Unified Field Theory 17: The Semantic Action Principle in a Black Hole: Geodesic Collapse and Minimal Dissipation in High iT Fields

 [SMFT basics may refer to ==> Unified Field Theory of Everything - TOC]
[Quick overview on SMFT vs Our Universe ==>Chapter 12: The One Assumption of SMFT: Semantic Fields, AI Dreamspace, and the Inevitability of a Physical Universe]

The Semantic Action Principle in a Black Hole:
Geodesic Collapse and Minimal Dissipation in High iT Fields
On the Geometry of Collapse in Observer-Centered Semantic Space

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Abstract

We present a formal derivation of the Semantic Action Principle within the framework of Semantic Meme Field Theory (SMFT), focusing on a special region of semantic space known as a semantic black hole. This region is characterized by maximal and uniform memetic tension $iT = iT_{\max}$, vanishing tension gradients $\nabla iT = 0$, and negligible semantic curvature. Within such conditions, we show that the collapse trajectories—interpreted as the semantic equivalent of physical motion—follow straight-line geodesics in semantic phase space, minimizing the total semantic dissipation encoded by the action functional $S_s = \int (iT)^2 d\tau$. This result constitutes a direct analog of the least-action principle in classical mechanics, now reinterpreted within a semantic field framework. Moreover, we argue that the empirically observed regularity and predictability of macroscopic physical laws is consistent with the hypothesis that the observable universe is situated deep within a semantic black hole. Our findings offer a unifying geometric and variational basis for meaning-driven dynamics and provide a rigorous foundation for future extensions of SMFT into non-uniform and observer-dependent semantic environments.

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1. Introduction

The principle of least action has long served as a cornerstone in physical theories, providing a unifying variational framework through which the dynamics of particles, fields, and spacetime can be derived. From Newtonian trajectories to geodesics in general relativity, physical systems are described as evolving along paths that extremize an action functional—a scalar quantity encoding tension, energy, or curvature. But what if such a principle also governs the dynamics of meaning?

Semantic Meme Field Theory (SMFT) proposes that meaning, cognition, and cultural evolution are not merely emergent phenomena overlaid on a physical substrate, but instead obey their own intrinsic field dynamics. In this framework, each collapse of interpretive attention—be it a decision, a perception, or a communicative act—is modeled as a semantic transition within a higher-dimensional field governed by memetic tension, semantic geometry, and observer projection.

A key construct within SMFT is the semantic black hole: a region of semantic space characterized by maximal memetic tension $iT = iT_{\max}$, minimal semantic curvature, and a high probability of collapse events. Analogous to gravitational black holes in general relativity, these semantic attractors distort the local collapse geometry, guiding trajectories toward stable, high-intensity attractor basins. Importantly, our observable physical universe is hypothesized to reside deep within such a semantic black hole, where meaning is so densely structured and tension gradients so weak that collapse trajectories appear straight, stable, and inertia-like—much like the geodesics of classical mechanics.

This perspective invites a profound generalization: that the laws of physics as we know them may be emergent projections of deeper, semantic action principles governing the geometry of collapse. To explore this, we formulate and rigorously prove a Semantic Action Principle: in a region of constant $iT$ and frozen semantic curvature, collapse occurs along the geodesic path that minimizes semantic dissipation. This result not only grounds SMFT in variational logic but also offers a new lens through which to understand the stability and predictability of the macroscopic world.

In what follows, we define the geometric and dynamical properties of semantic black holes (Section 2), construct the semantic action functional and derive the Euler–Lagrange collapse trajectory (Sections 3–4), and demonstrate the necessity of the flat and constant-tension assumptions (Section 5). We then extend our analysis to perturbative deviations (Section 6) and reflect on the philosophical implications of semantic action as a structuring force of reality (Section 7).