- Start: The bucket rotates, not the liquid: the water surface is flat
- Bucket and water rotate in an equilibrium: The water surface is a parabola (almost)
- Stop the bucket: The water continues to rotate and the surface is still parabolic.
The parabolic surface proves that the bucket is rotating: against the environment, against earth, against the next fixstars, against absolute space.
Newton selected absolute space as reference - the "sensorium" for God.
In fact, the experiment states physically just the existence of some (approximate) intertial system as the famous Foucault pendulum!
The Austrian Ernst Mach (born in Moravia as I was) asked:
What if the bucket would be surrounded by thick rotating walls? Thick means really thick, many kilometers of rotating matter while the bucket and the water would be at rest? He predicted that the water surface would also become curved; this means that inertia is the result of the matter in the universe.
General Relativity moved somehow in that direction with the frame-dragging effect (Lense-Thirring effect) ...
The picture from http://commons.wikimedia.org/wiki/File:Coriolis_effect11.jpg
is a modern version of Newton's bucket in a science museum using two immiscible liquids: The equilibrium interface is a parabola.