Eliezer_Yudkowsky comments on Mach's Principle: Anti-Epiphenomenal Physics - Less Wrong
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As I understand it, "centrifugal" is the force you get in a rotating reference frame. "Centripetal" is the only real force (rather than pseudo-force) when you're not in a rotating reference frame.
If water creeps up the walls of the bucket, obviously it's because the walls are pushing the water inward against the water's resistance; unless you're constructing a rotating reference frame, in which case the water is pushing out and running up against the walls' resistance.