I was reading up on Mach’s principle and the historical relation it had with the development of General Relativity. As I understand it, one formulation of Mach’s principle states that for all motion to be relative (even rotation/acceleration) the global mass-energy of the universe must somehow be affecting the motion of an inertial observer to create an apparent “pseudo-force”. This is in contrast to the view that the pseudo-forces seen in Accelerated frames are an indicator that the observer in that frame of reference is really in an absolute state of motion.
So to uphold this idea that “all motion is relative” Mach needed some sort of underlying mechanism to explain how the two situations could be equivalent, but whatever that underlying cause was was a mystery.
There’s an anecdote on Wikipedia that sums up the idea behind this pretty well:
“You are standing in a field looking at the stars. Your arms are resting freely at your side, and you see that the distant stars are not moving. Now start spinning. The stars are whirling around you and your arms are pulled away from your body. Why should your arms be pulled away when the stars are whirling? Why should they be dangling freely when the stars don't move?“
So my question is, in the actual mathematical framework is this reproduced? Would the stars whirling around a stationary observer somehow make their arms be pulled away, thus making the two situations, one where the observer is spinning and the stars are stationary and the other way around physically equivalent?
I’ve heard that there are frame-dragging effects in general relativity that reproduce something like this, but I’m unaware of whether or not this makes all forms of motion truly relative. I know that Einstein desired a theory such as this, but was it achieved with General Relativity and is it feasible?