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.
We analyze potential violations of causality in Unruh DeWitt-type detector models in relativistic quantum information. We proceed by first studying the relation between faster-than-light signaling and the causal factorization of the dynamics for multiple detector-field interactions. We show in what way spatially extended non-relativistic detector models predict superluminal propagation of the field's initial conditions. We draw parallels between this characteristic of detector models, stemming from their non-relativistic dynamics, and Sorkin's "impossible measurements on quantum fields" arXiv:…
Requiring causality on measurements in quantum field theory seems to impose strong conditions on a self-adjoint operator to be really measurable. This may seem limiting and artificial in the operator language of algebraic quantum field theory (AQFT), but is essential for a truly relativistic theory. Recent publications attempt to deal with this issue by including the apparatus into the formalism, connecting AQFT with measurement theory, but other options have been suggested. In this essay, I discuss the causality conditions on self-adjoint operators both in the language of AQFT and in the lang…
A crucial task for secure communication networks is to determine the minimum of physical requirements to certify a cryptographic protocol. A widely accepted candidate for certification is the principle of relativistic causality which is equivalent to the disallowance of causal loops. Contrary to expectations, we demonstrate how correlations allowed by relativistic causality could be exploited to break security for a broad class of multi-party protocols (all modern protocols belong to this class). As we show, deep roots of this dramatic lack of security lies in the fact that unlike in previous …
It is known that relativistic wavefunctions formally propagate beyond the light cone when the propagator is limited to the positive energy sector. By construction, this is the case for solutions of the Salpeter (or relativistic Schrödinger) equation or for Klein-Gordon and Dirac wavefunctions defined in the Foldy-Wouthuysen representation. In this work we investigate quantitatively the degree of non-causality for free propagation for different types of wavepackets all having initially a compact spatial support. In the studied examples we find that non-causality appears as a small transient eff…
The deformation of the relativistic dispersion relation caused by noncommutative (NC) Quantum Mechanics (QM) is studied using the extended phase-space formalism. The introduction of the additional commutation relations induces Lorentz invariance violation. It is shown that this deformation does not affect the propagation speed of free massless particles. From the deformation of the dispersion relation for massless particles, gamma ray burst data is used to establish an upper bound on the noncommutative parameter, $η$, namely $\sqrtη \lesssim 10^{-12} \,\mathrm{eV/c}$. Additionally, a putative …
