Sound may have negative gravitational mass and could repel ordinary matter

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(Inside Science) -- The sound of a sonic boom may produce about the same magnitude of gravitational pull as a 10-milligram weight, a new study finds. Oddly, the findings also suggest the pull is in the opposite direction of the gravitational pull generated by normal matter, meaning sound waves might fall up instead of down in Earth's gravitational field.

One might assume these findings are related to Einstein's famous equation E=mc2, which revealed that anything with energy could be converted to an equivalent amount of mass and vice versa. One consequence of this relationship according to Einstein's theory of relativity is that matter traveling near the speed of light will get heavier.

However, these new findings suggest that even in regular conditions that ignore relativity, sound possesses gravitational mass.

Any sound waves on Earth would have extraordinarily weak gravitational effects on their surroundings compared to the effect of the Earth itself, which has a mass of about 6 trillion trillion kilograms. "It is a tiny, tiny effect," said study lead author Angelo Esposito, a high-energy physicist at the Swiss Federal Polytechnic School of Lausanne.

Still, the finding challenges long-held assumptions about how sound works.

"It's surprising in this day and age that it is still possible to find new results in classical Newtonian physics," said particle physicist Ira Rothstein at Carnegie Mellon University in Pittsburgh, who did not take part in this study.

Sound waves are fluctuations of density within materials. In classical physics, their energy can make matter move back and forth, but they were not thought to possess mass.

However, this view began to change when scientists investigated a very slippery kind of fluid known as a superfluid, which flows with virtually zero friction or viscosity. Liquid helium can act like a superfluid when cooled to temperatures just a few degrees above absolute zero. In 2018, researchers reported sound waves in superfluid helium might interact with gravity in ways that require they possess mass.

Now, Esposito and his colleagues have found that sound waves traveling in more familiar materials such as solids and fluids also may possess gravitational mass, which means they respond to gravitational fields like matter does. According to the researchers' equations, sound that carries one watt of power for one second in air -- comparable to that from heavy thunder -- will generate an equivalent of 10 milligrams of gravitational mass.

These findings not only suggest that sound has gravitational mass, but that such mass is negative. All known matter has positive gravitational mass, and such masses attract each other. However, positive gravitational mass repels negative gravitational mass instead of attracting it.

"It follows that if I generate a sound wave traveling, say, horizontally in a standard material, this will tend to bend its path upward -- float -- under the influence of the Earth's gravitational field," said Esposito. However, since this work suggests that all sound waves have negative gravitational mass, they should gravitationally attract each other, the researchers added.

The researchers suggest that experiments may soon be able to detect whether this effect is real. For instance, the effect may be measureable in an exotic form of supercooled matter called a Bose-Einstein condensate. They calculate that a sound wave in a condensate of cesium atoms roughly 100 microns wide -- about the average diameter of a human hair -- might have a gravitational mass of up to one-thousandth that of the condensate, potentially within the limits of detection.

In addition, earthquakes generate sound waves in rock, and the scientists estimated that a quake of magnitude 9 on the Richter scale would generate 100 million metric tons of gravitational mass. This would exert a force about 100 trillion times weaker than Earth's gravitational pull, which atomic clocks and quantum gravimeters might be sensitive enough to detect in the near future, they said.

"It would be really interesting to see if these effects are measurable," Esposito said.

The scientists detailed their findings online March 1 in the journal Physical Review Letters.

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