Abstract
The relational interpretation of quantum mechanics (RQM) has received a growing interest since its first formulation in 1996. Usually presented as an interpretational layer over the usual quantum mechanics formalism, it appears as a philosophical perspective without proper mathematical counterparts. This state of affairs has direct consequences on the scientific debate on RQM which still suffers from misunderstandings and imprecise statements. In an attempt to clarify those debates, the present paper proposes a radical reformulation of the mathematical framework of quantum mechanics which is relational from the start: fact-nets. The core idea is that all statements about the world, facts, are binary entities involving two systems that can be symmetrically thought of as observed and observer. We initiate a study of the fact-nets formalism and outline how it can shed new relational light on some familiar quantum features.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
A multi-graph is a graph where we allow more than one edge between two vertices.
References
Schrödinger, E.: An undulatory theory of the mechanics of atoms and molecules. Phys. Rev. 28(6), 1049 (1926). https://doi.org/10.1103/PhysRev.28.1049
Bacciagaluppi, G., Valentini, A.: Quantum theory at the crossroads: reconsidering the 1927 Solvay Conference. Cambridge University Library (2006). arXiv:quant-ph/0609184
Von Neumann, J.: Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton (2018)
Rovelli, C.: Relational quantum mechanics. Int. J. Theor. Phys. 35(8), 1637 (1996). https://doi.org/10.1007/BF02302261
Laudisa, F.: Open problems in relational quantum mechanics. J. Gen. Philos. Sci. 50, 215–230 (2019). https://doi.org/10.1007/s10838-019-09450-0
Pienaar, J.L.: A quintet of quandaries: five no-go theorems for relational quantum mechanics. Found. Phys. (2021). https://doi.org/10.1007/s10701-021-00500-6
Brukner, Č.: Qubits are not observers—a no-go theorem. (2021) arXiv:2107.03513
Di Biagio, A., Rovelli, C.: Relational quantum mechanics is about facts, not states: a reply to Pienaar and Brukner. Found. Phys. (2022). https://doi.org/10.1007/s10701-022-00579-5
Stacey, B.C.: Is relational quantum mechanics about facts? If so, whose? A reply to Di Biagio and Rovelli’s comment on Brukner and Pienaar. (2021) arXiv:2112.07830
Adlam, E., Rovelli, C.: Information is physical: cross-perspective links in relational quantum mechanics. (2022) arXiv:2203.13342
Yang, J.M.: A relational formulation of quantum mechanics. Sci. Rep. 8(1), 13305 (2018). https://doi.org/10.1038/s41598-018-31481-8
Di Biagio, A., Rovelli, C.: Stable facts. Relative facts. Found. Phys. 51(1), 30 (2021). https://doi.org/10.1007/s10701-021-00429-w
Rovelli, C.: The relational interpretation of quantum physics. In: Freire, O., Bacciagaluppi, G., Darrigol, O., Hartz, T., Joas, C., Kojevnikov, A., Pessoa, O. (eds.) Oxford Handbook of the History of Interpretation of Quantum Physics. Oxford University Press, Oxford (2021)
Rovelli, C.: An argument against the realistic interpretation of the wave function. Found. Phys. 46(10), 1229 (2016). https://doi.org/10.1007/s10701-016-0032-9
Giacomini, F., Castro-Ruiz, E.: Brukner, Č: quantum mechanics and the covariance of physical laws in quantum reference frames. Nat. Commun. 10(1), 494 (2019). https://doi.org/10.1038/s41467-018-08155-0
de la Hamette, A.-C., Galley, T.D.: Quantum reference frames for general symmetry groups. Quantum 4, 367 (2020). https://doi.org/10.22331/q-2020-11-30-367
de la Hamette, A.-C., Galley, T.D., Hoehn, P.A., Loveridge, L., Mueller, M.P.: Perspective-neutral approach to quantum frame covariance for general symmetry groups. (2021) arXiv:2110.13824
Loveridge, L., Busch, P., Miyadera, T.: Relativity of quantum states and observables. EPL 117, 40004 (2017). https://doi.org/10.1209/0295-5075/117/40004
Acknowledgements
This research stems from discussions that occurred at the Sejny Summer Institute in July 2021, organized by the Basic Research Community for Physics. We must mention the essential contribution of Leon Loveridge and Anne-Catherine de la Hamette, and the helpful discussions with Andrea Di Biagio.We also thank Alexandra Elbakyan for her help in accessing the scientific literature.PMD is supported by the ID# 61,466 Grant from the John Templeton Foundation, as part of the project Quantum Information Structure of Spacetime (QISS). (qiss.fr). The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation.JG is supported by the Polish National Science Centre (NCN) through the OPUS Grant No. 2017/27/B/ST2/02959.This work was partly supported by the Czech Science Foundation, Grant No. GAČR 19–15744Y.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Martin-Dussaud, P., Carette, T., Głowacki, J. et al. Fact-nets: Towards a Mathematical Framework for Relational Quantum Mechanics. Found Phys 53, 26 (2023). https://doi.org/10.1007/s10701-022-00653-y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10701-022-00653-y