”The Unavoidable Interaction Between the Object and the Measuring Instruments”: Reality, Probability, and Nonlocality in Quantum Physics

This article aims to contribute to the ongoing task of clarifying the relationships between reality, probability, and nonlocality in quantum physics. It is in part stimulated by Khrennikov’s argument, in several communications, for “eliminating the issue of quantum nonlocality” from the analysis of quantum entanglement. I argue, however, that the question may not be that of eliminating but instead that of further illuminating this issue, a task that can be pursued by relating quantum nonlocality to other key features of quantum phenomena. I suggest that the following features of quantum phenomena and quantum mechanics, distinguishing them from classical phenomena and classical physics—(1) the irreducible role of measuring instruments in defining quantum phenomena, (2) discreteness, (3) complementarity, (4) entanglement, (5) quantum nonlocality, and (6) the irreducibly probabilistic nature of quantum predictions—are all interconnected, so that it is difficult to give an unconditional priority to any one of them. To argue this case, I shall consider quantum phenomena and quantum mechanics from a nonrealist or, in terms adopted here, “reality-without-realism” (RWR) perspective. This perspective extends Bohr’s view, grounded in his analysis of the irreducible role of measuring instruments in the constitution of quantum phenomena.

1. My argument will be restricted to the standard QM. Other theories of quantum phenomena, such as Bohmian mechanics, will only be mentioned in passing. I shall also put aside the complexities involved in using such terms as “theory,” “model,” or “mathematical model,” considered from the RWR perspective in [1, pp. 6–10]

2. Khrennikov, in [13, 14] in part responds to the argumentation of this author in [16, 17]. The present article is a revised version of [17]. While still responding to Khrennikov, it offers a more independent argument and new concepts, in particular that of quantum indefinitiveness.

3. Thus, he changed his view even before the lecture, given in September 1927, was published in April 1928 [20]. Bohr, notably, dated the published version 1927 when it was reprinted in his book, Atomic Theory and the Description of Nature [20], now the first volume of [19].

4. I have considered different versions of Bohr’s interpretation in [22]. It is worth noting that there is no single Copenhagen interpretation, as even Bohr changed his views a few times. It is more fitting to speak, as Heisenberg did, of “the Copenhagen spirit of the quantum theory” [23, p. iv]. This spirit designates a spectrum of interpretations that share some, but not all, of their features.

5. The literature on the subject is extensive, and my limits here only allow me to mention a very small portion of it.

6. It is worth noting that Khrennikov, too, brings into consideration complementarity and the role of Planck’s constant, h [15].

7. Two such cases are “the continuity axiom” of L. Hardy’s derivation [27] and “the purification postulate” of that of D’Ariano et al. [28].

8. See, for example, [29, 30]. I have discussed this subject in detail in [1, pp. 33–34].

9. While in physics the primary reality considered is that of matter, a reality, including a reality without realism, can be mental, for example, in mathematics [32, pp. 203–210].

10. Although terms “realist” and “ontological” sometimes designate more diverging concepts, they are close in their meaning and will be used interchangeably here.

11. One could in principle see the assumption of the existence or reality of something to which a theory can relate without representing it as a form of realism. This use of the term is found in advocating interpretations of QM that are nonrealist in the present sense (e.g., [34,35,36]), although none of these authors entertains the strong RWR view. In any event, I would argue that the present definition is more in accord with most understandings of realism in physics and philosophy.

12. Both Dirac [41] and von Neumann [42], followed Bohr’s Como argument or, in any event, adopted the same type of view, allowing for realism and classical causality in considering the independent behavior of quantum objects, with probabilities only introduced by measurement (see [25, pp. 197–214], [7, p. 1279].

13. These qualifications in part explain the history of questioning of the idea of causality in fundamental physics, while allowing for the type of view of classical physics or relativity termed here classically causal, beginning with Russell’s 1913 essay [44]. See [45] for a reconsideration of Russell’s argument from a contemporary perspective, allied with structural realism [33]. As will be seen, in the case of quantum causality, one could speak of events as causes.

14. There is yet another alternative, that of simply disregarding such questions, captured by N. D. Mermin’s often cited maxim “shut up and calculate,” an attitude not adopted by Mermin himself, who said on the same occassion: “But I will not shut up” [46, p. 24].

15. The concept of quantum indefinitiveness is different from A. Shimony’s realist concept of “objective indefiniteness,” which sounds similar [47]. Shimony’s concept implies a statement concerning a relation of between individual quantum events, a relation established by QM. The concept of quantum indefinitiveness is independent of QM. Shimony’s concept is noteworthy as revealing subtler dimensions of realism in quantum theory. See [48] for an instructive discussion.

16. For discussion of the concept of quantum field from the RWR perspective, see [5].

17. The concept “quantum object” could be defined otherwise, for example, on more realist lines, as, in part via Shimony’s concept of objective indefiniteness, mentioned above, in [48].

18. A somewhat similar argument concerning the stratified character of the reality defining quantum phenomena, if without adopting the RWR view, was proposed in [52].

19. The nature of this “amplification” is part of the problem of the transition from the quantum to the classical, which and related subjects, such as “decoherence, ” are beyond my scope here.

