Dispersion and the transverse aether drag

Abstract

THERE has been controversy about the correct expression of the displacement, d, introduced by the transverse motion of a dispersive dielectric slab on a light beam. Player¹ proposed the formula d=νt(n_g − n⁻¹)/c, where ν is the slab transverse velocity, t the slab thickness, n_g and n the group and wave refractive indices of the medium, respectively, and c the velocity of light in free space. This expression has been verified in very careful experiments reported by Jones². I point out here that a simple model demonstrates that (in agreement with Player's formula) d must vanish when ν_gv_ø=c², where ν_g≡c/n_g is the group velocity and ν_ø≡=c/n is the phase velocity in the slab.