical laws do not involve any such structure. In particular, as mentioned earlier, the fact that one could extract a preferred foliation from the wavefunction, does not imply that every quantum theory, in virtue of having a wavefunction, will also have a preferred foliation, because such foliation could be not dynamical.
See e.g., Dürr et al. (2016) on this point.
Tumulka (2009).
In GRWf and GRWm, as well as in rGRWf and rGRWm, the flashes are distributed as dictated by the collapses of the wavefunction and the matter density is defined as.
\(m\left(x,t\right)=\sum _{i=1}^{N}{m}_{i}\int d{q}_{1}\dots d{q}_{N}{\delta }^{3}\left({q}_{i}-x\right){\left|{\psi }_{t}\left({q}_{1}\dots {q}_{N},t\right)\right|}^{2},\)where \(N\) is the number of ‘particles,’ and \({m}_{i}\) are their masses.
They are doubly deterministic in the sense that both the particles and the wavefunction evolve deterministically (respectively according to the guidance equation and the Schrödinger equation).
As discussed in Goldstein and Tumulka (2001), and in Tumulka (2007), a theory using past light-cones is local.
See Allori (2020a) and references therein.
The first to propose to rewrite the locality condition in terms of two different conditions was Jarrett (1984), and he distinguished between ‘simple locality’ and ‘completeness.’ His conclusions have been criticized especially by Norsen (2009) and Maudlin (2011). The terminology ‘parameter independence’ and ‘outcome independence’ is by Shimony (1984) and seem to better characterize the content of these conditions.
Maudlin (2011), Goldstein p.c., Norsen p.c.
Assuming there is no retrocausation. See also Ghirardi et al. (1993).
See also Lewis (2003), McQuinn (2015) and references therein for more.
For a small macroscopic object made of roughly \({10}^{19}\) ‘particles,’ if each ‘particle’ undergoes a collapse every \({10}^{16}\) seconds, there is a flash roughly once every \({10}^{-3}\) seconds, and nothing at all in between.
However, within the primitive ontology framework some have maintained that fields should be seen as part of the law too, just as the wavefunction (Allori 2015). If so, the objection seems less severe.
However, Allori (2018) has argued that this is still possible.
See e.g., Monton (2002, 2006, 2013), Allori et al. (2008, 2011), Albert (2013, 2015), Allori (2013b), Emery (2017), Maudlin (2019). See replies in Albert (2015), Ney (2021) and references therein. Notice however, that these replies aim at recovering the appearances of macroscopic three-dimensional objects from the wavefunction, so they do not dispute the unfamiliarity of their ontology.
At east most of them, if one does not consider, for instance, Bell-type quantum field theories.
This is in a 1926 letter to Born; in Born and Einstein (1971).
See also Ghirardi and Grassi (1996), Esfeld and Gisin (2014), Myrvold (2016).
However, see Allori (2019b).
See also Einstein’s distinction between constructive and principle theories (1919). Constructive theories are theories in which the macroscopic phenomena are accounted for in terms of the microscopic dynamics, while principle theories constrain the phenomena with principles which govern what can and cannot happen. Flores (1999) has argued that constructive theories are compatible with Salmon’s mechanistic explanation (1987), principle theories can be tied to unification approaches such as the ones of Friedman (1974), Kitcher (1989). See also Felline (2011).
The current models of explanatory unification generalize the idea that explanations are arguments (developed by the deductive-nomological model), and therefore are committed to the so-called ‘expectability thesis:’ a unifying explanation must show how the explanandum is to be expected from the explanans. With stochastic laws, events with a low probability of happening cannot be expected. One possible reply is to use van Camp’s proposal (2011) that principle theories unify in the sense that they provide the conceptual schema necessary to talk about explanation within a theory in the first place. The idea is that principle theories play a distinctive conceptual role as necessary preconditions for explanation (see also DiSalle 2006).
Tumulka (2006b) similarly argues that the direction of influence is indeterminate.
See e.g., Lewis (2021).
Myrvold (2002).
See e.g., Maudlin (2011), Bedingham et al. (2013), Bassi and Ghirardi (2020).
