Hello AppMathsDoc,
I think I know what you are getting at. First things first.
No I haven't read that book but I have read,'The Elegant Universe' by the same author.
I have heard of Newton's bucket because it was one of many disputes between Newton and Leibniz. Newton thought the bucket experiment went a long way in proving absolute space. Thinking along the same lines Newton imagined what would happen if two heavy weights were tied to each end of a rope and sent into space away from any influence of gravity.
The answer is nothing unless the weights rotate around each other.
Once this happens then Newton thought that rotation makes sense if we reference it in relation to the background of empty space. Leibniz did not agree and though that absolute space was nonsense. Unfortunately Leibniz could no devise a though experiment or otherwise to disprove Newton's idea.
Mach and Einstein put an end to the idea of absolute space.
Well as it turns out Einstein probably produced more unanswered question than we would like to think. Quantum theory does provide for the possibility of absolute space once again.
From my reading of,'The Elegant Universe' it seems as though space is not as empty as we would like to think. The following is not Green's ideas.
Kant distinguished between things-in-themselves and things-for- us.
For Kant there are two realities, however we only get to see one (things-for-us). With a little imagination we could imagine that things-in-themselves is a wave function. Things-in-themselves are only potential possibilities. Things-for-us is what we might call conscious awareness or a collapse of the wave function due to observation.
Kant might turn over in his grave at this interpretation.