Clarifying issues about rotational motion in classical and quantum mechanics

K. Heyde

Alyssa Ney

The purpose of this introduction is to provide the reader who is unfamiliar with contemporary debates in the metaphysics of quantum mechanics with some background in the central issues that arise in this volume. The goal is to sketch one clean, direct, accessible path from classical physics to quantum theory that will serve to clarify the main interpretive issues that arise in the volume. Key technical concepts of quantum mechanics are introduced as well as the main interpretive options.

Tapan Kumar Das

Xu Gong

ly outlined statement is then extended to more general classical cases. Quantum mechanics is established by imposing the particular requirements of microsystems to Hamiltonian mechanics. Hence, this statement for classical regular motion is able to be further extended to corresponding quantum cases such that the quantum-classical correspondence is more clearly clarified.

J. Žák

Takuya Matsumoto

We address the fundamental question of how rotation angles arise in classical rigid body motion from a geometric viewpoint. As a fundamental kinematical setting, we consider a rotating-disc model. We show that the rotation angle accumulated in a cyclic motion can be naturally decomposed into a dynamical phase and a geometric phase, and that the latter is obtained from the $U(1)$ holonomy of the Hopf fibration equipped with its canonical connection through a natural weight-two representation of the fiber group. By introducing a Gauss map based on a normal vector fixed at the center of the rotating disc, the physical periodic motion is mapped to a closed curve on the two-sphere $S^2$, whose horizontal lift in the Hopf bundle $S^3 \to S^2$ determines the geometric phase through the weight-two representation. This framework provides a conceptually clear interpretation of rotation angles as geometric phases and clarifies the geometric origin of their decomposition.