This experiment has been first proposed by Einstein; see Norsen (2005).
Bricmont (2016b).
Norsen p.c.
I am grateful to an anonymous reviewer for pressing me on this point.
References
Albert, D.Z.: After Physics. Cambridge University Press (2015)
Allori, V.: “Primitive Beable is not Local Ontology: On the Relation between Primitive Ontology and Local Beables.” Crítica 53 (159): 15–43 (2021). (2021)
Allori, V.: “Spontaneous Localization Theories with a Particle Ontology.” In: V. Allori, A. Bassi, D, Dürr and N. Zanghì (eds.) Do Wavefunctions Jump? Perspectives on the Work of GianCarlo Ghirardi: 73–93. Springer (2020). (2020a)
Allori, V.: “Why Scientific Realists Should Reject the Second Dogma of Quantum Mechanics.” In: M. Hemmo and O. Shenker (eds.) Quantum, Probability, Logic: the Work and Influence of Itamar Pitowsky: 19–48. Springer (2020). (2020b)
Allori, V.: “Scientific Realism without the Wave-Function”. In: Saatsi, J., French, S. (eds.) Scientific Realism and the Quantum, pp. 212–228. Oxford University Press (2019a)
Allori, V.: Quantum Mechanics, Time and Ontology. Stud. History Philos. Mod. Phys. 66, 145–154 (2019b)
Allori, V.: Primitive Ontology and Scientific Realism. Or: The Pessimistic Meta-Induction and the Nature of the Wavefunction. Lato Sensu: Revue de la Société de Philosophie des Sciences. 5(1), 69–76 (2018)
Allori, V.: Primitive Ontology in a Nutshell. Int. J. Quantum Found. 1(3), 107–122 (2015)
Allori, V.: “Primitive Ontology and the Structure of Fundamental Physical Theories.”. In: Albert, D., Ney, A. (eds.) The Wavefunction: Essays in the Metaphysics of Quantum Mechanics, pp. 58–75. Oxford University Press (2013a)
Allori, V.: “On the Metaphysics of Quantum Mechanics.” In S. Lebihan (ed.) Precis de la Philosophie de la Physique: 116–151. Vuibert. (2013b)
Allori, V., Goldstein, S., Tumulka, R., Zanghì, N.: Predictions and Primitive Ontology in Quantum Foundations: A Study of Examples. Br. J. Philos. Sci. 65(2), 323–352 (2014)
Allori, V., Goldstein, S., Tumulka, R., Zanghì, N.: “Many-Worlds and Schrödinger’s First Quantum Theory.” The British Journal for the Philosophy of Science 62 (1), 1–27 (2011). (2011)
Allori, V., Goldstein, S., Tumulka, R., Zanghì, N.: “On the Common Structure of Bohmian Mechanics and The GRW Theory.” The British Journal for the Philosophy of Science 59 (3): 353–389. (2008)
Aspect, A., Dalibard, J.: and Gérard Roger. “Experimental Test of Bell’s Inequalities Using Time-varying Analyzers.” Physical Review Letters 49(25): 1804–1807. (1982)
Baas, A., Bihan, B.L., Forthcoming:). “What Does the World Look like According to Superdeterminism?”The British Journal for the Philosophy of Science
Barrett, J.: “Everett’s Relative-State Formulation of Quantum Mechanics.” The Stanford Encyclopedia of Philosophy (Winter 2014 Edition), Edward N. Zalta (ed.), (2018). https://plato.stanford.edu/entries/qm-everett/
Barrett, J., Byrne, P. (eds.): The Everett Interpretation of Quantum Mechanics: Collected Works 1955–1980 with Commentary. Princeton University Press (2012)
Bassi, A.: and GianCarlo Ghirardi. “Collapse Theories.” The Stanford Encyclopedia of Philosophy (Winter 2014 Edition), Edward N. Zalta (ed.), (2020). https://plato.stanford.edu/entries/qm-collapse/
