# Sound has Mass and thus, Gravity?

May 25, 2020

### By Dr. Inés Urdaneta / Physicist at Resonance Science Foundation

In order for sound to be affected by gravity and to exercise gravity, it has to carry some mass of its own. But our common observations showed that sound is vibration traveling through media; energy traveling through material carrying no mass of its own. Until now, intuitively we see that the mass, through which the sound wave or vibration is traveling, must affect the speed and propagation of the sound wave through that media. Sound waves travel at different speeds in different mediums — water, oil, wood. The displacement from an equilibrium position of mass (atoms in a material) is perceived as sound. Seems everything is understood, right? Well, here is where the piece that’s missing comes into play: the energy promoting the displacement of the atoms carries mass of its own! That’s what the results of the research presented below conclude.

Let’s see how… the atoms in a material under sound stimulation show mechanical displacements proportional to the energy of the sound wave or vibration, represented often as a spring. In the material at the atomic level, this mechanical energy vibration is known to be quantized in discrete amounts called phonons, just as an atom absorbs or emits the energy contained in the vibrations of the electromagnetic waves we call light, in discrete amounts called photons. And these phonons or “particles of sounds” just as the photons or “particles of light”, imply that the waves they belong to, propagate in discrete amounts called quanta. If a photon is a quantum of light, a phonon would be a quantum of sound. Both quanta are believed to be massless, but up to very recently — and almost by accident — it was found that phonons do in fact carry a very small amount of mass. They are massive.

This is no surprise, since Einstein’s famous equation E=mc2 tells us that there is an exact equivalence between energy and mass. To understand the meaning of the equation, we use the following image. Very roughly speaking, mass is confined vibration; it translates into a gravitational effect. Meanwhile, light is a propagating vibration, such that the boundary condition between propagating and confined vibration is precisely the proportional constant known as the speed of light c, which sets the limit to the speed a mass can travel, i.e., a limit for the vibrations to remain confined, and hence exercise gravity. For this reason, electromagnetic (light) vibrations are energy carriers that remain massless in motion because they propagate at the speed of light. Since sound concerns propagating vibrations through phonons traveling slower that the speed of light, some mass is implied, even if traveing in air.

##### You would expect classical physics results like this one to have been known for a long time by now – Angelo Esposito, Columbia University

Esposito and collaborators at Columbia University 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. 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.

It should be noted that the researchers did not actually measure mass being carried by a sound wave, instead they used math to prove it happens. The mass of a phonon is expected to be very small, comparable to the mass of the hydrogen atom, about 10–24 grams, and as tiny as it seems, it may be measurable. They suggest experiments for real measurements conducted with sound waves as they move through a superfluid or Bose-Einstein condensate made of very cold atoms, which would allow enough mass carried for measurement. Another better approach might be to measure the mass being carried by sound waves moving through the Earth during a quake, because it moves billions of kilograms of mass; the sound generated by it might be visible on devices that measure gravitational signals as the gravitational waves detected coming from the collision of two supermassive black holes.

Their work, published in the journal Physical Review Letters, states that sound waves that do not transport mass is only true at linear order. As the abstract of this publication claims: “Using effective field theory techniques, we confirm the result found by Nicolis and Penco [Phys. Rev. B 97, 134516 (2018)] for zero-temperature superfluids, and extend it to the case of solids and ordinary fluids. We show that, in fact, sound waves do carry mass—in particular, gravitational mass. This implies that a sound wave not only is affected by gravity but also generates a tiny gravitational field, an aspect not appreciated thus far. Our findings are valid for nonrelativistic media as well, and could have intriguing experimental implications.”

#### RSF in perspective

It seems that classical phenomenon has much more to reveal to our eyes and to our ears than we thought. Reality keeps nourishing our imagination…

The fact that the mass of the phonon is very close to that of the hydrogen atom (basically the mass of the proton itself) is very intriguing; it suggests a deeper connection, as probably it is no coincidence. This will be further explored by our research team. But more importantly, as reality is composed of a variety of states of matter, this realization connects to what is claimed by ancient cultures around the globe. They emphasize the role of the spoken word as a tool for manifesting reality… And speech is sound.