THE SANNER MODEL – Towards an Evolution Equation for the Aether Field

The Sanner Model (TSM) postulates a rigid, three-dimensional space filled with a massless, frictionless, density-free aether that accelerates radially inward toward mass centers. The foundation document presented the field equation as a static constraint: it determines the aether acceleration field for a given mass distribution, but it does not describe how the field changes in time. This paper extends that static constraint into a full evolution equation. The derivation uses only two ingredients: the aether velocity field is irrotational (curl-free), so it can be written as the gradient of a scalar velocity potential; and the total aether acceleration is then the gradient of a single scalar function built from that potential and its time derivative. Promoting the static constraint to a wave equation for this scalar function yields the evolution equation. The result is dimensionally consistent, reduces exactly to the known static solutions a = GM/r^2 and v = sqrt(2GM/r) in the static limit, and describes aether waves that propagate at the speed of light c. The paper shows that the system is well-posed as an initial value problem: given the velocity potential and its time derivative at an initial time, the evolution is determined. The non-linearity of TSM is contained in the relationship between the velocity potential and the dynamical scalar, not in the evolution equation itself — analogous to the Hamilton-Jacobi formulation of classical mechanics. The paper also discusses the connection to the quantum microstructure proposed in the companion paper on quantum aether dynamics, compares the structure of the evolution equation with that of general relativity, and addresses the role of back-reaction. Back-reaction — the effect of emitted radiation on the source that produced it — was not part of Einstein's original field equations either; it emerged later and remains an open problem in general relativity. The same is true in TSM. The paper concludes with open questions and three falsifiable challenges: numerical simulation of aether waves, comparison with LIGO/Virgo observations, and derivation of the evolution equation from the quantum microstructure.