Wigner's Friend Paradox Revisited

Markus Enz; Peter Reichert

REVIEW 3 major objections 4 minor 37 references

Wigner's Friend Paradox Revisited

T0 review · 3 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read A modified Copenhagen interpretation—with wave-function collapse as real time evolution inside isolated labs—eliminates Wigner's Friend inconsistencies and predicts a joint 'ok' probability of 1/4, replacing the previous 1/12.

desk verdict A clean probability calculation and a clear limitation statement, but the resolution fails at step 3: W's complementary-basis collapse leaves the friend's memory in a superposition, so Table 2's definite-knowledge claim doesn't follow. read the letter →

arxiv 2608.02635 v1 pith:ZTBBEU3O submitted 2026-07-30 quant-ph

Peter Reichert , Markus Enz This is my paper · ORCID

classification quant-ph

keywords Wigner'sFriendparadoxextendedCopenhageninterpretationwave-functioncollapseobserver-independentquantumstatemeasurementproblemBornrule

topics The Measurement Problem

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper proposes a modified Copenhagen interpretation that removes Wigner's Friend and extended Wigner's Friend inconsistencies. The key move is to treat wave-function collapse during measurement as genuine quantum time evolution that also occurs inside isolated labs, and to separate that objective state from the partial knowledge conscious observers may have about it. Under these assumptions the earlier extended-setup calculation changes: the probability that both outside observers see the outcome 'ok' becomes 1/4, not 1/12. Because the altered number comes from collapse rather than from a coherent superposition of branches, the difference is in principle observable. The authors acknowledge that a full mechanistic account of collapse remains an open problem.

What carries the argument

The machinery is the axiom that measurement consists of a projection onto the eigenspace of the observed eigenvalue, with the outcome realized according to Born probabilities, and that this projection is part of the system's time evolution even when the system is isolated from any external observer. Applied inside Wigner's friend labs, this axiom turns an entangled superposition of 'heads' and 'tails' branches into a set of definite alternative states, each with its own probability. The calculation in equation (13) is the point where the axiom changes the result: each definite branch overlaps with the external 'ok' state with amplitude 1/2, giving 3 × (1/3) × (1/2)^2 = 1/4, whereas the coher

What would settle it

Run the extended two-lab procedure many times, with internal measurements performed by automated devices, and tally how often both outside observers get 'ok'. The modified collapse picture predicts 25%; the coherent-branch picture predicts about 8.3%. A statistically clear rate at one of these values would settle between the two analyses.

Watch

Extended reading notes

Core claim

The central claim is that all inconsistencies in Wigner's Friend and extended Wigner's Friend setups disappear if measurement collapse is part of quantum mechanical time evolution even or especially in isolated labs, the quantum state is universal and observer-independent, and observer knowledge is tracked separately via intersubjective probabilities. The decisive calculation concerns the extended setup's final double measurement: after the friend in the second lab measures the spin along z, the lab state collapses to one of the three definite branches (12a)-(12c) instead of remaining a coherent superposition. Computed from these branches, the probability that both external observers registe

Load-bearing premise

The whole resolution hangs on the premise that measurement produces a genuine wave-function collapse inside an isolated system as part of time evolution; if collapse happens only when an outside observer looks, the branches stay coherent and the paradox returns.

Editorial extensions

If this is right

The extended Wigner's Friend setup becomes a consistency check rather than a contradiction: observers can disagree only in knowledge, not in state.
The joint 'ok'-and-'ok' outcome occurs with probability 1/4; each of the four outcome pairs is equally likely.
The same reasoning carries over to spontaneous collapse models and to unitary-plus-statistical-mechanics accounts of measurement, since both realize collapse without an observer.
If a future mechanistic theory replaces the collapse axiom, the argument is meant to remain valid because it only relies on the existence of some projection-like transition inside isolated labs.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The 1/4-versus-1/12 gap suggests a concrete experimental target: realize the two internal measurements with controllable 'friend' systems and count the joint 'ok' rate; the two branches of quantum mechanics predict different rates.
The paper's distinction between objective state and intersubjective knowledge could be exported to other quantum puzzles, such as delayed-choice and counterfactual measurement scenarios, where partial information is usually conflated with state update.
The framework implies that there is a definite time (when the macroscopic device registers the result) at which the branch structure changes; experiments that tune the size or sensitivity of the 'measurement device' might map the crossover from coherence to collapse-like behavior.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Dear [Colleague],

