  In this paper we show that if the refractive index, or rather (n(w) -1)
satisfies the dispersion relations then, it is implied by Titchmarsh's theorem
that n(w) -> 1 as w -> infinity. Any other limiting value for n(w) would
violate relativistic causality, by which we mean not only that cause must
precede effect but also that signals cannot travel faster-than-c (the velocity
of light) in a vacuum. This paper does not claim to be a mathematically
rigorous proof, but the authors hope to have succeeded in supplying a very
convincing argument against faster-than-c light signals.
  Keywords: Dispersion relations, Kramers Kronig relations, Causality,
faster-than-c signals.
