Abstract
First, this article considers the nature of quantum reality (the reality responsible for quantum phenomena) and the concept of realism (our ability to represent this reality) in quantum theory, in conjunction with the roles of locality, causality, and probability and statistics there. Second, it offers two interpretations of quantum mechanics, developed by the authors of this article, the second of which is also a different (from quantum mechanics) theory of quantum phenomena. Both of these interpretations are statistical. The first interpretation, by A. Plotnitsky, “the statistical Copenhagen interpretation,” is nonrealist, insofar as the description or even conception of the nature of quantum objects and processes is precluded. The second, by A. Khrennikov, is ultimately realist, because it assumes that the quantum-mechanical level of reality is underlain by a deeper level of reality, described, in a realist fashion, by a model, based in the pre-quantum classical statistical field theory, the predictions of which reproduce those of quantum mechanics. Moreover, because the continuous fields considered in this model are transformed into discrete clicks of detectors, experimental outcomes in this model depend on the context of measurement in accordance with N. Bohr’s interpretation and the statistical Copenhagen interpretation, which coincides with N. Bohr’s interpretation in this regard.
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Notes
The concepts of reality and realism will be explained in Sect. 2. By “quantum phenomena” we refer to those observable physical phenomena in considering which Planck’s constant, h, must be taken into account, although, as will be seen below, these phenomena themselves may be described by means of classical physics. Quantum objects, which are responsible for the appearance of quantum phenomena, could be macroscopic, although their quantum nature would be defined by their ultimate microscopic constitution and hence by the role of h in the corresponding phenomena. (We discuss the difference between objects and phenomena in quantum physics below). By “quantum theory” we refer collectively to theories accounting for quantum phenomena, among them the “standard quantum mechanics” (introduced by W. Heisenberg and E. Schrödinger in 1925–1926), henceforth designated as “quantum mechanics,” in contradistinction, for example, to “Bohmian mechanics,” which is a mathematically different theory, rather than a different interpretation of quantum mechanics. By “quantum physics” we refer to the totality of quantum phenomena and quantum theories. These concepts technically include high-energy (relativistic) quantum theories and physics, which will not be considered here. The terms “classical phenomena,” “classical mechanics,” “classical theory,” and “classical physics,” will be used in parallel. We are only concerned, in considering locality, with special relativity, and henceforth “relativity” refers to special relativity, unless stated otherwise.
We explain “locality” in more detail in the next section. For the moment, at stake is primarily the compatibility with (special) relativity, prohibiting an “action at a distance” (a physical influence propagating faster than the speed of light in a vacuum).
For a detailed analysis of the exchange see [5, pp. 237–312].
It is not possible to survey these interpretations here. Just as does the Copenhagen interpretation (one could think of several even in Bohr’s own case), each rubric, on by now a long list (e.g. the many-worlds, consistent-histories, modal, relational, transcendental-pragmatist, and so forth), contains numerous versions, which, however, revolve around the concepts just listed. The literature dealing with the subject is immense, although standard reference sources, such as Wikipedia [6], would list the most prominent ones. Given the role of the statistical considerations in this article, we might mention a compelling statistical interpretation proposed in [7], which has certain affinities with the statistical Copenhagen interpretation proposed here, again, acknowledging that there is a large number of other statistical interpretations available, difficult to survey here. The literature is nearly as immense when it comes to the Bell and the Kochen–Specker theorems and related findings. We will not be concerned with these problematics here. Among the standard treatments are [8–10]. We might add that they have been extensively discussed at Växjö conferences, and the proceedings of these conferences contain important contributions to the subject, and most other foundational issues concerning quantum physics. It is worth keeping in mind that these theorems and most of these findings pertain to quantum data as such, and do not depend on quantum mechanics or any particular theory of these data.
The description just given allows for different degrees to which our models “match” reality. For example, to what degree does the mathematical architecture of relativity correspond, even as an idealization, to the architecture of nature, as opposed to ultimately only serving as a mathematical model for correct predictions concerning relativistic phenomena? See [12]. Indeed, as Kant realized, these questions could be posed concerning classical mechanics, where, however, the descriptive idealizations used are more in accord with our phenomenal experience than in relativity or quantum theory. There is vast literature on the subject, which we cannot consider here. One might mention, however, E. Schrödinger’s account, arguably following H. Hertz, of “the physics of models” in classical physics in his cat-paradox paper, which addressed the limitations of our capacity to represent, to have a picture, Bild, of the ultimate reality even if the latter is assumed to be classical, which Schrödinger preferred it to be [13, pp. 152–153]. While he was thus close to Einstein in preferring the “classical ideal” to what transpired in quantum mechanics, he was more skeptical than Einstein as concerns the future of this ideal in fundamental physics.
As noted earlier, once one allows for “reality” in this sense, one could, in principle, speak of “realism.” I. Hacking’s influential concept of “entity-realism” (vs. “theory realism”) [17] and some of its avatars, developed during the last decade in the philosophy of science and debates concerning the question of reality there (debates influenced by quantum theory), may be argued to be examples of this type of realism. These concepts do not appear to us to be quite as radical as the concept of “reality without realism,” insofar as they still appear to conform to Kant’s concept of noumena as, while unknowable, still in principle thinkable. As noted here, Bohr’s position could be interpreted in either direction. The subject would require a further discussion, which is beyond our scope here. It may be added that one could, following G. Berkeley, conversely, understand nonrealism as the denial of the existence of external reality altogether. While this concept, used by Berkeley against Newton, is not without relevance to quantum theory, it is rarely adopted in physics or philosophy, and will be not considered here.
