Deciding between collapse for all observers and unitary evolution in isolated laboratories: the $1/12$ versus $1/4$ extended Wigner's-friend discrimination

The modified Copenhagen interpretation proposed by Reichert and Enz (2026) resolves Wigner's-friend inconsistencies by postulating an objective, observer-independent wave-function collapse that acts also inside isolated laboratories. It predicts joint outcome probabilities for the Frauchiger–Renner extended Wigner's-friend setup — all four outcomes equal to $1/4$, in particular $p_{\bar{\mathrm{ok}}\,\mathrm{ok}}=1/4$ — that differ from the standard unitary prediction $p_{\bar{\mathrm{ok}}\,\mathrm{ok}}=1/12$, making the two analysis classes empirically distinguishable in principle. No experiment has tested this divergence: existing Wigner's-friend experiments operate with microscopic 'friends' in the regime where both classes coincide, and whether a discriminating experiment — a laboratory whose internal measurement constitutes a genuine registration while the laboratory remains coherently measurable from outside in a superposition basis — is physically realizable is open. The problem is to determine feasibility and either perform the discrimination between objective collapse for all observers and unitary evolution of isolated laboratories, or establish a quantitative fundamental obstruction.

Background

Quantum mechanics rests on two postulates in tension. Isolated systems evolve unitarily and deterministically according to the Schrödinger equation, yet a measurement projects ('collapses') the state vector onto an eigenstate of the measured observable, with outcomes distributed according to the Born rule (probability equal to the squared modulus of the amplitude). The Copenhagen interpretation treats measurement and its collapse as a primitive postulate, with neither a physical mechanism nor a precise criterion for when it applies — an incompleteness that Wigner dramatized in 1961. In Wigner's friend thought experiment, a friend measures a spin prepared in a superposition inside an isolated laboratory and obtains a definite outcome, so for her the state has collapsed; Wigner, treating the entire laboratory (spin, device, friend) as an isolated quantum system, assigns it a coherent superposition of both outcome branches. Deutsch (1985) observed that this disagreement is in principle empirical: an always-unitary account (the Everett, or many-worlds, view that the state vector never collapses) and a collapse account make different predictions if Wigner subsequently measures the laboratory in a basis of superpositions of the outcome branches.

Extended Wigner's-friend scenarios add a second laboratory and external observers. In the Frauchiger–Renner (FR) setup, a first agent measures a quantum coin, prepares a spin conditioned on the outcome, and a second agent measures the spin; two external observers then measure each laboratory in bases containing the states $|\bar{\mathrm{ok}}\rangle$ and $|\mathrm{ok}\rangle$, which are superpositions of the laboratories' outcome branches. Applying standard quantum theory to all agents uniformly, FR derived the joint probability $p_{\bar{\mathrm{ok}}\,\mathrm{ok}}=1/12$ and argued that letting the agents reason about each other with the same theory leads to contradiction. Related no-go theorems (Brukner 2018; Bong et al. 2020) show that quantum predictions conflict with 'absoluteness of observed events' (every observed event exists absolutely, not relative to an observer) together with locality and no-superdeterminism (the requirement that the external observers' measurement choices be statistically independent of the laboratories' prior physical state); the associated Local Friendliness inequalities are violated in photonic experiments in which the 'friend' is a single degree of freedom of a photon.

Reichert and Enz (2026) propose a modified Copenhagen interpretation that resolves the Wigner's-friend inconsistencies within a collapse framework by postulating: (i) a universal, observer-independent state vector; (ii) collapse as an objective part of quantum time evolution that occurs also inside isolated systems whenever an outcome is registered in a macroscopic system (registration, not consciousness, triggers collapse); and (iii) a strict separation between the objective state and the observers' intersubjective knowledge, the latter described by probability distributions over states. In the FR setup, the objective collapse inside the second laboratory destroys the orthogonality that removes two of the three contributing branches in FR's calculation, so each branch contributes $1/12$ and $p_{\bar{\mathrm{ok}}\,\mathrm{ok}}=3/12=1/4$, with all four joint outcomes of the external observers equal to $1/4$. This is exactly the class of distinguishing experiments anticipated by Deutsch (1985). Objective-collapse models — stochastic modifications of the Schrödinger equation, such as GRW (Ghirardi–Rimini–Weber) and CSL (continuous spontaneous localization), that induce spontaneous localization at rates growing with system size (reviewed by Bassi et al. 2013) — would produce the same qualitative signature with intermediate, parameter-dependent statistics.

