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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.

David
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  • Possible dupe of :http://physics.stackexchange.com/questions/5483/is-machs-principle-wrong?rq=1 –  May 27 '16 at 09:25
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    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 09:33
  • 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. –  May 27 '16 at 09:56
  • @count_to_10 Maybe the question title is misleading? I am by no mean trying say Mach's principle could be right after all. The question is: in an empty universe, what does GR predict? It looks to me (I know I am wrong) that Mach's principle is verified (frame-dragging), but I know very little about GR and I know that GR disproof Mach's principle.

    I can accept GR and still want to understand why it dismisses other theories.

     – David May 27 '16 at 10:00
  • @count_to_10 In the link you mentioned I found other reasons showing Mach's principle is wrong (gravitational waves) but couldn't find why a rotating sphere in an empty universe is still "really" rotating according to GR. – David May 27 '16 at 10:05
  • And wikipedia says "it lends support to Machs Principle", so I will reverse my d/v and hopefully you get a proper answer from the people who know far more than I, such as CuriousOne –  May 27 '16 at 10:24
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    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
  • @CuriousOne

    I do need GR because it is my very question: "What does GR predict"

     – David May 27 '16 at 10:28
  • Ok, question is unclear, I will rephrase. – David May 27 '16 at 10:29
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    GR in the non-relativistic case predicts the exact same thing as Newton. – CuriousOne May 27 '16 at 11:06
  • Fine, and what do I miss then about frame-dragging in empty universe? – David May 27 '16 at 11:08
  • "Einstein found Mach principle attractive but failed to include it in his General Relativity (GR), and GR is incompatible with Mach's principle." - I would say that it was Mach's principle that failed to be included in a correct theory of Nature, not the correct theory of Nature. ;-) In science, Nature cannot fail by definition of science. – Luboš Motl May 27 '16 at 14:11
  • @LubošMotl Sure, I have to agree with that :) I edited just a little, I hope that's better – David May 27 '16 at 14:15
  • Great, @David, but just to be sure, I agree with everything CuriousOne wrote. According to GR, the predictions aren't affected by the existence of distant stars at all - whether or not Mach expected this influence to exist - and GR also says that Newton's laws are OK when all the speeds and escape speeds are much lower than the speed of light. A rotating sphere rotates, is attracted by some gravity but repelled by the centrifugal force, the latter is probably bigger for real-world spheres. A trivial thing. If the sphere is perfectly symmetric, no gravitational waves are emitted. – Luboš Motl May 27 '16 at 14:19
  • If the sphere has wiggles on it or any non-uniformity and it rotates, GR predicts that this sphere emits gravitational waves and the rotation is slowing down. Gravitational waves are incidentally predicted by Mach not to exist at all, so LIGO was -among other things - a spectacular falsification of Mach's principle. – Luboš Motl May 27 '16 at 14:19

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