Emergence of the Minkowski Metric from Ze Dynamics

Abstract

This paper presents a novel derivation of the Minkowski metric from first principles within the framework of Ze dynamics. I demonstrate that the fundamental structure of spacetime, characterized by the Lorentzian interval ds² = –c²dt² + dx², emerges not as an a priori geometric postulate but as a statistical invariant of a discrete, information-theoretic substrate. The primitive elements are counters updated by a stream of events, governed by a statistically conserved quadratic sum. A critical functional bifurcation separates the dynamics into a temporal channel, defined by sequential, order-dependent prediction error, and a spatial channel, defined by parallel, order-invariant structural differences. The inherent antagonism between these channels—where spatial stabilization is paid for by temporal destabilization—forces their contributions to combine with opposite signs in the conserved quantity, thereby deriving the minus sign of the metric signature. The constant c emerges as a conversion factor between the natural scales of the two counting processes. The resulting interval, computed via a concrete numerical algorithm, recovers the kinematics of Special Relativity in the continuum limit, with the light cone arising as a numerical stability boundary for coherent signal propagation within the network. This work reframes Minkowski spacetime as an effective geometry, positing that space and time are emergent operational modes of information processing rather than fundamental dimensions.