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Jim:

You said:

Then you’ll agree that the ubiquitous identification of gravitation with “true” force is based on non-empirical, non-four dimensional models which are routinely, implicitly, and illegitimately treated as givens.

First, I wouldn't say that any "identification of gravitation with 'true' force" is "ubiquitous" (except possibly in your mind). Secondly, for those who do "identif[y] gravitation with 'true' force", I cannot speak for why they may think this way or what their basis for such thinking may be. Thirdly, I have never seen any such "non-empirical, non-four dimensional models" "routinely, implicitly, and illegitimately treated as givens." They are only given/proposed/used/etc. as theories and/or models.

I can only point out that there is at least one approach that makes such an identification legitimate by way of making all motions geodesic motions. Furthermore, I would not say that any such is any less legitimate than any four dimensional model. Only careful predictions and experiment may tell the difference. (In fact, at the classical level, the level of General Relativity, there may, indeed, be no detectable difference. For such a case, the decidable criteria will be suitability for handling Quantum-type phenomena, or other cases beyond the classical.)

You then go on to say:

I’ve tried to get you to describe one of these pseudo forces, assuming you’re referring to something other than the Coriolis, or centrifugal or centripetal “forces”, which can most definitely be directly attributed to true forces and distinguished from gravitation. ...

First, centripetal force refers to the central pointing force that leads to the non-inertial nature of the reference frame in which one supposes there is such a thing as a centrifugal "force".

Second, what is the nature of the motion of a free neutral test particle undergoing any of your listed inertial (pseudo, "false") "forces" (free of any "true" forces)? Are not such motions geodesics? If so, then how are these geodesics to be distinguished from any other geodesics?

Often times you have suggested that the geodesics of such inertial (pseudo, "false") "forces" will be divergent while gravitational geodesics will be convergent (apparently relying upon an unspoken ansatz [one that appears to rely upon an assumption of a central concentration of mass]). This is why I brought up the observed ring/torus of "dark" matter.*

If your "box" was placed within a similar ring/torus, especially if the ring/torus was spinning/rotating (and practically everything we observe in this universe spins/rotates, besides, in order not to have such collapse under its own gravity one would almost certainly need it to spin/rotate) you would observe motions of free neutral test particles, within the box, that would be quite indistinguishable from having the box spin/rotate in a region of space devoid of such a massive ring/torus.

This is only one of an innumerable set of such possible examples. Basically, given any example of motions of free neutral test particles within a "box" under the influence of whatever inertial (pseudo, "false") "forces" one wishes to conjure up, one may find a distribution of mass-energy-momentum-stress** such that those same motions may be attributed to gravity. (Geodesics are geodesics, after all.)

This is also why I brought up the "box" in orbit around the Earth. (By the way, I'm glad to see you made some attempt at the exercise. I'll get back to your work on it another time. However, did you notice that the few test particles you used undergo divergent geodesics, similar to your assertions for non-gravitational inertial "forces"?)

See, no need to appeal to "hypothetical, dependent on non-empirical, non-four dimensional or multiple-universe models".

David

* The ring/torus of "dark" matter is not some otherworldly hypothetical construct. It was observed based upon gravitational lensing (another highly successful prediction of Einstein's General Theory of Relativity). The matter is called "dark" matter because there appears to be no way to observe it besides its gravitational effects (gravitational lensing, orbits of other objects, etc.)

** When I refer to "mass-energy-momentum-stress" or an "energy-momentum-stress tensor" I'm referring to the source of spacetime curvature (the distribution of mass, and such, in the universe). Please don't confuse such with my mentioning of attempts to illicit something similar from the gravitational field itself.

As I pointed out in my first post, such attempts at identifying some "energy-momentum-stress" in the gravitational field does not have a tensorial character, and, hence, is not well defined (or local).

Perhaps I should have never mentioned such attempts. Perhaps it has served nothing but to cloud your understanding of what I havbe been trying to help you understand.