Abstract
In Chap. 2, we located the importance of de Broglie’s research for the development of QM in his speculating about matter waves, and hence in his indirect contribution to Schrödinger’s discovery of the SE. But de Broglie’s contributions to the early development of QM of course exceeded this point. In particular, he also proposed a so called pilot wave theory, in which there would be waves and particles, and which he hoped to be a precursor to a future (fully developed) ‘theory of the double solution’. In the latter there would be additional singular solutions to the SE or the KGE, highly peaked field amplitudes with a phase coinciding with that of the regular solutions, replacing genuine, additional particles (cf. Bacciagaluppi and Valentini 2009, p. 60; Jammer 1966, pp. 292 and 357; Mehra and Rechenberg 1987, p. 1209). Pilot wave theory and the theory of the double solution were certainly both motivated by the duality of wave-like and particle-like aspects exhibited in experiments and discussed at some length in Chap. 2. In contrast to the naïve (collapse) approach discussed therein, however, de Broglie’s pilot wave theory would have particles be present at all times and only be guided or piloted by a simultaneously occurring wave-phenomenon. The theory of the double solution, he hoped, would then explain everything in terms of waves (fields) alone (cf. Dürr et al. 2012, p. 7; Mehra and Rechenberg 1987, p. 1209).
Go to any meeting, and it is like being in a holy city in great tumult. You will find all the religions with all their priests pitted in holy war […]. They all declare to see the light, the ultimate light. Each tells us that if we will accept their solution as our savior, then we too will see the light.
—C. Fuchs (2002, p. 1)
The term ‘ψ-ontology’, having a peircing phonetic ring to it (read: ‘siontology’), has been traced back to Chris Granade by M. Leifer (2011).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
You can easily verify this by restricting attention to one of the coordinates, differentiating ψ twice using product- and chain rule, and realizing that \(\nabla R \cdot \nabla S = \frac {\partial R}{\partial x}\cdot \frac {\partial S}{\partial x} + \frac {\partial R}{\partial y}\cdot \frac {\partial S}{\partial y}+\frac {\partial R}{\partial z}\cdot \frac {\partial S}{\partial z}\) (and so forth).
- 2.
Cf. Passon (2004, p. 7) for an overview of attempts to get around this feature.
- 3.
We will introduce the notion of a conditional wave function thoroughly below.
- 4.
A ‘measurement of the position operator’ need not be a measurement of the actual position of a particle though; cf. the example in Dürr et al. (2012, pp. 142–143).
- 5.
This only holds, of course, if the wavefunction is not factorizable, because otherwise all the factors in (6.8) that do not depend on x j can be ‘divided off’.
- 6.
However, cf. Norsen (2010) for an interesting first step towards a fully local view of BM.
- 7.
This will become clear after the discussion of decoherence in Sect. 6.3.2.
- 8.
It should be noted though that at least S. Goldstein (private communication) thinks that there are subtle but important conceptual differences.
- 9.
Cf. however Maudlin (2007, pp. 11–12) for some dissenting views.
- 10.
would here in fact be a functional on a space of three-metrics and \(\hat {\mathbb {H}}\) contains a functional derivative (cf. Kiefer 2007, p. 141 ff. for details). - 11.
Of course it may also seem quite counter-intuitive that, on the BSA, it appears to depend on the existence of minds, being the carriers of descriptive systems, whether there are laws of nature or not. Even Lewis (1994, p. 479; emphasis in original) admitted that “if nature were unkind, and if disagreeing rival systems were running neck-and-neck, then lawhood might be a psychological matter […].” We should appreciate, though, that at least the entities regularly exhibiting the same behavior do reside in the outside world and they do behave so mind-independently, even if they do not have to; and given certain standards, the best system may also be precisely (objectively) fixed. So there is certainly no radical subjectivism here (cf. also Psillos 2002, pp. 153–154).
- 12.
Cf. in particular Callender (2015) for a detailed treatment of some problems and potential solutions.
- 13.
Author’s note: I owe this objection essentially to Sheldon Goldstein and Christian Loew independently (private communication in both cases).
- 14.
Cf. also Friederich’s (2015) book-length investigation of a Wittgensteinian-therapeutic approach to QM, in this connection.
- 15.
Author’s note: I owe thanks to Andreas Hüttemann for making me aware of this issue.
- 16.
- 17.
Cf. the next section for difficulties of generalizing guidance equations.
- 18.
In fact, any universal is simultaneously instantiated at many points in space, or cast in relativistic terms, instantiated on multiple points of the same spacelike hypersurface. The key point is that in BM the dependence of one quantity (velocity) is on the multiple instantiations (particle positions) on that hypersurface, not on only one of them (the particle’s own one).
- 19.
Author’s note: Again thanks to Andreas Hüttemann are in order for the observation that the situation constitutes a dilemma.
- 20.
In fact, Maudlin (2013, p. 151) basically suggests the same about the quantum state – that it may be an entity sui generis.
- 21.
Cf. however Dorato (2015) for a quite different and somewhat more benevolent discussion on this context.
- 22.
One might thus be tempted to think of BM as a subjective collapse interpretation; but that would surely be misleading, since collapse plays no substantial role therein.
- 23.
Here is how (in brief; Chap. 7 presents the argument for QM in more detail): In Healey (2012a, p. 22 ff.) and Friederich (2015, p. 132) it is argued that there can be no interventions \( \underline {I}_{A}, \underline {I}_{B}\) for two agents (Alice and Bob) in remote places, sharing among them a pair of electrons in the singlet state, such that both Alice and Bob could perform their respective intervention to fix one of the possible values: “manipulability by the distant outcome always undermines the local control required for a genuine intervention.” (Boge 2016a, p. 4) This is why causal counterfactuals are not ‘sanctioned’ by QM (the argument goes), if one accepts interventionism as definitive of causation. Since dependence is mutual in BM, this argument seems to transfer seamlessly.
- 24.
- 25.
