From Light Propagation to Unification: A Master Equation That Reduces to Quantum Mechanics, Relativity, and Newtonian Mechanics

Abstract

Based on a single fundamental postulate that light propagates uniformly at constant speed in vacuum, this paper derives a universal master equation:\(h\nu_0 = h\nu_0 e^{-gn/c} + m_n c^2,\quad m_n = \frac{h\nu_0}{c^2}\left(1 - e^{-gn/c}\right),\)where n denotes dimensionless layer number, rather than temporal coordinate. The formula characterizes continuous photon-to-mass energy conversion during propagation across hierarchical cosmic layers, with strict global energy conservation. Under three asymptotic limits, it systematically reduces to the Schrödinger equation (quantum mechanics), Einstein mass-energy relation and relativistic energy-momentum formula (special relativity), and Newton’s second law (classical mechanics). The three cornerstone physical theories are not ad-hoc assembled, but emergent low-order approximations of identical dynamical law. The model predicts cosmic bulk acceleration \(\bar{g}_{\text{uni}} = 1.02\times10^{-10}\,\text{m/s}^2\), approximately 15% consistent with dark matter radial acceleration scale, and hadronic string tension \(0.936\,\text{GeV/fm}\), approximately 1.7% matching QCD lattice measurements. All predictions span 41 orders of magnitude with zero free fitting parameters. Four testable observational predictions are proposed, including cosmic infrared background anisotropy, redshift-dependent lensing bias, gravitational wave echoes of black holes, and a three-clock experiment to measure absolute cosmic motion. The framework naturally eliminates black hole spacetime singularities and fully resolves the black hole information paradox by storing all quantum information on the black hole horizon shell, with unitary information release via Hawking radiation. Without extra dimensions, new particles or free adjustable constants, this work unifies classical, quantum and relativistic dynamics under a single light-propagation axiom.

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