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The fundamental constants put a new speed limit on sound

The sound has a speed limit. Under normal circumstances, its waves cannot travel faster than about 36 kilometers per second, physicists propose on Oct. 9 in Science Advances.

The zipper sound 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 harbor sound waves that exceed this final limit, which is about 100 times the typical speed of sound traveling in the air.

Team reasoning rests on known equations of physics and mathematical relationships. “Given the simplicity of the argument, it suggests that (researchers) are putting their finger on something very deep,” says condensed matter physicist Kamran Behnia of the École Supérieure de Physique et de Chimie Industrielles in Paris.

The speed limit equation rests on fundamental constants, special numbers that govern the cosmos. One of these numbers, the speed of light, sets the maximum speed limit in the universe: nothing can go faster. Another, known as the fine-structure constant, determines the force with which electrically charged particles push and pull on each other. When combined in the correct arrangement with another constant – the ratio of the masses of the proton to the electron – these numbers produce the speed limit of sound.

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Sound waves, which consist of the vibrations of atoms or molecules, travel through one material while one particle expels another. The speed of the wave depends on several factors, including the types of chemical bonds that bind the material and how massive its atoms are.

None of the speed of sound previously measured in a variety of liquids and solids exceeds the proposed limit, found the physicist of condensed matter Kostya Trachenko and colleagues. The fastest speed measured, in diamond, was only half the theoretical maximum.

The limit applies only to solids and liquids at pressures normally found on Earth. At pressure millions of times that of the Earth's atmosphere, sound waves move faster and could exceed the limit.

A material that has a high speed of sound only exists at such high pressures: hydrogen squeezed strong enough to become a solid metal (SN: 28/06/19). That metal was never convincingly created, so the researchers calculated the expected speed instead of using a measurement. Calculations suggest that above about 6 million times the Earth's atmospheric pressure, the speed limit of sound would be broken.

The role of fundamental constants in the maximum speed of sound results from how waves move through materials. Sound travels thanks to the electromagnetic interactions of electrons from neighboring atoms, which is where the fine-structure constant comes into play. And the proton-electron mass ratio is important because even though electrons are interacting, the nuclei of atoms move as a result.

The fine-structure constant and the proton-electron mass ratio are dimensionless constants, meaning that there are no units attached to them (so their value does not depend on any particular system of units). These dimensionless constants fascinate physicists, because values ​​are crucial to the existence of the universe as we know it (SN: 02/11/16). For example, if the fine-structure constant were to be significantly altered, stars, planets, and life could not form. But no one can explain why these important numbers have the values ​​they have.

“When I have sleepless nights, I sometimes think about it,” says Trachenko of Queen Mary University in London. Thus, he and his colleagues extend this enigma from the cosmic realm to more common concepts such as the speed of sound. Trachenko and co-author Vadim Veniaminovich Brazhkin of the Institute of High Pressure Physics in Troitsk, Russia, also reported a minimum possible viscosity for liquids in the April 24 scientific advances.

That viscosity limit depends on the Planck constant, a number at the heart of quantum mechanics, the mathematics that governs physics on very small scales. If Planck's constant were 100 times greater, says Trachenko, "water would be like honey and would probably be the end of life because the processes in the cells would not flow as efficiently."

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