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David,

Thank you for responding. No problem about the “weasel” thing. I’m probably more like a domesticated marmot than a weasel anyway.

I may not have time to respond to your second post right now…

I’m inclined to believe there’s no place in the universe where curvature is actually zero, although it’s no doubt a legitimate construct for the purpose of illustrating a principle. I’ve used it myself to illustrate the nature of a “pure” inertial acceleration, “unadulterated” by gravitational curvature. But that relates to an issue you’ve brought into focus about the difference between empirical hypotheses or principles and mathematical models. I think it’s a mark of real progress that we’ve arrived at this point.

You wrote “depending on other circumstances, like the distribution of mass-energy-momentum-stress surrounding [a uniform gravitational field], there may, indeed, be a definable magnitude” of the field.

While there may be a workable mathematical model of such a region, I don’t believe we can point to a place in the “real world” where it’s been found to exist. It may be worthwhile to hold the model in stock to help explain some new discovery, or to apply in a novel way to some existing unexplained phenomenon, but it has no standing against any empirical hypothesis that is otherwise coherent and useful.

The same goes, I believe, with other constructs that would gray the distinction between gravitational and inertial accelerations, between gravity and force. The “extra, compact dimensions”, “potentially uncountably many… inertial (pseudo, ‘false’) ‘forces’”, and the scenario “when the whole spacetime manifold is flat” - these are perfectly legitimate as imaginations, some maybe even as hypotheses, but they should have no bearing on “real-world” questions or hypotheses.

Regarding your identification of gravitation with “pseudo” or “false” forces, I know of none of the latter in the “real world” that would not be betrayed as either manifestations of real forces, or as non-existent, if placed in a controlled experiment like the box we’ve been discussing. For example, a centrifugal “force” acting on the box, and indirectly on the test particles inside, unlike gravitation, would result in the particles initially seeming to accelerate toward a side (in this case separating as they did so, due to the radial acceleration of the box), and “sticking” there, and making impressions in the wall of the box if it were of a suitable material.

On the other hand, a “flat” gravitational field, even if one could be found, has no bearing on the question of whether gravity can legitimately be identified as a “force”. The test particles would simply remain unmoving in the interior of the box.

I’m out of time. If you (David or anyone) has the time and inclination to write before I can resume, if there’s a instance of “pure” gravitation where it could be shown to behave like a force in a controlled experiment, I would be most interested in learning about it.

Jim