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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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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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).

The above citations are from Crossref's cited-by service (last updated successfully 2024-06-21 23:02:58) and SAO/NASA ADS (last updated successfully 2024-06-21 23:02:59). The list may be incomplete as not all publishers provide suitable and complete citation data.