∂f is a generalized gradient for calculus on manifolds which can be locally written in a suitable coordinate representation (cf. Footnote 71 of Chap. 2) as
, with g
μν the manifold’s metric and where the 
are conceived of as vectors in a ‘tangent space’ at a given point in the manifold for which the local coordinates x
μ are defined (e.g. Frankel 2004, p. 45 ff.; Nakahara 2003). Frankel (2004, p. 47) uses the notation ‘∇f’ instead; we here follow that of Dürr et al. (2012, p. 227). - 26.
This is the adjoint spinor that makes for a Lorentz-invariant scalar product \(\bar {\psi }\psi \) (cf. Griffiths 2008, p. 236).
- 27.
The most important reference for further details is Struyve (2010).
- 28.
The functional derivative δF[f] δf of a functional F[f] obtains a quite ‘natural’ understanding in close analogy to derivatives in ordinary calculus as \(\lim \limits _{\epsilon \rightarrow 0} { \frac {1}{\epsilon }}(F[f(x) + \epsilon \delta (x-x')]-F[f(x)])\), with δ(x − x′) a Dirac-δ (e.g. Greiner and Reinhardt 1993, p. 37; Lancaster and Blundell 2014, p. 12), i.e. where one lets f vary with tiny ‘strengths’ (𝜖).
- 29.
E.g. Nakahara (2003, p. 40 ff.) for an introduction to Grassmann numbers.
- 30.
‘Covariance’, strictly speaking, is not the same as invariance; it rather means that “a […] quantity ‘changes in the same way’.” (Cheng 2005, p. 14) However, if all the quantities in an equation transform covariantly, the entire equation retains the same form (cf. ibid.), which is why the terms ‘Lorentz invariant’ and ‘Lorentz covariant’ are sometimes used interchangably in the literature, as regards equations and theories. Cf. also Friedman (1983, p. 45) for a deeper discussion and some subtleties in the transition from SR to GR.
- 31.
A lot more could be—and has been; cf. Passon (2004, p. 9) for references—said on this problem of ‘surreal’ trajectories, but for our present purposes the discussion seems fully sufficient. We briefly also mention the recent experimental work by Mahler et al. (2016), who show, by advanced experimental methods, that “the trajectories seem surreal only if one ignores their manifest nonlocality.” (p. 1) Interpreting the results as being concerned with particle trajectories at all, however, obviously presupposes a Bohmianm understanding of QM.
- 32.
The generalization to non-pure density matrices and multiple (distinguishable) particles is straightforward in virtue of the properties of tensor products and the linearity of sums.
- 33.
That the third line follows from the second can be verified by comparing the exponents; the fourth line may be derived by substituting a variable \(\xi := -\sqrt {\alpha }(x-x')\) in all three spatial dimensions, so that the measure is rescaled by \((\sqrt {\alpha })^{-1}\) and the exponent becomes just − ξ 2 in all three dimensions. The integral can then be computed using Gauß’s ‘trick’.
- 34.
Talk of ‘models’ here should be understood along the same lines as in Chap. 4: as highlighting the somewhat provisionary character. Ultimately all such ‘models’ here aim to provide an interpretation of the QM formalism, an explanation of our empirical success in using it. Of course the same considerations as in Sect. 6.1.1 hence come to mind; considerations of such collapse interpretations really constituting alternative theories.
- 35.
Ghirardi et al. (cf. 1988, p. 386) proposed a model for systems of ‘indistinguishable particles’, using a symmetrization of a then joint superoperator, so that individual positions of localization would not matter. The model however has the unsatisfying feature that it prescribes simultaneous localizations of all N particles, thereby leaving “no hope for a Lorentz-invariant version.” (Tumulka 2006b, p. 1906)
- 36.
- 37.
Allori et al. (2014, p. 330 ff.) have argued that it is contentious to use mass as the defining property, since one could set up a quite similar distribution using charges instead of masses, as was originally attempted by Schrödinger. It is hence preferable to use the more neutral term ‘matter density’.
- 38.
This is acknowledged by Egg and Esfeld (2015, p. 3240), who recognize a “considerable flexibility in implementing the thesis of Humean supervenience of the quantum state on the primitive ontology.” But they believe the “non-Humean options” to be “clearly […] less revisionary” (p. 3241), which is reason enough for them to prefer those options.
- 39.
- 40.
- 41.
For details on the stationarity of spacetimes e.g. Ruetsche (2011, p. 207).
- 42.
A first estimate for ΔE is also computed by Penrose from squared differences in gravitational accelerations for different spacetimes in a Newtonian limit (cf. Penrose 1996, p. 594 ff. for details).
- 43.
In particular, that would require a “precise measure of uncertainty that is to be assigned to the ‘superposed Killing vector’ and to the corresponding notion of ‘stationarity’ for the superposed space-time.” (Penrose 1996, p. 596)
- 44.
Cf. also Maudlin (2011, p. 243 ff.) for an accessible informal analysis of at least Tumulka’s relativistic model.
- 45.
Cf. also Saunders (2010) for a general introduction to the subject.
- 46.
For obvious reasons, we will here generically use \({\vert \mathbb {S}_{j}\rangle}\) to refer to system states, \({\vert \mathbb {A}_{j}\rangle}\) to apparatus states…and so on.
- 47.
Some of the following is discussed in more detail in Boge (2016b, p. 12 ff.).
- 48.
Why the (larger) environment? Because the treatment given below would not lead to stable states if it were applied to the state of system and apparatus only; the preferred basis is selected as the basis that is stable w.r.t. the action of the environment on the apparatus, i.e. as the basis of eigenstates (‘pointer states’) of some observable (‘pointer observable’) that commutes with the interaction Hamiltonian (cf. Joos et al. 2003, p. 166; Schlosshauer 2007, p. 77). Why only the interaction Hamiltonian? Because it can usually reasonably be assumed that this part dominates the total Hamiltonian; this is called the “quantum measurement limit” (cf. Schlosshauer 2007, p. 77; emphasis omitted).
