Self-Consistent Time Gradient as the Origin of Mass: A Gravitational-Quantum Cavity Model

Abstract: We propose that mass originates from a self-consistent distortion of spacetime time-flow created by a localized energy distribution. The resulting time gradient forms an effective temporal refractive index well that confines the field responsible for its own generation. Within this “temporal cavity,” stable standing-wave solutions of the coupled Einstein–Klein–Gordon system correspond to discrete mass eigenvalues. The simplest self-consistency condition, equating the Compton wavelength with the Schwarzschild radius, yields a unique Planck-scale mass m=ℏc/2Gm = √ c / 2Gm=ℏc/2G. This framework provides a geometric and dynamical interpretation of mass as a quantized self-consistent mode of spacetime, unifying quantum confinement and gravitational time dilation. Extensions to sub-Planckian masses using effective couplings Geff(m)G_eff(m)Geff(m) may offer a natural explanation for the observed hierarchy of particle masses. The model suggests that mass is not an intrinsic property of matter but the emergent frequency of spacetime’s own self-consistent vibration.