Dear Janko,
I am afraid I cannot answer what you ask since I share the views expressed by:
J.L. Synge in his excellent General relativity book: "The Principle of Equivalence performed the essential office of midwife at the birth of general relativity... I suggest that the midwife be now buried with appropriate honours and the facts of absolute space-time faced."
Einstein himself, later in his life, changed his opinion of Mach's principle and wrote: "Actually, one should no longer speak of Mach's principle at all."
And here is why I think Mach's ideas contradict spacetime physics (properly understood in terms of Minkowski's four-dimensional formulation of Einstein's special relativity). Only two examples:
1. According to Mach, if there existed a single particle in the universe, one could not say anything about its motion (e.g., whether it is moving with constant velocity or is accelerating). That is true in Einstein's original special relativity, but clearly wrong in its accepted Minkowski's formulation: if there existed a single particle in the universe, its worldline would be either straight (which, in three-dimensional language, means that the particle is moving with constant velocity) or curved (representing accelerated motion).
2. According to Mach, one cannot distinguish between the Copernican and the Ptolemaic systems because, on Mach's view, it is not clear what orbits what. This is plain wrong in spacetime physics because the worldlines (rather worldtubes) of the planets are helixes around the worldtube of the Sun (which, in three-dimensional language, means that it is the planet that orbit the Sun).
Best,
Vesselin
