Abstract
There is, it seems, a rather natural response to the conceptual problems raised by QM. This response, put frankly, is to say that ‘it’s all just epistemic!’ More precisely this would mean to deprive the quantum state of its ontological significance and to construe the theory not as a description of the actual, real situation of physical systems, but rather as a representation of the knowledge an actual or ideal observer or agent has about these. So for instance, when a quantum system passes a double slit, we cannot know exactly where it is going to turn up. But we can try to make precise predictions about its future behavior, based on our previous experience with similar situations and systems, and hence quantify, in a sense, our knowledge about its future behavior and about the occurrence of spots in various regions on the screen behind the slit. Again given past experience, a quantum mechanical state function may be the tool of choice to accomplish this task. But in the instant we see a dot appearing on the screen we can update our knowledge about the system’s actual state, since we can now be rather certain (assuming that we have not visited too many epistemology classes) that the system has occupied exactly that region on the screen at the moment of the appearance of the dot.
The field in a many-dimensional coordinate space does not smell like something real.
—A. Einstein, in a letter to Ehrenfest, 1926 (cf. Howard 1990, p. 83)
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Notes
- 1.
At that time, Einstein knew the cat thought-experiment from a letter Schrödinger had sent him, in which the latter described it in terms of an explosion rather than poisoning (cf. Mehra and Rechenberg 1987, p. 743).
- 2.
Fine (1984), however, gives a detailed critical analysis of the historical data concerning Einstein’s view of the quantum state and contends that the standard representation of Einsteins views is incorrect. In essence, the point is that Einstein seems to have used talk of ensembles merely as a means for grounding the belief in the incompleteness of QM, not as a serious suggestion for an alternative (cf. also Whitaker 1996, p. 239, on this point).
- 3.
Cf. also Whitaker (1996, p. 214) for an analysis of Schrödinger’s examples.
- 4.
Note that things might be phrased more accurately in terms of random variables \( \underline {\lambda }\)—or even random vectors \(\boldsymbol { \underline {\lambda }}\)—taking on values λ ∈ Λ (or λ in some suitable Cartesian product-space \(\times _{i=1}^{n}\Lambda _{i}\)) on systems S. Accordingly, when we occasionally speak about λ as a variable in what follows, this should be read as short for ‘value λ of variable \( \underline {\lambda }\)’.
- 5.
For completeness’ sake we note that Leifer (2014, p. 82), in his analysis of the approach, provides a treatment in terms of measure-theoretic notions, using a σ-algebra Σ (cf. Appendix A) over Λ, equipped with a σ-additive measure μ that maps from Σ into the interval [0, 1]. The epistemic state is then viewed as the (Radon-Nikodym) derivative of μ w.r.t. λ, which is only well-defined under certain conditions (cf. below) that not all conceivable models satisfy (cf. Leifer 2014, p. 90; Leifer and Maroney 2013, p. 4). Leaving out transition matrices, Leifer requires that \(\int {\mathrm{d}\mu _{\hat {\rho }}} \xi ^{k}_{M}(\lambda ) = \mathrm {Tr}(\hat {E}_{k}\hat {\rho })\), where \(\mu _{\hat {\rho }}\) is the probability measure over Σ induced by preparation \(P_{\hat {\rho }}\). This is only equivalent to the above condition (modulo transformation matrix) in case there is a measure λ which dominates all measures \(\mu _{\hat {\rho }}\) over the space Λ (cf. Appendix A), whence one can appeal to
in the integral (cf. Leifer and Maroney 2013, p. 4). Fortunately, we can here restrict our attention to models in which the assumption is valid and we need not bother with these details any further. - 6.
We slightly alter notation and wording, since Harrigan and Spekkens also call λ ψ and ψ “isomorphic”, which is meaningless for elements of spaces. We have also used our notion of true rather than ‘ontic’ states.
- 7.
These equivalence classes are then usually called ‘rays’ by physicists (cf. Heinosaari and Ziman 2012, p. 82), even though a ray is more precisely the set of all complex multiples of some vector. So the ‘ray’ in the sense of [ψ] is basically a ray of normalized vectors (cf. Gustafson and Sigal 2011, p. 193). The name ‘projective’ here obviously stems from the fact that any projector |ψ〉 〈ψ| projects equally onto |e iφψ〉 := e iφ|ψ〉, since |e iφψ〉 〈e iφψ| = e iφ |ψ〉 〈ψ|e −iφ = |ψ〉 〈ψ| (cf. also Heinosaari and Ziman 2012, p. 82).
- 8.
In some receptions (e.g. Lewis et al. 2012, p. 3 or Maroney 2012, p. 2) this requirement is refined such that an overlap between epistemic states is required only for non-orthogonal quantum states, as two orthogonal states |ϕ〉, |ψ〉 are usually construed as indicative of mutually exclusive preparation procedures, which one might (but need not) assume to result in mutually exclusive sets of true states. The negation of ψ-onticity merely implies the existence of two distinct quantum states that have densities associated to them with overlapping support. This is comparatively weak and makes a broad range of models possible. Refinements in terms of distance measures between the epistemic states have also been proposed (e.g. Pusey et al. 2012, p. 477; Aaronson et al. 2013, p. 2).
- 9.
In fact, in a concrete ψ-epistemic toy model investigated later, there will even be an equivocation norm operative, whence it may even be seen as presupposing objective Bayesiansim in Williamson’s sense.
- 10.
This reading is supported by further textual evidence: Harrigan and Rudolph (2007, p. 4), for instance, concede that the response functions “could occur because of our failure to take into account the precise ontological configurations of either [preparation or measurement]”; and similarly Spekkens constantly refers to an “unknown disturbance” (my emphasis—FB) of the system caused by the measurement in his 2007 paper, with obvious similarities to Heisenberg’s original formulation of the microscope thought experiment.
