Kelvin Absolute Temperature Scale Identified as Length Scale and Related to de Broglie Thermal Wavelength.

Thermodynamic equilibrium between matter and radiation leads to de Broglie wavelength $\lambda_{d\beta } =h/m_{\beta } v_{r\beta } $ and frequency $\nu_{d\beta } =k/m_{\beta } v_{r\beta } $ of matter waves and stochastic definitions of Planck $h=h_{k} =m_{k} <\lambda_{rk} >c$ and Boltzmann $k=k_{k} =m_{k} <\nu_{rk} >c$ constants, $\lambda_{rk} \nu_{rk} =c$, that respectively relate to spatial ($\lambda )$ and temporal ($\nu )$ aspects of vacuum fluctuations. Photon mass$m_{k} =\sqrt {hk/c^{3}} $, $amu=\sqrt {hkc} =1/N^{o}$, and universal gas constant $R^{o}=N^{o}k=\sqrt {k/hc} $ result in internal $U_{k} =Nh\nu_{rk} =Nm_{k} c^{2}=3Nm_{k} v_{mpk}^{2} =3NkT$and potential $pV=uN\hat{{v}}/3=N\hat{{u}}/3=NkT$ energy of photon gas in \textit{Casimir vacuum} such that $H=TS=4NkT$. Therefore, Kelvin absolute thermodynamic temperature scale [degree K] is identified as length scale [meter] and related to most probable wavelength and de Broglie thermal wavelength as $T_{\beta } =\lambda_{mp\beta } =\lambda_{d\beta } /3$. Parallel to Wien displacement law obtained from Planck distribution, the displacement law $\lambda_{wS} T=c_{2} /\sqrt 3 $ is obtained from Maxwell$-$Boltzmann distribution of speed of ``photon clusters''. The propagation speeds of sound waves in ideal gas versus light waves in photon gas are described in terms of $v_{r\beta } $ in harmony with perceptions of Huygens. Newton formula for speed of long waves in canals $\sqrt {p/\rho } $ is modified to $\sqrt {gh} =\sqrt {\gamma p/\rho } $ in accordance with adiabatic theory of Laplace.