Bedingham, D.: Relativistic State Reduction Dynamics. Foundation of Physics. 41, 686–704 (2011)
Bedingham, D., Dürr, D., Ghirardi, G.C., Goldstein, S., Tumulka, R., Zanghì, N.: Matter Density and Relativistic Models of Wavefunction Collapse. J. Stat. Phys. 154(1–2), 623–631 (2014)
Belot, G.: Quantum States for Primitive Ontologists. Eur. J. Philos. Sci. 2(1), 67–83 (2012)
Bell, J.S.: Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press, Cambridge (1987)
Bell, J.S.: Quantum Field Theory without Observers. Phys. Rep. 137, 49–54 (1986)
Bell, J.S.: “La Nouvelle Cuisine.”. In: Sarlemijn, A., Kroes, P. (eds.) Between Science and Technology. Elsevier (1990)
Benatti, F., Ghirardi, G.C., and Renata Grassi: Describing the Macroscopic World: Closing the Circle within the Dynamical Reduction Program. Found. Phys. 25, 5–38 (1995)
Berndl, K., Dürr, D., Goldstein, S., Zanghì, N.: Nonlocality, Lorentz Invariance, and Bohmian Quantum Theory. Phys. Rev. A. 53, 2062–2073 (1996)
Bohm, D.: “A Suggested Interpretation of the Quantum Theory in Terms of ‘Hidden’ Variables, I and II. ” Phys. Rev. 85, 166–193 (1952)
Born, M., and Albert Einstein: Born-Einstein Letters, 1916–1955: Friendship, Politics and Physics in Uncertain Times. MacMillan (1971)
Bricmont, J.: “Probabilistic Explanations and the Derivation of Macroscopic Laws.”. In: Allori, V. (ed.) Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature, pp. 31–64. World Scientific (2020)
Bricomnt, J.: “What Did Bell Really Prove?”. In: Gao, S., Bell, M. (eds.) Quantum Nonlocality and Reality, pp. 49–78. Cambridge University Press (2016a)
Bricmont, J.: Making Sense of Quantum Mechanics. Springer (2016b)
Bub, J. and Itamar Pitowsky: “Two Dogmas about Quantum Mechanics.”. In: Saunders, S., Barrett, J., Kent, A., Wallace, D. (eds.) Many Worlds?: Everett, Quantum Theory, and Reality, pp. 433–459. Oxford University Press (2010)
Butterfield, J.: Bell’s Theorem: What it Takes. Br. J. Philos. Sci. 43, 41–83 (1992)
Butterfield, J., Fleming, G.N., Ghirardi, G.C., Grassi, R.: Parameter Dependence in Dynamical Models for Statevector Reduction. Int. J. Theor. Phys. 32(12), 2287–2304 (1993)
Chen, E.K.: “Bell’s Theorem, Quantum Probabilities, and Superdeterminism.” In: E. Knox, and A. Wilson (eds.) The Routledge Companion to Philosophy of Physics. Routledge: 181–199. (2021)
Clauser, J.F., Horne, M.A., and Abner Shimony: An Exchange on Local Beables. Dialectica. 39, 86–110 (1985)
Colin, S.: A Deterrministic Bell Model. Phys. Lett. A. 317(5–6), 349–358 (2003)
Colin, S., and Ward Struyve: A Dirac Sea Pilot-wave Model for Quantum Field Theory. J. Phys. A. 40(26), 7309–7341 (2007)
Cushing, J., McMullin, E. (eds.): Philosophical Consequences of Quantum Theory. Notre Dame (1989)
DiSalle, R.: Understanding Space-Time. Cambridge University Press (2006)
Dewdney, C., Horton, G.: A Non-Local, Lorentz-Invariant, Hidden-Variable Interpretation of Relativistic Quantum Mechanics Based on Particle Trajectories. J. Phys. A. 34, 9871–9878 (2001)
Dorato, M., Esfeld, M.A.: GRW as an Ontology of Dispositions. Stud. History Philos. Sci. B. 41 (1), 41–49 (2010)
Dove, C., Squires, E.J.: Symmetric Versions of Explicit Wavefunction Collapse Models. Found. Physic. 25, 1267–1282 (1996)
Dowker, F., and Joe Henson: Spontaneous Collapse Models on a Lattice. J. Stat. Phys. 115, 1327–1339 (2004)