The discrimination has not been performed. Existing Wigner's-friend experiments use 'friends' far below any registration threshold; in that microscopic regime the collapse-for-all-observers and unitary predictions coincide, so the observed violations of Local Friendliness inequalities do not decide the question. A discriminating experiment requires a laboratory whose internal measurement constitutes a genuine macroscopic registration while the laboratory as a whole remains coherently measurable from outside in a superposition basis. Decoherence — the uncontrolled entanglement of the laboratory with its environment, which rapidly suppresses the off-diagonal terms carrying the distinction — and the creation of classical records are the central obstructions: Baumann (2023) shows that any classical record of the friend's outcome that is not included in the external observer's coherent whole-laboratory measurement — for example one leaked to the environment or communicated outside the laboratory — removes the discrimination entirely, since Wigner's unitary description then reproduces collapse statistics; internal registration degrees of freedom that remain inside the coherently measured laboratory are not covered by this result. Quantitative analyses (Relaño 2019; Rivlin et al. 2025) find strong environment-induced restrictions. Whether any platform (matter-wave interferometry, cavity quantum electrodynamics, quantum processors) can reach the discriminating regime, or whether a fundamental obstruction exists, is unsettled.

Problem Statement

Decide, empirically or by rigorous feasibility analysis, whether a measurement performed inside an isolated quantum laboratory is an objective physical process for all observers or a feature of description only — as crystallized by the divergent predictions for the Frauchiger–Renner extended Wigner's-friend setup, where $p_{\bar{\mathrm{ok}}\,\mathrm{ok}}$ denotes the joint probability that both external observers obtain the 'ok' outcome: $p_{\bar{\mathrm{ok}}\,\mathrm{ok}}=1/4$ (all four joint outcomes equal to $1/4$) if collapse acts objectively inside the isolated laboratory, versus $p_{\bar{\mathrm{ok}}\,\mathrm{ok}}=1/12$ under the standard unitary treatment of the laboratory, with parameterized objective-collapse models predicting intermediate statistics.

The problem comprises two linked deliverables serving this single objective:

1. A feasibility determination: either a quantitative experimental design in which the internal ('friend's') measurement constitutes a genuine registration in a macroscopic system while the whole laboratory — including the registration device and any internal record — remains coherently measurable by an external observer in a superposition-of-outcomes basis, with a resource and decoherence analysis showing the two prediction classes are statistically resolvable; or a quantitative no-go argument establishing, from stated physical assumptions, that no physically realizable configuration can discriminate them — distinguishing a fundamental obstruction from a current technical limitation. Because the criterion fixing a genuine macroscopic registration (hence the discriminating regime referred to in deliverable 2 and completion (a)) is model-dependent, the analysis must state the criterion it adopts — for example an amplification scale in mass or number of degrees of freedom, or the amplification criterion of a named parameterized collapse model at a stated rate — and is judged for internal consistency against it.

2. Given feasibility, the experimental discrimination itself: a completed experiment in the regime where the prediction classes differ, deciding which class holds at stated statistical significance, together with the model-level calculation of the predicted statistics for the chosen platform (including the collapse probability if a parameterized collapse model is used), so that the decision is quantitative rather than axiomatic; where execution in that regime is not attainable, a fully specified experiment together with the same model-level predicted statistics and the statistical significance it attains may be submitted in place of executed data.

The problem is complete when either (a) a valid discrimination experiment has decided the question in the regime where the prediction classes differ; (b) a rigorous quantitative analysis has established that no such experiment can exist; or (c) a quantitative feasibility analysis has established whether the discriminating regime is reachable and classified any obstruction as fundamental rather than technical. The broader measurement problem — replacing the collapse postulate by a mechanistic theory of measurement — is the background motivation and remains open, but is not part of this problem's completion boundary.

