On the possibility of an experiment on "nonlocality" of electrodynamics

It has been known since the 19th century that a circularly polarised electromagnetic wave carries an angular momentum. A simple experiment (Righi, 1882) apparently indicates that the angular momentum is distributed over the entire cross section of the beam. According to some modern ideas, the angular momentum of the beam with the given polarisation is localised near the beam "surface" and represents a spin of photons, while the energy in the beam is distributed throughout its cross section, which is inconsistent with the principle of locality. For the experimental determination of the localisation of the angular momentum, we propose a new scheme, in which we study the interference pattern of two coherent circularly polarised beams. Each beam first passes through a half-wave plate, one of the plates being divided into two coaxial parts. With (manual) rotation of one parts of the plate we change the frequency of the light passing through it: the plate absorbs the momentum and, therefore, work is done. This change in frequency should cause a movement of the interference fringes and show the distribution of the angular momentum over the beam cross section.