Speed of sound from fundamental physical constants

Abstract

Two dimensionless fundamental physical constants, the fine structure constant a and the proton-to-electron mass ratio m_mpe, 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 that provides the upper bound for the speed of sound in condensed phases, vu. We find that v_cu = a (2_mmep)2_1, 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 the current understanding of how fundamental constants can impose new bounds on important physical properties.