Sometimes the term “causality” is used in accordance with the requirements of relativity, which further restricts causes to those occurring in the backward (past) light cone of the event that is seen as an effect of this cause, while no event can be a cause of any event outside the forward (future) light cone of that event. These restrictions follow from the assumption that causal influences cannot travel faster than the speed of light in a vacuum, c. When speaking of the lack of causality, we only mean the inapplicability of the concept of causality found in classical physics and not about any incompatibility with relativity.
Among others who have pursued this line of inquiry are A. M. Cetto and L. de la Pena, M. Kupczynski, and T. Nieuwenhuizen (see [18]). Bohr came to see quantum field theory as extending quantum mechanics along a nonrealist gradient.
For an extensive analysis of this view and problems found in it, see [5, pp. 191–219].
The concept requires clarifications, which we put aside here. See [23], for a helpful discussion of this concept and the concept of quantum object in general from a realist perspective.
The standard use of the term “quantum statistics” refers to the behavior of large multiplicities of identical quantum objects, such as electrons and photons, which behave differently, in accordance with, respectively, the Fermi–Dirac and the Bose–Einstein statistics.
See Ref. [28] for an exposition of the last version of the theory developed by Bohm, in collaboration with B. Hiley.
Technically, as Kant realized, objects and phenomena are also different in classical physics. There, however, this difference could be disregarded. Multicomponent classical systems, such as those considered in classical statistical physics, introduces further complexities, such situations are still fundamentally different from those of quantum physics. This is because the elemental individual constituents of such systems could be treated by descriptive causal models of classical mechanics, which is impossible in quantum theory, at least in Bohr’s and related interpretations.
In part in view of the considerations given here, wave-particle complementarity, with which the concept of complementarity is associated most commonly, did not play a significant, if any, role in Bohr’s thinking. Indeed, Bohr does not appear to have ever spoken of this complementarity. His solution to the dilemma of whether quantum objects are particles or waves—or his “escape” from the paradoxical necessity of seeing them as both—is that they are neither. Instead, either feature is seen by Bohr as an effect or set of effects, particle-like (which may be individual or collective) or wave-like (which are always collective), of the interactions between quantum objects and measuring instruments, in which these effects are observed.
Given the data obtained in quantum experiments, this would have to be the case even if one assumes the underlying causality of quantum processes. This fact is reflected in Bohmian theories, in which a given quantum object is assumed to possess both position and the momentum, as defined exactly, at any moment of time, thus allowing one for realism and causality. However, these theories retain the uncertainty relations and, correlatively, reproduce the statistical predictions of quantum mechanics, because a given measurement always disturbs, actually disturbs, the object and displaces the value of one of these properties. By contrast, this type of concept of disturbing quantum objects and processes by observation (a concept that allows one to give a classical-like independent architecture to quantum objects and processes when they are not disturbed by observation) is inapplicable in Bohr’s interpretation or the statistical Copenhagen interpretation [2, v. 2, pp. 63–64].
The so-called quantum Bayesianism or QBism exemplifies the complexities of Bayesian thinking in quantum theory and beyond [36, 37]. While it adopts a nonrealist view of quantum objects and processes, and in this respect is in accord with Bohr’s interpretation and the statistical Copenhagen interpretation, it is different from both in other respects [37]. QBism is Bayesian and nonrealist, but not all Bayesian or all nonrealist positions are QBist. To properly address QBism, including in its Bayesian aspects, and to fairly assess its claims would require an extensive analysis that cannot be undertaken here.
Of course, in the Bayesian scheme of things, there may be some individual events to which one cannot assign probabilities, but, in general, one can and usually does.
In certain situations, such as those of the EPR type, we can, for all practical purposes, predict certain quantities exactly, but this is never true in full rigor either, for the reasons just considered. There is always a non-zero probability that the object in question will not be found where it is expected to be found at the moment of time for which the prediction is made. Unlike the Bell-Bohm version of the EPR experiment for spin (at stake in Bell’s and related theorems), the actual experiment proposed by EPR, dealing with continuous variables, cannot be physically realized, because the EPR-entangled quantum state is non-normalizable. This fact does not affect the fundamentals of the case, which can be considered in terms of the idealized experiment proposed by EPR. There are experiments (e.g., those involving photon pairs produced in parametric down conversion) that statistically approximate the idealized entangled state constructed by EPR for continuous variables. These experiments are consistent with the present argument. They also reflect the fact that the EPR thought experiment is a manifestation of correlated events for identically prepared experiments with EPR pairs, which can in this regard be understood on the model of the Bell–Bohm version of the EPR experiment. In any event, there are quantum experiments, such as, paradigmatically, the double-slit experiment, in which the assignment of probabilities to the outcomes of individual events is difficult and even impossible to assume.
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Acknowledgments
The authors are grateful to Irina Basieva, Ceslav Brukner, G. Mauro D’Ariano, Henry Folse, Gregg Jaeger, Jan-Åke Larsson, and Anton Zeilinger, for exceptionally productive discussions, and to both anonymous readers of the article for their insightful comments and helpful suggestions.
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Plotnitsky, A., Khrennikov, A. Reality Without Realism: On the Ontological and Epistemological Architecture of Quantum Mechanics. Found Phys 45, 1269–1300 (2015). https://doi.org/10.1007/s10701-015-9942-1
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DOI: https://doi.org/10.1007/s10701-015-9942-1