We have theoretical evidence to show that sound carries mass

Krishna: When we think of sound waves, we usually think of invisible vibrations moving weightless through the air - not carrying any mass.

But new theoretical work shows that Sound waves carry mass. Physicists have provided further evidence that particles of sound really can carry tiny amounts of mass. And that means they can produce their own gravitational fields (6). Even in these messy 'real world' conditions, according to them, the sound waves could carry mass. That mass isn't exactly huge, as you'd expect. We're talking roughly the same as the amount of energy in the phonon divided by the square of the speed of light. So … small. (6).

Ordinary sound waves carry a small amount of mass with them as they travel, according to a new theoretical study. The theory assumes Newtonian conditions, so the effect is unrelated to either quantum theory or the equivalence of energy and mass known from relativity. The researchers do not yet have a clear physical explanation of their mathematical results, but they say that the idea should be testable in experiments with ultracold atoms, or possibly in observations of earthquakes (4).

In 2019 high-energy physicists Alberto Nicolis of Columbia University in New York and Riccardo Penco, now at Carnegie Mellon University (CMU) in Pittsburgh, used quantum field theory to analyze the behavior of sound waves moving through superfluid helium(5). To their surprise, they found that the waves carry a small amount of mass, not only by virtue of Einstein’s famous formula equating energy with mass. The duo found that phonons, the quantum units of sound waves, interact with a gravitational field in a way that requires them to transport mass as they move.

Nicolis and two other theorists have extended the analysis to sound waves moving in more familiar materials, such as liquids or solids, finding much the same result. For a 1-second-long, 1-watt sound wave in water, the amount of mass would be about 0.1 milligrams (4).

Most physicists had assumed earlier that sound waves carry energy but not mass, meaning that they would not generate any gravitational field (as long as one ignores general relativity). Their analysis revealed the effect because it goes beyond the simplified linear models typically used in studying sound waves, where, for example, the displacement of a material is always exactly proportional to the force applied. Although this approximation is very good for most purposes, it misses the mass effect entirely (5). Some researchers studying sound waves may have overlooked the effect because they rarely think about interactions with gravity.

The new calculation indicates that for ordinary sound waves in most materials, the mass carried is equal to the sound wave energy multiplied by a factor that depends on the speed of sound and the medium’s mass density. And the mass carried by sound waves turns out to be negative. It is a depletion of mass, rather an addition of mass. So sound waves in a gravitational field should float upward somewhat, like any buoyant object in water.

But the physicists who say sound carry mass admit that they have more work to do in finding the right physical interpretation of the mass flow. For liquids, they note, the effect seems to imply that some small fraction of particles must travel against the motion of the sound wave. But this idea seems less plausible for solids (4).

The researchers hope the effect might be detectable soon. For example, they estimate that the mass carried by a sound wave in a Bose-Einstein condensate of extremely cold atoms could carry as much as 1 part in 1000 of the total mass of the system, near the limits of current detection techniques. More ambitiously, earthquakes generate strong sound waves traveling through Earth’s crust, and the mass associated with them could be as large as 100 billion kilograms, which could register in sensitive gravitational monitoring devices (5).

Using a theoretical approach called effective field theory, which is commonly used in particle and solid-state physics, scientists calculated the mass carried by a sound wave packet propagating though a superfluid. The calculations show that sound waves carry a tiny negative mass, which means that in the presence of a gravitational field, such as that of the Earth, their trajectory is bent upwards. Researchers found that sound waves also generate a small gravitational field (1).

Although the mass of sound waves is tiny, it could be measured in experiments with cold molecular or atomic gases. The work might be relevant for neutron star dynamics, because gravitational fields would affect the physical properties of the superfluid stellar core (2,3).

It's also important to keep in mind the mathematics behind the claim haven't actually been put to the test. Sound foundations aside, somebody now needs to measure gravitational shifts in atoms chilled to near zero, something which just might be possible as we explore such condensates in space. Alternatively, the researchers suggest it might be easier to weigh an earthquake. The sound generated by a large tremor could amount to billions of kilograms of mass (7).

Footnotes:

1. Sound carries mass - Nature Reviews Physics
2. http://Esposito, A., Krichevsky, R. & Nicolis, A. Gravitational mass carried by sound waves. Phys. Rev. Lett.
3. http://Esposito, A., Krichevsky, R. & Nicolis, A. The mass of sound. Preprint at arXiv https://arxiv.org/abs/1807.08771 (2018)
4. Sound Waves Carry Mass
5. http://A. Nicolis and R. Penco, “Mutual interactions of phonons, rotons, and gravity,” Phys. Rev. B 97, 134516 (2018).
6. Gravitational Mass Carried by Sound Waves
7. We Just Got More Evidence That Sound Waves Really Do Carry Mass