- 49.
On the other hand, if one employs collapses in addition to decoherece, this “might actually allow for an experimental disproof of collapse theories” (Schlosshauer 2004, p. 1296), since then there could be experimentally realizable situations in which a respective collapse model predicts localizations where decoherence would not. But such experimental protocols would be extremely difficult to realize, due to the approximate ‘omnipresence’ of decoherence effects (cf. Schlosshauer 2004, ibid.).
- 50.
We critically remark at this point, however, that the ontological significance of the projectors is somewhat opaque in the MWI; Saunders’ (2010, p. 42) appeal to von Neumann’s (1932, p. 409) construal of projectors as the “elementary building blocks of the macroscopic description of the world”, for instance, does not really help this fact. Maybe we can think of them, in virtue of the branching-decoherence theorem mentioned below, as representing ‘emergent structures’ due to decoherence in some sense. But it would certainly be desirable to find more clarity on this issue in the literature.
- 51.
More precisely, one can distinguish different degrees of decoherence in virtue of D(α, β) being complex valued: one can make a difference between the whole functional vanishing or only the real or imaginary part. The details do not matter for the present context though, so we refer the interested reader to Joos et al. (2003, p. 241 ff.).
- 52.
There may be important differences between the two authors’ views on the role of the wavefunction in the MWI though that will become apparent in the subsequent discussion.
- 53.
We here take it that π is real valued for convenience, but one can of course introduce an additional ‘intermediate’ map that assigns real values to consequences such as ‘I am being handed a sandwich’ (cf. Wallace 2002, p. 6).
- 54.
Note that a decoherence-based MWI effectively rules out mind-brain identity, because (as was our earlier observation) the brain states will still be (very weakly) overlapping, even if decoherence has taken place, but the conscious states will not: O 0 will never, we take it, have the experience of observing both, ↑ and ↓, not even ‘remotely’.
- 55.
Note briefly that there is also the possibility of interpreting the situation in terms of divergence (cf. Greaves 2007, p. 117): there could be multiple copies of oneself all along, coexisting together as O 0 up until the measurement and then just ‘leaving off’ into different branches. This would sanction the subjective uncertainty view, but it has the obvious deficit of introducing Albert-Loewer-like many minds after all, and hence undesirable ad hoc surplus structure.
- 56.
- 57.
…who in turn adapts the scenario from Adam Elgar (cf. Wallace 2012, p. 193). Note that Wallace (2012, ibid.) of course presents own arguments for why he thinks his strategy is immune to the criticism; but we here agree with Maudlin (2014a, p. 803), that “Wallace’s response […] fails to make contact with the case considered.”
- 58.
More technically phrased, Wallace (2012, p. 163) represents an ‘act’ by a unitary \(\hat {U}\) and one’s quantum state |ψ〈 is assumed to be in a ‘macrostate’ \(\mathbb {M}\) which is a subspace of the Hilbert space \(\mathbb {H}\), as is the ‘reward’, \(\mathbb {R}\), because not every detail about these quantum states matters. So to avoid the language of measurements, self-adjoint operators, and eigenvalues, Wallace (2012) appeals only to unitary operators and subspaces to model reward situations and actions. He then (p. 179) defines branching indifference such that if one’s own quantum state |ψ〉 is in \(\mathbb {M}\) and \(\mathbb {M}\subset \mathbb {R}\), then one is indifferent at |ψ〈 about either performing \(\hat {U}\) such that \(\hat {U}{\vert \psi \rangle}\in \mathbb {R}\) or leaving |ψ〈 alone (performing
). This makes the problem quite obvious: in our scenario above, the macrostate would lie in the ‘reward’ space (imminent catastrophe), but we could still dislike a unitary with the effect of ‘more catastrophes happening’ due to branching, i.e. we could rationally want to avoid multiplication within \(\mathbb {R}\). - 59.
Again, we will only give highlights; the reader interested in details of the proof may be referred either to the original papers or to Boge (2016b, p. 32–41) and references therein.
- 60.
- 61.
We omit the additional phase degree of freedom that is effectively 1 (cf. Zurek 2003, p. 2).
- 62.
Author’s note: I am indebted to Rochus Klesse for raising my awareness on this point.
- 63.
We here use the paraphrases also given in Boge (2016b, pp. 32–33).
- 64.
- 65.
- 66.
- 67.
We have been careful to appeal to a propensity rather than directly to frequencies, so that cases with moduli that are not square roots of rational numbers and are treated by a limiting procedure (cf. Zurek 2003, p. 3) may be understood on equal terms.
- 68.
Wallace and Timpson refer back to Healey (1991, p. 406) instead.
would here in fact be a functional on a space of three-metrics and 
, with g
μν the manifold’s metric and where the 
are conceived of as vectors in a ‘tangent space’ at a given point in the manifold for which the local coordinates x
μ are defined (e.g. Frankel 
). This makes the problem quite obvious: in our scenario above, the macrostate would lie in the ‘reward’ space (imminent catastrophe), but we could still dislike a unitary with the effect of ‘more catastrophes happening’ due to branching, i.e. we could rationally want to avoid multiplication within References
Albert, D. 2010. Probability in the Everett picture. In Many worlds? Everett, quantum theory, & reality, eds. S. Saunders, J. Barrett, A. Kent, and D. Wallace, 355–368. Oxford/New York: Oxford University Press.
Albert, D., and B. Loewer. 1988. Interpreting the many worlds interpretation. Synthese 77(2): 195–213.
Albert, D.Z. 1996. Elementary quantum metaphysics. In Bohmian mechanics and quantum theory: An appraisal, eds. J.T. Cushing, A. Fine, and S. Goldstein, 277–284. Berlin/Heidelberg: Springer.
