Information-Processing Invariance

Abstract

This paper proposes a unified theoretical framework that bridges quantum information theory and relativistic physics through a new Invariance Law of Spacetime. We introduce the Total Information Budget (χ), defined as the product of informational mass (m), system update rate (ν), and spatial information flux (L). By synthesizing this postulate with Einstein’s energy-mass equivalence (E = m · c²), we derive the invariant relationship c² = ν · L. This equation reveals c² to be the specific processing capacity of the vacuum, a fundamental constant that dictates a zero-sum trade-off between temporal resolution and spatial rendering. We validate this model using Planck-scale limits, demonstrating that at the saturation point of reality, the product
of the Planck frequency and the minimum spatial flux (c · l_p) converges precisely to c². Our findings provide a computational foundation for mass-energy equivalence and offer a novel interpretation of spacetime as a self-rendering informational system. This framework aligns with Vopson’s mass-energy-information equivalence principle and provides new insights into the informational nature of gravitational and temporal phenomena.