Similarities between the speed limit in relativity and the sound barrier in inviscid fluid flows
Abstract
The Prandtl-Glauert-Lorentz transformation establishes a deep mathematical correspondence between compressible potential flow theory and special relativity. Despite being implicit in the aerodynamic literature since the early twentieth century, this analogy remains largely unrecognised across the two communities and has never been surveyed in a unified manner. This review presents, in a self-contained and pedagogical framework accessible to both communities, the historical, mathematical, and applied dimensions of this correspondence. After tracing the parallel developments that gave rise to compressible aerodynamic theory and special relativity, we establish the formal equivalence between the Lorentz transformation and the Prandtl-Glauert coordinate change, and reinterpret relativistic concepts such as time dilation, the Doppler effect, and the Lorentz factor within the acoustic framework. Thanks to the added mass concept, we finally extend this analogy and show that the whole mathematical framework of special relativity is exactly mirrored by the linearised compressible potential flow theory.
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BibTeX
@misc{salmon2026similarities,
title = {{Similarities between the speed limit in relativity and the sound barrier in inviscid fluid flows}},
author = {F Salmon},
howpublished = {Physics of Fluids},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35198},
eprint = {2609.35198},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05765948v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Similarities between the speed limit in relativity and the sound barrier in inviscid fluid flows
AU - F Salmon
PY - 2026
DA - 2026/09/10
PB - Physics of Fluids
DO - 10.48550/arxiv.2609.35198
UR - https://hal.science/hal-05765948v1
AB - The Prandtl-Glauert-Lorentz transformation establishes a deep mathematical correspondence between compressible potential flow theory and special relativity. Despite being implicit in the aerodynamic literature since the early twentieth century, this analogy remains largely unrecognised across the two communities and has never been surveyed in a unified manner. This review presents, in a self-contained and pedagogical framework accessible to both communities, the historical, mathematical, and applied dimensions of this correspondence. After tracing the parallel developments that gave rise to compressible aerodynamic theory and special relativity, we establish the formal equivalence between the Lorentz transformation and the Prandtl-Glauert coordinate change, and reinterpret relativistic concepts such as time dilation, the Doppler effect, and the Lorentz factor within the acoustic framework. Thanks to the added mass concept, we finally extend this analogy and show that the whole mathematical framework of special relativity is exactly mirrored by the linearised compressible potential flow theory.
SN - 1070-6631
SN - 1089-7666
ER -