 We cannot go into the mathematical details necessary for a full discussion of the successes and failures of Mach-heavy in the GTR context. But one can see why the Machian interpretation Einstein hoped he could give to the curved spacetimes of his theory fails to be plausible, by considering a few simple ‘worlds’ permitted by GTR. In the first place, for our hovering rocket ship, if we are to attribute the gravity field it feels to matter, there has got to be all this other matter in the universe. But if we regard the rocket as a mere ‘test body’ (not itself substantially affecting the gravity present or absent in the universe), then we can note that according to GTR, if we remove all the stars, galaxies, planets etc. from the world, the gravitational field does not disappear. On the contrary, it stays basically the same locally, and globally, in the simplest solution of the field equations, it takes the form of empty Minkowski spacetime – precisely the quasi-absolute structure Einstein was hoping to eliminate. Solutions of the GTR field equations for arbitrary realistic configurations of matter (e.g., a rocket ship ejecting a stream of particles to push itself forward) are hard to come by, and in fact a realistic two-body exact solution has yet to be discovered. But numerical methods can be applied for many purposes, and physicists do not doubt that something like our accelerating rocket – in otherwise empty space – is possible according to the  theory.[7]  We see clearly, then, that GTR fails to satisfy Einstein’s own understanding of Mach’s Principle, according to which, in the absence of matter, space itself should not be able to exist.