TITLE:
Born’s Rule from Reversible Evolution and Record Formation
AUTHORS:
Oskar Axelsson
KEYWORDS:
Born’s Rule, Quantum Measurement, Reversible Dynamics, Irreversible Record Formation, Quantum Foundations
JOURNAL NAME:
Journal of Modern Physics,
Vol.17 No.10,
October
9,
2026
ABSTRACT: We show that the quadratic measure associated with the Born rule need not be introduced as an independent probabilistic postulate, but follows, under the stated structural and regularity assumptions, from the compatibility between reversible linear evolution and the formation of stable records. Physical processes alternate between reversible dynamics and episodes of record formation. Quantities that remain well defined throughout such processes must therefore admit a representation that remains consistent across both regimes. Prior to record formation, alternatives combine additively at the level of complex amplitudes, whereas successive record-forming distinctions admit a multiplicative representation through refinement. Requiring compatibility between these compositional structures constrains the admissible weight assignment to the family
| α |
p
. The finite-dimensional specialization of Lamperti’s isometry theorem then singles out
p=2
as the unique value compatible with continuous reversible linear mixing while preserving total weight. The Born rule therefore emerges as the unique weight assignment compatible with reversible linear composition, multiplicative record refinement, phase invariance, and continuous reversible invariance, without invoking probabilistic assumptions or a specific interpretation of quantum measurement.