Allori, V., S. Goldstein, R. Tumulka, and N. Zanghì. 2008. On the common structure of Bohmian mechanics and the Ghirardi–Rimini–Weber theory. The British Journal for the Philosophy of Science 59(3): 353–389.
Allori, V., S. Goldstein, R. Tumulka, and N. Zanghì. 2014. Predictions and primitive ontology in quantum foundations: A study of examples. The British Journal for the Philosophy of Science 65(2): 323–352.
Armstrong, D.M. 1978. Universals and scientific realism. Cambridge/New York: Cambridge University Press. [2 volumes].
Armstrong, D.M. 1989. Universals: An opinionated introduction. Boulder/San Francisco: Westview Press.
Bacciagaluppi, G. 2010. Collapse theories as beable theories. Manuscrito 33(1): 19–54. http://philsci-archive.pitt.edu/8876/.
Bacciagaluppi, G., and A. Valentini. 2009. Quantum theory at the crossroads: Reconsidering the 1927 Solvay conference. Cambrdige/New York: Cambridge University Press.
Baker, D.J. 2007. Measurement outcomes and probability in Everettian quantum mechanics. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38(1): 153–169.
Barnum, H. 2003. No-signalling-based version of Zurek’s derivation of quantum probabilities: A note on ‘Environment-assisted invariance, entanglement, and probabilities in quantum physics’. arXiv preprint quant-ph/0312150.
Bassi, A., and G. Ghirardi. 2003. Dynamical reduction models. Physics Reports 379(5): 257–426.
Bassi, A., K. Lochan, S. Satin, T.P. Singh, and H. Ulbricht. 2013. Models of wave-function collapse, underlying theories, and experimental tests. Reviews of Modern Physics 85(2): 471–527.
Bedingham, D., D. Dürr, G. Ghirardi, S. Goldstein, R. Tumulka, and N. Zanghì. 2014. Matter density and relativistic models of wave function collapse. Journal of Statistical Physics 154(1–2): 623–631.
Bedingham, D.J. 2009. Dynamical state reduction in an EPR experiment. Journal of Physics A: Mathematical and Theoretical 42(46): 465301.
Bedingham, D.J. 2011. Relativistic state reduction dynamics. Foundations of Physics 41(4): 686–704.
Bell, J.S. 1987. Are there quantum jumps? In Speakable and unspeakable in quantum mechanics, ed. J.S. Bell, 201–212. Cambridge/New York: Cambridge University Press.
Bell, J.S. 1987[1966]. On the problem of hidden-variables in quantum mechanics. In Speakable and unspeakable in quantum mechanics, ed. J.S. Bell, 1–13. Cambridge/New York: Cambridge University Press.
Bell, J.S. 1987[1971]. Introduction to the hidden-variable question. In Speakable and unspeakable in quantum mechanics, ed. J.S. Bell, 29–39. Cambridge/New York: Cambridge University Press.
Bell, J.S. 1987[1976]. The theory of local beables. In Speakable and unspeakable in quantum mechanics, ed. J.S. Bell, 52–62. Cambridge/New York: Cambridge University Press.
Bell, J.S. 1987[1980]. de Broglie-Bohm, delayed-choice double-slit experiment, and density matrix. In Speakable and unspeakable in quantum mechanics, ed. J.S. Bell, 111–116. Cambridge/New York: Cambridge University Press.
Bell, J.S. 1987[1981]b. Quantum mechanics for cosmologists. In Speakable and unspeakable in quantum mechanics, ed. J.S. Bell, 139–158. Cambridge/New York: Cambridge University Press.
Bell, J.S. 1987[1984]a. Beables for quantum field theory. In Speakable and unspeakable in quantum mechanics, ed. J.S. Bell, 173–180. Cambridge/New York: Cambridge University Press.
Bell, J.S. 1990a. Against ‘measurement’. In Sixty-two years of uncertainty. Historical, philosophical, and physical inquiries into the foundations of quantum mechanics, ed. A.I. Miller, 17–32. New York: Plenum Press.
Boge, F. 2016a. Book review: Simon Friederich: Interpreting quantum theory: A therapeutic approach. Erkenntnis. https://doi.org/s10670-016-9823-9.
Boge, F. 2016b. On probabilities in the many worlds interpretation of quantum mechanics. Bachelor thesis, Institue for Theoretical Physics, University of Cologne. http://kups.ub.uni-koeln.de/6889/.
Bohm, D. 1952a. A suggested interpretation of the quantum theory in terms of ‘hidden’ variables. I. Physical Review 85(2): 166–179.
Bohm, D. 1952b. A suggested interpretation of the quantum theory in terms of ‘Hidden’ variables. II. Physical Review 85(2): 180–193.
Bohm, D., and B. Hiley. 1993. The undivided universe: An ontological interpretation of quantum theory. London/New York: Routledge.
Brune, M., E. Hagley, J. Dreyer, X. Maitre, A. Maali, C. Wunderlich, J. Raimond, and S. Haroche. 1996. Observing the progressive decoherence of the ‘meter’ in a quantum measurement. Physical Review Letters 77(24): 4887.
Byrne, P. 2010a. Everett and wheeler: The untold story. In Many worlds? Everett, quantum theory, and reality, eds. S. Saunders, J. Barrett, A. Kent, and D. Wallace, 521–542. Oxford/New York: Oxford University Press.
Byrne, P. 2010b. The many worlds of Hugh Everett III: Multiple universes, mutual assured destruction, and the meltdown of a nuclear family. Oxford/New York: Oxford University Press.
Callender, C. 2015. One world, one beable. Synthese 192(10): 3153–3177.
Carroll, S.M., and C.T. Sebens. 2014. Many worlds, the born rule, and self-locating uncertainty. In Quantum theory: A two-time success story, eds. D.C. Struppa, and J.M. Tollaksen, 157–169. Milan: Springer.
Cartwright, N. 1983. How the laws of physics lie. Oxford/New York: Clarendon Press.
Cartwright, N. 1989. Nature’s capacities and their measurement. Oxford/New York: Oxford University Press. Reprinted 2002.
