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"To get a handle on Mach's viewpoint, imagine a particle spinning out in space. If there were no stars forming a backdrop against which to measure the particle's motion, can we really say that the particle is moving? To Mach, the answer was no, in an empty space there is no distinction between the particle spinning and the particle being stationary."
Of course it's hard to imagine a controlled experiment to test the above idea. The other problem is that virtual quanta inside the vacuum gravitate. Actually virtual fermion-antifermion pairs gravitate attractively like dark matter and virtual bosons anti-gravitate repulsively like dark energy. The point is that at most 4% of the stuff of the world are real quanta excited out of the covariant aether quantum vacuum. Therefore, Mach's picture of Newtonian bodies appears a bit naive in the hindsight of quantum field theory.
Einstein told Heisenberg in 1925 that the theory determines the observations as much as the observations determine the theory. In terms of Einstein's geometrodynamics there is no conceptual problem at all with the expansion of space as operationally defined by the temperature of the microwave background.
Of course, if Barbour & Company attempt to re-invent the wheel they must show how the conventional Einstein theory is a classical limiting case of their new paradigm, but perhaps they may have already done that? I have not read Barbour's papers.