Huygens Analogy Between Propagation of Light Waves in Ether and Sound Waves in Air

According to a scale-invariant model of Boltzmann statistical mechanics$^{\mathrm{1}}$ speed of light is identified as root-mean-square speed of photons in physical space identified as a compressible tachyon fluid, Planck compressible ether, that is de Broglie hidden thermostat or Casimir vacuum. In accordance with perceptions of Huygens$^{\mathrm{2}}$, propagation of light waves in ether is found to be analogous to that of sound waves in air with the ratio of \textit{longitudinal} to \textit{transverse} velocities given as $c_{l} /c_{t} =\sqrt 3 $. Photons are considered to have \textit{helical trajectories} due to their periodic (axial, angular, radial) motions along cylindrical ``\textit{strings}'' with three \textit{simultaneously independent} coordinates $(z,\theta ,r)$and by Boltzmann equipartition principle, have Wien$^{\mathrm{1}}$ velocities $(v_{wz} =c/\sqrt {3\mbox{\thinspace }} ,\thinspace v_{w\theta } =c/\sqrt {3\mbox{\thinspace }} ,\thinspace v_{wr} =c/\sqrt {3\mbox{\thinspace }} )$ leading to photon atomic internal energy $\hat{{u}}=m_{o} c^{2}=3kT$ and atomic enthalpy $\hat{{h}}=\hat{{u}}+p\hat{{v}}=mc^{2}=4kT$ hence Hasen\"{o}hrl $\gamma =4/3$ factor in $^{\mathrm{\thinspace }}m=(4/3)m_{o} $ (S. H. Sohrab, \textit{APS Bulletin, April}2017). With atomic potential energy $p\hat{{v}}=\hat{{u}}/3$ and ideal gas law $p=\rho RT$, speed of light waves $c=\sqrt {3kT/m_{o} } =\sqrt {3k{T}'/2m_{o} } $ in photon gas or Casimir vacuum is in close agreement with Laplace formula $c=\sqrt {\gamma R{T}'} $ for speed of sound waves in ideal gas$^{\mathrm{3}}$. $^{\mathrm{1}}$ Sohrab, S. H.,\textit{ ASME J. Energy Resources Technology} \textbf{138}: 1-12 (2016). $^{\mathrm{2}}$ Huygens, C., \textit{Treatise on Light}, p.14, Dover, 1912. $^{\mathrm{3}}$ Krout, K. A., and Sohrab, S. H., \textit{Int. J. Therm}odynamics \quad \textbf{19}: 29-34 (2016).