A Proposed Solution to the Hierarchy Problem in a Cyclic Universe Model: Phase Matching Between Dirac Proper Time and the Cosmic Horizon

This study investigates the hierarchy problem among fundamental physical interactions and the ratio of Coulomb electrostatic attraction to gravitational attraction (α g −1 ≈ 2.27×10 39 ) through the phase matching between the photon’s microscopic standing wave mode and its cosmic-scale free geodesic loop. When two photons collide to produce an electron-positron pair and the electron becomes confined in a stable “standing wave” phase within the potential well of a proton, a narrow ±t temporal oscillation (∆τ zbw = h/4m e c 2 ) derived from the Dirac equation is revealed. In standard cosmology, the geodesic of light originating from the early universe and entering a black hole horizon cannot be completed due to the classical singularity barrier; in contrast, the Black Hole–White Hole (BH-WW) cyclic universe hypothesis proposes that, just as individual protons drive electrons into local temporal cycles, macro gravitational concentrations drain light into the initial phase of time, thereby completing the circuit. By taking the ratio of the electron’s micro proper-time step to the closed geodesic timescale defined via the current standard ΛCDM comoving particle horizon (R horizon ), the ratio of electrostatics to gravitation is analytically obtained with a relative error of only 0.3% without requiring any free tuning parameters.