The paper is worth reading for the calculation: they get p(ok,ok)=1/4 under their collapse-in-isolated-systems Copenhagen, whereas Frauchiger–Renner get 1/12. The derivation is clear and the difference is exactly traced to replacing the coherent branch (eq. 14) with collapsed branches (12b,c). That is a genuine, testable-in-principle consequence of their axioms. The authors are also honest about the unresolved measurement problem and they don't hide the fact that they have weakened FR's criterion (Q) to (Q').

The problem is that the resolution fails at the final step. When W measures the whole lab in the |ok>/|fail> basis, their own collapse postulate projects the lab onto, say, |ok>_L = (|−1/2>_L − |+1/2>_L)/√2. That is a coherent superposition of two pointer/memory states. So the friend's memory and recorded outcome are not definite. Table 2, step 3, still assigns F perfect knowledge of 'the state in the corresponding lab.' That is inconsistent with the collapse rule they rely on. The collapse to an eigenstate of W's observable is not a collapse to an eigenstate of the friend's pointer observable, and their postulate doesn't magically make the friend's memory definite. This is the same issue that plagues naive collapse pictures when external measurements are in a complementary basis. The stress-test note gets this exactly right.

The weaker criterion (Q') is a second soft spot: they change the no-go theorem rather than satisfying it. That's not fatal if the new axioms are independently motivated, but it's a significant concession. The mechanistic definition of collapse (threshold, basis, timing) is also admittedly missing, and they explicitly punt on it.

So: the calculation is new and clean, the writing is transparent, and the limitations are stated. But the central claim—'we can resolve any inconsistencies'—is not supported. The paper deserves a serious referee because the calculation and the interpretation move are interesting and the mistake is instructive, but it should not be published as a resolution. A good referee might suggest testing the p=1/4 prediction in a small quantum simulation, but that won't fix the conceptual inconsistency.

For whom is this? People working on Wigner's friend and collapse models may want to cite it as an example of a collapse-based attempt that fails at the complementary-measurement step. I wouldn't cite it in my own work. I would send it to peer review rather than desk reject it, though the likely outcome is a clear rejection or a major rewrite that fixes the final step.

Recommendation: engage with it enough to point out the step-3 error; don't let it through as a resolution.

Referee Report

3 major / 4 minor

Summary. The paper proposes a modified Copenhagen interpretation of quantum mechanics based on three assumptions: (i) a universal, observer-independent quantum state; (ii) wave-function collapse as a real physical process that is part of quantum time evolution, including inside isolated systems; and (iii) a sharp distinction between the objective quantum state and the epistemic state of conscious observers. It applies this framework to Wigner's Friend and to the extended Wigner's Friend setup of Frauchiger and Renner. The central computation is Eq. (13), which gives p_ok,ok = 1/4 instead of Frauchiger-Renner's 1/12, and the paper claims that with these assumptions all inconsistencies are resolved. The paper explicitly acknowledges that the measurement problem is not solved and that the collapse postulate is an ill-defined placeholder.