Cartwright, N. 1999. The dappled world: A study of the boundaries of science. Cambridge/New York: Cambridge University Press.
Castelvecchi, D., and A. Witze. 2016. Einstein’s gravitational waves found at last. Nature news. 10.1038/nature.2016.19361.
Caves, C.M. 2004. Notes on Zurek’s derivation of the quantum probability rule. http://info.phys.unm.edu/~caves/reports/ZurekBornderivation.ps. Last modified 29 July 2005.
Cheng, T. 2005. Relativity, gravitation and cosmology: A basic introduction. Oxford/New York: Oxford University Press.
Cohen, J., and C. Callender. 2009. A better best system account of lawhood. Philosophical Studies 145(1): 1–34.
Collett, B., and P. Pearle. 2003. Wavefunction collapse and random walk. Foundations of Physics 33(10): 1495–1541.
Couder, Y., and E. Fort. 2006. Single-particle diffraction and interference at a macroscopic scale. Physical Review Letters 97(15): 154101.
Dawid, R., and K.P.Y. Thébault. 2015. Many worlds: Decoherent or incoherent? Synthese 192(5): 1559–1580.
de Broglie, L. 1927. La mécanique ondulatoire et la structure atomique de la matière et du rayonnement. Journal de Physique et le Radium 8(5): 225–241.
de Laplace, P.S. 1902 [1814]. A philosophical essay on probabilities. Trans. from the 6th French ed. by F.W. Truscott, and F.L. Emory. London: Chapman & Hall, Ltd.
d’Espagnat, B. 1990. Towards a separable ‘empirical reality’? Foundations of Physics 20(10): 1147–1172.
Deutsch, D. 1999. Quantum theory of probability and decisions. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 455(1988): 3129–3137.
DeWitt, B.S. 1967. Quantum theory of gravity. I. The canonical theory. Physical Review 160(5): 1113.
DeWitt, B.S. 1973[1970]. Quantum mechanics and reality. In The many worlds interpretation of quantum mechanics, Princeton series in physics, eds. B. Dewitt, and N. Graham, 155–165. Princeton: Princeton University Press.
DeWitt, B.S. 1973[1971]. The many-universes interpretation of quantum mechanics. In The many worlds interpretation of quantum mechanics, eds. B. Dewitt, and N. Graham, 167–218. Princeton: Princeton University Press.
Diósi, L. 1987. A universal master equation for the gravitational violation of quantum mechanics. Physics Letters A 120(8): 377–381.
Diósi, L. 1988. Continuous quantum measurement and Itô formalism. Physics Letters A 129(8): 419–423.
Diósi, L. 1989. Models for universal reduction of macroscopic quantum fluctuations. Physical Review A 40(3): 1165–1174.
Diósi, L., and B. Lukács. 1987. In favor of a Newtonian quantum gravity. Annalen der Physik 499(7): 488–492.
Dizadji-Bahmani, F. 2013. The probability problem in Everettian quantum mechanics persists. The British Journal for the Philosophy of Science 66(2): 257–283.
Dorato, M. 2015. Laws of nature and the reality of the wave function. Synthese 192(10): 3179–3201.
Dowker, F., and I. Herbauts. 2005. The status of the wave function in dynamical collapse models. Foundations of Physics Letters 18(6): 499–518.
Dretske, F.I. 1977. Laws of nature. Philosophy of Science 44(2): 248–268.
Dürr, D., S. Goldstein, T. Norsen, W. Struyve, and N. Zanghì. 2014. Can Bohmian mechanics be made relativistic? Proceedings of the Royal Society A 470(2162): 20130699.
Dürr, D., S. Goldstein, and N. Zanghì. 2012. Quantum physics without quantum philosophy. Berlin/Heidelberg: Springer.
Dürr, D., and S. Teufel. 2009. Bohmian mechanics: The physics and mathematics of quantum theory. Berlin/Heidelberg: Springer.
Egg, M., and M. Esfeld. 2014. Non-local common cause explanations for EPR. European Journal for Philosophy of Science 4(2): 181–196.
Egg, M., and M. Esfeld. 2015. Primitive ontology and quantum state in the GRW matter density theory. Synthese 192(10): 3229–3245.
Englert, B.-G., M.O. Scully, G. Süssmann, and H. Walther. 1992. Surrealistic Bohm trajectories. Zeitschrift für Naturforschung A 47(12): 1175–1186.
Esfeld, M., M. Hubert, D. Lazarovici, and D. Dürr. 2014. The ontology of Bohmian mechanics. The British Journal for the Philosophy of Science 65(4): 773–796.
Everett III, H. 1957. “Relative state” formulation of quantum mechanics. Reviews of Modern Physics 29(3): 454.
Everett III, H. 1973. The theory of the universal wavefunction. In The many worlds interpretation of quantum mechanics, eds. B. Dewitt, and N. Graham, 3–140. Princeton: Princeton University Press.
Feintzeig, B. 2014. Can the ontological models framework accommodate Bohmian mechanics? Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 48: 59–67.
Frankel, T. 2004. The geometry of physics: An introduction, 2nd ed. Cambrdige/New York: Cambridge University Press.
Friebe, C., M. Kuhlmann, H. Lyre, P. Näger, O. Passon, and M. Stöckler. 2015. Philosophie der Quantenphysik. Berlin/Heidelberg: Springer.
Friederich, S. 2015. Interpreting quantum theory: A therapeutic approach. Basingstoke: Palgrave Macmillan.
Friedman, M. 1983. Foundations of space-time theories. Relativistic physics and philosophy of science. Princeton: Princeton University Press.
Fuchs, C.A. 2002. Quantum mechanics as quantum information (and only a little more). arXiv preprint quant-ph/0205039.
Fuchs, C.A. 2014. Introducing QBism. In New directions in the philosophy of science, eds. M.C. Galavotti, D. Dieks, W.J. Gonzalez, S. Hartmann, T. Uebel, and M. Weber, 385–402. Heidelberg/New York: Springer.