- 11.
We will treat their exposition of it as the only relevant reference for our purposes.
- 12.
We have here appealed to a few properties such as
, and 
, 
(cf. Heinosaari and Ziman 2012, p. 62 ff.). These properties are not difficult to prove; so the interested reader is encouraged to prove them herself. - 13.
One should not generally confuse |0〉 with the vacuum state in this context though. 0 is merely a label here, reminiscent of the binary bit-language of 1s and 0s.
- 14.
Actually, Spekkens lets quantum states directly correspond to the probability distributions; but we are here using the OM framework, whence they should be representative of preparations P instead.
- 15.
Note that it is not in contradiction to the Kolmogorov axioms that the entries in ξ sum up to 2 instead of 1, as ξ expressed in this way is variable in λ, i.e., in the true state on which it is conditional, not in the outcome. Only the sum over all outcome probabilities, given fixed parameters (λ, M) must sum to one.
- 16.
This is the equivocation norm that we had claimed was operative in the model.
- 17.
For completeness’ sake, note that Spekkens (2007, p. 5) also introduces a notion of convex combination for the model so that 1 ∨ 2 ∨ 3 ∨ 4 comes out as the toy-analogue of a completely mixed state which can be decomposed into 1 ∨ 2 and 3 ∨ 4 or 1 ∨ 3 and 2 ∨ 4 or…
- 18.
In fact, unitary operators together with antiunitary ones exhaust the state-automorphisms or symmetries on the set of all density matrices on a separable Hilbert space (e.g. Heinosaari and Ziman 2012, pp. 29 and 92 ff.). Antiunitary operators, however, “can describe only abstract symmetries (e.g. time inversion), not physically realizable symmetries such as rotations or translations.” (Heinosaari and Ziman 2012, p. 91)
- 19.
Such a phase shifter can, for instance, be implemented by a piece of matter with a refraction index different from that of air, in which light would travel at an altered velocity (e.g. Walker et al. 2012, p. 1050).
- 20.
Note that we have assumed both arms of the interferometer to be of equal length, so that none of the two states can pick up a phase due to a spatial delay. In fact, the spatially induced phase difference is what accounts for the interfence pattern in the double slit experiment (Sect. 2.1.1).
- 21.
In fact, varying the phase somewhat more than just
, one can appeal to probabilities of detection in either d
1 or d
2, where (say) 
for 
, as results from the setup with a general phase shift. One can equally use a difference in path length, as mentioned in Footnote 20, and this is what Grangier et al. (1986) actually did to confirm that the number of counts would conform to the predicted \(\cos ^{2}\)-regularity (cf. their p. 178). - 22.
Spekkens uses ‘⋅’ instead and refrains from labeling the systems, i.e. lets the conjunction be ordering sensitive (cf. 2007, p. 11).
- 23.
This is the much-used term that Schrödinger (1935a, p. 556) introduced to describe the situation.
- 24.
It would hence be more appropriate to use exclusive disjunction \(\dot {\vee }\) instead of ∨.
- 25.
It is however not clear that the model fits into the OM approach or whether it can be made to do so. This does not really pose a problem for us, though, since we are in principle more generally concerned with epistemic approaches to QM here.
- 26.
Recall that, in concert with the Bogen-Woodward understanding of ‘phenomena’ which we endorsed from Chap. 2 on, this may simply mean ‘implications of QM or QIT’.
- 27.
Indeed, this definition is not maximally general again, since we have appealed directly to probability densities. Leifer (2014, p. 99) instead uses the condition that the probability measure on the space ΛΨ = Λ1 × Λ2 is the product measure \(\mu _{1}\times \mu _{2}(\Lambda _{\Psi }) = \int _{\Lambda _{2}} \mu _{1}(\Omega _{\lambda _{2}}){\mathrm{d}\mu _{2}(\lambda _{2})}\), where
. For our discussion, no harm comes from using the simpler definition above. - 28.
This of course means that
, with k
(2) the preparation for the second system, and analogously for p
k(λ
2). - 29.
For notational simplicity we will later also use this letter to refer to the measurement (POVM) associated with the outcome states in \(\mathbb {R}\).
- 30.
These charges of transformability between the two types of models are, however, challenged by Leifer (2014, p. 113–114).
- 31.
Leifer (2014) gives a detailed overview of at least some of the recent development.
- 32.
Here he is referring especially to elaborations from a talk given by Spekkens (2008).
- 33.
It is of course open to debate whether one prefers to call something that is testable ‘physics’, and reserves the term ‘metaphysics’ for a priori investigations. But that is rather a matter of linguistic taste and intuition.
- 34.
Of course we could also use a quantum mechanically more complete description here, by including spatial degrees of freedom etc. But this has no influence on the relevant predictions; it would only make the description more complicated, since the spatial quantum state for two indistinguishable systems has to be appropriately (anti-)symmetrized as well: two indistinguishable fermions, say, would here have to be described by a state such as \({\left\vert \Psi \right\rangle} = \frac {1}{\sqrt {2}}({\left\vert L\right\rangle}{\left\vert R\right\rangle} +{\left\vert R\right\rangle}{\left\vert L\right\rangle})\otimes {\left\vert \chi \right\rangle}\), where |L〉 and |R〉 are two states in position space with non-overlapping supports in \(\mathbb {R}^{3}\), and |χ〉 is the singlet state (e.g. Ghirardi et al. 2002, p. 81 ff; Ghirardi and Marinatto 2003, p. 384).
