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arXiv · quant-ph/0310059

Dispersion Relations and Relativistic Causality

H. Fearn·R. H. Gibb
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Abstract

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.

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H. Fearn, R. H. Gibb. 2003-10-30. Dispersion Relations and Relativistic Causality. https://arxiv.org/abs/quant-ph/0310059

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