Dispersion Relations and Relativistic Causality
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.
Cite
@article{arxiv.quant-ph/0310059,
title = {Dispersion Relations and Relativistic Causality},
author = {H. Fearn and R. H. Gibb},
journal= {arXiv preprint arXiv:quant-ph/0310059},
year = {2007}
}
Comments
13 pages no figures (condensed format) Changes has been made to the Scharnhorst section