Abstract
Can there be ‘peaceful coexistence’ between quantum theory and special relativity? Thirty years ago, Shimony hoped that isolating the culprit (i.e. the false assumption) in proofs of Bell inequalities as Outcome Independence would secure such peaceful coexistence: or, if not secure it, at least show a way—maybe the best or only way—to secure it. In this paper, I begin by being sceptical of Shimony’s approach, urging that we need a relativistic solution to the quantum measurement problem (Sect. 2). Then I analyse Outcome Independence in Kent’s realist one-world Lorentz-invariant interpretation of quantum theory (Sects. 3 and 4). Then I consider Shimony’s other condition, Parameter Independence, both in Kent’s proposal and more generally, in the light of recent remarkable theorems by Colbeck, Renner and Leegwater (Sect. 5). For both Outcome Independence and Parameter Independence, there is a striking analogy with the situation in pilot-wave theory. Finally, I will suggest that these recent theorems make some kind of peaceful coexistence mandatory for someone who, like Shimony, endorses Parameter Independence.
Dedicated to the memory of Abner Shimony (1928–2015).
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Notes
- 1.
- 2.
My (2015) is another such effort. But there are several other proposals deserving more attention from philosophers, such as those of [1], and Landsman and co-authors (2013, 2013a, 2017 Chapters 10.1–3, 11.4).
- 3.
As is also well-known, he asked himself this question in print, in the closing paragraph of his ground-breaking first paper on hidden variables: a paper which, due to an editorial oversight at Reviews of Modern Physics, was only published in 1966, i.e. after he had given a ‘Yes’ answer to the question for deterministic hidden variables, in his 1964 proof of a Bell inequality.
- 4.
- 5.
This condition is found in, for example: Bell’s 1971 paper (2004: pp. 36–38), Clauser and Horne ([16]: Eq. (2’), p. 528), and Shimony ([64]: Sect. 2 Eq. (10), and Sect. 4 Eq. (37)). The facts that this condition (i) occurs in both the Bell, and the Clauser and Horne, papers, and (ii) suffices, together with our earlier ‘no conspiracy’ assumption (that \(\rho \) in Eq. 2 is independent of which quantity is measured), for a Bell inquality, were first clarified by Shimony, Horne, Clauser and Bell in a famous 1976 exchange. It is reprinted as [5], and as Chap. 12 of [62].
- 6.
Reference [35] is the most thorough early source for this ‘conjunction’ point. But we should recall van Fraassen’s brief but masterly exposition, which dubs Parameter Independence ‘Hidden Locality’, and Outcome Independence ‘Causality’ (1982: principles IV and III, respectively, p. 31). Incidentally, Shimony himself came to agree that ‘parameter’ was too general a word for ‘distant setting’. His (2009a: Eqs. 8 and 9) replaces the label ‘Parameter Independence’ by ‘Remote Context Independence’, and correspondingly ‘Outcome Independence’ by ‘Remote Outcome Independence’. But I shall stick to using the established labels.
- 7.
- 8.
Similarly, some authors ([32, 65]) suggested that the moral of OD was that quantum theory exhibited a species of holism or non-separability. Cf. Morganti ([47]: Sect. 2) as an example of the ongoing philosophical discussion. But as the sequel indicates, I concur with Henson ([30]: pp. 1021–1028, Sect. 3.1–3.4) that this moral does not, as Henson puts it, ‘relieve the problem of Bell’s theorem’.
- 9.
This point echoes Bell’s viewpoint, mentioned in Sect. 1. But perhaps one should say, so as to reflect one’s hope of reconciling the quantum with relativity: not ‘coincidence’, but ‘manna from Heaven’.
- 10.
- 11.
As we will see, the spacetime need not be Minkowski: any appropriately causally well-behaved spacetime will do. There is a more substantial constraint, arising from his appeal to a final boundary condition: viz. that there should be a well-defined limit to a sequence of probability distributions, associated with a sequence of successively later and later spacelike hypersurfaces. But as Kent discusses, there is good reason to think this will be satisfied in favoured cosmological models.
- 12.
Remark: Kent’s focus is on the measurement problem, which he prefers to call the reality problem, ‘since few physicists now believe that the fundamental laws of nature involve measuring devices per se or that progress can be made by analysing them’ (2014, 012107–1). Hence the title of his paper. I agree with his preference for ‘reality problem’ over ‘measurement problem’: but I will keep to the traditional term, reflecting his wider concern by talking about seeking an ‘interpretation of quantum theory’.
- 13.
After expounding stages (i)–(iii), Kent discusses taking S ever later in spacetime, i.e. letting S go to future infinity; and therefore his proposal needs the probability distributions associated to ever later S to have an appropriate limit: cf. footnote 11. But I shall not discuss this aspect.
- 14.
