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Is vacuum dispersive?

The question we ask is: does the speed of light {\it{in vacuo}} depend on its frequency? While the answer is NO in the frame of classical physics, we point out that the opposite could be true if one takes into account the polarization of Dirac sea. We estimate the dependence of the index of refraction of vacuum + Dirac sea versus the wavelength of an incoming beam, and suggest a way to test this effect.