- 35.
The operators \(\hat {p}_{1/2}\) correspond to
respectively, yielding eigenvalue 0 for the total operator \(\hat {p}_{1}+\hat {p}_{2}\); i.e. p
2 = −p
1. The respective position operators yield x and x + x
0 respectively, so that \(\hat {x}_{1}-\hat {x}_{2}\) gives the distance x
0 between the two, and a position measurement on system 1 with result x will imply position x + x
0 for system 2 (see also Aharonov and Rohrlich (2005, p. 27) and Schrödinger (1935a, p. 559) on this point). - 36.
The notation ‘λ ∈ T’ appealed to below is a bit sloppy, but it should be clear what is meant.
- 37.
The opinion that this is so however goes contrary to that of Maudlin (2014b, p. 6), who thinks that “the criterion is, in the parlance of philosophers, analytic.” (emphasis in original) ‘Predicting the value of a physical quantity with certainty’ could mean to predict the outcome of some experiment which could still not be indicative of what the investigated system ‘really did beforehand’, which may be the targeted ‘element of reality’. Moreover, predicting with certainty on theoretical grounds could have no actual experimental counterpart (incompatible experimental setups) and thus not refer to anything. These are reasons to doubt that the statement is analytic, and in fact we will see how to put these intuitions to work in Chap. 7.
- 38.
German original: “Es scheint mir keinem Zweifel zu unterliegen, dass die Physiker, welche die Beschreibungsweise der Quanten-Mechanik für prinzipiell definitiv halten, auf diese Ueberlegung wie folgt reagieren werden: Sie werden die Forderung […] von der unabhängigen Existenz des in verschiedenen Raum-Teilen vorhandenen Physikalisch-Realen fallen lassen; sie können sich mit Recht darauf berufen, dass die Quanten-Theorie von dieser Forderung nirgends explicite Gebrauch mache.”
- 39.
This kind of notation is also used by Graßhoff et al. (2005).
- 40.
The name ‘parameter independence’ is possibly misleading, since many things should certainly count as causal or probabilistic parameters. The intended ‘parameter’ here is the distant setting, whence Pawłowski et al. (2010, p. 2), for instance, use the name “setting independence” instead. We will however stick to the more widespread terminology.
- 41.
In contrast to e.g. Wiseman (2014) and Bell (1990b), and in the spirit of our above discussion of OMs, we have omitted direct reference to a preparation procedure P and instead only appealed to the quantum state χ, interpreted as a P-state. P would denote “the values of any number of other variables describing the experimental set-up, as admitted by ordinary quantum mechanics […]”, (Bell 1990b, p. 108) and would hence add no relevant information beyond χ in this context.
- 42.
In contrast to Friebe et al. (2015, p. 141), we have allowed for λ to depend on χ, since the OM approach requires this to be possible: χ is construed as the P-state therein, a representation of what was done to the system in a preparation procedure.
- 43.
- 44.
- 45.
Näger’s result is more straightforwardly concerned with causal influences and the latter results concern information, so to count these arguments as in favor of the same thing, a case has to be made that causation and information are related in an appropriate manner. Cf. Näger (2013a, p. 42 ff.) for discussion on these issues.
- 46.
German original: “Ohne die Annahme einer solchen Unabhängigkeit der Existenz (des ‘So-Seins’) der räumlich distanten Dinge voneinander, die zunächst dem Alltags-Denken entstammt, wäre physikalisches Denken in dem uns geläufigen Sinne nicht möglich.”
- 47.
Terminological warning: One sometimes encounters a differentiation between EPR-correlations and Bell-correlations, the former denoting the perfect correlation implied for the EPR-state or measurements along the same axis on the singlet, the latter referring to the precise correlations appealed to in Bell-inequalities, i.e. with different misalignment angles and violated by QM (e.g. Maudlin 2010b, p. 124). When we use the term ‘EPRB’-correlations, the ‘B’ stands for Bohm; but we allow to include the correlations predicted by QM for different misalignment angles, i.e. the ‘violating’ correlations rather than the violated ones.
- 48.
Reichenbach also required that (i) ¬C would equally screen off A and B, and that (ii) p(A|C) > p(A), p(B|C) > p(B). But as Butterfield (2007, p. 818) remarks, (ii) is simply appealed to by Reichenbach to account for positive correlation, and we are here equally interested in negative correlations. And the screening off by ¬C will be replaced shortly by a more general constraint.
- 49.
We remark here that today experiments have been realized in which a violation of a Bell-type inequality was reported using photons in a fiber that allowed them to be separated by a distance >300 km (Inagaki et al. 2013).
- 50.
Both models are also discussed at length and improved in Maudlin (2011, p. 160 ff.), and the elaborations and drawings therein are instructive. See also Maudlin’s criticism of this kind of model (his pp. 165–166).
- 51.
Cf. Redhead (1987, pp. 121 and 123) for an actual derivation of these from (FUNC).
- 52.
- 53.
The product rule applies since \(\hat {P}_{j}\) of course commutes with itself. And more generally, any two projectors that project onto orthogonal rays commute as well:
(for 〈i|j〉 = δ
ij). - 54.
You can easily convince yourself of this fact by assuming otherwise and multiplying by either |ψ〉 or |ϕ〉 from the right. You will find a contradiction with the assumption of non-collinearity.
- 55.
- 56.
is obviously degenerate since any state |a
j〈⊗|ϕ〉 with \(\hat {A}{\vert a_{j}\rangle} = a_{j}{\vert a_{j}\rangle}\) will give a
j for 
, regardless of |ϕ〉. - 57.
- 58.
