Space and Time as Orthogonal Projections of a Conserved State Vector

Abstract

This article presents a novel theoretical framework that reinterprets the fundamental nature of space and time. I propose that they are not independent, pre-existing continua but are emergent as orthogonal and anti-parallel projections of a single, conserved state vector in a higher-dimensional space. The model is built upon the core axiom of an invariant norm, ||Ψ||^2 = constant, and a strong geometric condition: the vectorial projections for space (S) and time (T) are equal in magnitude but opposite in direction, expressed as S = -κT, where κ is a fundamental constant. From this foundation, I demonstrate how key features of modern physics emerge naturally. The Lorentz transformations and phenomena of time dilation are derived from the compensatory exchange between the S and T components during state evolution. The mass-energy equivalence E=mc² is reformulated as a geometric conversion law, with the speed of light c acting as the exchange constant κ. Furthermore, the cosmological arrow of time is linked to a global drift of the state vector from an initial condition of high temporal potential toward increased spatial expression. The framework offers integrated explanations for causality, black hole structure, and provides pathways for unification with quantum mechanics, suggesting that spacetime itself is a quantum-informational construct.