Jim:

I hope you've had a good Merry Christmas. :-)

I'm amalgamating some of my responses to three of your latest posts* here, since you have an issue in common in all three.

The issue is that you continue to act as if you haven't recognized that (other than theories/models that use curvature to explain all forces**) I have never argued that one cannot distinguish between purely gravitational effects (geodesic motion), at least when the local curvature is non-zero, and the effects of non-zero net "true" forces (deviations from geodesic motion, what you appear to want to label as "inertial acceleration").

Even though I do point out that there is no operational or theoretically available distinction between gravitational effects and the effects of any of an innumerable set of inertial (pseudo, "false") "forces"*** (at least so long as the spacetime is not completely flat, since all produce geodesic motion, in the absence of "true" forces), I have never suggested (other than the "everything is curvature" theories) that any such could not be distinguished from "true" forces (that cause a deviation from geodesic motion).

The problem is that you continue as if I had argued otherwise. This is why I have stated, before, that you treat me as if I was your enemy/nemesis/whatever.

If we are to have any sort of productive exchange you must recognize what I'm actually saying.

I say it again. Other than to point out that there are theories/models wherein all forces are handled via curvature (so all motions are geodesic), I have never tried to suggest that within a purely four dimensional framework (such as General Relativity) one would not be able to distinguish between the purely geodesic motions of pure gravitation (independent of whether the curvature is non-zero) and the non-geodesic motions caused by non-zero net "true" forces.****

David

* The three posts are Re: The phenomenology of Shinola and other stuff, part 2, Shinola exercises, and Re: Re: The phenomenology of Shinola and other stuff.

** Basically, such "everything is curvature" theories/models take the approach that if it worked for gravitation, why not the other forces? One may certainly argue as to whether such theories have, thus far, been successful, or not, and whether such is "the right approach". However, they exists, and have been at least somewhat successful, at least at the same classical level as General Relativity.

I would hope that you recognize that different free neutral test particles released with different initial velocities (from the same spacetime point) will follow different geodesics. Well, the same is true in these "everything is curvature" theories: The reason different types of particles (non-neutral particles with various "charges") follow different geodesics, even if their initial four-velocities are the same (at least proportionately), is that their various "charges" give rise to various additional components of their full (higher dimensional) velocity. So they follow different geodesics because in the full set of dimensions their initial velocities are different.

*** I recognize that you appear to think that such is distinguishable. However, such distinguishability is illusory, unless, possibly, one knows, a priori, what the local spacetime curvature is (basically via an ansatz, as you yourself have engaged at various times). All inertial (pseudo, "false") "forces" enter into the motions in precisely the same way as gravity. The only time one has any ability to transform these away is when the entire spacetime is flat. (If the local spacetime is flat, then one may transform them all away locally, including gravity, but this still leaves its mark on the surrounding spacetime in such a way that questions of what is gravity and what are "other" inertial "forces" is still undecidable, without some ansatz.)

(Actually, even when the local spacetime is not flat one is always able to transform all inertial "forces", including gravity, away "locally". Its just that "locally" becomes far more restricted. Under this condition, exact cancellation can only occur at a single point, while for any finite level of precision there is a neighborhood of this point that exhibits no inertial "forces", including gravity, up to said level of precision.)

**** What I believe is the most general and true statement is that since the success of General Relativity one can no longer hold to the Newtonian concept that gravity is just as much a "true" force as electromagnetism and the nuclear forces (strong and weak), while asserting that all inertial (pseudo, "false") "forces" are most definitely not forces.