Galvan, B. 2015. Relativistic Bohmian mechanics without a preferred foliation. arXiv preprint arXiv:1509.03463.
Gell-Mann, M., and J.B. Hartle. 1989. Quantum mechanics in the light of quantum cosmology. In Proceedings of the 3rd international symposium on the foundations of quantum mechanics, 321–343. Reading: Addison Wesley.
Ghirardi, G. 2016. Collapse theories. In The Stanford encyclopedia of philosophy, ed. E.N. Zalta. The Metaphysics Research Lab, Center for the Study of Language and Information (CSLI), Stanford University. http://plato.stanford.edu/entries/qm-collapse/.
Ghirardi, G., R. Grassi, and A. Rimini. 1990a. Continuous-spontaneous-reduction model involving gravity. Physical Review A 42(3): 1057–1064.
Ghirardi, G., and P. Pearle. 1990a. Dynamical reduction theories: Changing quantum theory so the statevector represents reality. In PSA: Proceedings of the Biennial meeting of the philosophy of science association, 19–33.
Ghirardi, G., and P. Pearle. 1990b. Elements of physical reality, nonlocality and stochasticity in relativistic dynamical reduction models. In PSA: Proceedings of the Biennial meeting of the philosophy of science association, 35–47.
Ghirardi, G.C., R. Grassi, and F. Benatti. 1995. Describing the macroscopic world: Closing the circle within the dynamical reduction program. Foundations of Physics 25(1): 5–38.
Ghirardi, G.C., O. Nicrosini, A. Rimini, and T. Weber. 1988. Spontaneous localization of a system of identical particles. Il Nuovo Cimento B 102(4): 383–396.
Ghirardi, G.C., P. Pearle, and A. Rimini. 1990b. Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles. Physical Review A 42(1): 78–89.
Ghirardi, G.C., A. Rimini, and T. Weber. 1986. Unified dynamics for microscopic and macroscopic systems. Physical Review D 34(2): 470–491.
Ghirardi, G.C., A. Rimini, and T. Weber. 1987. Disentanglement of quantum wave functions: Answer to ‘Comment on ‘Unified dynamics for microscopic and macroscopic systems’’. Physical Review D 36(10): 3287–3289.
Goldstein, S., R. Tumulka, and N. Zanghì. 2012. The quantum formalism and the GRW formalism. Journal of Statistical Physics 149(1): 142–201.
Graham, N. 1973. The measurement of relative frequency. In The many worlds interpretation of quantum mechanics, eds. B. Dewitt, and N. Graham, 229–253. Princeton: Princeton University Press.
Greaves, H. 2004. Understanding Deutsch’s probability in a deterministic multiverse. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35(3): 423–456.
Greaves, H. 2007. Probability in the Everett interpretation. Philosophy Compass 2(1): 109–128.
Greiner, W., and J. Reinhardt. 1993. Field quantization. Berlin/Heidelberg: Springer.
Grice, H.P. 1975. Logic and conversation. In Syntax and semantics, vol. 3: Speech acts, eds. P. Cole, and J.L. Morgan, 41–58. New York: Academic Press.
Griffiths, D. 2008. Introduction to elementary particles, 2nd rev. ed. Weinheim: Wiley-VCH.
Griffiths, D.J. 1999. Introduction to electrodynamics. New Jersey: Prentice Hall.
Hackermüller, L., K. Hornberger, B. Brezger, A. Zeilinger, and M. Arndt. 2004. Decoherence of matter waves by thermal emission of radiation. Nature 427(6976): 711–714.
Harrigan, N., and R.W. Spekkens. 2010. Einstein, incompleteness, and the epistemic view of quantum states. Foundations of Physics 40: 125–157.
Hartle, J.B. 2003. Gravity: An introduction to Einstein’s general relativity. San Francisco/Boston: Addison Wesley.
Healey, R. 2009. Holism in quantum mechanics. In Compendium of quantum physics. Concepts, experiments, history and philosophy, eds. D. Greenberger, K. Hentschel, and F. Weinert, 295–298. Berlin: Springer.
Healey, R. 2012a. How to use quantum theory locally to explain ‘non-local’ correlations. arXiv preprint arXiv:1207.7064.
Healey, R.A. 1991. Holism and nonseparability. The Journal of Philosophy 88(8): 393–421.
Hiley, B.J. 1999. Active information and teleportation. In Epistemological and experimental perspectives on quantum physics, eds. D. Greenberger, W.L. Reiter, and A. Zeilinger, 113–126. Dordrecht: Springer Science + Business Media.
Holland, P. 1995. The quantum theory of motion: An account of the de Broglie-Bohm causal interpretation of quantum mechanics. Cambridge/New York: Cambridge University Press.
Hughes, R.I.G. 1989. The structure and interpretation of quantum mechanics. Cambridge/London: Harvard University Press.
Hume, D. 1999 [1748]. An enquiry concerning human understanding. Edited by T.L. Beauchamp. Oxford/New York: Oxford University Press.
Ivanova, M. 2014. Is there a place for epistemic virtues in theory choice? In Virtue epistemology naturalized, ed. A. Fairweather, 207–226. Berlin/Heidelberg: Springer.
Jackson, J.D. 1990. Classical electrodynamics, 3rd ed. Hoboken: Wiley.
Jammer, M. 1966. The conceptual development of quantum mechanics. New York/St. Louis: McGraw-Hill Book Company.
Jammer, M. 1974. The philosophy of quantum mechanics: The interpretations of QM in historical perspective. Hoboken: Wiley.
Joos, E., H. Zeh, C. Kiefer, D. Giulini, J. Kupsch, and I.-O. Stamatescu. 2003. Decoherence and the appearance of a classical world in quantum theory, 2nd ed. Berlin/Heidelberg: Springer.
