Lobachevsky-Poincaré-Dirac Space and Quantum Nature of Internal Spacetime versus External Space and Time in Cosmology

Some implications of an invariant model of Boltzmann statistical mechanics to thermodynamics [1] and quantum nature of space and time are described. Kelvin absolute temperature is identified as Wien wavelength λ_wb of thermal oscillations (kT_β = kλ_wβ  = m_β(v_wβ)² , v_wβ = λ_wβν_wβ) and applied to introduce internal measures of space and time called spacetime (λ_wβ-1, τ_wβ-1) and external measures of space and time (x_β = N_xλ_wβ-1, t_β = N_tτ_wβ-1). Because of its hyperbolic geometry, its discrete fabric, and its stochastic atomic motions, physical space is called Lobachevsky-Poincaré-Dirac-Space. When Casimir vacuum is identified as Planck compressible ether, Lorentz-FitzGerald contractions become causal, Pauli [2], in accordance with Poincaré-Lorentz dynamic as opposed to Einstein kinematic theory of relativity [3]. Mach, Lorentz, Michelson numbers (v/c_m, v/c_e, v/c_k) lead to a unified description of supersonic, super-electronic, and superluminal flows involving (Mach, Lorentz, Poincaré-Minkowski) cones.  The “time problem” of GTR and Gödel closed time-like world lines are also discussed.

¹ Sohrab, S. H., ASME J. Energy Resoures Technology 138: 1-12 (2016).

² Pauli, W., Theory of Relativity, Dover (1958).

³ Sohrab, S. H., Chaotic Modeling and Simulation (CMSIM) 3, 231-245 (2016).