 There is one key element left out of this success story, however, and it is crucial to understanding why most physicists reject Einstein’s claim to have eliminated absolute states of motion in GTR. Going back to our accelerating rocket, we accepted Einstein’s claim that we could regard the ship as hovering at rest in a universe-filling gravitational field. But a gravitational field, we usually suppose, is generated by matter. How is this universe-filling field linked to generating matter? The answer may be supplied by Mach-heavy. Regarding the ‘accelerating’ rocket which we decide to regard as ‘at rest’ in a gravitational field, the Machian says: all those stars and galaxies, etc., jointly accelerating downward (relative to the rocket), ‘produce’ that gravitational field. The mathematical specifics of how this field is generated will have to be different from Newton’s law of gravity, of course; but it should give essentially the same results when applied to low-mass, slow-moving problems such as the orbits of the planets, so as to capture the empirical successes of Newtonian gravity. Einstein thought, in 1916 at least, that the field equations of GTR are precisely this mathematical replacement for Newton’s law of gravity, and that they fully satisfied the desiderata of Mach-heavy relationism. But it was not so. (See the entry on  early philosophical interpretations of general relativity.)