> Damien Broderick wrote [07 Oct 2000]:
> ...............what happens to inertia
> in a big emptying bubble like that?
> If inertia is an effect of the mass
> of the rest of the universe, presumably
> it also diminishes over time, finally to
> nothing. Hmmm...
Ludwig Boltzmann [1] in the mid-1890s took, as basic notions, a set of point masses, and the network od Euclidean distances
between those point masses. If you have just one point mass, then no distances are available to define its location.
Consequently there is no inertia.
John Archibald Wheeler and Ignazio Ciufolini [2] pointed out that D.W. Sciama [3] and D.J. Raine [4] transformed the idea
"no other masses, then no inertia" to the view that no solution of Einstein's field equation can give a reasonable account
of inertia if the geometry nowhere displays an identifiable center of mass. That's because without other masses there is no
way to measure distances, and no way to define inertia.
But (see ref. [2], p. 297] these days to think of material masses as the ultimate primordial entity and space-time geometry
as derivative (from those masses) is wrong. Space-time geometry, in and by itself, defines the location of the mass, its
velocity, its acceleration, the local intertial frame, and therefore its inertia.
There are models of empty universes (just the mass-energy of gravitational waves) in which there is inertia (see. i.e., the
Taub model [5]).
In conclusion J.A. Wheeler summarize: " the mass-energy tells space-time how to curve, and the space-time tells the
mass-energy how to move, so the mass-energy *there* also rules the inertia *here* ".
[1] "Uber die Grundprinzipien und Grundgleichungen dei Mechanik", translated in "Ludwig Boltzmann: Theoretical Physics and
Philosophical Problem: Selected Writings", B. McGuinness (ed.), Reidel, Dordrecht, 1974.
[2] in "Gravitation and Inertia", Princeton U.P., 1995, page 296.
[3] in "Physical Foundations of General Relativity", Doubleday, London, 1969.
[4] in "Mach's principle and space-time structure", Rep. Prog. Phys., 44:1152-1195 (1981).
[5] A.H. Taub, "Empty space-times admitting a three parameter group of motions", Ann. Math., 53:472-490 (1951).
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