Dispersion Relations and Relativistic Causality

Details Dispersion Relations and Relativistic Causality Dispersion Relations and Relativistic Causality

2003-10-09

arxiv.org/abs/quant-ph/0310059v3

Physics

Quantum Physics

13 pages no figures (condensed format) Changes has been made to the Scharnhorst section

Scientific paper

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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