The measurement problem and Wigner's friend thought experiment
Artistic representation of how a friend's perception of a prior measurement result (left) changes (right) following Wigner's intervention (middle).
Quantum mechanics (QM) is our most successful physical theory in terms of experimental predictions. However, after almost a century from its conception, the interpretation of its formalism continues to raise a number of conceptual challenges. Among these, the quantum measurement problem is one of the most fundamental, and proposed solutions to this issue lie at the heart of the controversy surrounding alternative interpretations of quantum theory. The measurement problem can be intuitively framed as the question of how, when, and under what circumstances definite values of physical variables are realized from among potential outcomes.
The problem is most notably exemplified by the Wigner's friend thought experiment, which illustrates the paradoxical implications of quantum theory when different observers might disagree on whether a measurement outcome has been realized. In recent years, the topic has gained renewed interest due to new multi-agent extended versions of Wigner’s friend gedankenexperiment, such as Brukner’s no-go theorem for “facts of the world” [1], the Frauchiger-Renner no-go theorem on the self-consistency of quantum theory [2], and Bong et al. no-go theorem for “Local Friendliness” [3]. These works have been jointly awarded the 2023 Paul Ehrenfest Best Paper Award for Quantum Foundations. Wigner’s friend-like scenarios comprise observations of observers, highlighting the ambiguity of the two dynamics of quantum theory: Unitary evolution of isolated quantum systems and the non-unitary measurement-update rule (or collapse postulate). These (thought) experiments are designed such that the regular observers – the Friends – would describe their interaction with another quantum system as a measurement and, therefore, apply the collapse postulate, while so-called superobservers – the Wigners – describe the Friends as quantum systems and, thus, their interactions unitarily.
Since 2015, our group has worked towards a better understanding of the measurement problem, by exploring the limits of applicability of quantum theory in exotic scenarios in which observers both perform measurements and are measured by superobservers. We were the first ones to derive a no-go theorem for “facts of the world”, based on a combination of Wigner's friend with Bell-like setups [2], and since there we further developed ideas in a number of works [4-11].
The no-go theorem for “facts of the world” [1], shows that the assumptions on “locality”, “freedom of choice” and of “observer-independent facts” (i.e. the possibility of simultaneously decide on the truth value of statements about the experimental outcomes observed by different observers) are incompatible with quantum mechanical predictions. This has even stronger implications than standard Bell’s theorem, since it excludes the possibility of a coexistence of outcomes for different observers: “there are no facts of the world per se, but only relative to observers” [1] (given all the other assumptions hold). The scope and details of this work have been further developed by our group in Refs. [4,7,9], and have provided the theoretical basis for the celebrated strong no-go theorem of Bong at al. [3].
Moreover, we showed that different dynamical descriptions of the same measurement, together with the standard probability rules, give rise to observable contradictions when certain classical records are exchanged between Wigner and the Friend [7]. This allowed us to explore further this asymmetry between the description of the friend and of Wigner, and we were be able to show that, in certain cases, observers may be entitled to adopt and verify the state assignment from another observer’s environment if they condition their predictions on all information that is in principle available to them [11].
We were also able to generalize the standard Born rule, such that to reconcile the two different probability assignments in the descriptions by Wigner and his friend. This was achieved by describing the Wigner’s friend experiment in a timeless framework (Page-Wootters mechanism) which allows to assign an overall state from which both Wigner and the Friend can unambiguously compute the probabilities [8]. In Ref. [8], we put forward the first no-go theorem that does not require multiple Wigner-friend pairs. Therein, we showed that, under seemingly natural assumptions, the perceptions that the friend has of her own measurement outcomes at different times cannot “share the same reality”. Finally, we recently showed that if the friend is even slightly aware of a possible measurement being carried out on her by the superobserver, Wigner, this would conflict with the no-signaling principle [10].
This research program highlights that much remains to be understood about quantum theory when exploring its conceptual limits. The measurement problem stands as one of the most profound and fascinating challenges in modern physics; finding compelling solutions to the Wigner’s friend paradox would mark a significant step toward unraveling the deeper mysteries of the measurement problem.