Dürr, Detlef: Sheldon Goldstein, Karin Münch-Berndl, and Nino Zanghì. 1999. “Hypersurface Bohm–Dirac Models.”Physical Review A60:2729–2736
Dürr Detlef, S., Goldstein, T., Norsen, W., Struyve: and Nino Zanghì. “Can Bohmian Mechanics be Made Relativistic?” Proceedings of the Royal Society A 470(2162): 20130699. (2014)
Dürr Detlef, S., Goldstein, R., Tumulka, Zanghì, N.: Bell-Type Quantum Field Theories. J. Phys. A. 38, R1–R43 (2005)
Dürr Detlef, S., Goldstein, R., Tumulka, Nino, Zanghì: Bohmian Mechanics and Quantum Field Theory. Phys. Rev. Lett. 93, 090402 (2004)
Dürr Detlef, S., Goldstein, T., Norsen, W., Struyve, Zanghì, N.: “Can Bohmian Mechanics be Made Relativistic?” Proceedings of the Royal Society A 470: 20130699. (2013)
Dürr Detlef, S., Goldstein, Zanghì, N.: Quantum Equilibrium and the Origin of Absolute Uncertainty. J. Stat. Phys. 67, 843–907 (1992)
Egg, M.: “Quantum Ontology without Speculation.” European Journal for the Philosophy of Science 11 (32). (2021)
Egg, M., Esfeld, M.A.: Primitive Ontology and Quantum State in the GRW Matter Density Theory. Synthese. 192(10), 3229–3245 (2015)
Egg, M., and Juha Saatsi: Scientific Realism and Underdetermination in Quantum Theory. Philos. Compass. 16(11), e12773 (2021)
Einstein, A.: “What is the Theory of Relativity?”The London Times. (1919)
Einstein, A.: Quantum Mechanics and Reality. Dialectica. 2, 320–324 (1948)
Einstein, A., Max Born: The Born-Einstein Letters: 1916–1955. Friendship, Politics and Physics in Uncertain Times. Walker and Company (1971)
Einstein, A., Podolsky, B., and Nathan Rosen: Can Quantum-mechanical Description of Physical Reality be Considered Complete? Phys. Rev. 47, 777–780 (1935)
Emery, N.: Against Radical Quantum Ontologies. Philos. Phenomenol. Res. 95(3), 564–591 (2017)
Esfeld, M.A.: “From the Measurement Problem to the Primitive Ontology Programme.“. In: Allori, V., Bassi, A., Dürr, D., Zanghì, N. (eds.) Do Wavefunctions Jump? Perspectives of the Work of GianCarlo Ghirardi, pp. 95–108. Springer (2020)
Esfeld, M.A., and Nicolas Gisin: “The GRW Flash Theory: a Relativistic Quantum Ontology of Matter in Spacetime? Philos. Sci. 81(2), 248–264 (2014)
Esfeld, M.A., Lazarovici, D., Lam, V., and Mario Hubert: The Physics and Metaphysics of Primitive Stuff. Br. J. Philos. Sci. 68(1), 133–161 (2017)
Felline, L.: Scientific Explanation between Principle and Constructive Theories. Philos. Sci. 78(5), 989–1000 (2011)
Flores, F.: Einstein’s Theory of Theories and Types of Theoretical Explanation. Int. Stud. Philos. Sci. 13(2), 123–134 (1999)
Forrest, P.: Quantum Metaphysics. Blackwell, Oxford (1988)
Friedman, S.: “Retrocausality in Quantum Mechanics.” The Stanford Encyclopedia of Philosophy (Winter 2014 Edition), Edward N. Zalta (ed.), (2019). https://plato.stanford.edu/entries/qm-retrocausality/
Friedman, M.: “Explanation and Scientific Understanding.”Journal of Philosophy:5–19. (1974)
Frigg, R., and Carl Hoefer: Probability in GRW Theory. Stud. History Philos. Sci. B. 38(2), 371–389 (2007)
Gao, S., Bell, M. (eds.): Quantum Nonlocality and Reality:50 Years of Bell’s Theorem. Cambridge University Press. (2016)
Ghirardi, G.C.: Does Quantum Nonlocality Irremediably Conflict with Special Relativity? Found. Phys. 40, 1379–1395 (2012)
