Does GR contradict Mach's principle?

[Q-reeus]

...This illustrates that the experimental proof that the G value used in GR is a constant for purposes of solar system experiments does not on its own rule out Machian theories which involve a value of G that varies with location.

Can it be taken here that G_s is specifically applied to both active gravitational mass m_a and passive mass m_p, and that the latter follows from applying WEP - ie m_p = m_i. So there is a chain of logic leading from Mach's principle that originally dealt only with inertia hence inertial mass m_i, and the other two are 'derived' from that?

 

[Jonathan Scott]

Can it be taken here that G_s is specifically applied to both active gravitational mass m_a and passive mass m_p, and that the latter follows from applying WEP - ie m_p = m_i. So there is a chain of logic leading from Mach's principle that originally dealt only with inertia hence inertial mass m_i, and the other two are 'derived' from that?

Sorry, I can't give you a good answer at the moment. I often have difficulty handling these sort of questions nowadays, because once you start talking about ideas which are not part of GR, it's tricky to remember exactly what holds and what doesn't, and it's years since I had time to really think about this area. Also, I've just had Sunday lunch.

I certainly generally assume active and passive mass are the same, and I seem to remember that in Sciama's type of Machian approach, all masses and distances are relative anyway; if you double all mass values in the universe, or all distances, nothing different happens.

 

[Q-reeus]

...Also, I've just had Sunday lunch...

Can't argue with that - hope it was nice.

...I certainly generally assume active and passive mass are the same, and I seem to remember that in Sciama's type of Machian approach, all masses and distances are relative anyway; if you double all mass values in the universe, or all distances, nothing different happens.

Presumably this is relative to some given time-like hyperslice. Not at all sure but had thought Hubble redshift could be interpreted as Mach's principle operating across different eras - ie back then with matter being crowded together, inertia was much greater wrt 'now', hence 'time/light-frequency much slower'. I realize 'expanding space' is the usual interpretation, but just like with ordinary gravitational redshift there can be alternate pov's ('tiring' light or slower clocks in that case).