Born rule
Compiled with AI assistance and selectively reviewed. Please consult the cited passages; the books remain the authoritative source. About this companion
Editorial synthesis · provisional
Definition
The Born rule assigns quantum outcome probabilities through squared-amplitude weights. In the transactional reading, the conjugate pairing is interpreted as the joint contribution of offer and confirmation, not derived merely from there being two participants. PB formalizes positive, normalized weights under specified assumptions. Across these treatments, assigning an outcome a probability remains distinct from the further event of its actualization.
Explanation
AB gives the odds a physical reading through emitter–absorber participation, while declining to claim that two participants force a square. Its notes distinguish interpretation from mathematical uniqueness. RB1 separates interference among indistinguishable routes from probabilities of final outcomes and treats divided-receiver consistency as conditional, not evidence favoring TI over rivals.
PB defines the weight as an amplitude composed with its dagger: in finite-dimensional complex Hilbert spaces, the squared modulus of the outcome amplitude. Positivity, unitary invariance and normalization follow within the stated structure, with a complete absorber family and normalized offer. General categorical scalars require interpretation as real probabilities. The quadratic pairing is grounded, not derived from non-probabilistic axioms; unitary invariance is not Lorentz covariance. The confirmation-effect is outcome-specific, not generally the offer's adjoint.
RB3 applies the rule to eligible absorber responses subject to conservation constraints, without teleological direction. Its adoption of RTI remains explicit rather than proved. RB1's selection analogy and reported free-will compatibility do not establish another probability rule or agent causation. Weighting, physical interpretation and actualization remain distinct.
Scope and attribution
AB, PB, RB1 and RB3 own direct treatments. RB2's generic quantum discussion, references to Born and ordinary birth/Reborn matches are not Born-rule evidence. OB-CON-00372 Born-weight normalization remains a separate identity.
AB — The Actual Book
Offer and confirmation physically interpret the odds. Body and notes deny that two participants alone prove the square, and separate odds from actual resolution.
Occurrence locators: 30, 32, 33; Notes: 235, 236, 240.
PB — The Possible Book
The module defines squared-modulus weights and proves positivity, unitary invariance and normalization with stated assumptions. Outcome-specific confirmation and the absence of selection keep the formal mathematics distinct from a proof of RTI.
Occurrence locators: 148, 149, 150, 160, 168, 169, 170, 171, 172, 173, 174.
RB1 — The Real Book, Volume I: The Possible Is Real
The physical reading distinguishes interference, uniqueness and actualization. Subdivision consistency is conditional and interpretation-neutral; criticism of MWI does not exempt RTI from derivational scrutiny.
Occurrence locators: 51, 54, 55, 59, 60, 61, 73, 76, 77, 91, 124, 252, 253, 260, 296, 299; Notes: 59, 75.
RB3 — The Real Book, Volume III: Murmurations
Conservation-compatible absorber responses receive Born-rule probabilities without purposeful direction. The interpretation remains adopted, not established.
Occurrence locators: 55; Notes: 393.
Background used in the editorial explanation
Domain-specific mechanisms and wider analogies remain distinguished. Original definitions retain their scope; local cross-references do not rewrite them. Named theories and mechanisms are distinguished from neighboring background, homonyms and the author’s own synthesis. Reproduced AI passages retain their separate voice.