Ghirardi, G., and Renata Grassi: “Bohm’s Theory Versus Dynamical Reduction.”. In: Cushing, J., Fine, A., Goldstein, S. (eds.) Bohmian Mechanics and Quantum Theory: An Appraisal, pp. 353–377. Springer (1996)
Ghirardi, G., Grassi, R., and Philip Pearle: Relativistic Dynamical Reduction Models: General Framework and Examples. Found. Phys. 20, 1271–1316 (1990)
Gisin, N.: Quantum Measurements and Stochastic Processes. Phys. Rev. Lett. 52(19), 1657–1660 (1984)
Goldstein, S.: “Bohmian Mechanics. The Stanford Encyclopedia of Philosophy (Winter 2014 Edition), Edward N. Zalta (ed.), (2017). https://plato.stanford.edu/entries/qm-bohm/
Goldstein, S.: “Typicality and Notions of Probability in Physics.”. In: Ben-Menahem, Y., Hemmo, M. (eds.) Probability in Physics:, pp. 59–71. Springer (2012)
Goldstein, S., Norsen, T.: Daniel Tausk, and Nino Zanghí. 2011. “Bell’s Theorem.”Scholarpedia6(10):8378
Goldstein, S., and Roderich Tumulka: Opposite Arrows of Time Can Reconcile Relativity and Nonlocality. Class. Quantum Gravity. 20, 557 (2001)
Goldstein, S., and Nino Zanghí: “Reality and the Role of the Wavefunction. In Quantum Theory.”. In: Albert, D., Ney, A. (eds.) The Wave-function: Essays on the Metaphysics of Quantum Mechanics, pp. 91–109. Oxford University Press, New York (2013)
Hellwig, K.E., Kraus, K.: Formal Description of Measurements in Local Quantum Field Theory. Phys. Rev. D. 1, 566–571 (1970)
Hossenfelder, S., and Tim Palmer: Rethinking Superdeterminism. Front. Phys. 8, 139 (2020)
Hubert, M.: and Davide Romano. “The Wave-Function as a Multi-Field.”European Journal for Philosophy of Science:1–17. (2018)
Jarrett, J.: On the Physical Significance of the Locality Conditions in the Bell Arguments. Nous. 18, 569–589 (1984)
Kitcher, P.: “Explanatory Unification and the Causal Structure of the World.” In: P. Kitcher and W. Salmon (eds.) Minnesota Studies in the Philosophy of Science 13: 410–503. University of Minnesota Press. (1989)
Lazarovici, D., and Paula Reichert: Typicality, Irreversibility and the Status of Macroscopic Laws. Erkenntnis. 80(4), 689–716 (2015)
Lewis, P.J.: “Collapse Theories.” In: E. Knox, and A. Wilson (eds.) The Routledge Companion to Philosophy of Physics. Routledge: 247–256. (2021)
Lewis, P.J.: “On Closing the Circle.”. In: Allori, V., Bassi, A., Dürr, D., Zanghí, N. (eds.) Do Wavefunctions Jump? Perspectives of the Work of GianCarlo Ghirardi, pp. 121–134. Springer (2020)
Lewis, P.J.: In Search of Local Beables. Int. J. Quantum Found. 1, 215–229 (2015)
Lewis, P.J.: Four Strategies for Dealing with the Counting Anomaly in Spontaneous Collapse Theories of Quantum Mechanics. Int. Stud. Philos. Sci. 17(2), 137–142 (2003)
Lienert, Matthias, Sören Petrat, and Roderich Tumulka. 2020. Multi-time Wavefunctions: An Introduction.Springer
Maudlin, T.: Philosophy of Physics: Quantum Theory. Princeton University Press (2019)
Maudlin, T.: Quantum Non-Locality and Relativity (Third Edition). Blackwell. (2011)
Maudlin, T.: “Space-Time in the Quantum World.”. In: Cushing, J., Fine, A., Goldstein, S. (eds.) Bohmian Mechanics and Quantum Theory: An Appraisal, pp. 285–306. Springer (1996)
