Relative Facts of Relational Quantum Mechanics are Incompatible with Quantum Mechanics

Jay Lawrence1, Marcin Markiewicz2, and Marek Żukowski2

1Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755, USA
2International Centre for Theory of Quantum Technologies (ICTQT), University of Gdansk, 80-308 Gdansk, Poland

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Abstract

Relational Quantum Mechanics (RQM) claims to be an interpretation of quantum theory [20]. However, there are significant departures from quantum theory: (i) in RQM measurement outcomes arise from interactions which entangle a system $S$ and an observer $A$ without decoherence, and (ii) such an outcome is a "fact" relative to the observer $A$, but it is not a fact relative to another observer $B$ who has not interacted with $S$ or $A$ during the foregoing measurement process. For $B$ the system $S \otimes A$ remains entangled. We derive a GHZ-like contradiction showing that relative facts described by these statements are incompatible with quantum theory. Hence Relational Quantum Mechanics should not be considered an interpretation of quantum theory, according to a criterion for interpretations that we have introduced. The criterion states that whenever an interpretation introduces a notion of outcomes, these outcomes, whatever they are, must follow the probability distribution specified by the Born rule.

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► References

[1] Adlam, Emily (2021), Foundations of Quantum Mechanics, Elements in the Philosophy of Physics (Cambridge University Press).
https:/​/​doi.org/​10.1017/​9781108885515

[2] Adlam, Emily, and Carlo Rovelli (2022), ``Information is physical: Cross-perspective links in relational quantum mechanics,'' 10.48550/​ARXIV.2203.13342.
https:/​/​doi.org/​10.48550/​ARXIV.2203.13342

[3] Brukner, Časlav (2022), ``Wigner's friend and relational objectivity,'' Nature Reviews Physics 4 (10), 628–630.
https:/​/​doi.org/​10.1038/​s42254-022-00505-8

[4] Brukner, Časlav (2018), ``A no-go theorem for observer-independent facts,'' Entropy 20 (5), 10.3390/​e20050350.
https:/​/​doi.org/​10.3390/​e20050350

[5] Cabello, Adán (2017), ``Interpretations of quantum theory: A map of madness,'' in What is Quantum Information?, edited by Olimpia Lombardi, Sebastian Fortin, Federico Holik, and Cristian López (Cambridge University Press) p. 138–144.
https:/​/​doi.org/​10.1017/​9781316494233.009

[6] Cavalcanti, Eric G (2021), ``The view from a Wigner Bubble,'' Foundations of Physics 51 (2), 39.
https:/​/​doi.org/​10.1007/​s10701-021-00417-0

[7] Deutsch, David (1985), ``Quantum theory as a universal physical theory,'' International Journal of Theoretical Physics 24 (1), 1–41.
https:/​/​doi.org/​10.1007/​BF00670071

[8] Di Biagio, Andrea, and Carlo Rovelli (2022), ``Relational quantum mechanics is about facts, not states: A reply to Pienaar and Brukner,'' Foundations of Physics 52 (3), 62.
https:/​/​doi.org/​10.1007/​s10701-022-00579-5

[9] Frauchiger, Daniela, and Renato Renner (2018), ``Quantum theory cannot consistently describe the use of itself,'' Nature Communications 9 (1), 3711.
https:/​/​doi.org/​10.1038/​s41467-018-05739-8

[10] Greenberger, Daniel M, Michael A. Horne, and Anton Zeilinger (1989), ``Going Beyond Bell's Theorem,'' in Bell's Theorem, Quantum Theory and Conceptions of the Universe, edited by Menas Kafatos (Springer Netherlands, Dordrecht) pp. 69–72.
https:/​/​doi.org/​10.1007/​978-94-017-0849-4_10

[11] Haake, Fritz, and Marek Żukowski (1993), ``Classical motion of meter variables in the quantum theory of measurement,'' Phys. Rev. A 47, 2506–2517.
https:/​/​doi.org/​10.1103/​PhysRevA.47.2506

[12] Ma, Xiao-song, Johannes Kofler, and Anton Zeilinger (2016), ``Delayed-choice gedanken experiments and their realizations,'' Rev. Mod. Phys. 88, 015005.
https:/​/​doi.org/​10.1103/​RevModPhys.88.015005

[13] Mermin, N David (1990), ``Simple unified form for the major no-hidden-variables theorems,'' Phys. Rev. Lett. 65, 3373–3376.
https:/​/​doi.org/​10.1103/​PhysRevLett.65.3373

[14] Miller, W. A., and J. A. Wheeler (1984), ``Delayed-choice experiments and Bohr’s elementary quantum phenomenon,'' in Foundations of Quantum Mechanics in the light of New Technology, edited by S. Kamefuchi et al. (eds.) (Physical Society of Japan, Tokyo).

[15] von Neumann, John (1955), Mathematical Foundations of Quantum Mechanics (Princeton Univ. Press, Princeton, N.J.).