E.g. Schurz (2014, p. 49) for some details on induction.
- 59.
There are, however, a few difficulties with the actual preparation and measurement of EPR states in the sense of the original paper: the state is not time dependent, and the descriptions used to set up the argument for incompleteness would only be valid at t = 0, whereas time evolution makes it unstable; and since a plane wave representation is used, there would be a non-vanishing probability of the two particles being basically anywhere in space, so that the assumption of spatial separatedness is actually unwarranted (cf. Home and Selleri 1991, p. 13). However, Praxmeyer et al. (2005) have constructed a scheme in which the EPR state appears as the limit of a two-mode squeezed state, and observables on it are considered which can be used to violate a Bell-type inequality.
- 60.
Depending on the specific setup used to implement the states appealed to in the EPR paper, this becomes a debatable claim; cf. Footnote 59.
in the integral (cf. Leifer and Maroney 
, and 
, 
(cf. Heinosaari and Ziman 
, one can appeal to probabilities of detection in either d
1 or d
2, where (say) 
for 
, as results from the setup with a general phase shift. One can equally use a difference in path length, as mentioned in Footnote 20, and this is what Grangier et al. (
. For our discussion, no harm comes from using the simpler definition above.
, with k
(2) the preparation for the second system, and analogously for p
k(λ
2).
respectively, yielding eigenvalue 0 for the total operator 
(for 〈i|j〉 = δ
ij).
is obviously degenerate since any state |a
j〈⊗|ϕ〉 with 
, regardless of |ϕ〉.References
Aaronson, S., A. Bouland, L. Chua, and G. Lowther. 2013. ψ-epistemic theories: The role of symmetry. Physical Review A 88(1–12): 032111.
Adams, S. 1997. Relativity. An introduction to space-time physics. London/Philadelphia: Taylor & Francis.
Aharonov, Y., and D. Rohrlich. 2005. Quantum paradoxes. Quantum theory for the perplexed. Weinheim: Wiley-VCH.
Albert, D.Z. 1992. Quantum mechanics and experience. Cambridge/London: Harvard University Press.
Aspect, A., J. Dalibard, and G. Roger. 1982. Experimental test of Bell’s inequalities using time-varying analyzers. Physical Review Letters 49(25): 1804–1807.
Audretsch, J. 2007. Entangled systems. New directions in quantum physics. Weinheim: Wiley-VCH.
Baaquie, B.E. 2013. The theoretical foundations of quantum mechanics. New York/Heidelberg: Springer.
Ballentine, L. 2014. Ontological models in quantum mechanics: What do they tell us? arXiv preprint arXiv:1402.5689.
Ballentine, L.E. 1970. The statistical interpretation of quantum mechanics. Reviews of Modern Physics 42(4): 358–381.
Bartlett, S.D., T. Rudolph, and R.W. Spekkens. 2012. Reconstruction of Gaussian quantum mechanics from Liouville mechanics with an epistemic restriction. Physical Review A 86(1): 012103(25 pp).
Basdevant, J.-L., and J. Dalibard. 2002. Quantum mechanics. Berlin/Heidelberg: Springer.
Belinfante, F.J. 1973. A survey of hidden variables theories. Oxford/New York: Pergamon Press.
Bell, J.S. 1987[1964]. On the Einstein-Podolsky-Rosen paradox. In Speakable and unspeakable in quantum mechanics, ed. J.S. Bell, 14–21. 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[1981]a. Bertlmann’s socks and the nature of reality. In Speakable and unspeakable in quantum mechanics, ed. J.S. Bell, 139–158. Cambridge/New York: Cambridge University Press.
Bell, J.S. 1990b. La Nouvelle cuisine. In Between science and technology. Proceedings of the international conference between science and technology. Eindhoven University of Technology, The Netherlands, 29–30 June 1989, eds. A. Sarlemijn, and P. Kroes, 97–115. Amsterdam/Oxford: North-Holland (Elsevier Science Publishers B.V.).
Bird, A., and E. Tobin. 2015. Natural kinds. 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/natural-kinds/.
Bohm, D. 1951. Quantum theory. New York: Dover Publications Inc.
Branciard, C. 2011. Detection loophole in Bell experiments: How postselection modifies the requirements to observe nonlocality. Physical Review A 83(3): 032123.
Bub, J. 1974. The interpretation of quantum mechanics. Dordrecht/Boston: D. Reidel Publishing Co.
Buchler, J., ed. 1955. Philosophical writings of Peirce. New York: Dover Publications Inc.
Busch, P., M. Grabowski, and P.J. Lahti. 1995. Operational quantum physics. Berlin/Heidelberg: Springer.
Butterfield, J. 2007. Stochastic Einstein locality revisited. British Journal for the Philosophy of Science 58(4): 805–867.
Cartwright, N. 1989. Nature’s capacities and their measurement. Oxford/New York: Oxford University Press. Reprinted 2002.
Case, W.B. 2007. Wigner functions and Weyl transforms for pedestrians. American Journal of Physics 76(10): 937–946.
Chalmers, D. 2012. Constructing the world. Oxford/New York: Oxford University Press.
Chen, G., D.A. Church, B.-G. Englert, C. Henkel, B. Rohwedder, M.O. Scully, and M.S. Zubairy. 2007. Quantum computing devices. Principles, designs, and analysis. Boca Raton/London: Chapman Hall/CRC.
Clauser, J.F., and M.A. Horne. 1974. Experimental consequences of objective local theories. Physical Review D 10(2): 526–535.
Clauser, J.F., M.A. Horne, A. Shimony, and R.A. Holt. 1969. Proposed experiment to test local hidden-variable theories. Physical Review Letters 23(15): 880–884.
