Uncertainty principles and the speed of light in atomic dipole transitions: a heuristic derivation

The constancy of the speed of light in vacuum across inertial frames is a cornerstone of special relativity, yet its physical origin remains unresolved. While Maxwell's equations link light speed to vacuum permittivity and permeability, recent studies suggest these properties arise from quantum vacuum fluctuations involving transient particle-antiparticle pairs. These fluctuations, stationary to inertial observers and Lorentz symmetric, may explain both the value and invariance of light speed. This work presents a heuristic argument for the speed of light and its invariance in the specific case of atomic dipole transitions. The analysis is based on position–momentum and energy–time uncertainty relations associated with dipole-allowed photon emission. In this framework, a time operator describing photon propagation in vacuum is introduced, reproducing the speed of light and demonstrating its invariance across inertial frames. The uncertainty relations preserve their form under Lorentz transformations, supporting light–speed invariance. The Lorentz transformations and longitudinal Doppler effect are also derived within this operator framework, suggesting that the constancy of light speed may originate from the foundational role of uncertainty principles and quantum vacuum.