[1] C. Brukner, On the quantum measurement problem, Quantum [Un]-Speakables II. Springer International Publishing, 95-117 (2017).
[2] Frauchiger, D. and Renner, R., Quantum theory cannot consistently describe the use of itself. Nature communications, 9(1), p.3711 (2018).
[3] Bong, K.W., Utreras-Alarcón, A., Ghafari, F., Liang, Y.C., Tischler, N., Cavalcanti, E.G., Pryde, G.J. and Wiseman, H.M., 2020. A strong no-go theorem on the Wigner’s friend paradox. Nature Physics, 16(12), pp.1199-1205.
[4] V. Baumann, F. D. Santo, and C. Brukner, Comment on Healey's \Quantum Theory and the Limits of Objectivity, Foundations of Physics 49, 741 (2019).
[5] V. Baumann and C. Brukner, Wigner’s Friend as a Rational Agent, Chapter in “Quantum, Probability, Logic”, Springer (2020).
[6] Baumann, V., Del Santo, F., Smith, A.R., Giacomini, F., Castro-Ruiz, E. and Brukner, C.. Generalized probability rules from a timeless formulation of Wigner's friend scenarios. Quantum, 5, 524 (2021).
[7] C. Brukner. Facts are relative. Nature Physiscs 16, 1172–1174 (2020).
[8] Allard Guérin, P., Baumann, V., Del Santo, F. and Brukner, Č. A no-go theorem for the persistent reality of Wigner’s friend’s perception. Communications Physics, 4(1), 93 (2021).
[9] C. Brukner. Wigner’s friend and relational objectivity. Nat Rev Phys 4, 628–630 (2022).
[10] Baumann, V. and Brukner, C., . Wigner's friend's memory and the no-signaling principle. Quantum, 8, p.1481 (2024).
[11] Del Santo, F., Manzano, G. and Brukner, C. Wigner's friend scenarios: on what to condition and how to verify the predictions. arXiv preprint arXiv:2407.06279 (2024).
[2] Frauchiger, D. and Renner, R., Quantum theory cannot consistently describe the use of itself. Nature communications, 9(1), p.3711 (2018).
[3] Bong, K.W., Utreras-Alarcón, A., Ghafari, F., Liang, Y.C., Tischler, N., Cavalcanti, E.G., Pryde, G.J. and Wiseman, H.M., 2020. A strong no-go theorem on the Wigner’s friend paradox. Nature Physics, 16(12), pp.1199-1205.
[4] V. Baumann, F. D. Santo, and C. Brukner, Comment on Healey's \Quantum Theory and the Limits of Objectivity, Foundations of Physics 49, 741 (2019).
[5] V. Baumann and C. Brukner, Wigner’s Friend as a Rational Agent, Chapter in “Quantum, Probability, Logic”, Springer (2020).
[6] Baumann, V., Del Santo, F., Smith, A.R., Giacomini, F., Castro-Ruiz, E. and Brukner, C.. Generalized probability rules from a timeless formulation of Wigner's friend scenarios. Quantum, 5, 524 (2021).
[7] C. Brukner. Facts are relative. Nature Physiscs 16, 1172–1174 (2020).
[8] Allard Guérin, P., Baumann, V., Del Santo, F. and Brukner, Č. A no-go theorem for the persistent reality of Wigner’s friend’s perception. Communications Physics, 4(1), 93 (2021).
[9] C. Brukner. Wigner’s friend and relational objectivity. Nat Rev Phys 4, 628–630 (2022).
[10] Baumann, V. and Brukner, C., . Wigner's friend's memory and the no-signaling principle. Quantum, 8, p.1481 (2024).
[11] Del Santo, F., Manzano, G. and Brukner, C. Wigner's friend scenarios: on what to condition and how to verify the predictions. arXiv preprint arXiv:2407.06279 (2024).