A Stability Principle for Atomic Orbits: A Classical Interpretation of the Fine-Structure Constant and a Classical Origin for Atomic Stability

This work proposes a stability principle for atomic orbits based on a dimensionless geometric–temporal invariant defined as the fraction of an orbital period spent by bound electrons in regions of high acceleration near the nucleus. This invariant, denoted β, is phenomenologically identified with the fine-structure constant α for stable atomic configurations. The principle does not modify established spectroscopic formulas but offers a classical physical interpretation for the emergence of α in atomic structure, linking orbital geometry, radiation, and vacuum interaction. Elliptical orbits and multi-electron occupancy are naturally accommodated. The work establishes β = α as an experimentally inferred consistency condition that any microscopic theory of atomic stability must reproduce, while explicitly identifying the precise point at which further vacuum-coupling derivations become necessary