On the $c$ equivalence principle and its relation to the weak equivalence principle of general relativity

Abstract: We clarify the status of the $c$ equivalence principle ($c_u=c$) recently proposed by Heras et al \cite{JoseAJP2010,JoseEJP2010} and show that its proposal leads to an extension of the current framework of classical relativistic electrodynamics (CRE). This is because in the MLT (mass, length and time) system of units, CRE theory can contain only one fundamental constant of nature and special relativity dictates that this must be $c$, the standard speed of light in vacuum, a point not sufficiently emphasized in most textbooks with the exception of a few such as Panofsky and Phillips \cite{PanofskyPhillips}. The $c$ equivalence principle Heras \cite{JoseAJP2010,JoseEJP2010} can be shown to be linked to the second postulate of special relativity which extends the constancy of the unique velocity of light to all of physics (especially to mechanics) other than electromagnetism. An interesting corollary is that both the weak equivalence principle of general relativity and the $c$ equivalence principle are in fact one and the same, which we demonstrate within the context of Newtonian gravity.