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Ontology and the foundations of quantum theory

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Abstract

A brief review of the historical main line of investigation of the ontology of quantum theory is given with an emphasis on elementary particles. Einstein et al. considered possible elements of reality and questioned the completeness of the quantum state, prompting later studies of local causality in relation to their physical properties. Later reconsiderations of quantum mechanical law have involved differing attitudes toward the objective existence not only of the properties of distantly located particles, but even of entire universes of systems including them. Experimental foundational investigations have mainly involved quantum mechanics at low energies but some have begun to explore higher energies, where quantum field theory is required, and its ontology has been seen to involve quantum fields as well as elementary particles.

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Notes

  1. Discussions of the range of interpretations are found in, e.g., [15, 16].

  2. A good contemporary characterization of a realist interpretation of quantum theory sensitive to the semantic aspect of interpretation is: “[A]ccepting that [quantum theory] is true, that the objects [it] refers to (electrons, protons, etc.) exist, that the properties it refers to are ‘real,’ and in particular that the physical quantities it refers to are ‘real’; in short it also means that we can...take all its referential terms as genuinely referring and not just as convenient fictions or metaphors for the real” ([26], p. 126)—reference meant here in the linguistic sense. See [27] for a discussion of philosophical challenges to realism.

  3. Two, quite difference approaches to this serve as illustrative examples of the diversity of approaches currently under pursuit: see the articles [28,29,30,31] and references therein.

  4. This condition is closely related to causality if indeterminism is the condition that “the state of a system at time t cannot in general be predicted with certainty given the history of its states priority to t” [13], p. 19.

  5. The term ‘context,’ however, was to arise in the later search for supplements to the quantum mechanical description of measurements performed on compound, spatially distributed systems. Abner Shimony introduced the terminological distinction between the so-called “contextual(istic)” and “noncontextual(istic)” hidden-variable models (cf. [44], Ref. 8) in 1971: “The name “contextualistic” was introduced by A. Shimony: Experimental test of local hidden variable theories, in [45], and a shortening to “contextual” was performed by [46]” [44]. Shimony identified these sorts of models as being first explicitly considered by Bell in1966 [47], but the distinction appears to have occurred first to Heisenberg in 1935.

  6. A proof of Belinfante and others effectively demonstrated the viability of contextual hidden-variables models and quantum mechanics in a 1973 publication [48], cf. [44] Ref. 12. See [37] for a discussion of contextuality as then understood.

  7. When asked, would you “prefer to retain the notion of objective reality and throw away one of the tenets of relativity: that signals cannot travel faster than the speed of light?”, Bell responded in accordance with Einstein’s views: “Yes. One wants to be able to take a realistic view of the world, to talk about the world as being there even when it is not observed. I certainly believe in a world that was here before me, and will be here after me, and I believe that you are part of it! And I believe that most physicists take this point of view when they are being pushed into a corner by philosophers”, ibid.

  8. Some variants are said not to involve universe-splitting, such as Bub’s “new orthodoxy,” which is to include aspects of the Copenhagen-type interpretation [58]. But Copenhagen-type interpretations have the observer distinct from the observed object by a scale or complexity boundary (‘cut’), the location of which is not determined by physics alone and taking the observer and measurement apparatus to be described classically, not quantum mechanically [54].

  9. As with the Copenhagen approach, there is disagreement among advocates of approaches to quantum theory taking time-evolution as always unitary to quantum ontology. Note also that Bell did not view (at least the Many-worlds version of) the Collapse-Free approach as a solution to the difficulties presented by quantum phenomena, despite its capability of being presented realistically, because he viewed that interpretation as “radically solipsistic,” despite contrary claims about it by various advocates (cf. [61], p. 136).

  10. “In the reality assumption the phrase ‘can predict’ occurs. The phrase...may be understood in the strong sense, that data are at hand for making the prediction, or in the weak sense, that a measurement could be made to provide data for the prediction. EPR assume the weak sense, and indeed unless they did so they could not argue that an element of physical reality exists for all components of spin, those which could have been measured as well as the one that actually was measured...The preference for one rather than the other of these two interpretations of the phrase is not merely a semantical matter...Bohr believed that the concept of reality cannot be applied legitimately to a property unless there is an experimental arrangement for observing it...” [62].

  11. Controversy continues to surround the Bell-type inequalities. See, for example, the discussions in [65,66,67] and of the references therein. It has also been argued that context is essential for the understanding of such expressions, cf., e.g., [68].

  12. For a detailed discussion of associated complementarity relations, see [72].

  13. For a critical assessment of Wheeler’s position on the relation of quantum phenomena to reality, see [75].

  14. Moreover, the character of elementary quantum objects has a decisive influence on the structures found throughout the entire physical world at all of its levels, for example, those of chemistry and biology, because matter can be in specific senses broken down into and constructed from such parts, which are of therefore of great importance. A discussion of this structure and its analysis in relation to space and time can be found in [76].

  15. Some realist philosophers, noting that only certain mathematical structures in physical theory appear to remain entirely unchanged as physics has developed, have taken the position of ontological structural realism, according to which mathematical structures are ontologically prior to physical ones, and even to quantum fields that have been considered by some as prior to particles. See [87, 88].

  16. Busch subsequently found that local commutativity is a necessary consequence of Einstein causality for unsharp measurements as well as for sharp measurements as long as they admit local measurements [90, 91].

  17. The elementary particle is found at the very foundation of the notion of the relativistic quantum system, as Weinberg explains regarding his own portrayal QFT: “I start with particles...because what we know about particles is more certain more directly derivable from the principles of quantum mechanics and relativity. If it turned out that some physical system could not be described by a quantum field theory, it would be a sensation; if it turned out that the system did not obey the rules of quantum mechanics and relativity, it would be a cataclysm. In fact, lately there has been a reaction against looking at quantum field theory as fundamental ...From this point of view...the reason our field theories work so well is not that they are fundamental truths, but that any relativistic quantum theory will look like a field theory when applied to particles at low energy” [93] 1–2; also see [94] 15, 85.

  18. And the allowed (discrete) spin values are integral (permutation-symmetric) or half-integral (permutation anti-symmetric).

  19. That failure was shown in [95].

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  1. Quantum Communication and Measurement Laboratory, Department of Electrical and Computer Engineering, Boston University, 8 St. Mary’s St., Boston, 02215, MA, USA

    Gregg Jaeger

  2. Division of Natural Science and Mathematics, Boston University, 871 Commonwealth Ave., Boston, 02215, MA, USA

    Gregg Jaeger

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Jaeger, G. Ontology and the foundations of quantum theory. Eur. Phys. J. Spec. Top. 232, 3273–3284 (2023). https://doi.org/10.1140/epjs/s11734-023-00970-x

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