Significance. If the proposed interpretation were internally consistent, the paper would be a useful contribution: it offers a concrete, falsifiable probability difference (Eq. 13, p_ok,ok = 1/4 vs 1/12), engages seriously with collapse models and the Frauchiger-Renner theorem, and is transparent about its limitations. However, the central consistency claim fails at the final step of the extended Wigner's Friend setup. The paper's own collapse rule, applied to the external measurement of the lab in the |ok>/|fail> basis, leaves the friend's memory in a superposition. Table 2 nevertheless ascribes definite internal knowledge to the friend. This is not a minor presentation issue; it is the load-bearing step of the claimed resolution. The paper also weakens Frauchiger-Renner's criterion (Q) to (Q'), which reduces the force of the 'resolution' unless the modified axioms are independently well motivated.

major comments (3)

[§4, Eq. (6b) and Table 2, step 3] The collapse of lab L onto |ok>_L = (|-1/2>_L - |+1/2>_L)/√2 is a projection onto a coherent superposition of the two pointer/memory states (5a) and (5b). Under Assumption 2, this is a real physical collapse: the friend's measurement device and the friend's memory are left in the superposition (|'-1/2'>_F - |'+1/2'>_F)/√2. Table 2 nonetheless reports the internal registered result as 'ok' and states that knowledge is perfect about the state in the corresponding lab. That is inconsistent with the collapse postulate: F does not occupy a definite belief state after W's measurement, so the epistemic probabilities in Table 2 are undefined. This invalidates the paper's claim that the modified assumptions resolve all inconsistencies at all times.
[§5, criterion (Q')] The paper replaces Frauchiger and Renner's criterion (Q) with a weaker criterion (Q'), requiring consistency of 'a suggested version of quantum mechanics' rather than a pre-defined version. The paper itself concedes that 'It is trivial that modified assumptions (and modified criteria) can lead to different conclusions.' The original Frauchiger-Renner theorem is about the consistency of a fixed, given quantum theory. Demonstrating that a different theory with a modified criterion avoids the contradiction does not resolve the original paradox unless the modified axioms are independently justified at the required level of precision. The collapse postulate is explicitly acknowledged to be not well defined, so the justification is currently incomplete.
[§2, Assumption 2] Assumption 2 makes collapse a real process 'also within isolated systems,' but it does not specify when a measurement process occurs, what counts as a macroscopic registration, or what selects the measurement basis and the timing of collapse. The paper acknowledges this ('As such a measurement process is not well-defined, this is not satisfying'), but the central probability shift in Eq. (13) depends on collapse occurring at the specific internal steps and not at the coherent-branch level of Frauchiger-Renner. Without a precise criterion, the universal consistency claim cannot be uniquely evaluated. This is a foundational gap, though the more immediate technical inconsistency in Table 2 step 3 is the decisive problem.

minor comments (4)

[§2] Typographical errors: 'underlay' should be 'undergo'; 'ocurred' should be 'occurred'.
[§5] Typographical errors: 'There is a an intensive discussion' should be 'There is an intensive discussion'; 'intergral' should be 'integral'.
[Table 2] The column headers for 'registered result' are confusing because 'ok'/'fail' in step 3 are results of the external measurements, not of the internal devices D and D. The footnote clarifies, but the table's layout makes it easy to misread the content of the cells.
[Eq. (13)] The notation uses the same subscript L for the two labs (⟨ok|_L ⊗ ⟨ok|_L), although earlier in the paper the two labs are distinguished as L and L (or L and ar L). This makes Eq. (13) unnecessarily ambiguous.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the 1/4 prediction follows directly from the stated collapse axiom and is a falsifiable consequence, not a fitted or self-referential input.

full rationale

The paper's central derivation, equation (13), computes p_ok,ok = 1/4 by applying the explicitly stated Assumption 2 (collapse inside isolated labs) to replace Frauchiger–Renner's coherent tail state (14) with the collapsed branches (12a)–(12c), then evaluating Born amplitudes on those branches. No parameter is fitted to the target probability; the target probability is derived, and the paper explicitly contrasts it with FR's 1/12 as a testable difference. The only apparent 'definitional' move is the replacement of criterion (Q) with (Q'), allowing the paper's own version of quantum mechanics to count as valid; this is openly acknowledged, including the sentence 'It is trivial that modified assumptions (and modified criteria) can lead to different conclusions.' The paper does not claim to satisfy the original (Q), so the resolution is a conditional theory-construction rather than a hidden circular reduction. There is no load-bearing self-citation, no ansatz smuggled in by citation, and no uniqueness theorem imported from the authors' prior work. The skeptic's objection that the friend's memory would be left in a superposition after W's |ok>/|fail> measurement is a correctness or coherence challenge to the collapse axiom, not evidence that the derivation reduces to its own inputs. Thus no circular steps are identified.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The central calculation depends on the collapse-in-isolated-systems axiom and the weakened criterion (Q'). No fitted parameters appear. The step-3 handling of internal observer knowledge assumes that collapse produces definite pointer states, which the projection postulate does not guarantee for complementary-basis measurements.

