Deriving Newton's Laws from Information Dynamics

This paper presents a novel derivation of Newton's laws of motion and universal gravitation from first principles based on quantum information dynamics rather than traditional mechanical postulates. Working within the Pentagonal Quantum Information Substrate (PQIS) framework, we demonstrate that classical mechanics emerges naturally from the dynamics of information processing in a discrete network with pentagonal (D₅) symmetry. Through systematic mathematical analysis, we establish that stable information patterns correspond to classical objects with mass and position, while their evolution through the network yields precisely Newton's laws in appropriate limits. We rigorously define the classical regime where quantum effects become negligible, derive inertia from information pattern stability, and show how forces emerge from context field gradients. The law of universal gravitation emerges from nonlocal information terms, with the gravitational constant G calculated explicitly from network parameters. Our derivation accounts for the equivalence principle through the identical information-theoretic origin of inertial and gravitational mass, and incorporates fractal probability structures that naturally explain the 87.6%/12.4% split observed in gravitational coupling. This work demonstrates that classical mechanics is not a fundamental description but rather an emergent approximation of more basic information dynamics, providing new insights into the nature of space, time, matter, and force.