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

TL;DR

The paper investigates the distinction between active and passive rotations in quantum systems motivated by Newton's bucket and rotating-frame QCD. It develops a symmetry-based criterion, $[\mathbf{J}, H_0]=0$, and analyzes several potentials (Coulomb, position-dependent B-fields, rotating wells) to determine when active and passive rotations coincide or diverge. It finds that for most realistic, non-spherical potentials the two notions are not equivalent, though equivalence can emerge in highly symmetric cases or under equilibrium/Killing-vector arguments, with notable caveats in field theory and gravity. The work further discusses extensions to quantum field theory, highlighting how active rotation can induce quantum fluctuations and how non-inertial frames relate to quantum reference-frame concepts and the quantization of gravity.

Abstract

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.