The rotation of magnetic field does not impact vacuum birefringence

We study how the rotation of a classical magnetic field influences vacuum birefringence. In spite of the fact that solutions of the wave equation depend in a non-trivial way on the relative magnitude of the strength of vacuum birefringence and the angular rotation frequency of the magnetic field, the induced ellipticity of the light ray does not depend on the magnetic field angular rotation frequency. Hence, in contrast to recent claims, the result of the PVLAS experiment cannot be explained by conventional non-linear quantum electrodynamics.