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arXiv:1905.02235 · Physical review. D/Physical review. D.

Faster-than-light signaling in the rotating-wave approximation

Nicholas Funai, Eduardo Martín-Martínez

Published Sep 25, 2019• 23 citations
arXivHTMLPDF

Abstract

We present new results on the causality violations introduced by the rotating wave approximation commonly used in quantum optics and high-energy physics. We find that the causality violations and faster-than-light signaling induced by the approximation have ``fat tails,'' i.e., they are polynomially decaying with the distance from the light-cone of the emitter. Furthermore, we also show that the fundamental problems with the incompatibility between the approximation and relativity are not cured even in the long interaction time regime (where the approximation is often taken). This renders the approximation unsuitable for any regime where we are concerned about relativistic causality and information transmission via the electromagnetic field.

DOI
10.1103/physrevd.100.065021

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We present new results on the causality violations introduced by the rotating wave approximation commonly used in quantum optics and high-energy physics. We find that the causality violations and faster-than-light signaling induced by the approximation have ``fat tails,'' i.e., they are polynomially decaying with the distance from the light-cone of the emitter. Furthermore, we also show that the fundamental problems with the incompatibility between the approximation and relativity are not cured even in the long interaction time regime (where the approximation is often taken). This renders the approximation unsuitable for any regime where we are concerned about relativistic causality and information transmission via the electromagnetic field.
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In this paper we analyze the problem of ``apparent'' superluminal signalling and retrocausation that can appear for particle detector models when considering noncompactly supported field-detector interactions in quantum field theory in curved spacetimes and in relativistic quantum information protocols. For this purpose, we define a signalling estimator based on an adapted version of the quantum Fisher information to perturbative regimes. This allows us to study how the internal dynamics of the detectors (for example the gap between the detector energy levels) have an impact on the ability of particle detectors to communicate with one another. Moreover, we show that, very generally, even for detectors with infinite tails in space and time, if the tails decay exponentially, one can define an effective light cone, outside of which signalling is negligible. This provides concrete evidence supporting the use of noncompact (but exponentially decaying) detector smearings in protocols of relativistic quantum information.
In relativistic theories the principle of microscopic causality states that ``information cannot travel faster than the speed of light'' \cite{kaku}. In the present work we show that the time evolution of relativistic wave functions violates this principle. We consider here the wave functions of massless and massive particles. In the case of massless particles the wave functions which violate the microscopic causality have an analytic form while in the case of massive particles we have to rely on numerical calculations. In both cases the wave functions which are strictly localized at t=0t=0t=0, at later times do not vanish {\it outside} the future light cone. \end{abstract}
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 nonrelativistic detector models predict superluminal propagation of the field's initial conditions. We draw parallels between this characteristic of detector models, stemming from their nonrelativistic dynamics, and Sorkin's ``impossible measurements on quantum fields'' [R. D. Sorkin, in Directions in General Relativity: Proceedings of the 1993 International Symposium, Maryland (Cambridge University Press, 1993), Vol. 2, pp. 293--305.]. Based on these features, we discuss the validity of measurements in quantum field theory when performed with nonrelativistic particle detectors.
Conventional definition of the time-normal operator ordering (Kelley P. L. and Kleiner W. H., Phys. Rev. , 136 (1964) A316 ) is prone to causality violations (de Haan M., Physica A , 132 (1985) 375 ; 397 ). We show that such violations disappear if this definition is amended outside the rotating wave approximation. Nonrelativistic causality of an arbitrary time-normal product turns out to be a property of quantum kinematics, while relativistic causality is demonstrated for a time-normal product of two operators under the most general assumptions about quantum dynamics (commutativity of operators at space-like intervals). This eliminates the key obstacle preventing phase-space techniques of quantum optics from being extended to arbitrary quantum fields including fermions.
A formal implementation of the concepts of mesoscopic electromagnetic interaction and of the propagating wave in quantum electrodynamics beyond the rotating wave approximation is discussed. Used as a guide, these concepts lead to a natural resolution of a long-standing controversy: causality violations in the Glauber–Kelley–Kleiner photodetection theory. The Glauber–Kelley–Kleiner definition of the time-normal operator ordering must be amended without the rotating wave approximation, which eliminates all causality problems.