assumptions (4)

ad hoc to paper Measurement processes with wave function collapse are part of quantum mechanical time evolution, also within isolated systems, projecting onto the eigenspace of the observed eigenvalue with Born probabilities.
Section 2, Assumption 2. This is the key postulate that changes the FR probability calculation (eqs. 12-13). It is unmechanistically defined, lacking a criterion for what counts as a measurement, in which basis, and at what time.
domain assumption The quantum state is universal and observer-independent.
Section 2, Assumption 1. Adopted from a family of psi-ontic interpretations; contested by QBism and relational interpretations. The paper relies on this to eliminate observer-dependent states.
domain assumption Conscious observers' knowledge is represented by intersubjective probability distributions over states.
Section 2 and Section 5, item 3. Needed to separate the objective state from observer knowledge; presupposes Bayesian/Cox consistency arguments.
ad hoc to paper Frauchiger-Renner criterion (Q) is replaced by (Q'), requiring consistent application of a suggested version of quantum mechanics rather than a pre-defined one.
Section 5. This attenuation of the no-go theorem's premise is what allows all three criteria to be jointly satisfied; it changes the problem rather than resolving it.

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Cite this review

Pith. "Pith review of Wigner's Friend Paradox Revisited." pith.science (2026). https://pith.science/paper/ZTBBEU3O

@misc{pith2026260802635,
  author       = {Pith},
  title        = {Pith review of: Wigner's Friend Paradox Revisited},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZTBBEU3O}},
  note         = {Machine review of arXiv:2608.02635}
}

read the original abstract

By assuming (i) a universal, observer-independent quantum state, by considering (ii) measurement processes with wave function collapse as part of quantum mechanical time evolution (also within isolated systems), and by (iii) clearly distinguishing the state of a quantum system from the knowledge of conscious observers about this state, we suggest a modified Copenhagen interpretation of quantum mechanics that resolves Wigner's Friend and extended Wigner's Friend paradoxes. The suggested interpretation leads to differences in some outcome probabilities compared to previous analyses which, in principle, make it possible to falsify the suggested modifications or the previous analyses (or both). The fundamental problem of the incompleteness of quantum mechanics in the Copenhagen interpretation regarding the lack of a precise definition and a mechanistic description of the measurement process (including the collapse of the wave function) is not addressed in this study. However, the argumentation regarding the resolution of Wigner's Friend paradoxes also applies to attempts for such a mechanistic description using collapse models with stochastic extensions to the Schr\"odinger equation or trying to model wave function collapse with unitary time evolution and irreversibility of the measurement process resulting from quantum statistical mechanics.

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Reviewed August 5, 2026 · model on record in the stance chip above.

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Allahverdyan, A. E. and Balian, R. and Nieuwenhuizenc, T. M. Curie- W eiss model of the quantum measurement process. Europhysics Letters

work page

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Allahverdyan, A. E. and Balian, R. and Nieuwenhuizenc, T. M. Understanding quantum measurement from the solution of dynamical models. Physics Reports

work page

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Models of wave-function collapse, underlying theories, and experimental tests , author =. Rev. Mod. Phys. , volume =. 2013 , month =. doi:10.1103/RevModPhys.85.471 , url =

doi:10.1103/revmodphys.85.471 2013

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doi:10.1103/physrev.48.696 1935

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