Absolute rotation

The second is the effect of centrifugal force upon the tension in a string joining two spheres rotating about their center of mass.

The centrifugal force pushes the water toward the sides of the bucket, where it piles up deeper and deeper, Pile-up is arrested when any further climb costs as much work against gravity as is the energy gained from the centrifugal force, which is greater at larger radius.

[1] Other thinkers suggest that pure logic implies only relative rotation makes sense.

Whether or not the effects from inertia are attributed to a fictitious centrifugal force is a matter of choice.

Sagnac set up this experiment to prove the existence of the luminiferous aether that Einstein's 1905 theory of special relativity had discarded.

The idea is that the local motion of a rotating reference frame is determined by the large-scale distribution of matter in the universe.

Mach's principle says that there is a physical law that relates the motion of the distant stars to the local inertial frame.

If you see all the stars whirling around you, Mach suggests that there is some physical law which would make it so you would feel a centrifugal force.

Bouncing ball in a rotating space station: The objective reality of the ball bouncing off the outer hull is confirmed both by a rotating and by a non-rotating observer, hence the rotation of the space station is an "absolute", objective fact regardless of the chosen frame of reference.
Figure 1: The interface of two immiscible liquids of different density (a denser colorless liquid and a lighter orange-colored liquid) rotating around a vertical axis is an upward-opening circular paraboloid.
Figure 2: Two spheres tied with a string and rotating at an angular rate ω. Because of the rotation, the string tying the spheres together is under tension.