From Metric to Vector

Abstract

The geometric-differential paradigm of spacetime, while foundational to modern physics, faces intrinsic challenges in quantum gravity and provides a limited framework for understanding state evolution as a computational process. This article proposes a shift in ontological foundations, presenting Ze, a discrete computational framework that implements the dynamics of a fundamental state vector Ψ. We argue that Ze is not merely an algorithm but a model of physical becoming, where space and time are not pre-existing coordinates but emerge as anti-parallel channels for the redistribution of information flow. Within Ze, the state vector is represented by a global configuration of statistical counters, and its evolution is driven by a process of passive learning through the minimization of prediction error. The framework naturally maps key physical entities: the temporal component corresponds to the sequential, irreversible flow of events and counter growth, while the spatial component corresponds to the synchronous, correlational structure of the internal model. This anti-parallelism is formalized in a discrete Ze-Lagrangian, a variational principle balancing structural stabilization against predictive error. We demonstrate how this setup allows for the emergence of relativistic invariants, a statistical and vector-based causality akin to causal sets, and quantum phenomena such as quantization (from discrete accounting) and interference (from superposition of predictive contexts). The theory reframes the observer as a self-norm-preserving system and suggests that Special and General Relativity are limiting descriptions of stable regimes in the Ze dynamics. The work offers a unified, vector-based ontology that derives physics from first principles of information processing.