Though much could be said about this topic, this is not the place: except for two short points, the first historical and the second conceptual. (1): Though I duly cited d’Espagnat’s clear and influential presentation of the point, and nowadays the decoherence literature often says it clearly (e.g. Zeh, Joos et al. (2003, p. 36, 43); Janssen (2008, Sects. 1.2.2, 3.3.2)), it is humbling to recall that Schrödinger already was clear on it in his amazing 1935 papers: cf. especially the analogy with a school examination (1935, Sect. 13, p. 335 f.). (2): Although I thus condemn this ‘one fell swoop’ solution (joining, of course, much wiser authorities including Bell): I of course agree that the result here—obtaining an improper mixture nearly diagonal in a quantity you ‘want’ to have definite values—can form an important part of a principled, and clear-headed, solution to the measurement problem. The obvious example is the modal interpretation, in its early versions from the mid-1990s (cf. [22]): which, roughly speaking, proposed as a postulate, going beyond quantum theory, that the eigenprojections of any system’s density matrix have definite values.
- 15.
For clarity and simplicity, I will again suppress the need to let the late spacelike hypersurface S go to future infinity. Cf. footnotes 11 and 13.
- 16.
So in terms of the formalism: Kent’s idea is like an appeal to one ‘branch’ of the state of an environmental particle, i.e. one component of its improper mixture, to pick out as factual the corresponding (strictly correlated) component of the improper mixture of the system of interest. But only ‘like’, not ‘identical with’! As I stressed in Sect. 3.2.2’s Contrasts with ‘decoherence as usual’: the difference is that Kent avoids the error of assuming an improper mixture is ignorance-interpretable. He knowingly postulates the beables, and their probabilities, that secure an actual quasiclassical history, while avoiding this error.
- 17.
Again, there is an interesting comparison with the pilot-wave theory. For my question to Kent is the analogue of a question sometimes raised about the pilot-wave theory. Namely: does the ‘psycho-physical parallelism’ ([69], Chap. VI.1 p. 418f.) between some mental states, such as states of perceptual knowledge, and some physical states of our sensory organs (e.g. depression of a touch receptor in my fingertip, or photons impinging on my retina) mean that a perception being definite—one way rather than another—involves a point-particle being in one wave-packet rather than another? (For example, cf. Brown and Wallace (2005: Sect. 7, pp. 533–537).) But I think that on this topic, Kent’s situation is much more comfortable than the pilot-wave theorist’s. For according to modern psychophysics, it is much more plausible that mental states being one way rather than another correspond to (i) values of components of stress-energy at locations in the brain being one way rather another, than to (ii) point-particles being in one location rather than another.
- 18.
There is nothing suspect about such tenseless verbs. They are not a philosophers’ fiction or contrivance: the verbs in proverbs, e.g. ‘a stich in time saves nine’, and in pure mathematics, e.g. ‘1 + 1 \(=\) 2’, are tenseless.
- 19.
Here again, the words ‘registering’, and ‘recording that it reflected’, are to be understood tenselessly, in line with the warning at the end of Sect. 4.1. That is: there is indeed an actual fact as to which reflection happens (tenselessly!). But this fact is not independent of, nor is it ‘made true’ or ‘settled’ before the time of, the actual final condition.
- 20.
This difference implies no criticism of Kent: the pilot-wave theory is long-established, and most expositions of its recovery of orthodoxy do not involve any cosmological, and so inevitably speculative, considerations of the kind Kent’s proposal must tangle with.
- 21.
Furthermore, Leegwater allows the measure over hidden variables to depend on more than just the quantum state (although not which quantity is measured). For example, it can depend on the specific method that was used to prepare the state. I stress that discerning the no-conspiracy assumption is not original to me: Landsman and Leegwater are perfectly clear that they make this assumption, even though it is not given a formal label or acronym ([43], pp. 122103–2, assumption CQ and its footnote 14; 2017, p. 221, Definition 6.20 and following text; [45], p. 21 footnote 7 and its preceding text).
- 22.
Note the obvious contrast with the dynamical reduction programme, i.e. with the view that the universal quantum state evolves non-unitarily, collapsing appropriately throughout history so as to yield a quasiclassical world (cf. footnote 2 and Sect. 5.2). On that view, the quasiclassical world no doubt includes which quantity, or quantities, are measured at all the various times, and so the final universal quantum state certainly will depend on such facts. So in such a universe, a Kentian algorithm applied to the final condition would violate no-conspiracy.
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Acknowledgements
Dedicated to the memory of Abner Shimony. As all who met him soon realized, it was a pleasure and a privilege to know him, both as a person and as an intellect. It is a pleasure to thank Masanao Ozawa for the invitation to the Nagoya conference; and to thank him, Francesco Buscemi and the other local organizers, for a very enjoyable and valuable meeting. I am very grateful to Adrian Kent for generous advice and encouragement; and to Bryan Roberts for the splendid diagram. For comments on a previous version, I thank an anonymous referee, audiences in Cambridge, Wayne Myrvold, James Read, Bryan Roberts and four Dutch wizards: Dennis Dieks, Fred Muller and especially Guido Bacciagaluppi and Gijs Leegwater.
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Butterfield, J. (2018). Peaceful Coexistence: Examining Kent’s Relativistic Solution to the Quantum Measurement Problem. In: Ozawa, M., Butterfield, J., Halvorson, H., Rédei, M., Kitajima, Y., Buscemi, F. (eds) Reality and Measurement in Algebraic Quantum Theory. NWW 2015. Springer Proceedings in Mathematics & Statistics, vol 261. Springer, Singapore. https://doi.org/10.1007/978-981-13-2487-1_11
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