🧮 Motion Theory: Mathematical Foundations

I. Essence and Absolute Motion

The core entity of the theory, the essence, is defined by absolute motion. This motion is expressed as:

\[ \Phi_{\mu}(x^\nu) = \frac{d x^\mu}{d \tau} \]

where \( \Phi_{\mu} \) is the motion vector, \( x^\mu \) are spacetime coordinates, and \(\tau \) is intrinsic time.

II. Deviation and Field Tensor

Deviations in absolute motion generate form, represented by the antisymmetric field tensor:

\[ \Phi_{\mu\nu} = \partial_\mu \Phi_\nu - \partial_\nu \Phi_\mu \]

If \( \Phi_{\mu\nu} = 0 \), motion is pure. If \( \Phi_{\mu\nu} \neq 0 \), form and curvature arise.

III. Potential and Field Energy

Motion deviation induces a potential field, representing form energy:

\[ V(\Phi) = \frac{1}{2} \Phi_{\mu\nu} \wedge \Phi^{\mu\nu} \]

IV. Time as a Derived Quantity

Time is emergent, defined as a derivative of essence motion:

\[ t_{\text{obs}} = \int_{\tau_0}^{\tau} |\Phi_{\mu}| d\tau \]

V. Uncertainty from Motion

Uncertainty emerges naturally due to motion and temporal contact:

\[ \Delta x^\mu \cdot \Delta \Phi_\mu \geq \frac{1}{2} \]

VI. Entropic Dissolution

Forms dissolve over time, returning to pure motion:

\[ \frac{d \Phi_{\mu\nu}}{d\tau} = - \alpha \cdot \Phi_{\mu\nu}, \quad \alpha > 0 \]

This document is a formal mathematical representation of the core framework of the Motion Theory, based on the ontological primacy of essence and motion.

This page is part of the living architecture of Nowonacra: The Flux.
To go deeper, see the full technical paper:

MOTION THEORY (Full Text)