Colbeck, R., and R. Renner. 2012. Is a system’s wave function in one-to-one correspondence with its elements of reality? Physical Review Letters 108(15): 150402(1–4).
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.
De Zela, F. 2008. A non-local hidden-variable model that violates Leggett-type inequalities. Journal of Physics A: Mathematical and Theoretical 41: 505301(9pp).
d’Espagnat, B. 1979. The quantum theory and reality. Scientific American 241: 158–181.
d’Espagnat, B. 1995. Veiled reality. An analysis of present day quantum mechanical concepts. Reading: Addison-Wesley Publishing Co.
Dickson, M. 2007. Non-relativistic quantum mechanics. In Philosophy of physics. Part A, eds. J. Butterfield, and J. Earman, 275–416. Amsterdam/Boston: Elsevier.
Dieks, D. 2002. Events and covariance in the interpretation of quantum field theory. In Ontological aspects of quantum field theory, eds. M. Kuhlmann, H. Lyre, and A. Wayne. New Jersey/London: World Scientific Publishing.
Dowling, J., and G. Milburn. 2003. Quantum technology: The second quantum revolution. Philosophical Transactions of the Royal Society of London 361: 1655–1674.
Drezet, A. 2012. Should the wave-function be a part of the quantum ontological state? Progress in Physics 4: 14–17.
Dunningham, J., and V. Vedral. 2007. Nonlocality of a single particle. Physical Review Letters 99: 180404.
Einstein, A. 1926. Letter to Sommerfeld. Einstein Archive 21–356.
Einstein, A. 1935. Letter to Schrödinger. Archived at the duplicate Einstein Archive, Mudd Manuscript Library, Princeton University.
Einstein, A. 1936. Phyiscs and reality, Trans. J. Piccard. Journal of the Franklin Institute 221(3): 349–382.
Einstein, A. 1948. Quanten-Mechanik und Wirklichkeit. Dialectica 2(3–4): 320–324.
Einstein, A. 1949a. Atobiographical notes. In Albert Einstein. Philosopher-Scientist, ed. P.A. Schilpp, 1–94. New York: MJF Books.
Einstein, A. 1949b. Reply to criticism. In Albert Einstein. Philosopher-Scientist, ed. P.A. Schilpp, 665–688. New York: MJF Books.
Einstein, A. 2011 [1939]. Letter to Schrödinger. In Letters on wave mechanics: Correspondence with H. A. Lorentz, Max Planck, and Erwin Schrödinger, ed. K. Przibram. New York: Open Road Media.
Einstein, A., B. Podolsky, and N. Rosen. 1935. Can quantum-mechanical description of physical reality be considered complete? Physical Review 47: 777–780.
Emerson, J., D. Serbin, C. Sutherland, and V. Veitch. 2013. The whole is greater than the sum of the parts: On the possibility of purely statistical interpretations of quantum theory. arXiv preprint arXiv:1312.1345.
Fine, A. 1982. Some local models for correlation experiments. Synthese 50(2): 279–294.
Fine, A. 1984. What is Einstein’s statistical interpretation, or, is it Einstein for Whom Bell’s theorem tolls? Topoi 3(1): 23–36.
Fleming, G.N. 2000. Reeh-Schlieder meets Newton-Wigner. Philosophy of Science 67:S495–S515.
Friebe, C., M. Kuhlmann, H. Lyre, P. Näger, O. Passon, and M. Stöckler. 2015. Philosophie der Quantenphysik. Berlin/Heidelberg: Springer.
Friedman, M. 1999. Reconsidering logical positivism. Cambridge/New York: Cambridge University Press.
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.
Garner, A.J.P., O.C.O. Dahlsten, Y. Nakata, M. Murao, and V. Vedral. 2013. A framework for phase and interference in generalized probabilistic theories. New Journal of Physics 15: 093044(26pp).
Ghirardi, G., and L. Marinatto. 2003. Entanglement and properties. Fortschritte der Physik 51(4–5): 379–387.
Ghirardi, G., L. Marinatto, and T. Weber. 2002. Entanglement and properties of composite quantum systems: A conceptual and mathematical analysis. Journal of Statistical Physics 108(1–2): 49–122.
Gillies, D. 2000. Philosophical theories of probability. London/New York: Routledge.
Giovannetti, V., S. Lloyd, and L. Maccone. 2004. Quantum-enhanced measurements: Beating the standard quantum limit. Science 306(5700): 1330–1336.
Giustina, M., M.A. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-Å. Larsson, C. Abellán, et al. 2015. Significant-Loophole-Free test of Bell’s theorem with entangled photons. Physical Review Letters 115(25): 250401.
Goodman, N. 1983 [1955]. The new riddle of induction. In Fact, fiction, and forecast, ed. N. Goodman, 59–83, 4th ed. Cambridge: Harvard University Press.
Grangier, P. 2001. Count them all. Nature 409(6822): 774–775.
Grangier, P., G. Roger, and A. Aspect. 1986. Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences. Europhysics Letters 1(4): 173–179.
Graßhoff, G., S. Portmann, and A. Wüthrich. 2005. Minimal assumption derivation of a bell-type inequality. The British Journal for the Philosophy of Science 56(4): 663–680.
Gustafson, S.J., and I.M. Sigal. 2011. Mathematical concepts of quantum mechanics, 2nd ed. Berlin/Heidelberg: Springer.
Hardy, L. 1994. Nonlocality of a single photon revisited. Physical Review Letters 73: 2279–2283.
Hardy, L. 2013. Are quantum states real? International Journal of Modern Physics B 27(1–3): 1345012 (19pp).