Kent, A. 1990. Against many-worlds interpretations. International Journal of Modern Physics A 5(09): 1745–1762.
Kent, A. 2010. One world versus many: The inadequacy of everettian accounts of evolution, probability, and scientific confirmation. In Many worlds? Everett, quantum theory, and reality, eds. S. Saunders, J. Barrett, A. Kent, and D. Wallace, 307–368. Oxford/New York: Oxford University Press.
Kent, A. 2015. Does it make sense to speak of self-locating uncertainty in the universal wave function? Remarks on Sebens and Carroll. Foundations of Physics 45(2): 211–217.
Kiefer, C. 2007. Quantum gravity, 2nd ed. Oxford/New York: Oxford University Press.
Lancaster, T., and S.J. Blundell. 2014. Quantum field theory for the Gifted Amateur. Oxford/New York: Oxford University Press.
Le Bellac, M. 2006. Quantum physics. Trans. by P. de Forcrand-Millard. Cambridge/New York: Cambridge University Press.
Leifer, M.S. 2011. Can the quantum state be interpreted statistically? Web log post: http://mattleifer.info/2011/11/20/can-the-quantum-state-be-interpreted-statistically/.
Lewis, D.K. 1994. Humean supervenience debugged. Mind 103(412): 473–490.
Lewis, P.G., D. Jennings, J. Barrett, and T. Rudolph. 2012. Distinct quantum states can be compatible with a single state of reality. Physical Review Letters 109(15): 150404(1–5).
Lewis, P.J. 2007. Quantum sleeping beauty. Analysis 67(1): 59–65.
Lockwood, M. 1996. ‘Many Minds’ interpretations of quantum mechanics. The British Journal for the Philosophy of Science 47(2): 159–188.
Loewer, B. 1996. Humean supervenience. Philosophical Topics 24(1): 101–127.
Lombardi, O., and D. Dieks. 2012. Modal interpretations of quantum mechanics. In The Stanford encyclopedia of philosophy, ed. E.N. Zalta. The Metaphysics Research Lab, Center for the Study of Language and Information (CSLI), Stanford University. http://plato.stanford.edu/entries/qm-modal/.
Mahler, D.H., L. Rozema, K. Fisher, L. Vermeyden, K.J. Resch, H.M. Wiseman, and A. Steinberg. 2016. Experimental nonlocal and surreal Bohmian trajectories. Science Advances 2(2):e1501466.
Maudlin, T. 2007. The metaphysics within physics. Oxford/New York: Oxford University Press.
Maudlin, T. 2010a. Can the world be only wavefunction? In Many worlds? Everett, quantum theory, and reality, eds. S. Saunders, J. Barrett, A. Kent, and D. Wallace, 121–143. Oxford/New York: Oxford University Press.
Maudlin, T. 2011. Quantum non-locality and relativity. Metaphysical intimations of modern physics, 3rd ed. Malden/Oxford: Wiley-Blackwell.
Maudlin, T. 2013. The nature of the quantum state. In The wave function. Essays on the metahphysics of quantum mechanics, eds. A. Ney, and D. Albert, 126–153. Oxford/New York: Oxford University Press.
Maudlin, T. 2014a. Critical study: David Wallace, the emergent multiverse: Quantum theory according to the everett interpretation. Noûs 48(4): 794–808.
McLaughlin, B., and K. Bennett. 2011. Supervenience. In The Stanford encyclopedia of philosophy, ed. E.N. Zalta. The Metaphysics Research Lab, Center for the Study of Language and Information (CSLI), Stanford University. http://plato.stanford.edu/entries/supervenience/.
Mehra, J., and H. Rechenberg. 1987. The historical development of quantum theory, vol. 5: Erwin Schrödinger and the rise of wave mechanics. Part 2: The creation of wave mechanics: Early response and applications 1925–1926. New York/Heidelberg: Springer.
Mohrhoff, U. 2004. Probabilities from envariance? International Journal of Quantum Information 2(02): 221–229.
Monton, B. 2002. Wave function ontology. Synthese 130(2): 265–277.
Monton, B. 2004. The problem of ontology for spontaneous collapse theories. Studies in History and Philosophy of Modern Physics 35(3): 407–421.
Mumford, S. 2004. Laws in nature. London/New York: Routledge.
Nakahara, M. 2003. Geometry, topology and physics, 2nd ed. Bristol/Philadelphia: IOP Publishing.
Nicrosini, O., and A. Rimini. 1990. On the relationship between continuous and discontinuous stochastic processes in Hilbert space. Foundations of Physics 20(11): 1317–1327.
Nielsen, M., and I. Chuang. 2010. Quantum computation and quantum information, 10th anniversary ed. Cambridge/New York: Cambridge University Press.
Norsen, T. 2010. The theory of (exclusively) local beables. Foundations of Physics 40(12): 1858–1884.
Parfit, D. 1984. Reasons and persons. Oxford: Clarendon Press.
Passon, O. 2004. Why isn’t every physicist a Bohmian? arXiv preprint quant-ph/0412119.
Pearle, P. 1989. Combining stochastic dynamical state-vector reduction with spontaneous localization. Physical Review A 39(5): 2277.
Pearle, P., and E. Squires. 1994. Bound state excitation, nucleon decay experiments and models of wave function collapse. Physical Review Letters 73(1): 1–5.
Pearle, P., and E. Squires. 1996. Gravity, energy conservation, and parameter values in collapse models. Foundations of Physics 26(3): 291–305.
Penrose, R. 1996. On gravity’s role in quantum state reduction. General Relativity and Gravitation 28(5): 581–600.
Peskin, M.E., and D.V. Schroeder. 1995. An introduction to quantum field theory. Reading: Perseus Books.
Psillos, S. 2002. Causation and explanation. Stocksfield: Acumen.
Rae, A.I. 2004. Quantum physics: Illusion or reality?, 2nd ed. Cambridge/New York: Cambridge University Press.
