Abstract

We present a kinetic-theory estimate of the mass of a particle and apply it to the neutrino. The method rests on two relations of the kinetic theory of gases, recently placed on a rigorous binary-collision footing: a mass—speed relation $m_1u_1^2=m_2u_2^2$, linking two coexisting species through their root-mean-square collision speeds, and a wave--speed relation $u=c\sqrt{3/\gamma}$, converting a medium's propagation speed into its particle collision speed. If neutrinos and ordinary gas molecules are modelled as two species of a common kinetic system obeying Avogadro's law, these relations fix the neutrino mass at $0.025$--$0.042\ \mathrm{eV}/c^2$---at the level of the tightest current neutrino-mass bounds and, as we show, independent of the reference gas. The argument uses the standard control volumes (``boxes'') of the kinetic theory of gases and is a statistical-mechanics estimate: it requires neither the physical confinement of neutrinos nor any direct measurement of neutrino pressure. The estimate is linear in the assumed shared temperature; we set out the governing assumptions explicitly---including the reference temperature and the classical (non-relativistic) kinetic treatment---and identify their relaxation, and the resulting refinements, as directions for future work.

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