Invariant model of statistical mechanics, quantum mechanics, and physical nature of space and time

Some of the implications of a scale invariant model of statistical mechanics to the physical and quantum nature of both space and time as well as quantum mechanics are described. At thermodynamic equilibrium, the velocity, energy, and speed of particles are shown to be governed by invariant Gaussian, Planck, and Maxwell-Boltzmann distribution functions. Physical space or Casimir vacuum is identified as a compressible tachyon fluid, Planck compressible ether, such that Lorentz-FitzGerald contractions become causal (Pauli) in accordance with Poincare-Lorentz dynamic theory of relativity as opposed to Einstein kinematic theory of relativity. Also, some of the implications of the model to the physical foundation of Riemann hypothesis are discussed. In particular, normalized spacing between non-trivial zeroes of Riemann zeta function are found to follow normalized Maxwell-Boltzmann distribution function.