The Born rule is one of quantum mechanics' most fundamental postulates: the probability of finding a particle at position x is proportional to |Ψ(x)|². It cannot be derived within standard quantum mechanics - it is an axiom. Many interpretations of quantum mechanics accept it as primitive.
BFUT Paper 19A derives it from the physical identification of the wavefunction as substrate deformation geometry.
The Physical Identification
In BFUT, the wavefunction Ψ(x,t) is the amplitude of the Spaticle substrate deformation at position x and time t. The energy density of a deformation wave in a continuous medium is proportional to the square of the wave amplitude - this is standard wave mechanics. For the Spaticle substrate:
The probability of finding a condensation at position x is the probability that the substrate deformation energy at x is sufficient to trigger an irreversible coupling event in a detector at x. Since the coupling probability is proportional to the available deformation energy, and the deformation energy is proportional to |Ψ|², the Born rule follows directly.
Not a Postulate, a Consequence
The Born rule in BFUT is a consequence of two physical facts: (1) the wavefunction is substrate deformation amplitude, (2) coupling probability is proportional to available deformation energy. Both are physically motivated. Neither requires a separate postulate.
This gives the Born rule a physical interpretation it has never had: |Ψ(x)|² is not a bare probability assigned by convention. It is the physical deformation energy density at x. Where the substrate is more strongly deformed, coupling is more probable. The probability is real, local, and physical.
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