The c equivalence principle and the correct form of writing Maxwell's equations

Abstract: It is well-known that the speed $c_u=1/\sqrt{\epsilon_0\mu_0}$ is obtained in the process of defining SI units via action-at-a-distance forces, like the force between two static charges and the force between two long and parallel currents. The speed $c_u$ is then physically different from the observed speed of propagation $c$ associated with electromagnetic waves in vacuum. However, repeated experiments have led to the numerical equality $c_u=c,$ which we have called the $c$ equivalence principle. In this paper we point out that $$\nabla\times{\bf E}=-[1/(\epsilon_0\mu_0 c^{2)]\partial{\bf} B}/\partial t$$ is the correct form of writing Faraday's law when the $c$ equivalence principle is not assumed. We also discuss the covariant form of Maxwell's equations without assuming the $c$ equivalence principle.