Question

How the constancy of the velocity of the light is foreseen by the MAxwell's equations?

Answer 1

Maxwell's equations do not in themselves predict a specific value for the constant (or variable) c which appears in them. This value is determined experimentally as the relative velocity at which a photon must strike an observer in order to be absorbed. By modifying the second postulate to state: "The observed velocity of light is c from all frames of reference," the radiation continuum model (RCM) of electromagnetic radiation is developed. On the basis of this model, a Galilean invariant form of Maxwell's equations is obtained. Equations for transverse and radial Doppler shift are derived. An analysis of the force on a moving charge above a neutral current carrying wire is provided from varying reference frames without resorting to SRT or Lorentz transformations. An application to particle accelerators explains the apparent mass increase with velocity.

Answer 2

Some formulations of Maxwell's equations utilize a permittivity of free space \(\epsilon_0\) and permeability of free space \(\mu_0\) such that the speed of propogation of magnetic waves in a vacuum \(c\) is related in the following manner.\[c=\frac{1}{\sqrt{\epsilon_0\mu_0}}\]The actual values for the permittivity of free space and permeability of free space are both by physical observation and definition. Maxwell's equations, however, do not point to the fact that \(c\) is a constant for all observers...this is simply a consequence of the geometry of spacetime.