Gravity Coherence Fall

Coherence fall

Gravity coherence fall is the state of motion in which an extended object experiences no difference in total potential between its head and its feet. In Recognition Science, an extended object is modeled as a body with a center of mass and a positive spatial extent. A processing field assigns a potential to every position. The coherence defect is the absolute difference in total potential between the two ends of the object, measured in a frame that may itself be accelerating.

The module defines the total potential in a frame accelerating with acceleration a as the gravitational potential at the object's center plus a linear inertial term. The coherence defect then simplifies to a closed form: twice the extent times the sum of the potential gradient and the frame acceleration, taken in absolute value. The central theorem, falling_restores_coherence, proves that for any processing field and any extended object, there exists a unique acceleration that makes this defect zero. That unique acceleration is exactly the negative of the potential gradient, which is the gravitational acceleration g.

The plain-language consequence is that gravity is not a force pulling on the object, but a requirement on motion. Standing still in a gravitational field leaves a coherence defect: the head and feet sample different potentials. Free falling at the unique acceleration cancels the defect, so the object's local processing environment is uniform. This is why free fall feels like nothing: it is the coherent state, the one motion in which the extended object is not torn by potential differences.

THEOREM coherence_defect_simplify · IndisputableMonolith/Gravity/CoherenceFall.lean

THEOREM falling_restores_coherence · IndisputableMonolith/Gravity/CoherenceFall.lean

THEOREM falling_restores_coherence · IndisputableMonolith/Gravity/CoherenceFall.lean

What this page does not claim

This page does not claim that gravity is derived from the forcing chain of the core theory. This page does not claim that the coherence defect is a measure of spacetime curvature. This page does not claim that the module proves the existence of gravity as an empirical force.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Gravity/CoherenceFall.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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