# Do these PR Letter authors suggest sound transports mass, or only that it can be a source of gravitation?

Question: Do the authors of this PR Letter suggest sound transports mass, or only that it can be a source of gravitation?

The Phys.org article More evidence of sound waves carrying mass says:

Using effective field theory, they showed that a single-watt sound wave that moved for one second in water would carry with it a mass of approximately 0.1 milligrams. They further note that the mass was found to be a fraction of the total mass of a system that moved with the wave, as it was displaced from one site to another.

Importantly, the researchers did not actually measure mass being carried by a sound wave—they used math to prove it happens.

I'm having trouble understanding that. "carry with it a mass" and "displaced from one site to another" sound to me like the Phys.org article is suggesting that the sound is transporting mass from point A to point B. But that's not what I get from reading the actual paper:

Phys.org links to the open access Phys Rev Letter Esposito, Krichevsky, and Nicolis 2019 Gravitational Mass Carried by Sound Waves:

Conclusions.— We showed that contrary to common belief, sound waves carry gravitational mass in a standard Newtonian sense: they are affected by gravity, but they also source gravity...

Another possibility might be to consider seismic phenomena. The wave generated by an earthquake of Richter magnitude m=9 carries an energy E ∼ 10$${}^{18}$$ Joules which, for c$${}_s$$ ∼ 5 km/s, corresponds to M ∼ 10$${}^{11}$$ kg, and a change in gravitational acceleration δg ∼ 10$${}^{-4}$$ nm/s$${}^2$$. Atomic clocks and quantum gravimeters can currently detect tiny changes in the gravitational acceleration, up to fractions of nm/s$${}^2$$ [26–28]. Given the rapid improvement of these techniques, one can imagine that in the not-too-distant future they will reach the sensitivity needed to detect the gravitational fields of seismic waves

The point is that they are claiming the sound wave carries a small amount of net mass, and because of Newtonian gravity this means that it causes a net change in gravitational field as well.

No complicated general relativity here.

• but what does "carries a small amount of net mass" really mean? Is it actually transporting mass from one point to another, depleting something at the source and accumulating somewhere else (mass transport), or does it just mean that sound is a source of gravitation? – uhoh Mar 9 at 8:43
• @uhoh In an extreme example, think of an explosion, it is the sound hitting glass that breaks it. This break is a transport of mass from the original position , in the direction of sound, is the way I rationalize it. usual sound displacement will be tiny, probabily within the uncertainty principle on xp – anna v Mar 9 at 9:42
• @annav if you are comfortable that that is a good example of the new and unexpected results described in the PRL, then please write it up as an answer! You've describe a transient and interface with a second medium with a non-linear response and a result predictable with basic physics. Gravitational measurements from seismic events are already known but I think the second block quote in my question especially is talking about something different. If I'm wrong, help me understand how so, thanks! – uhoh Mar 9 at 10:27
• It is just a speculation on how Newtonan masses could propagate with the sound, No I m not comfortable enough with it. – anna v Mar 9 at 11:45
• glancing through the paper, it seems that the gravitational mass could be negative, depending on the medium, so it is much more complicated than my analogy of dust falling off at impact of sound. – anna v Mar 9 at 11:55