# Frame dragging VS Mach's principle: rotating body in an empty universe

What I understand about Mach's principle VS modern physics:

According to classical physics, there are ways to distinguish weather a body is rotating or not. For example if it is rotating, the Coriolis force experienced by an observer at the surface of the body is a function of the location, and the body will exhibit an equatorial bulge.

Some people find this is odd when we consider a rotating body in an otherwise empty universe because this imply the existence of preferred reference frames for rotation, namely the inertial frames, independent of all the universe matter.

Mach proposed (Mach's principle) that a body inertia is actually caused by its interaction with the entire universe mass distribution. A rotating sphere experience Coriolis forces because of its acceleration with respect to the rest of the universe mass. However, in a universe containing only a rotating sphere, since the sphere constitutes the total universe mass, it does not make sense to claim that the sphere is rotating. As a consequence, Coriolis forces and the equatorial bulge will vanish and no experiment will be able to demonstrate a rotating motion.

Einstein found Mach's principle attractive but couldn't include it in his General Relativity (GR): Mach's principle is incompatible with GR.

I wish to understand why, and here is my problem: what is the prediction of GR for a rotating sphere in an empty universe? According to frame-dragging, shouldn't the spacetime be "dragged" by the rotating body, and eventually "catch-up", so that at steady-state the whole body+spacetime is rotating as a solid block? In such case it becomes meaning less to say that the sphere is rotating. Where do I get it wrong? I have a very superficial GR knowledge.

• Possible dupe of :physics.stackexchange.com/questions/5483/… – user108787 May 27 '16 at 9:25
• Your phone can tell when it's rotating. It has a semiconductor sensor for that. People who find this odd simply didn't learn their Newton correctly. Mach's counterexample (if he really made it this way) is still wrong because the tension in the sphere would be inhomogeneous and it would bulge out. – CuriousOne May 27 '16 at 9:33
• David, I down voted this because, after reading various books on the development of GR, I think Einstein gave up on Mach when he realised that, have gone into the subject far more than Mach ever did, he knew what theories were valid, as opposed to philosophical musings. – user108787 May 27 '16 at 9:56
• You don't need general relativity for this. Newton's laws are perfectly fine and all rotation sensors on this planet use Newton, not Einstein. None of them is looking at the stars, by the way. They can sense rotation locally because of their acceleration. – CuriousOne May 27 '16 at 10:25
• GR in the non-relativistic case predicts the exact same thing as Newton. – CuriousOne May 27 '16 at 11:06