Discrete Elastic-Medium Spacetime: A Necessary Inference from Observational Facts

Why is physical space discrete? And why does its discrete structure carry the gluonic character of the strong interaction? This paper assembles multiple independent lines of evidence to address both questions. First, continuous spacetime harbors a set of systematic structural pathologies in its mathematical foundations—non-measurable sets, the Banach–Tarski volume-doubling paradox, zero-measure Kakeya sets containing all directions, and the Cantor set's separation of cardinality from measure—all rooted in the infinite divisibility of the continuum, which violates the requirement that physical space be a measurable reality. Introducing a fundamental minimal length eliminates them simultaneously. Second, ultraviolet divergences in quantum field theory and spacetime singularities in general relativity, as two traditional evidence chains, converge independently with the mathematical argument toward the same conclusion: spacetime must be granular at microscopic scales. Third, the isotropy of electromagnetic propagation (Michelson–Morley to 10⁻¹⁸) and the constancy of the speed of light constrain the structure of any discrete-spacetime model. Regarding the constitution of the discrete units, the two observational pillars of the strong interaction—quark confinement and asymptotic freedom—indicate that attraction and repulsion balance precisely at the deepest level of space, with the equilibrium scale falling at the hadronic scale (about a femtometer), naturally yielding a vacuum zero-point energy and a glueball mass scale in mutual agreement. Together, these lines of evidence point to a lattice-like quantum-gravitational substrate of spacetime whose constituents possess gluonic properties.