Malament, D.: In Defense of Dogma: Why There Cannot be a Relativistic Quantum Mechanics of (Localizable) Particles. In: Clifton, R. (ed.) Perspectives on Quantum Reality: Non-Relativistic, Relativistic, and Field-Theoretic, pp. 1–10. Kluwer Academic Publishers (1996)
McQueen, K.J.: Four Tails Problems for Dynamical Collapse Theories. Stud. History Philos. Mod. Phys. 49, 10–18 (2015)
Monton, B.: Wave Function Ontology. Synthese. 130(2), 265–277 (2002)
Monton, B.: Quantum Mechanics and 3 N- Dimensional Space. Philos. Sci. 73, 778–789 (2006)
Monton, B.: “Against 3-N-Dimensional Space.”. In: Albert, D.Z., Ney, A. (eds.) The Wavefunction: Essays in the Metaphysics of Quantum Mechanics, pp. 154–167. Oxford University Press (2013)
Myrvold, W.: Relativistic Constraints on Interpretations of Quantum Mechanics. In: E. Knox, and A. Wilson (eds.) The Routledge Companion to Philosophy of Physics. Routledge: 99–121. (2021)
Myrvold, W.: “Ontology for Relativistic Collapse Theories. In: Lombardi, O., Fortin, S., Lòpez, C., Holik, F. (eds.) Quantum Worlds: Perspectives on the Ontology of Quantum Mechanics. Cambridge University Press (2019)
Myrvold, W.: “Ontology for Collapse Theories.”. In: Gao, S. (ed.) Collapse of the Wave Function: Models, Ontology, Origin, and Implications, pp. 97–123. Cambridge University Press (2018)
Myrvold, W.: “Lessons of Bell’s Theorem: Nonlocality, Yes; Action at a Distance, Not Necessarily.”. In: Gao, S., Bell, M. (eds.) Quantum Nonlocality and Reality, pp. 238–260. Cambridge University Press (2016)
Myrvold, W.: Chasing Chimeras. Br. J. Philos. Sci. 60, 635–646 (2009)
Myrvold, W.: Modal Interpretations and Relativity. Found. Phys. 32, 1773–1784 (2002a)
Myrvold, W.: “On Peaceful Coexistence: Is the Collapse Postulate Incompatible with Relativity? Stud. History Philos. Mod. Phys. 33, 435–466 (2002b)
Nelson, E.: Quantum Fluctuations. Princeton University Press (1985)
Ney, A., and Kathryn Phillips: Does an Adequate Physical Theory Demand a Primitive Ontology? Philos. Sci. 80(3), 454–474 (2013)
Nikolić, H.: QFT as Pilot-wave Theory of Particle Creation and Destruction. Int. J. Mod. Phys. A. 25(7), 1477–1505 (2010)
Nikolić, H.: “Relativistic Quantum Mechanics and the Bohmian Interpretation.” Foundations of Physics Letters 18: 549–561 (2005). (2005)
Norsen, T.: “Quantum Solipsism and Nonlocality.”. In: Gao, S., Bell, M. (eds.) Quantum Nonlocality and Reality, pp. 204–237. Cambridge University Press (2016)
Norsen, T.: John S. Bell’s Concept of Local Causality. Am. J. Phys. 79, 1261 (2011)
Norsen, T.: The Theory of (Exclusively) Local Beables. Found. Phys. 40(12), 1858–1884 (2010a)
Norsen, T.:“Parameter Independence and Outcome Independence(2010b)
in Dynamical Collapse Theories.” Manuscript
Norsen, T.: Local Causality and Completeness: Bell vs. Jarrett. Found. Phys. 39(3), 273–294 (2009)
Norsen, T.: Einstein’s Boxes. Am. J. Phys. 73, 164 (2005)
Oldofredi, A.: “Stochasticity and Bell-type Quantum. Field Theory.” Synthese. 197(2):731–750 (2020)
Pearle, P.: Relativistic Dynamical Collapse Model. Phys. Rev. D. 41, 105012 (2015)
Pearle, P.: “Toward a Relativistic Theory of Statevector Reduction.”. In: Miller, A.I. (ed.) Sixty-Two Years of Uncertainty: Historical, Philosophical, and Physical Inquiries into the Foundations of Quantum Mechanics, pp. 193–214. Plenum Press (1990)
