Causal Budget Framework, Part I: Cellular Automata as Computational Quantum Mechanics

This work introduces the foundational computational mechanics of the Causal Budget Framework (CBF), a novel approach to quantum mechanics based on cellular automata principles. CBF models particles as spheres of independent wave cells that follow discrete update rules governed by a fundamental budget constraint: C = T + M = 1, where computational resources must be allocated between translation (T) and maintenance (M) each tick.

The framework demonstrates how familiar quantum phenomena including wave propagation, diffraction, and interference emerge naturally from simple cellular automata rules rather than being imposed as fundamental postulates. Using the double-slit experiment as a working example, this work shows how discrete particle shells heal into expanding wave fronts through local computational processes.

Key contributions include: (1) A vector cellular automaton approach where physics occurs only at particle surfaces, not throughout spacetime, (2) A causal budget constraint that unifies particle motion with relativistic effects, (3) Demonstration that particles structured as wave cell spheres naturally evolve into growing wave patterns through discrete computational rules.

This is Part I of a series establishing CBF as a computational foundation for fundamental physics, where quantum mechanics emerges from underlying discrete processes rather than being assumed from the start.