Phonon Scharnhorst effect: Acoustic analogue of the vacuum-fluctuation-boosted speed of light
Abstract
The Scharnhorst effect in quantum electrodynamics predicts a superluminal velocity shift δc>0 at low photon frequencies due to vacuum fluctuations between two mirrors. Although theoretically robust (no causality violation), the effect is extraordinarily small (δc/c≈ 10−32 for mirrors 1 μm apart) and outside current experimental reach. Here we propose a condensed matter analogue, replacing the photons in the electromagnetic vacuum by phonon excitations of a Bose-Einstein condensate. In an idealized geometry, the two-dimensional surface of a cylinder (circumference L) at zero temperature, the axial speed of sound is increased due to zero-point fluctuations of the condensate by δc/c≃ 5× 10−3 g̃ at L≃ 2 ξ, to first order in the dimensionless interaction constant g̃≃ 10−1 of the Bose gas of healing length ξ≃ 1 μm. This is 28 orders of magnitude larger than the photonic effect, basically because phonons have a self-interaction while photons only interact via massive electrons. We discuss the prospects for observation of the acoustic Scharnhorst effect, the main restriction being the low-temperature requirement.
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BibTeX
@misc{beenakker2026phonon,
title = {{Phonon Scharnhorst effect: Acoustic analogue of the vacuum-fluctuation-boosted speed of light}},
author = {C. W. J. Beenakker},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14155},
eprint = {2609.14155},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14155},
}
RIS
TY - UNPB
TI - Phonon Scharnhorst effect: Acoustic analogue of the vacuum-fluctuation-boosted speed of light
AU - C. W. J. Beenakker
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2609.14155
UR - https://arxiv.org/abs/2609.14155
AB - The Scharnhorst effect in quantum electrodynamics predicts a superluminal velocity shift δc>0 at low photon frequencies due to vacuum fluctuations between two mirrors. Although theoretically robust (no causality violation), the effect is extraordinarily small (δc/c≈ 10^−32 for mirrors 1 μm apart) and outside current experimental reach. Here we propose a condensed matter analogue, replacing the photons in the electromagnetic vacuum by phonon excitations of a Bose-Einstein condensate. In an idealized geometry, the two-dimensional surface of a cylinder (circumference L) at zero temperature, the axial speed of sound is increased due to zero-point fluctuations of the condensate by δc/c≃ 5× 10^−3 g̃ at L≃ 2 ξ, to first order in the dimensionless interaction constant g̃≃ 10^−1 of the Bose gas of healing length ξ≃ 1 μm. This is 28 orders of magnitude larger than the photonic effect, basically because phonons have a self-interaction while photons only interact via massive electrons. We discuss the prospects for observation of the acoustic Scharnhorst effect, the main restriction being the low-temperature requirement.
ER -