# Researchers calculate that sound has negative mass and negative gravity

Researchers claim sound waves do carry mass – gravitational mass. This implies that a sound wave not only is affected by gravity but also generates a tiny gravitational field. Our findings are valid for non-relativistic media as well, and could have intriguing experimental implications.

They claim that phonons might have negative mass and also have negative gravity.

Arxiv – The mass of sound

It is usually said that sound waves do not transport mass. They carry momentum and energy, and lead to temporary oscillations of the local mass density of any region they happen to pass through, but it is an accepted fact that the net mass transported by a sound wave vanishes.

A first indication that sound waves can in fact carry a nonzero net mass is contained in the results: using an effective point-particle theory, it was shown that phonons in zero-temperature superfluids have an effective coupling to gravity, which depends solely on their energy (or momentum) and on the superfluid’s equation of state. For ordinary equations of state, such a coupling corresponds to a negative effective gravitational mass: in the presence of an external gravitational field, such as that of Earth, a phonon’s trajectory bends upwards.

Now, this effect is completely equivalent to standard refraction in the form of Snell’s law: in the presence of gravity, the pressure of the superfluid depends on depth, and so does the speed of sound. As a result, in the geometric acoustics limit sound waves do not propagate along straight lines. Because of this, one might be tempted to dismiss any interpretation of this phenomenon in terms of “gravitational mass”.

They calculate the transported mass is in general quite small, of order M ∼ E/c2 s. For example, a very energetic phonon in superfluid helium-4 with momentum k ∼ 1 keV/c carries a mass roughly of order M ∼ 1 GeV/c2 , i.e. that of a single helium atom

It is possible to envision experimental setups where this effect could be detected. One possibility is to employ ultra-cold atomic or molecular gases. In these systems, in fact, not only might one be able to
achieve very small sound speeds and enhance the effect, but also use suitable trappings to simulate strong gravitational potentials.

Moreover, atomic clocks and quantum gravimeters can currently detect tiny changes in the gravitational acceleration of Earth, up to fractions of nm/s2. It is possible to imagine that, in a not too distant future, such techniques will reach the sensitivity necessary to detect the gravitational field associated with seismic w