Fundamental constants place a new speed limit on sound
Sound has a speed limit. Under normal circumstances, its waves can travel no faster than about 36 kilometers per second, physicists propose October 9 in Science Advances.
Sound zips along at different rates in different materials — moving faster in water than in air for example. But under conditions found naturally on Earth, no material can host sound waves that outpace this ultimate limit, which is about 100 times the typical speed of sound traveling in air.
The team’s reasoning rests on well-known equations of physics and mathematical relationships. “Given the simplicity of the argument, it suggests that [the researchers] are putting their finger on something very deep,” says condensed matter physicist Kamran Behnia of École Supérieure de Physique et de Chimie Industrielles in Paris.
The equation for the speed limit rests on fundamental constants, special numbers that rule the cosmos. One such number, the speed of light, sets the universe’s ultimate speed limit — nothing can go faster. Another, known as the fine-structure constant, determines the strength with which electrically charged particles push and pull one another. When combined in the right arrangement with another constant — the ratio of the masses of the proton and electron — these numbers yield sound’s speed limit.
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Sound waves, which consist of the vibrations of atoms or molecules, travel through a material as one particle jostles another. The wave’s speed depends on various factors, including the types of chemical bonds holding the material together and how massive its atoms are.
None of the sound speeds previously measured in a variety of liquids and solids surpass the proposed limit, condensed matter physicist Kostya Trachenko and colleagues found. The fastest speed measured, in diamond, was only about half the theoretical maximum.
The limit applies only to solids and liquids at pressures typically found on Earth. At pressures millions of times that of Earth’s atmosphere, sound waves move faster and could surpass the limit.
One material expected to boast a high sound speed exists only at such high pressures: hydrogen squeezed hard enough to turn into a solid metal (SN: 6/28/19). That metal has never been convincingly created, so the researchers calculated the expected speed instead of using a measurement. Above about 6 million times Earth’s atmospheric pressure, the sound speed limit would be broken, the calculations suggest.
The role of the fundamental constants in sound’s maximum speed results from how the waves move through materials. Sound travels thanks to the electromagnetic interactions of neighboring atoms’ electrons, which is where the fine-structure constant comes into play. And the proton-electron mass ratio is important because, although the electrons are interacting, the nuclei of the atoms move as a result.
The fine-structure constant and the proton-electron mass ratio are dimensionless constants, meaning there are no units attached to them (so their value does not depend on any particular system of units). Such dimensionless constants fascinate physicists, because the values are crucial to the existence of the universe as we know it (SN: 11/2/16). For example, if the fine-structure constant were significantly altered, stars, planets and life couldn’t have formed. But no one can explain why these all-important numbers have the values they do.
“When I have sleepless nights, I sometimes think about this,” says Trachenko, of Queen Mary University of London. So he and colleagues are extending this puzzle from the cosmic realm to more commonplace concepts like the speed of sound. Trachenko and coauthor Vadim Veniaminovich Brazhkin of the Institute for High Pressure Physics, in Troitsk, Russia, also reported a minimum possible viscosity for liquids in the April 24 Science Advances.
That viscosity limit depends on the Planck constant, a number at the heart of quantum mechanics, the math that governs physics on very small scales. If the Planck constant were 100 times larger, Trachenko says, “water would be like honey, and that probably would be the end of life because the processes in cells would not flow as efficiently.” More
