Source
Rovelli (1996), LIT-1635, arXiv quant-ph/9609002v2; read in NOTE-1227. Page numbers are the preprint’s.
What was actually shown
No deducible relation. “The absolute state of affairs of the world is a meaningless notion; asking about the absolute relation between two descriptions is precisely asking about such an absolute state of affairs of the world. … In particular, there is no way of deducing the view of one from the view of the other” (§II.D, p. 8). The relation “must be addressed within the view of one of the two observers (or of a third one)”, because “the process of comparison is always a physical interaction, and all physical interactions are quantum mechanical in nature” (p. 8).
No description in toto. A further observer can describe a complex situation, but that description is “deficient in two directions: upward, because an even more general observer is needed to describe the global observer itself, and –more importantly– downward, because the in toto observer knows the content of the information that the single component systems possess about each other only probabilistically” (§IV.A, p. 16). Everett’s universal wave function “represents the perspective of a non-existent observer”; “There is no description of the universe in-toto, only a quantum-interrelated net of partial descriptions” (§IV.B, p. 19).
Where the relativity analogy stops. The paper’s analogy is Einstein’s reading of the Lorentz transformations (§I, p. 2) and the relativity of velocity (p. 6). In relativity a frame’s description is obtained from another’s by a transformation. Here it is not: what one observer can have about another’s view is P-relative, probabilistic information that O has measured (the operator M, eq. 3), not what O found (“I know that you know the amount of your salary, but I do not know what you know about the amount of your salary”, p. 8). What does not vary between observers is the system’s characterization, W(S) (THEORY-1068), not a state of it.
Consistency. If P measures q on S and then O’s pointer, the two agree, “as was first noticed by von Neumann, and as is clear from (2)” (p. 9). That is the case shown. The general claim, that with rules (i) and (ii) “there is no way in which contradiction may develop”, is introduced with “The reader may convince himself” (§III.D, p. 15). Rovelli also suspects that this consistency “could be taken as the missing input” for the reconstruction, and has “no definite result” (§III.C, p. 14).
What this does not say
- That consistency fails. Nothing in the paper suggests a conflict; the gap is that the general case is not proved.
- That there is nothing invariant. The systems and their question sets are not observer-relative, and the probabilities a third system assigns are given by standard quantum mechanics.
- That this is solipsism. Views can be compared, by interaction (p. 8).
- Anything about communicative acts. Its bearing on QUESTION-021 is by analogy: a physical theory built on a relativity analogy that keeps a frame-independent kind (W(S), compare CLAIM-137) and denies a frame-independent state.
- How the later account handles consistency. THEORY-621 is the 2021 statement, with the same gap noted in its promote_when.