Hidden Kinematics and Dual Quantum References in Magnetic Resonance
Sunghyun Kim
TL;DR
This work reframes spin resonance by showing that transition probabilities are relational quantities between two quantum reference standards that share a common quantization operator but differ in kinematic versus dynamical roles. By performing sequential spin-operator transformations at the Schrödinger level, it unifies the conventional rotating-frame results with the lab-frame description into a single framework that includes both a dynamical rotation about the effective field and a kinematic rotation of the reference frame. The paper derives a complete transition-probability expression, $W(-\tfrac{1}{2},\tfrac{1}{2})$, that reduces to the familiar $W_{1954}$ and $W_{1937}$ in appropriate limits, and it highlights how energy accounting redistributes between dynamical and frame-motion contributions without changing the total energy. These insights clarify foundational aspects of spin dynamics in rotating fields and have implications for interpreting magnetic resonance experiments and quantum technologies where frame motion and reference standards play a role.
Abstract
Spin resonance phenomena are conventionally described using transition probabilities formulated in a rotating frame, whose physical meaning implicitly depends on the choice of quantum reference standard. In this Colloquium, we show that a spin in a rotating magnetic field constitutes a configuration involving two quantum descriptions that share a common quantization operator but differ in their kinematic and dynamical roles. The transition probability therefore emerges as a relational quantity between quantum reference standards rather than an intrinsic property of a single evolving spin state. By incorporating the kinematic motion of the spin vector together with the dynamical evolution, this framework restores consistent energy accounting and reveals the dual-reference structure underlying spin dynamics in rotating magnetic fields.