The Quantum Fisher Coupling in Reconstructive Dynamics

This paper clarifies the role of the quantum Fisher coupling in reconstructive dynamics. Article 5 showed that the reconstructive action reproduces the Madelung equations, and hence the Schrödinger equation, when the Fisher term carries the coupling λ = ℏ²/8m. The present article argues that the fundamental object to be derived is not ℏ or m separately, but their natural combination:

κ = ℏ²/m.

Three results are established. First, κ is the unique coupling of dimension energy times length squared compatible with the Fisher information term in the Madelung Hamiltonian. Second, κ/2 appears as the scale of the biharmonic flow obtained by linearising the Fisher gradient flow around a flat reference state. Third, the decomposition κ = ℏ²/m requires additional geometric input: m as the inertial coefficient of Wasserstein transport, and ℏ as the prequantisation constant associated with a non-trivial symplectic loop.

The paper does not derive κ from hypotheses H1–H5. Rather, it establishes that κ is the natural single object to be derived and identifies the geometric conditions under which its decomposition into ℏ and m may become accessible.