THEORY-621: Indexing each quantum fact to the system it is a fact for, and computing probabilities only between facts relative to the same system, removes the contradiction between the collapse and unitary probability rules in Wigner's-friend cases; the price is that values are not held at all times or by all systems alike, there is no global view, and no quantum state of the universe

Source

Rovelli (2021), LIT-177, a handbook chapter, read in full in NOTE-174.

What was actually shown

The contradiction (pp. 2–3). For a fact a and mutually exclusive facts bᵢ, P_collapse(c|a) = Σᵢ |W(c,bᵢ)|²|W(bᵢ,a)|² (eq. 3), while P_unitary(c|a) = |Σᵢ W(c,bᵢ)W(bᵢ,a)|² (eq. 4). These differ by interference.

The rule. Facts are sparse, occurring only in interactions, and relative, labelled by the interacting systems. Amplitudes W(b,a) have physical meaning only if a and b are relative to the same system. Eq. (3) “does not hold if the bᵢ have different labels than c”. What Wigner’s friend sees is a fact for the friend; for Wigner it is a correlation, which can still interfere. Any physical system can be an observer (p. 7).

Stable facts (p. 3). When decoherence makes P_collapse ≈ P_unitary, labels can be ignored. On this view, ontologies built on stable facts alone (Copenhagen, QBism) rest on an approximation: “we are all actually Wigner’s friends”. The decoherence result is cited, not shown (NOTE-174, C3).

ψ (pp. 3–4). ψ is a relative state with no ontological weight, compared to a Hamilton–Jacobi function. RQM posits no ontic state and so “circumvents” PBR, whose hidden premise is said to be strong realism.

The costs (pp. 6–7). Strong realism is given up in three respects: variables do not take values at all times, and take them at different times for different systems; values held relative to different systems can be compared only by a further physical interaction, so “there is no coherent global view available”; and “there is no meaning in ‘the quantum state of the full universe’”.

What could have come out otherwise. A relabelled rule could have left some Wigner’s-friend prediction inconsistent. Inside the chapter none is derived, because eq. (3) is never applied across labels.

What this does not say

• That the relative-labelling rule is derived. It is postulated as RQM’s “core idea” (NOTE-174, C2). It removes the contradiction by restricting when eq. (3) applies.
• That perspectives cohere. Inter-observer consistency, the chief objection in the literature, gets one sentence. Whether what one system records about another agrees with what it later learns is not addressed.
• That no-go theorems for absolute facts favour RQM. Calling them “direct evidence in favour of RQM” (p. 6) outruns them: they rule out observer-independent facts under their assumptions, a premise QBism and Everett also deny (C8).
• That all of quantum phenomenology follows from qp − pq = iħ. The chapter also needs a representation, a composition rule and the Born rule (C7).
• That ψ-realism is answered. The chapter argues against the 1926 “waves in space” reading and by analogy; Wallace- and Carroll-style realism is not engaged.

Connections

• Rivals THEORY-630. Gao’s protective-measurement argument makes ψ ontic and adds a preferred frame; here ψ has no ontological weight and there is no global view. Both cannot be right about ψ.
• PBR (THEORY-605) is sidestepped by positing no ontic state. Whether that is a third option or falls outside the framework is the question THEORY-586 raises.
• Dorato (LIT-176) classes RQM as a ψ-antirealist ontology of events (THEORY-656). Cuffaro & Hartmann’s open-systems view shares the denial of a closed universal system (THEORY-631). Carroll’s Hilbert-space fundamentalism (LIT-123) is the opposite pole.

Note of 2026-10-27 (evening): the readings of the U15–U23 works

Two readings bear on this reading’s open points.

• The decoherence step, “cited, not shown”, is shown. Di Biagio and Rovelli 2021 (NOTE-1226, eqs. 5–8, p. 4) give it, with an O(ε) error that is stated without a bound. The same-context rule is still asserted (“it is always the case”, p. 3), and agreement between observers still gets one sentence (p. 10), so the promote_when is not met.
• A correction to the title’s price. “Values are not held at all times” belongs to the 2021 sparse-facts formulation. Di Biagio and Rovelli 2025 (NOTE-1214, p. 7) say their reformulation “allows talk of relative facts also in-between interactions”. A relative fact is now a property of the joint distribution at any time.

The title is left as it stands, as a reading of the 2021 text. Whether it should be superseded by one of the 2025 formulation is open.