Emergence XI: Acceleration as Primitive in the Emergence Model

This paper is part of the Emergence series (Papers I–XI). It examines a direct consequence of the canvas wave equation (Paper I): the second derivative — acceleration — is primitive, while velocity and position are emergent.

The wave equation ∂²Φ/∂v² = ∂²Φ/∂u² is second order in both coordinates. A first‑order equation would not allow wave propagation, finite speed c, or emergent Lorentz invariance. Thus, the second derivative is not arbitrary; it is a physical necessity for a universe with a finite speed of light.

Within the Emergence model, velocity emerges from moving wave intersections. Position emerges from closed waves (particles) occupying voxels in the emergent lattice. Acceleration is first; position is last.

This paper clarifies the ontological hierarchy of the Emergence model. It is a conceptual and foundational analysis, not a derivation of new physics. It is intended for readers interested in the philosophical and structural assumptions of the model.

Keywords: acceleration, primitive, emergence, wave equation, ontology, foundations of physics