The Scharnhorst Effect: Superluminality and Causality in Effective Field Theories

Abstract

We present two re-derivations of the Scharnhorst effect. The latter was first obtained in 1990 by Klaus Scharnhorst, soon followed by Gabriel Barton, and consists in the theoretical prediction that the phase velocity of photons propagating in a Casimir vacuum normal to the plates would be larger than c. The first derivation given in the present work is relevant for the debates that have taken place in the physics literature regarding a possible greater-than-c value of the signal velocity. Indeed because the phase velocity result also held for the group velocity, the issue soon arose as to whether the same could be said for the signal velocity. Several arguments were presented against this notion, notably to the effect that measurement uncertainties would preclude such a measurement. These notably relied on the fact that the known phase velocity result is only valid within a certain frequency regime. Scharnhorst and Barton responded by arguing that given their previous result, the Kramers-Kronig relations imply one of two options: either the greater-than-c result holds for the signal velocity as well, or the Casimir vacuum behaves like an amplifying medium for some frequencies. Furthermore, the effect was later rederived and generalized within the framework of an effective metric approach, which has been argued to obviate the worries regarding causal paradoxes often associated with the possibility of faster-than-c signalling. However concerns related to theory errors as well as to the measurement uncertainties that had surfaced in the earlier debate have remained salient. By re-deriving the phase velocity using Soft-Collinear Effective Theory (SCET), one can address some of these concerns. Indeed, with regard to theory errors, SCET provides us with a framework where higher order corrections are known to be power-suppressed because SCET ensures that the expansion parameters are multiplied by factors of order 1. As a result, with due qualifications inherent to the nature of effective field theory, the result obtained within the SCET approach cannot be invalidated by higher order corrections. Furthermore, the theoretical description offered by SCET provides an argument relevant to the point that measurement uncertainties would prevent measuring the signal speed to be faster-than-c. Indeed, SCET implies the interaction between the Casimir vacuum and the propagating photon to be such that the latter would have the same phase velocity irrespective of its frequency. This in turn would entail that its signal velocity would be equal to this phase velocity, which is faster-than-c. The second calculation presented is concerned with the physical interpretation of the Scharnhorst effect, and constitutes an attempt at re-deriving it within source theory. Existing derivations imply that the Scharnhorst effect can be attributed to vacuum fluctuations. Other physical effects that share this feature have also been derived without any reference to the vacuum, but as due to source fields instead. We attempt a similar derivation for the Scharnhorst effect.