Harrigan, N., and T. Rudolph. 2007. Ontological models and the interpretation of contextuality. arXiv preprint arXiv:0709.4266.
Harrigan, N., and R.W. Spekkens. 2010. Einstein, incompleteness, and the epistemic view of quantum states. Foundations of Physics 40: 125–157.
Hartmann, S. 1996. The world as a process. In Modelling and simulation in the social sciences from the philosophy of science point of view, eds. R. Hegelsmann, U. Mueller, and K.G. Troitzsch, 77–100. Dordrecht: Springer Science + Business Media.
Heil, J. 2003. From an ontological point of view. Oxford/New York: Oxford University Press.
Heinosaari, T., and M. Ziman. 2012. The mathematical language of quantum theory. From uncertainty to entanglement. Cambridge/New York: Cambridge University Press.
Held, C. 2013. The Kochen-Specker theorem. 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/bell-theorem/.
Hensen, B., H. Bernien, A. Dréau, A. Reiserer, N. Kalb, M. Blok, J. Ruitenberg, R. Vermeulen, R. Schouten, C. Abellán, et al. 2015. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature 526(7575): 682–686.
Hessmo, B., P. Usachev, H. Heydari, and G. Björk. 2004. Experimental demonstration of single photon nonlocality. Physical Review Letters 92: 180401.
Hofer-Szabó, G., and P. Vecsernyés. 2014. Bell’s local causality for philosophers. philsci eprint: http://philsci-archive.pitt.edu/10795/1/LocalizationofCC7.pdf.
Home, D., and F. Selleri. 1991. Bell’s theorem and the EPR paradox. Rivista del Nuovo Cimento 14(9): 1–95.
Home, D., and M.A.B. Whitaker. 1992. Ensemble interpretation of quantum mechanics. A modern perspective. Physics Reports 210(4): 223–317.
Howard, D. 1985. Einstein on locality and separability. Studies in History and Philosophy of Science Part A 16(3): 171–201.
Howard, D. 1989. Holism, separability, and the metaphysical implications of the Bell experiments. In Philosophical consequences of quantum theory. Reflections on Bell’s theorem, eds. J.T. Cushing, and E. McMullin, 224–253. Notre Dame: University of Notre Dame Press.
Howard, D. 1990. ‘Nicht sein kann was nicht sein darf,’ or the Preshistory of EPR, 1909–1935: Einstein’s early worries about the quantum mechanics of composite systems. In Sixty-two years of uncertainty. Historical, philosophical, and physical inquiries into the foundations of quantum mechanics, ed. A.I. Miller, 61–112. New York/London: Plenum Press.
Hughes, G.E., and M.J. Cresswell. 1996. A new introduction to modal logic. London/New York: Routledge.
Hughes, R.I.G. 1989. The structure and interpretation of quantum mechanics. Cambridge/London: Harvard University Press.
Inagaki, T., N. Matsuda, O. Tadanaga, M. Asobe, and H. Takesue. 2013. Entanglement distribution over 300 km of fiber. Optics Express 21(20): 23241–23249.
Isham, C.J., and J. Butterfield. 1998. Topos perspective on the Kochen-Specker theorem: I. Quantum states as generalized valuations. International Journal of Theoretical Physics 37(11): 2669–2733.
Jaeger, G. 2007. Quantum information. An overview. New York: Springer Science + Business Media, LLC.
Jammer, M. 1974. The philosophy of quantum mechanics: The interpretations of QM in historical perspective. Hoboken: Wiley.
Jarrett, J.P. 1984. On the physical significance of the locality conditions in the bell arguments. Noûs 18(4): 569–589.
Jarrett, J.P. 1989. Bell’s theorem: A guide to the implications. In Philosophical consequences of quantum theory. Reflections on Bell’s theorem, eds. J.T. Cushing, and E. McMullin, 60–79. Notre Dame: University of Notre Dame Press.
Jaynes, E.T. 2003. Probability theory. The logic of science. Cambridge/New York: Cambridge University Press.
Jennings, D., and M. Leifer. 2015. No return to classical reality. Contemporary Physics 57(1): 60–82.
Kiefer, C. 2003. Quantentheorie, 2nd ed. Frankfurt a. M.: Fischer Taschenbuch Verlag.
Kochen, S., and E.P. Specker. 1975 [1967]. The problem of hidden variables in quantum mechanics. In The logico-algebaic approach to quantum mechanics, vol. I. Historical evolution, ed. C.A. Hooker. Dordrecht/Boston: D. Reidel Publishing Company.
Leifer, M. 2014. Is the quantum state real? An extended review of ψ-ontology theorems. Quanta 3(1): 67–155.
Leifer, M.S., and O.J.E. Maroney. 2013. Maximally epistemic interpretations of the quantum state and contextuality. Physical Review Letters 110: 120401(1–5).
Leitgeb, H. 2011. New life for Carnap’s Aufbau? Synthese 180(2): 265–299.
Lewis, D.K. 1983. New work for a theory of universals. Australasian Journal of Philosophy 61(4): 343–377.
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).
Mann, C., and R. Crease. 1988. John Bell, particle physicist (interview). Omni 10(8): 84–92, 121.
Maroney, O.J., and C.G. Timpson. 2014. Quantum- vs. macro-realism: What does the Leggett-Garg inequality actually test? arXiv preprint arXiv:1412.6139.
Maroney, O.J.E. 2012. How statistical are quantum states? arXiv preprint arXiv:1207.6906.
Maudlin, T. 2007. The metaphysics within physics. Oxford/New York: Oxford University Press.