[16] Nurgalieva, Nuriya, and Renato Renner (2020), ``Testing quantum theory with thought experiments,'' Contemporary Physics 61 (3), 193–216.
https:/​/​doi.org/​10.1080/​00107514.2021.1880075

[17] Pienaar, Jacques (2021a), ``QBism and relational quantum mechanics compared,'' Foundations of Physics 51 (5), 96.
https:/​/​doi.org/​10.1007/​s10701-021-00501-5

[18] Pienaar, Jacques (2021b), ``A quintet of quandaries: Five no-go theorems for relational quantum mechanics,'' Foundations of Physics 51 (5), 97.
https:/​/​doi.org/​10.1007/​s10701-021-00500-6

[19] Rovelli, Carlo (1996), ``Relational quantum mechanics,'' International Journal of Theoretical Physics 35 (8), 1637–1678.
https:/​/​doi.org/​10.1007/​BF02302261

[20] Rovelli, Carlo (2022), ``The relational interpretation,'' in Oxford Handbook of the History of Interpretation of Quantum Physics, edited by Olival Freire Jr et al. (Oxford University Press) pp. 1055–1072.

[21] Schlosshauer, Maximilian (2005), ``Decoherence, the measurement problem, and interpretations of quantum mechanics,'' Rev. Mod. Phys. 76, 1267–1305.
https:/​/​doi.org/​10.1103/​RevModPhys.76.1267

[22] Schlosshauer, Maximilian (2019), ``Quantum decoherence,'' Physics Reports 831, 1–57.
https:/​/​doi.org/​10.1016/​j.physrep.2019.10.001

[23] Wheeler, John Archibald, and Wojciech Hubert Zurek, Eds. (1983), Quantum Theory and Measurement (Princeton University Press, Princeton).

[24] Wigner, Eugene Paul (1995), ``Remarks on the mind-body question,'' in Philosophical Reflections and Syntheses, edited by Jagdish Mehra (Springer Berlin Heidelberg, Berlin, Heidelberg) pp. 247–260.
https:/​/​doi.org/​10.1007/​978-3-642-78374-6_20

[25] Żukowski, Marek, and Marcin Markiewicz (2021), ``Physics and metaphysics of Wigner's friends: Even performed premeasurements have no results,'' Phys. Rev. Lett. 126, 130402.
https:/​/​doi.org/​10.1103/​PhysRevLett.126.130402

[26] Zurek, Wojciech Hubert (1982), ``Environment-induced superselection rules,'' Phys. Rev. D 26, 1862–1880.
https:/​/​doi.org/​10.1103/​PhysRevD.26.1862

[27] Zurek, Wojciech Hubert (2022), ``Quantum theory of the classical: Einselection, envariance, quantum darwinism and extantons,'' Entropy 24 (11), 1520.
https:/​/​doi.org/​10.3390/​e24111520

Cited by

[1] Emily Adlam, "What Does ‘(Non)-absoluteness of Observed Events’ Mean?", Foundations of Physics 54 1, 13 (2024).

[2] Alex Khang, Kali Charan Rath, P. T. N. Anh, Sunil Kumar Rath, and Srijan Bhattacharya, Advances in Medical Diagnosis, Treatment, and Care 1 (2024) ISBN:9798369321058.

[3] Aurélien Drezet, "A Critical Analysis of ‘Relative Facts Do Not Exist: Relational Quantum Mechanics Is Incompatible with Quantum Mechanics’ by Jay Lawrence, Marcin Markiewicz and Marek Źukowski", Foundations of Physics 54 1, 5 (2024).

[4] Aurélien Drezet, "Can a Bohmian be a Rovellian for all practical purposes?", Foundations of Physics 53 1, 30 (2023).

[5] Eric G. Cavalcanti, Andrea Di Biagio, and Carlo Rovelli, "On the consistency of relative facts", European Journal for Philosophy of Science 13 4, 55 (2023).

[6] Pekka Lahti and Juha-Pekka Pellonpää, "An Attempt to Understand Relational Quantum Mechanics", International Journal of Theoretical Physics 62 8, 170 (2023).

[7] Matthew J. Lake and Marek Miller, "Quantum reference frames, revisited", arXiv:2312.03811, (2023).

[8] Eric G. Cavalcanti, Andrea Di Biagio, and Carlo Rovelli, "On the consistency of relative facts", arXiv:2305.07343, (2023).

[9] Martin Bojowald and Artur Tsobanjan, "Algebraic properties of quantum reference frames: Does time fluctuate?", arXiv:2211.04520, (2022).

[10] Jay Lawrence, Marcin Markiewicz, and Marek Żukowski, "Relative facts do not exist. Relational Quantum Mechanics is Incompatible with Quantum Mechanics. Response to the critique by Aurélien Drezet", arXiv:2210.09025, (2022).

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