When circularly polarized light is passed through a quarter-wave plate, the plate experiences a torque. I understand this is true because angular momentum must be conserved, but I don't understand what is happening in the plate. From a classical perspective, how is the light interacting with the electrons in the plate in order to create the torque? I prefer a physical description over a mathematical one. Thanks.
The global polarization state of the light is the result of the spins of individual photons. Spin is an angular momentum ($\pm \hbar$). Passing through a medium, the polarization changes if the spin of individual photons -and the associated angular momentum- is affected. This can happen by birefringence (visualize it as a interference-dependent "twist" of the photon from $\hbar$ to $-\hbar$ if you like) or even absorption ($\hbar$ to just $0$). The change in angular momentum is the torque applied or transferred to the plate.