Source
Di Biagio and Rovelli (2025), LIT-1676, arXiv 2510.11349v2, §VI (pp. 4–5), App. D (pp. 9–10) and App. E (pp. 10–11); read in NOTE-1214.
What was actually shown
The merge. Relative to us, |+⟩|a0⟩|b0⟩ (eq. 13) becomes (|0⟩|a0⟩ + |1⟩|a1⟩)|b0⟩/√2 when A correlates with Z (eq. 14), and then (|0⟩|a0⟩|b0⟩ + |1⟩|a1⟩|b1⟩)/√2 when B correlates with A or Z (eq. 15). Then I_{Z|A} = I_{Z|B} = I_Z^max and I_{A|B} = I_A^max: “A and B agree on the value of Z and about each other’s value” (p. 5).
The disturbance. If B instead correlates with X of the qubit, the state is eq. (16). X is a fact relative to B, A is not a fact relative to B, and “Z is not a fact relative to A anymore, even though A did nothing in this last timestep … because the interaction between B and S disturbed Z and changed its correlations with A” (p. 5). This case could have come out otherwise, and it is the one the paper uses against Frauchiger–Renner: the superobservers “change the correlation structure of the variables of the friends” (p. 5).
Wigner’s friend. Relative to an outside O, after Wigner asks his friend, H_Z = H_F = H_W = log 2 with I_{Z|F} = I_{Z|W} = I_Z^max and I_{F|W} = I_F^max (D8). “the value of Z relative to F is the same as the value of Z relative to W”, which O can verify “by interacting with Z, F, and W in any order” (p. 10). Wigner’s check M = |ψ1⟩⟨ψ1| does not commute with F, yet it leaves F’s relation to S untouched and gives Wigner no information about Z or F (p. 10).
The extended scenario. RQM keeps (E2): what Alice learns on opening the box is what Charlie saw, “guaranteed by quantum theory”. It denies (E1): “at no time will p_QM satisfy (E1)” for the interference choice, and Charlie’s outcome “is not a stable fact with respect to Alice” (p. 11).
The general claims are asserted. “The merging of perspectives offers a solution to RQM’s combination problem … If the variables couple correctly so as to get correlated, their perspectives will agree” (p. 5). There is no general statement of “correctly” and no proof.
What this does not say
- That perspectives relative to different outside systems agree. Each agreement above is read off one joint distribution, relative to “us” or to O. Inside one classical distribution, if Z is fixed by F and Z is fixed by W, the two agree by probability theory. The open question, which THEORY-621 and THEORY-1080 also leave open, is agreement between descriptions held relative to different systems. The paper sets it aside with its rejection of questions about what “really” happened (§IX).
- That merging is guaranteed. It requires coupling “properly”, and a coupling to a complementary variable does the opposite (eq. 16).
- That relative facts can be combined into one global distribution. App. E says they cannot (E3).
- That intersubjective agreement among many observers is derived. For that the paper relies on Zurek’s quantum Darwinism (§VIII), cited and not shown.