Best Matching

Julian Barbour explains here, the need for best matching in order to implement Mach's principle.

I had read his book, The End of Time, but is only now, after I thought of a New Scientific Method, that I understand his thoughts.

Mach postulated that an absolute Universe, with an absolute space and time, did have to emerge, if at all, from actual local observables. As Barbour explains in this note, Newton himself had one trouble with his dynamics, but could not solve it; he was forced then to assume, wrongly, that time is absolute.

For Barbour time is not essential in the description, what is essential is to find a guide, his best matching principle, to tell us which motion is real. Time is a local parameter, necessary to find the best match, not very different, than the parameter Topologists use to compare loops that continuously vary to get one shape from another. To change a cup into a doughnut. Time, it would seem, is then just a mathematical abstraction to get the best match.

Neat!