Fundamental Constants Put New Speedlimit On Sound
Under normal circumstances, sound waves cannot travel faster than 36 kilometers per second
Sound travels at different speeds through different materials - for example, it travels faster in water than air. But under conditions naturally occurring on Earth, no material can accommodate sound waves that exceed this ultimate limit, which is about 100 times the typical speed of sound traveling in the air.
The team's reasoning is based on known equations of physical and mathematical relationships. "Given the simplicity of the argument, it suggests that they 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 speed limit equation is based on fundamental constants,special numbers that rule the cosmos. One of those numbers, the speed of light, determines the ultimate speed limit of the universe - nothing can go faster. Another, known as the fine-structure constant, determines the force with which electrically charged particles push and pull each other. When combined with another constant - the ratio between the masses of the proton and electron - these numbers give the speed limit of the sound.
Sound waves, which consist of the vibrations of atoms or molecules, travel through a material as one particle displaces another. The speed of the wave depends on several factors, including the types of chemical bonds that hold the material together and how massive the atoms are. None of the previously measured sound speeds in a variety of liquids and solids exceed the proposed limit, condensed matter physicist Kostya Trachenko and colleagues discovered. The highest speed measured, in diamonds, was only about half the theoretical maximum. The limit only applies to solids and liquids at pressures typical of Earth. At pressures millions of times higher than the Earth's atmosphere, sound waves move faster and can exceed the limit.
One material that is expected to have a high speed of sound only exists at such high pressures: hydrogen is pressed hard enough to turn into a solid metal. That metal was never convincingly made, so instead of taking a measurement, the researchers calculated the expected speed. Above about 6 million times Earth's atmospheric pressure, the limit for the speed of sound would be exceeded, the calculations suggest.
The role of the fundamental constants in the maximum speed of sound stems from how the waves move through materials. Sound travels thanks to the electromagnetic interactions of the electrons of neighboring atoms, and that's where the fine structure constant comes into play. And the proton-electron mass ratio is important because although the electrons interact, the nuclei move through it.
The fine structure constant and the proton-electron mass ratio are dimensionless constants, which means that they have no units attached (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. For example, if the fine-structure constant had changed significantly, stars, planets and life would not have formed. But no one can explain why these all-important numbers have the values they have.
“When I have sleepless nights, I sometimes think about this,” says Trachenko, of Queen Mary University in London. So he and his colleagues are expanding this puzzle from the cosmic realm to more mundane 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 Science Advances.
That viscosity limit depends on Planck's constant, a number that is at the heart of quantum mechanics, the mathematics that controls physics on a very small scale. If Planck's constant were 100 times greater, Trachenko says, "water would be like honey, and that would probably be the end of life, because the processes in cells wouldn't run as efficiently."