Speed of sound from fundamental physical constants

Abstract

Two dimensionless fundamental physical constants, the fine structure constant $\alpha$ and the proton-to-electron mass ratio $\frac{m_p}{m_e}$ are attributed a particular importance from the point of view of nuclear synthesis, formation of heavy elements, planets, and life-supporting structures. Here, we show that a combination of these two constants results in a new dimensionless constant which provides the upper bound for the speed of sound in condensed phases, $v_u$. We find that $\frac{v_u}{c}=\alpha {\left(\frac{m_e}{2m_p}\right)}^{\frac{1}{2}}$, where $c$ is the speed of light in vacuum. We support this result by a large set of experimental data and first principles computations for atomic hydrogen. Our result expands current understanding of how fundamental constants can impose new bounds on important physical properties.

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• Microscopic dynamics and Bose-Einstein condensation in liquid helium
• Thermal diffusivity and its lower bound in orthorhombic SnSe
• Regular black holes with improved energy conditions and their analogues in fluids
• Atom-in-jellium predictions of the shear modulus at high pressure
• A truly relativistic gravity mediated entanglement protocol using superpositions of rotational energies
• Fundamental physical constants, operation of physical phenomena and entropy increase
• Electronic and optical properties of crystalline nitrogen versus black phosphorus: A comparative first-principles study