Some Implications of Invariant Model of Boltzmann Statistical Mechanics to Quantum Gravity

According to an invariant model of Boltzmann statistical mechanics, a factor of 10¹⁷ separates the scales of five major statistical fields of tachyon (graviton)-dynamics10^-35 m, electrodynamics 10^-18 m, hydrodynamics 10⁰ m, astrophysics 10¹⁸ m, and galactic-dynamics 10³⁵ m with “atomic” particles, graviton, electron, fluid-element, star, and galaxy [1] that are governed by an invariant Schrödinger equation. The nature of matter/anti-matter is described in terms of compression/rarefaction of physical space or Casimir vacuum identified as a compressible tachyonic fluid [1]. Origin of compressibility factor z_c = 3/8 of van der Waals fluid is identified. Spectrum of quantized volume elements of physical space is described in harmony with modern concepts of quantum gravity [2-5]. The model also leads to Everett multiverse at scale (l, λ, L) = (10²⁶, 10³⁵, 10⁴³), and entropy S = 4Nk of black hole with total thermal energy TS [1] in agreement with general relativistic statistical mechanics [4,5]. [1] Sohrab, S. H., ASME J. Energy Resources Technology 138, 1-12 (2016). [2] ‘t Hooft, G., Class. Quantum Grav. 16, 3263 (1999). [3] Ashtekar, A., Current Science 89, 12, 2064-2074 (2005). [4] Rovelli, C., Class. Quantum Grav.10, 1549-1566 (1993). [5] Major, S.A. and Setter, K. L., Class. Quantum Grav. 18, 5125-5142 (2001).