The PNP Theory of Cause and Effect

Fred Nedrock, Leera Vale, Max Freet, An M. Rodriguez (ORCID)

Preferred Frame Writing — January 2026

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One-Sentence Summary

Causality emerges in the PNP framework because a topologically non-trivial scalar field configuration cannot remain static without violating stress–energy conservation, forcing ordered evolution.

Summary

We derive causality from first principles within the Point–Not–Point (PNP) framework. At its core lies the topological irreducibility of the fundamental $(1)$ mode: the simplest closed oscillation of a scalar field $U$ exhibiting a $\pi$ phase inversion, or "bounce." This $\mathbb{Z}_2$ invariant enforces loop persistence and forbids extinction without a phase slip. We explicitly ground this mode in the discrete solution space of source-free Maxwell dynamics (the toroidal hydrogenic spectrum). From this physically motivated topology, we prove that such a mode cannot remain static, formalizing cause–effect not as a postulate, but as the inevitable action of the field propagator on a persistent topological sector.

Keywords

Keywords: PNP Framework, Topological Persistence, Causal Geometry, Scalar Field Theory, Z2 Invariant, Emergent Time

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