The quantum Newton's bucket: Active and passive rotations in quantum theory

Motivated both by classical physics problems associated with Newton's bucket'' and recent developments related to QCD in rotating frames of reference relevant to heavy ion collisions, we discuss the difference between active’’ and ``passive’’ rotations in quantum systems. We examine some relevant potentials and give general symmetry arguments to give criteria where such rotations give the same results. We close with a discussion of how this can be translated to quantum field theory.