Maudlin, T. 2010b. What Bell proved: A reply to blaylock. American Journal of Physics 78(1): 121–125.
Maudlin, T. 2011. Quantum non-locality and relativity. Metaphysical intimations of modern physics, 3rd ed. Malden/Oxford: Wiley-Blackwell.
Maudlin, T. 2014b. What Bell did. Journal of Physics A: Mathematical and Theoretical 47(42): 424010(24pp).
Ma̧czyński, M.J. 1971. Boolean properties of observables in axiomatic quantum mechanics. Reports on Mathematical Physics 2(2): 135–150.
McIntyre, D.H. 2012. Quantum mechanics. A paradigms approach. Boston/Columbus: Pearson.
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.
Mermin, N.D. 1993. Hidden variables and the two theorems of John Bell. Reviews of Modern Physics 65(3): 803–815.
Näger, P. 2013a. Causal graphs for EPR experiments. philsci e-print: http://philsci-archive.pitt.edu/9915/3/Naeger_PM_2013_%2D_Causal_Graphs_for_EPR_Experiments.pdf.
Näger, P.M. 2013b. A stronger bell argument for quantum non-locality. arXiv preprint arXiv:1308.3455.
Nielsen, M., and I. Chuang. 2010. Quantum computation and quantum information, 10th anniversary ed. Cambridge/New York: Cambridge University Press.
Nigg, D., T. Monz, P. Schindler, E.A. Martinez, M. Chwalla, M. Hennrich, R. Blatt, M.F. Pusey, T. Rudolph, and J. Barrett. 2012. Can different quantum state vectors correspond to the same physical state? An experimental test. arXiv preprint arXiv:1211.0942.
Norsen, T. 2007. Against ‘Realism’. Foundations of Physics 37(3): 311–340.
Norsen, T. 2009. Local causality and completeness: Bell vs. Jarrett. Foundations of Physics 39(3): 273–294.
Norsen, T. 2011. John S. Bell’s concept of local causality. American Journal of Physics 79(12): 1261–1275.
Patra, M.K., S. Pironio, and S. Massar. 2013. No-Go theorems for ψ-epistemic models based on a continuity assumption. Physical Review Letters 111: 090402(1–4).
Pawłowski, M., J. Kofler, T. Paterek, M. Seevinck, and C. Brukner. 2010. Non-local setting and outcome information for violation of Bell’s inequality. New Journal of Physics 12: 083051(9pp).
Pearle, P. 1968. Reply to Dr. Sach’s letter. American Journal of Physics 36: 464–465.
Peirce, C.S. [1878]. Deduction, induction, and hypothesis. In The essential Peirce. Selected philosophical writings, vol. 1 (1867–1893), eds. N. Houser, and C. Kloesel, 186–199. Bloomington/Indianapolis: Indiana University Press.
Peres, A. 1991. Two simple proofs of the Kochen-Specker theorem. Journal of Physics A: Mathematical and General 24(4):L175–L178.
Peres, A. 1999. All the Bell inequalities. Foundations of Physics 29(4): 589–614.
Peres, A. 2002. Quantum theory: Concepts and methods. New York/Boston: Kluwer.
Peters, D. 2014. What elements of successful scientific theories are the correct targets for ‘selective’ scientific realism? Philosophy of Science 81(3): 377–397.
Portmann, S., and A. Wüthrich. 2007. Minimal assumption derivation of a weak Clauser-Horne inequality. Studies in History and Philosophy of Modern Physics 38: 844–862.
Praxmeyer, L., B.-G. Englert, and K. Wódkiewicz. 2005. Violation of Bell’s inequality for continuous-variable EPR states. The European Physical Journal D 32(2): 227–231.
Pusey, M.F., J. Barrett, and T. Rudolph. 2011. On the reality of the quantum state. arXiv preprint arXiv:1111.3328.
Pusey, M.F., J. Barrett, and T. Rudolph. 2012. On the reality of the quantum state. Nature Physics 8(6): 475–478.
Redhead, M. 1987. Incompleteness, nonlocality, and realism. A prolegomenon to the philosophy of quantum mechanics. Oxford: Clarendon Press.
Reeh, H., and S. Schlieder. 1961. Bemerkungen zur Unitäräquivalenz von Lorentzinvarianten Feldern. Nuovo Cimento 22(5): 1051–1068.
Reichenbach, H. 1944. Philosophic foundations of quantum mechanics. Mineloa/New York: Dover Publications, Inc.
Reichenbach, H. 1961. Experience and prediction. An analysis of the foundations and structure of knowledge. Chicago/London: The University of Chicago Press.
Reichenbach, H. 1965. The direction of time. Edited by Maria Reichenbach. Mineloa/New York: Dover Publications, Inc.
Ruetsche, L. 2011. Interpreting quantum theories. Oxford/New York: Oxford University Press.
Sakurai, J.J. 1994. Modern quantum mechanics, rev. ed. Reading/New York: Addison-Wesley.
Schlosshauer, M., and A. Fine. 2012. Implications of the Pusey-Barrett-Rudolph quantum no-go theorem. Physical Review Letters 108: 260404(1–4).
Schlosshauer, M., and A. Fine. 2014. No-go theorem for the composition of quantum systems. Physical Review Letters 112: 070407(1–4).
Schrödinger, E. 1935a. Discussion of probability relations between separated systems. Mathematical Proceedings of the Cambridge Philosophical Society 31(4): 555–563.
Schrödinger, E. 1983 [1935]b. The present situation in quantum mechanics. A translation of Schrödinger’s ‘Cat Paradox’ paper. In Quantum theory and measurement, eds. J.A. Wheeler, and W.H. Zurek. Trans. by J.D. Trimmer. Princeton: Princeton University Press.
