The Born Rule from Torsion Density Measurement

The Born rule — P(outcome i) = |⟨i|ψ⟩|2 — is the only postulate of quantum mechanics
without a derivation from deeper principles within the standard framework. Existing
derivations (Gleason 1957, Zurek 2003, Deutsch 1999) recover the rule from assumptions
about Hilbert space structure, symmetry, or decision theory, but none derive it from a
mechanical substrate. This paper derives the Born rule within the Cohesion Unified
Field Theory from two results already established in the series: (1) torsion density —
the energy density of the recursion field — is quadratic in the recursion field amplitude,
following from E = pr applied to a linear recursion field; and (2) a macroscopic
measuring device responds to torsion density (energy deposited in each pointer state
configuration), not to field amplitude directly, because its structural time rate is slow
relative to the system’s recursion frequency and it averages over rapid field oscillations.
The squared modulus in the Born rule is therefore not a postulate: it is a consequence
of wave energy being quadratic in amplitude, applied to the moment of structural time
synchronisation between system and device. The derivation is complete at the level of
wave mechanics; the remaining open problem is an explicit derivation of the recursion
field wave equation from the Cohesion UFT field equations, rather than an appeal to
the universal quadratic property of wave energy. This paper closes the primary open
problem of the quantum measurement paper and the quantum field paper of this series.