Quantum Nature of Physical Space, Aristotle Fifth Element or Casimir Vacuum, Connects Constants of Chaos Theory ($\delta $, $\alpha )$ in Mathematics to Universal Gas Constant and Atomic Mass Unit ($R^{\mathrm{o}}$, \textit{amu}) in Physics

Physical space, Aristotle fifth element, Casimir vacuum, the primordial void, or ``\textit{Tohu Vavohu}'' meaning \textit{total chaos} [1], is identified as compressible tachyon fluid, Planck compressible ether, and Lorentz-FitzGerald contractions become causal (Pauli, 1958) in accordance with Poincar\'{e}-Lorentz \textit{dynamic} versus Einstein \textit{kinematic} theory of relativity [1]. Closing the gap between radiation and gas theories results in space composed of a spectrum of photon-clusters, Planck ``quantum spheres of action'' (Darrigol, 1991), with finite gravitational viscosity [2]. Normalized spacing between nontrivial zeros of Riemann zeta function and eigenvalues of GUE (Odlyzko, 1987) are found to follow \textit{Normalized Maxwell-Boltzmann} distribution. Thus, numbers in mathematics are related to counting photons. Constants of chaos theory $\delta =(1+R^{o})/2=4.6692$ and $\alpha =2+(2m_{k} c^{2}-0.5\times 10^{-26})/(m_{k} c^{2}-0.5\times 10^{-26})\approx 2.502904$ are related to De Pretto number 8338 J/kcal (universal gas constant $R^{\mathrm{o}} \quad =$ 8338.4 J/kmol-m) and $amu=m_{k} c^{2}=\sqrt {hkc} $. When \textit{physical space} is identified as a \textit{fluid} with energy spectrum given by Schr\"{o}dinger equation of quantum mechanics, in view of Heisenberg \textit{matrix mechanics}, it must be described by \textit{noncommutative geometry} [3]. $^{\mathrm{1}}$ Sohrab, S. H.,\textit{ Int. J. Thermodynamics} \textbf{17}, 233 (2014). $^{\mathrm{2}}$ `t Hooft, G., \textit{Class. Quantum Grav. }\textbf{16}, 3263 (1999). $^{\mathrm{3}}$ Connes, A., \textit{Lett. Math. Phys.} \textbf{34}, 238 (1995).