Comment on Phys.Rev. Lett. {\bf 122}, 084501 (2019) by A. Esposito, R. Krichevsky and A. Nicolis

TL;DR

This paper provides a critical commentary on a previous study about gravitational mass carried by sound waves, analyzing and discussing its findings and implications.

Contribution

It offers a detailed critique and discussion of the original work on gravitational effects of sound waves, clarifying its assumptions and conclusions.

Findings

Highlights potential issues in the original analysis

Provides alternative interpretations of sound wave gravitational effects

Clarifies the theoretical implications of sound wave mass transfer

Abstract

This is a comment on the PRL: Gravitational mass $M$ carried by sound waves by A. Esposito, R. Krichevsky and A. Nicolis, Phys.Rev. Lett. {\bf 122}, 084501 (2019).

Equations

$$M=-\frac{d\log c_s}{d\log {\rho }_m}\frac{E}{c_L^2}$$

Full text

Comment on Phys.Rev. Lett. 122, 084501 (2019) by A. Esposito, R. Krichevsky and A. Nicolis

C. Tannous

LABSTICC - UBO, UMR-6285 CNRS, Brest, F-29200 FRANCE ††thanks: Tel.: (33) 2.98.01.62.28, E-mail: tannous@univ-brest.fr

  

J. Gieraltowski

Laboratoire Géosciences Océan - IUEM, UMR-6538 CNRS, Plouzané, 29280 FRANCE

In Phys.Rev. Lett. 122, 084501 (2019), Esposito et al. introduce the notion of a gravitational mass $M$ carried by sound waves as given by:

[TABLE]

where $c_{s}$ is sound speed for the (longitudinal $L$ or transverse $T$) type of sound wave considered. $E$ is sound wave energy and $\rho_{m}$ the mass density of the wave carrier medium.

They apply this notion to earthquakes and deduce that for a Richter scale seism of magnitude $R=9$ there is an induced change $\delta g=10^{-4}$ nm/s2 in gravitational acceleration, concluding that presently $\delta g$ is too small to be measured. However, they point out that it might be possible soon to detect these changes since a considerable progress has been achieved recently with the detection of gravitational waves with the LIGO experiment LIGO .

Surprisingly, Esposito et al. have, in fact, hinted at an acoustic version of Einstein formula $E=Mc_{s}^{2}$ with $E$ the quake energy when one approximates the $-\frac{d\log c_{s}}{d\log\rho_{m}}$ factor by 1.

The energy $E$ produces a mass variation $\delta M_{\oplus}$ inducing a local change $\delta g=\frac{G\delta M_{\oplus}}{R_{\oplus}^{2}}$ in the gravitational acceleration $g$, with $R_{\oplus},M_{\oplus}$ Earth radius and mass respectively.

An earthquake releases energies through various channels such as heat, radiation or frictional weakening and inelastic deformation processes in rocks leading e.g. to formation of cracks. Presently, the characterization of seisms is based on moment-magnitude scale Bormann which is more accurate than the Richter scale especially in the case of strong earthquakes.

In the Richter scale, quake energy is obtained from the Gutenberg-Richter Bormann formula $E~{}=~{}10^{1.5\times R+4.8}$, while in the moment-magnitude $M_{w}$ scale, it is given by $E~{}=~{}10^{1.5\times M_{w}+4.32}$. This allows us to plot simultaneously versus $M_{w}$, the gravitational acceleration change and seism energy as displayed in fig 1.

According to the graph, the strongest quake ($M_{w}$=10) produces $\delta g=10^{-3}$ nm/s2 slightly below the current sensitivity $10^{-2}$ nm/s2 of superconducting gravimeters.

By comparison, the Sumatra-Andaman quake Sumatra is one of the strongest ever recorded over the last 65 years. It actually occurred in the Indian Ocean on December 26, 2004, releasing approximately 1.1 $\times 10^{17}$ joules as obtained from moment-magnitude scale Bormann analysis. It corresponds on our graph to $\delta g=10^{-5}$ nm/s2. While this value is beyond current sensitivity, there are several possible avenues to attain it soon such as Strontium optical lattice clocks, Cold atom or laser interferometric techniques inspired from LIGO experiment.

Acknowledgments: Discussions with Prof. Jacques Déverchère were very helpful to put this work into perspective.