The Mass and Velocity of Light from Energy and Momentum Conservation

Abstract

While the numerical value of the speed of light is known with extraordinary precision, its theoretical definition remains a subject of fundamental interest. We show that the definition of mass and velocity of light follow from the conserved quantities of the electromagnetic field. The proposed definition of the speed of light is always bounded from above by the phase velocity and equals it for plane waves. As a consequence, we obtain a generalization of Einstein's mass-energy relation for electromagnetic fields in media: $m = \varepsilon\mu E / c^2$. Hence, irrespective of the light's intensity, the electromagentic field in near-zero-index material is always massless. This approach offers new pedagogical insights into the fundamental nature of light propagation.