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The Relational Dissolution of the Quantum Measurement Problems

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Abstract

The Quantum Measurement Problem is arguably one of the most debated issues in the philosophy of Quantum Mechanics, since it represents not only a technical difficulty for the standard formulation of the theory, but also a source of interpretational disputes concerning the meaning of the quantum postulates. Another conundrum intimately connected with the QMP is the Wigner friend paradox, a thought experiment underlining the incoherence between the two dynamical laws governing the behavior of quantum systems, i.e the Schrödinger equation and the projection rule. Thus, every alternative interpretation aiming to be considered a sound formulation of QM must provide an explanation to these puzzles associated with quantum measurements. It is the aim of the present essay to discuss them in the context of Relational Quantum Mechanics. In fact, it is shown here how this interpretative framework dissolves the QMP. More precisely, two variants of this issue are considered: on the one hand, I focus on the “the problem of outcomes” contained in Maudlin (1995)—in which the projection postulate is not mentioned—on the other hand, I take into account Rovelli’s reformulation of this problem proposed in Rovelli (2022), where the tension between the Schrödinger equation and the stochastic nature of the collapse rule is explicitly considered. Moreover, the relational explanation to the Wigner’s friend paradox is reviewed, taking also into account some interesting objections contra Rovelli’s theory contained in Laudisa (2019). I contend that answering these critical remarks leads to an improvement of our understanding of RQM. Finally, a possible objection against the relational solution to the QMP is presented and addressed.

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Notes

  1. In Rovelli [13] RQM is introduced for the first time; in this paper I assume that the reader is familiar with its physical and metaphysical principles. For space reasons I will not discuss them here; however, excellent introductions and presentations of this interpretation are contained in Rovelli [4, 14, 15] and Laudisa and Rovelli [16].

  2. Analyzing Rovelli’s papers on RQM it clearly emerges how Einstein’s relativity theories and their axioms influenced the relational interpretation of QM. For an interesting discussion on this topic the reader may refer to Pienaar [17] and Di Biagio and Rovelli [18].

  3. For simplicity, in the present essay I will consider events and facts as synonyms. The subtle difference between these two notions in RQM is not relevant for the purposes of this work and can be overlooked.

  4. For a new perspective about the event ontology of RQM the reader may refer to Adlam and Rovelli [20], where the authors introduce an additional interpretative postulate to the existing corpus of principles shaping the theory. As a consequence of it, the authors argue that observer-independent facts do exists although they are described by relational quantum states. Due to spatial constraints I cannot discuss here in detail this new interpretation of RQM, thus, it will not mentioned in the remainder of the paper.

  5. I thank the anonymous referee for pointing out this distinction.

  6. In this essay Laudisa critically discusses two open problems of relational QM: (i) the QMP and (ii) the issue of locality. Here I will be concerned only with the former; for a recent discussion of locality in RQM the reader may refer to Martin-Dussaud et al. [22], Pienaar [23], Adlam and Rovelli [20].

  7. For a simple proof of this fact the reader should refer to Maudlin [3], pp. 7–8.

  8. The interpretation of the collapse postulate in RQM is similar to that provided by QBism. For discussion cf. Pienaar [24].

  9. The ontological status of the wave function in RQM has been discussed in several places, the reader may refer to Smerlak and Rovelli [25], Rovelli [14], Laudisa and Rovelli [16], Oldofredi [26].

  10. As a consequence in RQM also the notion of “wave function of the universe” present in several interpretations of quantum theory—as for instance in Everett’s relative state formulation of QM, the Many worlds interpretation, Bohmian mechanics, etc.—is rejected.

  11. Cf. Dorato [27] for a good discussion of this issue.

  12. Another crucial difference between these two interpretations is that in RQM the wave function of the universe, which play a central ontological role in MWI, does not exist.

  13. For further details on Wigner’s view cf. Wigner [5].

  14. Cf. Frauchiger and Renner [29], Bong et al. [30], Allard Guérin et al. [31].

  15. Three main consequences can be drawn from our discussion. Firstly, in RQM the separation between observed system and observer cannot be univocally determined, bona pace Wigner—in our example agent O observes s, but it is part of the composite observed system \(s+O\) according to Wigner’s perspective (more abut this issue in Section 4). Secondly, as we already underlined, according to Rovelli’s theory there is no privileged observer since all physical systems are equivalent: “[n]othing a priori distinguishes macroscopic systems from quantum systems. If the observer O can give a quantum description of the system s, then it is also legitimate for an observer W to give a quantum description of the system formed by the observer O” (Rovelli [13], p. 1644, notation adapted). Thirdly, RQM provides a complete description of the world, because there is neither a deeper theory, nor hidden parameters describing how an absolute reality behaves, as we have already pointed out in the previous section studying the first proposition of the problem of outcomes.

  16. It is worth recalling that such interactions involve wave function collapses.

  17. According to these authors stable facts are a proper subset of relative facts, i.e. all stable facts are also relative, but the converse does not hold: not every relative fact is stable.