Popper, K.: “The Propensity Interpretation of the Calculus of Probability and of the Quantum Theory.” In Korner and Price (eds.) Observation and Interpretation: 65–70. Buttersworth Scientific Publications. (1957)
Redhead, M.: Incompleteness, Nonlocality, and Realism: A Prolegomenon to the Philosophy of Quantum Mechanics. Oxford University Press (1987)
Rovelli, C.: Relational Quantum Mechanics,. Int. J. Theor. Phys. 35, 1637 (1996)
Salmon, W.C.: Scientific Explanation and the Causal Structure of the World. Princeton University Press (1984)
Shimony, A.: “Controllable and Uncontrollable Nonlocality.”. In: Kamefuchi, S., et al. (eds.) Foundations of Quantum Mechanics in the Light of New Technology. Physical Society of Japan, Tokyo (1984)
Struyve, W.: and Hans Westman. “A New Pilot-Wave Model for Quantum Field Theory.” AIP Conference Proceedings 844: 321. (2006)
Suárez, M.: Bohmian Dispositions. Synthese. 192(10), 3203–3228 (2105)
Tumulka, R.: “A Relativistic GRW Flash Process with Interaction.”. In: Allori, V., Bassi, A., Dürr, D., Zanghí, N. (eds.) Do Wavefunctions Jump? Perspectives of the Work of GianCarlo Ghirardi, pp. 321–348. Springer (2020)
Tumulka, R.: The Point Processes of the GRW Theory of Wavefunction Collapse. Rev. Math. Phys. 21, 155–227 (2009)
Tumulka, R.: The Unromantic Pictures of Quantum Theory. J. Phys. A. 40, 3245–3273 (2007)
Tumulka, R.: “Collapse and Relativity.”AIP Conference Proceedings, 844: 340–352. (2006b)
Tumulka, R.: A Relativistic Version of the Ghirardi-Rimini-Weber Model. J. Stat. Phys. 125, 821–840 (2006a)
Vaidman, L.: “The Bell Inequality and the Many-Worlds Interpretation.”. In: Gao, S., Bell, M. (eds.) Quantum Nonlocality and Reality, pp. 195–203. Cambridge University Press (2016)
Vaidman, L.: “Many-Worlds Interpretation of Quantum Mechanics.” The Stanford Encyclopedia of Philosophy (Winter 2014 Edition), Edward N. Zalta (ed.), (2014). https://plato.stanford.edu/entries/qm-manyworlds/
Valentini, A.: “Signal-locality, Uncertainty, and the Sub-quantum H-theorem, I.” Physics Letters A 156 (5). (1991)
Van Camp, W.: Principle Theories, Constructive Theories, and Explanation in Modern Physics. ” Stud. History Philos. Mod. Phys. 42, 23–31 (2011)
Wallace, D.: “On the Plurality of Quantum Theories: Quantum theory as a Framework, and its Implications for the Quantum Measurement Problem.“. In: French, S., Saatsi, J. (eds.) Scientific Realism and the Quantum:, pp. 78–102. Oxford University Press (2020)
Wallace, D.: The Emergent Multiverse: Quantum Theory according to the Everett Interpretation. Oxford University Press (2012)
Wilhelm, I.: Typical: A Theory of Typicality and Typicality Explanation. Br. J. Philos. Sci. (2019). https://doi.org/10.1093/bjps/axz016
Acknowledgements
I am particularly grateful to Jean Bricmont for discussing these matters with me at length. I also wish to thank Travis Norsen and Roderich Tumulka for their helpful insights on some issues considered in this paper.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Allori, V. What is It Like to be a Relativistic GRW Theory? Or: Quantum Mechanics and Relativity, Still in Conflict After All These Years. Found Phys 52, 79 (2022). https://doi.org/10.1007/s10701-022-00595-5
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10701-022-00595-5