  We show that QED nonlinear effects imply a phase correction to the linear
evolution of electromagnetic waves in vacuum. We provide explicit solutions of
the modified Maxwell's equations for the propagation of a superposition of two
plane waves, and calculate analytically and numerically the corresponding phase
shift. This provides a new framework for the search of all-optical signatures
of photon-photon scattering in vacuum. In particular, we propose an experiment
for measuring the phase shift in projected high-power laser facilities.
