Dispersion relations and causality: does relativistic causality require that n(ω) → 1 as ω → ∞ ?

@article{Fearn2006DispersionRA,
  title={Dispersion relations and causality: does relativistic causality require that n($\omega$) → 1 as $\omega$ → ∞ ?},
  author={Heidi Fearn},
  journal={Journal of Modern Optics},
  year={2006},
  volume={53},
  pages={2569 - 2581}
}
  • H. Fearn
  • Published 10 November 2006
  • Philosophy
  • Journal of Modern Optics
In this paper it is shown that if the refractive index, or rather, [ n(ω) -1 ] satisfies the dispersion relations then, it is implied by Titchmarsh's theorem that, n(ω) → 1 as ω→ ∞. Any other limiting value for n(ω) would violate relativistic causality, by which is meant not only that cause must precede effect but also that signals cannot travel faster-than-c, the velocity of light in a vacuum. 
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