References

1. Peter Reichert and Markus Enz, 'Wigner's Friend Paradox Revisited' (2026), arXiv:2608.02635, https://arxiv.org/abs/2608.02635
2. Eugene P. Wigner, 'Remarks on the Mind-Body Question' (first published 1961), reprinted in Philosophical Reflections and Syntheses (Springer, 1995), pp. 247-260, DOI 10.1007/978-3-642-78374-6_20, https://doi.org/10.1007/978-3-642-78374-6_20
3. David Deutsch, 'Quantum theory as a universal physical theory', International Journal of Theoretical Physics 24, 1-41 (1985), DOI 10.1007/BF00670071, https://doi.org/10.1007/BF00670071
4. Daniela Frauchiger and Renato Renner, 'Quantum theory cannot consistently describe the use of itself', Nature Communications 9, 3711 (2018), DOI 10.1038/s41467-018-05739-8, https://doi.org/10.1038/s41467-018-05739-8
5. Časlav Brukner, 'A No-Go Theorem for Observer-Independent Facts', Entropy 20, 350 (2018), DOI 10.3390/e20050350, https://doi.org/10.3390/e20050350
6. Massimiliano Proietti, Alexander Pickston, Francesco Graffitti, Peter Barrow, Dmytro Kundys, Cyril Branciard, Martin Ringbauer, Alessandro Fedrizzi, 'Experimental test of local observer independence', Science Advances 5, eaaw9832 (2019), DOI 10.1126/sciadv.aaw9832, https://doi.org/10.1126/sciadv.aaw9832
7. Kok-Wei Bong, Aníbal Utreras-Alarcón, Farzad Ghafari, Yeong-Cherng Liang, Nora Tischler, Eric G. Cavalcanti, Geoff J. Pryde, Howard M. Wiseman, 'A strong no-go theorem on the Wigner's friend paradox', Nature Physics 16, 1199-1205 (2020), DOI 10.1038/s41567-020-0990-x, https://doi.org/10.1038/s41567-020-0990-x
8. Angelo Bassi, Kinjalk Lochan, Seema Satin, Tejinder P. Singh, Hendrik Ulbricht, 'Models of wave-function collapse, underlying theories, and experimental tests', Reviews of Modern Physics 85, 471-527 (2013), DOI 10.1103/RevModPhys.85.471, https://doi.org/10.1103/RevModPhys.85.471
9. Armando Relaño, 'Decoherence framework for Wigner's-friend experiments', Physical Review A 101, 032107 (2020) (preprint 2019, arXiv:1908.09737), DOI 10.1103/PhysRevA.101.032107, https://doi.org/10.1103/PhysRevA.101.032107
10. Veronika Baumann, 'Classical Information and Collapse in Wigner's Friend Setups', Entropy 25, 1420 (2023), DOI 10.3390/e25101420, https://doi.org/10.3390/e25101420
11. David Schmid, Yìlè Yīng, Matthew Leifer, 'A review and analysis of six extended Wigner's friend arguments' (2023), arXiv:2308.16220, https://arxiv.org/abs/2308.16220
12. William J. Zeng, Farrokh Labib, Vincent Russo, 'Towards violations of Local Friendliness with quantum computers', Quantum 9, 1851 (2025) (preprint 2024, arXiv:2409.15302), DOI 10.22331/q-2025-09-05-1851, https://doi.org/10.22331/q-2025-09-05-1851
13. Tom Rivlin, Sophie Engineer, Veronika Baumann, 'Emergence of Classicality in Wigner's Friend Scenarios' (2025), arXiv:2507.21221, https://arxiv.org/abs/2507.21221
14. Julio C. F. Silva, B. F. Rizzuti, Cristhiano Duarte, 'Agreement and Compatibility in Wigner's Friend Paradox' (2026), arXiv:2605.27424, https://arxiv.org/abs/2605.27424