20. The difference between the statistical and probabilistic (such as Bayesian) views of QM would require a separate treatment. Khrennikov, in the works cited here, adoptes a statistical view, on more realist lines, as does, on RWR lines, the present author [4, 7]. Quantum Bayesianism, QBism, offers an RWR-type Bayesian approach [35]. RWR-type statistical interpretations of QM are uncommon. A compelling example of a statistical interpretation that may be interpreted along RWR lines, even if it is not by the authors themselves, is offered in [54]. Their position appears to allow for this interpretation because they argue that one should only interpret outcomes of pointer indications, and leave the richer quantum structure, which has many ways of expressing the same identities, without interpretation. In RWR-type interpretations, this structure would only be seen as that enabling statistical predictions, without representing the ultimate reality responsible for the outcomes of quantum experiments and hence pointer indications. Finally, there are also arguments (which are, it follows, realist) for classical causality in the case of discrete events, arguments advocated, for example, by L. Smolin, following R. Sorkin [55, pp. 257–261]. These arguments, in my view, pose problems, beginning with that of establishing discontinuous physical mechanisms by means of which classical causality can be established for such events, although one could have mathematics for predictions concerning them. It is not discreteness but classical causality that is the main difficulty.

21. See [56], for an assessment of Heisenberg’s overall later views of QM, including in [49].

22. This observation, as Wheeler notes, anticipates the delayed choice experiment [21, pp. 182–192].

23. This point appears to have been missed or not addressed either in commentaries on Bohr or by treatments of quantum measurement elsewhere. Subtle as it is, Schrödinger’s analysis of quantum measurement in his cat-paradox paper does not consider this point [53, pp. 158–159]. Von Neumann’s analysis comes close, but, while it is conceivable that von Neumann realized this point, he did not comment on it, and some of his statements suggest a realist view, which attributes the measured quantity to the object at the time of measurement [42, pp. 355–356].

24. I am indebted to D’Ariano for drawing my attention to the significance of considering composite systems in quantum theory, the point emphasized in his recent works (some of which are cited here), in contrast to other quantum-informational approaches to quantum foundations.

25. This situation is also responsible for what is known as “contextuality,” which is a statistical concept. I have considered the relationships between complementarity and contextuality from the RWR perspective in [6].

26. One might also note, along Bayesian lines, that predictions with any probability are only meaningful insofar as those who made them or know of them are still alive.

27. That a prediction with probability equal to unity is not the same as establishing the reality of what is so predicted has been stressed by quantum Bayesians (QBists), on the grounds of the subjective nature of Bayesian probability, rather than the reasoning used here (e.g., [35, 46, pp. 231–238]).

28. I only cite some key earlier experiments. There have been numerous experiments performed since, some in order to find loopholes in these and subsequent experiments.

29. The literature dealing with these subjects is immense. Among the standard treatments are [69,70,71,72,73]. There are also realist and causal views of quantum entanglement and correlations, either in realist interpretations of QM, such as the many worlds interpretation, or in alternative theories, such as Bohmian mechanics or that of classical random fields [7, 74]. Superdeterminism is another realist view, which explains away the complexities discussed here by denying an independent decision of performing one or the other EPR measurements (e.g., [75, 76]).

30. I have considered Bohr’s reply in detail previously [3, pp. 136–154], [22, pp. 107–136], [25, pp. 237–312] . The present discussion, however, modifies these treatments in several respects.

31. EPR’s actual argument is more elaborate. They derive a contradiction between the assumption that QM is complete and the assumption of the impossibility of attaching definite values to both variables in question, which, since this impossibility is inherent in QM, implies that QM is uncomplete. But this conclusion is essentially the same as stated by Bohr here. Even though one can predict (exactly) the two quantities considered only alternatively, EPR still contend that both quantities correspond to the elements of reality jointly pertaining to \(S_{2}\), according to their criterion, which does not require simultaneity of such measurements or predictions, a requrement that would, in their their view, impliy Einstein-nonlocality [8, p. 141] . QM, however, only allows one to predict either one or the other of these two quantities. Hence, it is incomplete, because it cannot predict all that is possible to establish as real, unless it is Einstein-nonlocal.

32. This fact was important for Khrennikov’s arguments concerning quantum nonlocality. It was also recently stressed, on more realist lines, by Grangier (e.g., [77]).

33. As has been noted by several authors, Schrödinger arguably the first of them [53, p. 160] , one could simultaneously make the position measurement on \(S_{1}\) and the momentum measurement on \(S_{2}\), and thus simultaneously predict (ideally exactly) the second variable for each system, the momentum for \(S_{1}\) and the position for \(S_{2}\). This determination, however, is not simultaneous in the same location, and measuring the complementary variable instead of the predicted one in either location would irrevocably preclude one from verifying this prediction and would define a different reality.

34. The argumentation just given complicates speaking, as is common, of entangled objects as forming “an indivisible whole.” Bohr never does so, although his reply to EPR has been misread in this way, by confusing Bohr’s use of this language for describing a phenomenon in his sense as forming an indivisible whole with the quantum object considered. Bohr’s concept of phenomenon was introduced later. But, if one applies, and one can, this concept to Bohr’s argument in his reply to EPR, a measurement performed on \(S_{1}\) forms an indivisible whole composed of \(S_{1}\) and the measuring instrument used, but does not in any way involve \(S_{2}\). It only enables one to make a prediction concerning \(S_{2}\) and the corresponding possible future phenomenon. A prediction is, however, not a phenomenon, only a measurement is; and a measurement on \(S_{2}\) would establish its own phenomenon, with its own indivisible wholeness between \(S_{2}\) and the measuring instrument.

I am grateful to G. M. D’Ariano, C. A. Fuchs, P. Grangier, L. Hardy, G. Jaeger, A. Khrennikov, and T. Nieuwenhuizen for helpful discussions concerning the subjects considered in this article.

Authors and Affiliations

1. Literature, Theory, and Cultural Studies Program, College of Liberal Arts, Purdue University, West Lafayette, USA

   Arkady Plotnitsky

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Correspondence to Arkady Plotnitsky.

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