Ruetsche, L. 2011. Interpreting quantum theories. Oxford/New York: Oxford University Press.
Saunders, S. 1998. Time, quantum mechanics, and probability. Synthese 114(3): 373–404.
Saunders, S. 2010. Many words? An introduction. In Many worlds? Everett, quantum theory, and reality, eds. S. Saunders, J. Barrett, A. Kent, and D. Wallace, 1–49. Oxford/New York: Oxford University Press.
Schlosshauer, M. 2004. Decoherence, the measurement problem, and interpretations of quantum mechanics. Reviews of Modern Physics 76(4): 1267–1305.
Schlosshauer, M. 2007. Decoherence and the quantum to classical transition, 2nd ed. Berlin/Heidelberg: Springer.
Schlosshauer, M., and A. Fine. 2005. On Zurek’s derivation of the Born rule. Foundations of Physics 35(2): 197–213.
Schlosshauer, M., J. Kofler, and A. Zeilinger. 2013. A snapshot of foundational attitudes toward quantum mechanics. Studies in History and Philosophy of Modern Physics 44(3): 222–230.
Schrenk, M. 2014. Better best systems and the issue of CP-laws. Erkenntnis 79(10): 1787–1799.
Schrödinger, E. 1926b. Quantisierung als Eigenwertproblem. (Zweite Mitteilung.). Annalen der Physik 384(6): 489–527.
Schrödinger, E. 1935a. Discussion of probability relations between separated systems. Mathematical Proceedings of the Cambridge Philosophical Society 31(4): 555–563.
Schwabl, F. 2006. Statistical mechanics, 2nd ed. Berlin/Heidelberg: Springer.
Smart, J.J.C. 1993. Laws of nature as a species of regularities. In Ontology, causality and mind: Essays in honour of D. M. Armstrong, eds. J. Bacon, K. Campbell, and L. Reinhardt, 152–168. Cambrdige/New York: Cambridge University Press.
Spekkens, R.W. 2007. Evidence for the epistemic view of quantum states: A toy theory. Physical Review A 75: 032110.
Squires, E.J. 1992. Explicit collapse and superluminal signals. Physics Letters A 163(5–6): 356–358.
Struyve, W. 2010. Pilot-wave theory and quantum fields. Reports on Progress in Physics 73(10): 106001.
Struyve, W., and H. Westman. 2007. A minimalist pilot-wave model for quantum electrodynamics. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 463(2088): 3115–3129.
Tegmark, M. 1993. Apparent wave function collapse caused by scattering. Foundations of Physics Letters 6(6): 571–590.
Tegmark, M. 1998. The interpretation of quantum mechanics: Many worlds or many words? Fortschritte der Physik 46(6–8): 855–862.
Teller, P. 1986. Relational holism and quantum mechanics. British Journal for the Philosophy of Science 37(1): 71–81.
Tooley, M. 1977. The nature of laws. Canadian Journal of Philosophy 7(4): 667–698.
Tumulka, R. 2006a. A relativistic version of the Ghirardi-Rimini-Weber model. Journal of Statistical Physics 125(4): 821–840.
Tumulka, R. 2006b. On spontaneous wave function collapse and quantum field theory. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 462(2070): 1897–1908.
Vaidman, L. 2012. Probability in the many-worlds interpretation of quantum mechanics. In Probability in physics, eds. Y. Ben-Menahem, and M. Hemmo, 299–311. Dordrecht: Springer.
Valentini, A. 1996. Pilot-wave theory of fields, gravitation and cosmology. In Bohmian mechanics and quantum theory: An appraisal, eds. J.T. Cushing, A. Fine, and S. Goldstein, 45–66. Berlin/Heidelberg: Springer.
van Fraassen, B. 1989. Laws and symmetry. Oxford/New York: Oxford University Press.
von Neumann, J. 1955 [1932]. Mathematical foundations of quantum mechanics. Trans. by R.T. Beyer. Princeton: Princeton University Press.
Wallace, D. 2002. Quantum probability and decision theory, revisited. arXiv preprint quant-ph/0211104.
Wallace, D. 2003. Everettian rationality: Defending Deutsch’s approach to probability in the Everett interpretation. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34(3): 415–439.
Wallace, D. 2008. Philosophy of quantum mechanics. In The Ashgate companion to contemporary philosophy of phyiscs, ed. D. Rickles, 16–98. Hants/Burlington: Ashgate.
Wallace, D. 2012. The emergent multiverse. Quantum theory according to the Everett interpretation. Oxford: Oxford University Press.
Wallace, D. 2014. Life and death in the tails of the GRW wave function. arXiv preprint arXiv:1407.4746.
Wallace, D., and C.G. Timpson. 2010. Quantum mechanics on spacetime I: Spacetime state realism. The British Journal for the Philosophy of Science 61(4): 697–727.
Williamson, J. 2010. In defence of objective Bayesianism. Oxford/New York: Oxford University Press.
Zeh, H. 2000. The problem of conscious observation in quantum mechanical description. Foundations of Physics Letters 13(3): 221–233.
Zeh, H.D. 1970. On the interpretation of measurement in quantum theory. Foundations of Physics 1(1): 69–76.
Zurek, W.H. 1982. Environment-induced superselection rules. Physical Review D 26(8): 1862.
Zurek, W.H. 2003. Environment-assisted invariance, entanglement, and probabilities in quantum physics. Physical Review Letters 90(12): 120404.
Zurek, W.H. 2005. Probabilities from entanglement, Born’s rule p k = |ψ k|2 from envariance. Physical Review A 71(5): 052105.
Zurek, W.H. 2009. Quantum darwinism. Nature Physics 5(3): 181–188.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Boge, F.J. (2018). ψ-Ontology, or, Making Sense of Quantum Mechanics. In: Quantum Mechanics Between Ontology and Epistemology. European Studies in Philosophy of Science, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-95765-4_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-95765-4_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-95764-7
Online ISBN: 978-3-319-95765-4
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)