**6. Coordinate choice in general relativity**

The most popular coordinate choice in general relativity is de Donder (harmonic) coordinates. When this choice is made, a factor of 4 appears in the term involving the analog, *g*oi., of the vector potential, *A*. This messes up the simple *ϕ*/*c* <sup>2</sup> = 1 relationship between *ϕ* and *c* 2 . But that relationship can be recovered by asserting that the gravelectric field equation be that just stated above [Eq. (6)] and only coordinates that return it are permissible. As did, for example, Braginski, Caves and Thorne [BCT] in their 1977 paper on "Laboratory experiments to test relativistic gravity" [10]. BCT, working with the coordinate choice of Misner, Thorne and Wheeler in chapter 39 of their massive *Gravitatjon* [11], worked through the details of the choice of Eq. (6) here for the potentials and metric. Their coordinate choice and gravelectric field equation determination leads to the correct Faradayan induction term in the equation of motion to account for inertial reaction forces. Edward Harris took particular note of BCT's treatment of inductive effects before adopting the gauge invariance rejection of Faradayan induction in the weak field, slow motion, but time-dependent Maxwellian analog interpretation of general relativity that led to the creation of the now fashionable sub-discipline of "gravitoelectromagnetism"; so-called GEM theory. That led in turn to the rejection of Faradayan induction effects in general relativity generally noted by Pfister and King.

The demand of explicit gravitational induction of inertial reaction forces does more than simply limit one's choice of coordinates. It can also be used in conjunction with Brans'spectator matter argument as a selection criterion for acceptable cosmologies. k = � 1 FLRW cosmologies, for example, do not conform to this criterion for in them, the gravitational and "kinetic" energies of test particles are not equal as *ϕ* 6¼ *c* 2 . If this is correct, then the remarkable *stability* of the k = 0 FLRW cosmology, remarked upon by Dicke and explained by Guth, is not a consequence of inflation. It is a consequence of the gravitational induction of inertial forces and Brans'spectator matter argument that makes *ϕ* a locally measured invariant equal to *c* 2 .

What is important is that whatever one's choice in the matter is, that choice depends crucially on Carl Brans'spectator matter argument that, in turn, depends on the correctness of the Equivalence Principle – arguably the simplest expression of the *principle* of relativity for proper accelerations. If one chooses to go with Einstein regarding the role of inertia in general relativity, then Brans' argument dictates a coordinate choice like that of BCT. The question is: was Einstein right about the role of inertia in general relativity? That is a question that ultimately can only be answered by experiment.
