- #51

PeterDonis

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I think the Milne universe which occurs in Minkowski spacetime and which is mathematically equivalent to the empty FRW universe is expanding too.

It's "expanding" if you pick a particular set of worldlines and call them the "comoving" ones. But those worldlines, from the viewpoint of a standard inertial frame on Minkowski spacetime, are just the worldlines of a set of inertial observers who all pass each other at a particular event (the spacetime origin) and then recede from each other at a constant speed in all possible directions.

Would you agree that this "particle" (I think the usual term is test particle) is understood to possess negligible mass such that it doesn't contribute to any ambient gravitational field (which is lacking here anyhow) in the "otherwise empty universe".

Yes. But then the statements you and @andrewkirk were making about the points of the non-rotating ring not traveling on geodesics because they are experiencing a tiny gravitational force inward are not correct. The points of the non-rotating ring are "test particles" in the sense you have described, so they don't cause any spacetime curvature and don't cause any gravitational field. So the "empty universe" is just flat Minkowski spacetime.

Max Jammer doesn't mention any specific spacetime though, just "empty".

Yes, that's a good example of why pop science sources are not good ones for learning actual science. Any actual textbook or peer-reviewed paper would have to specify exactly which spacetime geometry they mean by "empty universe".

He also doesn't mentionhowit could be shown that the particle can possess inertia. Could you explain in ordinary language how in principle this can be shown?

The principle that the spacetime geometry determines the inertial properties of worldlines (which ones are geodesics and which ones are not) is not "shown"; it's just part of what we mean by "spacetime geometry". In GR there is no other principle from which this one is derived.