  18. In those particular cases in which (9) holds for also for another observer W, then we can say that \(a_i^{(O)}\) is stable also for W.

  19. Here I am simplifying the physical description of the actual situation since small interference effects should be taken into consideration. For a more detailed account of this discussion see Di Biagio and Rovelli [33] Section 3.

  20. A similar idea was already stated in Rovelli [13] as follows: “if W knows that O has measured \(S_z\), and then she measures \(S_z\), and then she measures what O has obtained in measuring \(S_z\), consistency requires that the results obtained by W about the variable \(S_z\) and the pointer are correlated” (p. 1652, notation adapted).

  21. It should be noted that also in the original Wigner’s friend scenario, Wigner is not part in the description of the experimental situation taking place in the lab.

  22. This objection can be found e.g. in Laudisa [21], as underlined in Rovelli [4], p. 1066. In the latter essay Rovelli responds arguing that RQM rejects a strong form of realism where physical objects have well-defined values for their properties at all times. Moreover, he continues, not only in relational QM there is no such a thing as the wave function of the universe, but also “there is no coherent global view available”. Referring to this, Laudisa and Rovelli [16] claim that if “by realism we mean the assumption that the world is “out there”, irrespectively of our mental states, or perceptions, there is nothing in RQM that contradicts realism. But if by realism we mean the stronger assumption that each variables of each subsystem of the world has a single value at each and every time, then this strong version of realism is weakened by RQM”.

  23. It goes without saying that for many authors this feature of RQM constitutes an inherent defect of the theory, and thus, a justified motivation to discard it. It should be noted, however, that other well-known, established interpretations of the quantum formalism involving either a branching process, or a relativization of states seem to have a descriptive limit similar to RQM. For instance, the many worlds interpretation does not explain the physical details responsible for the branching process. Analogously, Everett’s interpretation requires that in measurement situations every possible outcome is actualized in relative states corresponding to different branches of the wave function. However, the details concerning the actualization of determined records in such relative states are not provided.

  24. This kind of ontology has a robust philosophical basis, for a general introduction the reader may refer to Casati and Varzi [34].

  25. Such ontologies not only have a long and prestigious philosophical tradition, but also they are endorsed by several authors in the contemporary philosophy of quantum mechanics, as for instance in da Costa et al. [36], Lombardi and Dieks [37] and Kuhlmann [38].

  26. One may easily rephrase the relational solution to the Wigner friend paradox and the QMP in terms of the various proposals mentioned in this section; however, this exercise is left to the reader.

References

  1. Bell, J.S.: Speakable and unspeakable in quantum mechanics. Cambridge University Press (1987)

    MATH  Google Scholar 

  2. Bricmont, J.: Making sense of quantum mechanics. Springer (2016)

    Book  MATH  Google Scholar 

  3. Maudlin, T.: Three measurement problems. Topoi 14, 7–15 (1995)

    Article  MathSciNet  Google Scholar 

  4. Rovelli, C.: The relational interpretation. In: Freire, O.J. (ed.) The Oxford Handbook of the History of Quantum Interpretations, pp. 1055–1071. Oxford University Press (2022)

    Google Scholar 

  5. Wigner, E.: Remarks on the mind-body question. In: Mehra, J. (ed.) Philosophical reflections and syntheses. The collected works of Eugene Paul Wigner (Part B historical, philosophical and socio-political papers). Springer (1995)

    MATH  Google Scholar 

  6. Bohm, D.: A suggested interpretation of the quantum theory in terms of “hidden’’ variables. II. Phys Rev 85(2), 180–193 (1952)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Holland, P.: The quantum theory of motion. An account of the de Broglie-Bohm causal interpretation of quantum mechanics. Cambridge University Press, Cambridge (1993)

    Book  Google Scholar 

  8. Dürr, D., Teufel, S.: Bohmian mechanics: the physics and mathematics of quantum theory. Springer, Berlin (2009)

    MATH  Google Scholar 

  9. Ghirardi, G.C.: Collapse theories. Stanford Encyclopedia of Philosophy (2016)

    MATH  Google Scholar 

  10. Bassi, A., Ghirardi, G.C.: Dynamical reduction models. Phys Rep 379, 257–426 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Everett, H.: “Relative state” formulation of quantum mechanics. Reviews of Modern Physics, 29(3):454–462. Reprinted in DeWitt, B. S., Graham, N., editors (1973). The many-worlds interpretation of quantum mechanics, pages 141–149. Princeton: Princeton University Press (1957)

  12. Wallace, D.: The emergent multiverse. Quantum theory according to the Everett interpretation. Oxford University Press, Oxford (2012)

    Book  MATH  Google Scholar 

  13. Rovelli, C.: Relational quantum mechanics. Int J Theor Phys 35(8), 1637–1678 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  14. Rovelli, C.: An argument against the realistic interpretation of the wave function. Found Phys 46, 1229–1237 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. Rovelli, C.: Space is blue and birds fly through it. Philos Trans Royal Soc A, Phys Eng Sci 376(2123), 2017.0312 (2018)

