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According to Mach we can attribute the fact that in a spinning bucket with water the water rises to the edges of the bucket just as well to the whole Universe rotating around the bucket, as to the spinning of the bucket itself. But how can the whole Universe be rotating? With respect to what? And doesn't it take a lot of energy to make the Universe spinning? Or has the Universe has been spinning all the time, so that if we make a bucket spinning we create a spinning difference between the bucket and the spinning Universe?

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Well from the buckets perspective that is what's happening. That's more or less the point as far as I can tell.

It doesn't take much energy to make the universe spin around the bucket though; the bucket has a fairly low inertia and can be given that circular motion fairly easy by a human. That's all it takes to make the universe spin from the perspective of the bucket.

Does that answer your question?

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  • $\begingroup$ @JMac-Mach wasn't talking indeed about the whole Universe rotating around the bucket. But suppose you could make the Universe (all the material that's in it) rotate around the bucket. You are at rest with respect to the bucket, so you feel no acceleration. Or does frame dragging (of which Mach didn't know) provide the acceleration, which would let the water level rise just the same? And in the case you spin around your axis, don't you feel yourself spinning anymore if all the stars are removed (as according to Mach the rotation can only exist relative to the stars)? GR wasn't there yet! $\endgroup$ – descheleschilder Feb 7 '17 at 23:08
  • $\begingroup$ @descheleschilder : In an empty Universe, you must eject something from your body in order to rotate. From Mach's viewpoint it would be correct to say that the ejected matter rotates relative to you (as you and the ejected matter would be the only objects in the empty Universe). But you would feel yourself spin only because portions of your body rotate with unequal angular velocities relative to their common axis and to each other. Frame dragging would measurably affect empty space & your relative trajectories if you and the ejected matter were massive enough. $\endgroup$ – Ernie Feb 8 '17 at 0:55
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The Universe (including the water in "Newton's bucket") is rotating only in relation to the bucket. In this sense, the energy required to set the Universe spinning is not a lot.

The water in "Newton's bucket" is part of the Universe, and the bucket is spinning with regard to the water and the rest of the Universe. But friction between the bucket and the Universe outside the bucket is insufficient to cause measurable effects in the rest of the Universe. Only the water part of the Universe inside the bucket has sufficient friction with the bucket to measure the effect of the rotating Universe's contact with the bucket.

If there were significant friction between the outside of the bucket and the rest of the Universe, it would take more energy to create a measurable effect on the rest of the Universe.

Mach took the position that all motion is relative. However, it would be counter to his argument to say that the Universe is an abstract and absolute entity that rotates. Rather, his argument signifies that it's equally correct to say that space and all objects in the Universe rotate in relation to the bucket, as it is to say that the bucket rotates in relation to the rest of the Universe.

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