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

TL;DR

This paper examines the $c$ equivalence principle, linking it to the weak equivalence principle of general relativity, and shows they are fundamentally the same within Newtonian gravity, extending the understanding of fundamental constants in physics.

Contribution

It clarifies the status of the $c$ equivalence principle and demonstrates its equivalence to the weak equivalence principle in the context of Newtonian gravity.

Findings

The $c$ equivalence principle is connected to the second postulate of special relativity.

Both the $c$ equivalence principle and the weak equivalence principle are shown to be equivalent.

The extension of classical relativistic electrodynamics to include the $c$ equivalence principle is discussed.

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.