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If rotation was relative, we could say that the Universe is revolving around the earth. But how could this be true, since at some distant point the speed of a star would be greater than the speed of light ? How does Mach answer to this question ?

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  • $\begingroup$ Rotation isn't relative in Newtonian mechanics, in Mach's Principle, or general relativity. $\endgroup$ – David Hammen Dec 19 '17 at 6:11
  • $\begingroup$ Mach wasn't aware that there was an upper speed limit, that only came with Einsteins insight; so the question is ahistorical. $\endgroup$ – Mozibur Ullah Dec 19 '17 at 10:04
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One answer is: you won't know until you try.

Another answer could be that the aggregate influences of all matter are what create the rotational rest frame. If there were no other matter than our tiny planet in the Universe, would there be any way to detect rotation?

I'm not wording that well, but it might add to your insight.

"It is justified to consider Mach as the precursor of the General Theory of Relativity." Albert Einstein

The Ehrenfest paradox may interest you:

https://en.wikipedia.org/wiki/Ehrenfest_paradox

It was one of the thought experiments that help Einstein may the leap the General Relativity.

There is a modified Mach's principle in General Relativity. I haven't read this paper, but it is a topic of great interest to me.

https://arxiv.org/abs/gr-qc/9607046

"We define a new parameter `cumulative drag index' for a particle in circular orbit in a stationary, axisymmetric gravitational field and study its behaviour in the two well known solutions of general relativity {\it viz.}, the Kerr spacetime and the G\"odel spacetime, wherein the inertial frame dragging has an important role. As it shows similar behaviour for both co and counter rotating particles, it may indeed be an indication of the influence of the faraway universe on local physics and thus Machian. "

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  • $\begingroup$ Thanks for the links. Yes my question is related to the links you sent. But my question is more historical. Why didn't physicists reply to Mach with this argument : if rotation were relative, then some stars would exceed the speed of light. As this is not possible, his view is not tenable. This would have ended the debate. Since this was not the case, I am not sure if the argument is valid, and if so, why isn't it valid ? Maybe it has something to do with Ehrenfests paradox... $\endgroup$ – Anarchasis Dec 20 '17 at 0:09
  • $\begingroup$ Well, when Mach stated his principle, there was no special relativity to challenged the idea of something going faster than the speed of light. So that's the main reason they didn't use that objection. Nonetheless, the objection isn't valid. The principle is that the distant massive bodies determine what rotation means. So if they were all rotating that fast, they would change spacetime in such a way as to make it look exactly the way it looks. $\endgroup$ – Steven Thomas Hatton Dec 20 '17 at 0:59

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