    Article  Google Scholar 

  16. Laudisa, F., Rovelli, C.: Relational quantum mechanics. Stanford Encyclopedia of Philosophy (2019)

    Google Scholar 

  17. Pienaar, J.: A quintet of quandaries: five no-go theorems for relational quantum mechanics. Found Phys 51, 97 (2021)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. Di Biagio, A., Rovelli, C.: Stable facts, relative facts. Found Phys 51, 30 (2021)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Rovelli, C., Vidotto, F.: Covariant loop quantum gravity: an elementary introduction to quantum gravity and spinfoam theory. Cambridge University Press (2014)

    Book  MATH  Google Scholar 

  20. Adlam, E., Rovelli, C.: Information is Physical: Cross-perspective Links in Relational Quantum Mechanics, pp. 1–22. arxiv:2203.13342 (2022)

    Google Scholar 

  21. Laudisa, F.: Open problems in relational quantum mechanics. J Gener Philos Sci 50, 215–230 (2019)

    Article  MathSciNet  Google Scholar 

  22. Martin-Dussaud, P., Rovelli, C., Zalamea, F.: The notion of locality in relational quantum mechanics. Found Phys 49, 96–106 (2019)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Pienaar, J.: Comment on “The notion of locality in relational quantum mechanics.” Found Phys 49, 1404–1414 (2019)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. Pienaar, J.: QBsim and relational quantum mechanics compared. Found Phys 51, 96 (2021)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Smerlak, M., Rovelli, C.: Relational EPR. Found Phys 37, 427–445 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. Oldofredi, A.: The bundle theory approach to relational quantum mechanics. Found Phys 51(1), 1–22 (2020)

    MathSciNet  Google Scholar 

  27. Dorato, M.: Rovelli’s relational quantum mechanics, anti-monism, and quantum becoming. In: Marmodoro, A., Yates, D. (eds.) The metaphysics of relations, pp. 235–262. Oxford University Press (2016)

    Chapter  Google Scholar 

  28. Barrett, J.: Everett’s relative-state formulation of quantum mechanics. Stanford Encyclopedia of Philosophy (2018)

    Google Scholar 

  29. Frauchiger, D., Renner, R.: Quantum theory cannot consistently describe the use of itself. Nat Commun 9, 1–10 (2018)

    Article  Google Scholar 

  30. Bong, K.W., Utreras-Alarcón, A., Ghafari, F., Liang, Y.C., Tischler, N., Cavalcanti, E., Pryde, G., Wiseman, H.: A strong no-go theorem on the Wigner’s friend paradox. Nat Commun 16, 1199–2005 (2020)

    Google Scholar 

  31. Allard Guérin, P., Baumann, V., Del Santo, F., Brukner, C.: A no-go theorem for the persisten reality of Wigner’s friend’s perception. Nat Commun Phys 2021, 4 (2021)

    Google Scholar 

  32. Lazarovici, D., Hubert, M.: How quantum mechanics can consistently describe the use of itself. Sci Rep 470(9), 1–8 (2019)

    Google Scholar 

  33. Di Biagio, A., Rovelli, C.: Relational quantum mechanics is about facts, not states: a reply to Pienaar and Brukner. Found Phys 52, 62 (2022)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  34. Casati, R., Varzi, A.: Events. Stanford Encyclopedia of Philosophy (2020)

    Google Scholar 

  35. Candiotto, L.: The reality of relations. G Metafi 2, 537–551 (2017)

    Google Scholar 

  36. da Costa, N., Lombardi, O., Lastiri, M.: A modal ontology of properties for quantum mechanics. Synthese 190, 3671–3693 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  37. Lombardi, O., Dieks, D.: Particles in a quantum ontology of properties. In: Bigaj, T., Wüthrich, C. (eds.) Metaphysics in contemporary physics, pp. 123–144. Brill Rodopi (2016)

    Chapter  Google Scholar 

  38. Kuhlmann, M.: The ultimate constituents of the material world. In search of an ontology for fundamental physics. Ontos, Frankfurt (2010)

    Book  Google Scholar 

  39. Calosi, C., Mariani, C.: Quantum relational indeterminacy. Stud Hist Philos Sci Part B Stud Hist Philos Mod Phys 71, 158–169 (2020)

    Article  ADS  MathSciNet  Google Scholar 

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Acknowledgements

I warmly thank the Guest Editor of this special issue Claudio Calosi for having invited me to contribute. My sincere thanks go also to the referee of this paper, whose comments and remarks improved the quality of the essay. AO is grateful to the Fundação para a Ciência e a Tecnologia (FCT) for financial support (Grant no. 2020.02858.CEECIND).

Funding

This study was supported by Fundação para a Ciência e a Tecnologia (Grant No. 2020.02858.CEECIND).

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    Andrea Oldofredi

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Oldofredi, A. The Relational Dissolution of the Quantum Measurement Problems. Found Phys 53, 10 (2023). https://doi.org/10.1007/s10701-022-00652-z

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