The Stern–Gerlach experiment and the effects of spin relaxation

Abstract

The classical Stern–Gerlach experiment is analyzed with an emphasis on the spin dynamics. The central question asked is whether there occurs a relaxation of the spin angular momentum during the time the particle passes through the Stern–Gerlach magnet. We examine in particular the transverse relaxation, involving angular momentum exchange between the spin of the particles and the spins of the magnet. A method is presented describing relaxation effects at an individual particle level. This leads to a stochastic equation of motion for the spins. This is coupled to a classical equation of motion for the particle translation. The experimental situation is then modeled through simulations of individual trajectories using two sets of parameter choices and three different sets of initial conditions. The two main conclusions are: (A) if the coupling between the magnet and the spin is solely described by the Zeeman interaction with the average magnetic field the simulations show a clear disagreement with the experimental observation of Stern and Gerlach. (B) If one, on the other hand, also allows for a T₂ relaxation time shorter than the passage time one can obtain a practically quantitative agreement with the experimental observations. These conclusions are at variance with the standard textbook explanation of the Stern–Gerlach experiment.