Schurz, G. 2008. Patterns of abduction. Synthese 164(2): 201–234.
Schurz, G. 2014. Philosophy of science. A unified approach. New York/London: Routledge.
Shalm, L.K., E. Meyer-Scott, B.G. Christensen, P. Bierhorst, M.A. Wayne, M.J. Stevens, T. Gerrits, S. Glancy, D.R. Hamel, M.S. Allman, et al. 2015. Strong loophole-free test of local realism. Physical Review Letters 115(25): 250402.
Shankar, R. 1994. Principles of quantum mechanics, 2nd ed. New York: Plenum Publishers.
Shimony, A. 1984. Contextual hidden variables theories and Bell’s inequalities. The British Journal for the Philosophy of Science 35(1): 25–45.
Shimony, A. 1990. An exposition of Bell’s theorem. In Sixty-two years of uncertainty. Historical, philosophical, and physical inquiries into the foundations of quantum mechanics, ed. A.I. Miller, 33–44. New York/London: Plenum Press.
Shimony, A. 2009. Bell’s theorem. 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/bell-theorem/.
Spekkens, R. 2014. Quasi-quantization: Classical statistical theories with an epistemic restriction. arXiv preprint arXiv:1409.5041.
Spekkens, R.W. 2005. Contextuality for preparations, transformations, and unsharp measurements. Physical Review A 75: 052108.
Spekkens, R.W. 2007. Evidence for the epistemic view of quantum states: A toy theory. Physical Review A 75: 032110.
Spekkens, R.W. 2008. Why the quantum? Insights from classical theories with a statistical restriction. PIRSA: 08020051.
Spekkens, R.W. 2012. Why I am not a ψ-ontologist. PIRSA: 12050021.
Strapp, H.P. 1975. Bell’s theorem and world process. Il Nuovo Cimento 29(2): 270–276.
Summers, S.J., and R. Werner. 1985. The vacuum violates Bell’s inequalities. Physics Letters 110A(5): 257–259.
Suppes, P. 1998. Pragmatism in physics. In The role of pragmatics in contemporary philosophy, eds. P. Weingartner, G. Schurz, and G. Dorn, 236–252. Vienna: Hölder-Pichler-Tempsky.
Takeda, S., M. Zwierz, H.M. Wiseman, and A. Furusawa. 2015. Experimental proof of nonlocal wavefunction collapse for a single particle using homodyne measurements. Nature Communications 6: 6665.
Tan, S.M., D.F. Walls, and M.J. Collett. 1991. Nonlocality of a single photon. Physical Review Letters 66: 252–255.
Taylor, E.F., and J.A. Wheeler. 1963. Spacetime physics. San Francisco: W. H. Freeman and Company.
Thaller, B. 2005. Advanced visual quantum mechanics. Berlin/Heidelberg: Springer.
Timpson, C.G. 2013. Quantum information theory and the foundations of quantum mechanics. Oxford: Oxford University Press.
van Enk, S. 2007. A toy model for quantum mechanics. Foundations of Physics 37(10): 1447–1460.
van Fraassen, B.C. 1982b. The Charybdis of realism: Epistemological implications of Bell’s inequality. Synthese 52(1): 25–38.
Vervoort, L. 2013. Bell’s theorem: Two neglected solutions. Foundations of Physics 43(6): 769–791.
von Neumann, J. 1955 [1932]. Mathematical foundations of quantum mechanics. Trans. by R.T. Beyer. Princeton: Princeton University Press.
Vértesi, T., and N. Brunner. 2014. Disproving the Peres conjecture by showing Bell nonlocality from bound entanglement. Nature Communications 5: 5297(1–5).
Walker, J., D. Halliday, and R. Resnick. 2012. Fundamentals of physics, 10th ed. Hoboken: Wiley.
Wallace, D. 2006. In defence of naiveté: The conceptual status of Lagrangian quantum field theory. Synthese 151(1): 33–80.
Werner, R.F. 1989. Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. Physical Review A 40(8): 4277–4281.
Werner, S.A., R. Colella, A.W. Overhauser, and C. Eagen. 1975. Observation of the phase shift of a neutron due to precession in a magnetic field. Physical Review Letters 35(16): 1053–1055.
Whitaker, A. 1996. Einstein, Bohr and the quantum dilemma. Cambridge/New York: Cambridge University Press.
Wigner, E.P. 1970. On hidden variables and quantum mechanical probabilities. American Journal of Physics 38(8): 1005–1009.
Wiseman, H.M. 2014. The two Bell’s theorems of John Bell. Journal of Physics A: Mathematical and Theoretical 47(42): 424001(31pp).
Wiseman, H.M., S.J. Jones, and A.C. Doherty. 2007. Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox. Physical Review Letters 98(14): 140402.
Wiseman, H.M., and G.J. Milburn. 2010. Quantum measurement and control. Cambridge/New York: Cambridge University Press.
Wittmann, B., S. Ramelow, F. Steinlechner, N.K. Langford, N. Brunner, H.M. Wiseman, R. Ursin, and A. Zeilinger. 2012. Loophole-free Einstein-Podolsky-Rosen experiment via quantum steering. New Journal of Physics 14: 053030(12pp).
Wootters, W.K. 2006. Distinguishing unentangled states with an unentangled measurement. International Journal of Quantum Information 04(01): 219.
Wroński, L. 2014. Reichenbach’s paradise. Constructing the realm of probabilistic common ‘causes’. Warsaw/Berlin: De Gruyter Open.
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Boge, F.J. (2018). Just a Matter of Knowledge?. 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_4
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