Physicists just confirmed the upper limit for the speed of sound in the Universe

Einstein’s theory of special relativity gave us the speed limit of the Universe – that of light in a vacuum. But the absolute top speed of sound, through any medium, has been somewhat trickier to constrain.

It’s impossible to measure the speed of sound in every single material in existence, but scientists have now managed to pin down an upper limit based on fundamental constants, the universal parameters by which we understand the physics of the Universe.

That speed limit, according to the new calculations, is 36 kilometres per second (22 miles per second). That’s about twice the speed of sound travelling through diamond.

Both sound and light travel as waves, but they behave slightly differently. Visible light is a form of electromagnetic radiation, so-named because light waves consist of oscillating electric and magnetic fields. These fields generate a self-perpetuating electromagnetic wave that can travel in a vacuum – and its top speed is around 300,000 kilometres per second. Travelling through a medium, like water or an atmosphere, slows it down.

Sound is a mechanical wave, which is caused by a vibration in a medium. As the wave travels through the medium, that medium’s molecules collide with each other, transferring energy as they go.

Hence, the more rigid the medium – the more difficult it is to compress – the faster sound travels. For example, water has more tightly packed particles than air, and that’s partially why whales can communicate across such vast distances in the ocean.

In a rigid solid, like a diamond, sound can travel even faster. We leverage this property to study the inside of Earth when sound waves from earthquakes travel through it. We can even use it to understand the interiors of stars.

“Soundwaves in solids are already hugely important across many scientific fields,” said materials scientist Chris Pickard of the University of Cambridge in the UK.

“For example, seismologists use sound waves initiated by earthquakes deep in the Earth interior to understand the nature of seismic events and the properties of Earth composition. They’re also of interest to materials scientists because sound waves are related to important elastic properties including the ability to resist stress.”

By now, you can probably see the problem with constraining the speed of sound. How do we account for all the possible materials in the Universe in order to determine an absolute upper limit on the speed of sound?

This is where fundamental constants are useful. To calculate the speed limit of sound, a team of scientists from Queen Mary University of London, the University of Cambridge in the UK, and the Institute for High Pressure Physics in Russia found the speed limit depends on two fundamental constants.

These are the fine structure constant, which characterises the strength of electromagnetic interactions between elementary charged particles; and the proton-to-electron mass ratio, which is the rest mass of the proton divided by the rest mass of the electron.

“The finely tuned values of the fine structure constant and the proton-to-electron mass ratio, and the balance between them, govern nuclear reactions such as proton decay and nuclear synthesis in stars, leading to the creation of the essential biochemical elements, including carbon. This balance provides a narrow ‘habitable zone’ in the space where stars and planets can form and life-supporting molecular structures can emerge,” the researchers wrote in their paper.

“We show that a simple combination of the fine structure constant and the proton-to-electron mass ratio results in another dimensionless quantity that has an unexpected and specific implication for a key property of condensed phases – the speed at which waves travel in solids and liquids, or the speed of sound.”

To confirm their equation, the team experimentally measured the speed of sound in a large number of elemental solids and liquids, and returned results consistent with their predictions.

One specific prediction of the team’s theory is that the speed of sound should decrease with the mass of the atom. According to this prediction, sound should move fastest through solid atomic hydrogen – which can only exist at extremely high pressures, above around 1 million times Earth’s atmospheric pressure at sea level (100 gigapascals).

Obtaining a sample to verify this prediction experimentally would be extremely difficult, so the team relied on calculations based on the properties of solid atomic hydrogen between 250 and 1,000 gigapascals. And they found that, again, the results agreed with their predictions.

If the results of applying the team’s equation remain consistent, it could prove to be a valuable tool, not just for understanding individual materials, but the broader Universe.

“We believe the findings of this study,” said physicist Kostya Trachenko of Queen Mary University of London, “could have further scientific applications by helping us to find and understand limits of different properties such as viscosity and thermal conductivity relevant for high-temperature superconductivity, quark-gluon plasma and even black hole physics.”

The research has been published in Science Advances.

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