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. 
View on Taylor & Francis
8 Citations
Background Citations
4

8 Citations

Citation Type

Citation Type

Can light signals travel faster than c in nontrivial vacua in flat space-time? Relativistic causality II
In this paper, we show that the Scharnhorst effect (vacuum with boundaries or a Casimir-type vacuum) cannot be used to generate signals showing measurable faster-than-c speeds. Furthermore, we aim to…
The propagation of terminated waves in dispersion media and the resulting time-dependent dielectric functions
In this paper we examine the physics of terminated wave propagation in a dispersive medium. A forced harmonic oscillator model is used to describe the molecule's motion. This model leads to a…
Broadband and giant nonreciprocity at the subwavelength scale in magnetoplasmonic materials
We unveil a previously overlooked wave propagation regime in magnetized plasmonic (gyrotropic) materials with comparable plasma and cyclotron frequencies, which enables a giant and broadband…
Broadband and Giant Nonreciprocity in Subwavelength Plasmonic Structures
We unveil a previously overlooked wave propagation regime in magnetized plasmonic (gyrotropic) materials with comparable plasma and cyclotron frequencies, which enables a giant and broadband…
Numerical demonstration of three-dimensional terahertz metamaterials based on the causality principle
A parameter retrieval algorithm based on the causality principle and Kramers—Kronig (KK) relations is employed to calculate the effective parameters of three-dimensional (3D) metamaterials. Using KK…
Can fast-light cloaks achieve arbitrarily broadband invisibility?
TLDR
It is clarified that invisibility cloaks based on fast-light media suffer from fundamental bandwidth restrictions that arise due to causality, the nature of superluminal wave propagation, and the stability issues of active systems.
Instantaneous Spreading Versus Space Localization for Nonrelativistic Quantum Systems
A theorem of Hegerfeldt (Kielanowski et al. 1998) establishes, for a class of quantum systems, a dichotomy between those which are permanently localized in a bounded region of space, and those…
Physical limitations on broadband invisibility based on fast-light media
TLDR
It is clarified that invisibility cloaks based on fast-light media suffer from fundamental bandwidth restrictions that arise due to causality, the nature of superluminal wave propagation, and the stability issues of active systems.

References

SHOWING 1-10 OF 67 REFERENCES
Dispersion Relations and Relativistic Causality
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…
Causality and the Dispersion Relation: Logical Foundations
TLDR
A rigorous proof is given of the logical equivalence of strict causality ("no output before the input") and the validity of a dispersion relation, e.g., the relation expressing the real part of a generalized scattering amplitude as an integral involving the imaginary part.
QED between parallel mirrors: Light signals faster than c, or amplified by the vacuum
Because it is scattered by the zero-point oscillations of the quantized fields, light of frequency omega travelling normally to two parallel mirrors experiences the vacuum between them as a…
Faster-than-c Signals, Special Relativity, and Causality
Motivated by the recent attention on superluminal phenomena, we investigate the compatibility between faster-than-c propagation and the fundamental principles of relativity and causality. We first…
``Faster than Light'' Photons in Gravitational Fields -- Causality, Anomalies and Horizons
Faster Than Light
It is widely believed that relativity -- both special and general -- requires that no physical signal travel at a speed faster than that of light. For instance, the assumption that there could be…
On the Theory of Dispersion of X-Rays
After a brief summary of the ideas underlying the quantum theory of dispersion it is shown that it can be applied to the refraction of x-rays, although the assumption that the number of atoms in a…
Signal velocity, causality, and quantum noise in superluminal light pulse propagation.
TLDR
This work considers pulse propagation in a linear anomalously dispersive medium where the group velocity exceeds the speed of light in vacuum or even becomes negative, and finds that quantum fluctuations limit the signal velocity to values less than c.
Dispersion relations for linear wave propagation in homogeneous and inhomogeneous media
For the dispersion of waves in a homogeneous medium there exist the Kramers–Kronig relations for the wave number K(ω) = ω/c(ω). The usual mathematical proof of such relations depends on assumptions…
QED Vacuum Polarization in a Background Gravitational Field and Its Effect on the Velocity of Photons
We calculate in QED the contribution to the photon effective action from one-loop vacuum polarization on a general curved background manifold, and use it to investigate the corrections to the local…
...
...