Spin has long been regarded as a fundamentally quantum phenomena that is incapable of being described classically. To bridge the gap and show that aspects of spin's quantum nature can be described classically, this work uses a classical Lagrangian based on the coupled oscillations of Foucault's pendulum as an analog for the electron spin state in an external magnetic field. With this analog it is possible to demonstrate that Foucault's pendulum not only serves as a basis for explaining geometric phase, but is also a basis for reproducing a broad range of behavior from Zeeman-like frequency splitting to precession of the spin state. By demonstrating that unmeasured electron spin states can be fully described in classical terms, this research opens the door to using the tools of classical physics to examine an inherently quantum phenomenon.
The contest entry was a spring-coupled triple pendulum. It was used to demonstrate the character of normal modes and in particular a mode that has high Q even with the center pendulum highly damped. The coupling of one of the springs to a pair of pendulums could be varied while they were swinging and with this adiabaticity in the effect upon a normal mode was observed. In the discussion the mathematical simularity to the equations of three coupled quantum mechanical levels is pointed out. The eigenstate in metastable hydrogen atoms that survives passage through the spin filter of a polarized ion source is compared to the high-Q mode observed in the triple pendulum.