An Invariant Statistical Theory of Field Applied to Hydrodynamic Foundation of Maxwell Electromagnetism, Quantum Gravity, and Quantum Cosmology

Applying an invariant statistical theory of field [1] and following Huygens [2] analogy between propagation of sound and light, propagation of light is shown to involve an exceedingly thin longitudinal component. Following Maxwell and Lorentz, an invariant hydrodynamic model of Maxwell equations is presented by identifying vector potential as velocity field A_β = v_β, and relating magnetic and electric field strengths to vorticity B_β = −▽xA_β and acceleration E_β = ∂A_β / ∂t_β = a_ρ thus leading to Lorentz force F_β = ρ_β (a_β.−2v_β x ω_β). Ratio of longitudinal (superluminal) to transverse wave propagation velocities [3] becomes C_L / C_T = [(λ+2η)/η]^1/2 = 2/3^1/2 when two Lame constants of Casimir vacuum of elastic physical space satisfy Stokes assumption λ + 2η/3 = 0. Elementary charge of electron is given as e ≈ 1843 m_e c/π ≈ 1.60215 x 10^-19 C with proton to electron mass ratio m_p/m_e ≈ 1943 from [1], whereas the classical ratio m_p/m_e ≈ 1836.2 leads to e ≈ 1.59624 x 10^-19 C. New perspectives on relativity theory and the nature of internal spacetime as opposed to external space and time [1], with the latter identified as Rovelli thermal time, and Dirac relativistic wave equation are described. Impact of the model on quantum cosmology, Maxwellian nature of speed distribution of galaxies, and Big Bang model of Lemaître primordial atom of our universe and its rotation in harmony with Gödel 1949 closed time-like solution of Einstein field equations with non-vanishing cosmological constant as well as Kerr solution of rotaing black holes are discussed. Thermodynamics of universe suggests possible relevance of Nordström scalar and Abraham vector theories of gravitation beside Einstein tensor theory [4]. The results are found to be in accordance with classical quantum gravity as dissipative deterministic system [5]. Following Helmholtz energy decomposition, dark energy and dark matter are respectively identified as internal energy U = 3NkT and potential energy PV - NkT of cosmic field [1]. Finally, some implications of the model to loop quantum gravity, Everett multiverse, and Newtonian law of gravitation expressed as gradient of zero-point pressure of Casimir vacuum F_g = −m_e▽p_e/ρ_e = m_eg are also discussed.
[1] Sohrab, S. H., Examples of Applications of an Invariant Statistical Theory of Field to Cosmology, Astrophysics, Hydrodynamics, Electrodynamics, and Photonics, C.H. Skiadas and Y. Dimotikalis (eds.), 15th Chaotic Modeling and Simulation international Conference, Springer Proceedings in Complexity, 2023.
[2] Huygens, C. Treatise on Light, p. 14, Dover, 2012.
[3] Achenbach, J. D., Wave Propagation in Elastic Solids, p.124, North-Holland, 1973.
[4] Nugayev, M. R., The Genesis of General Relativity: Interaction between Einstein’s, Abraham’s and Nordström’s Research Programs, Kairos Journal of Philosophy & Science 19, (2017).
[5] ‘t Hooft, G., Quantum Gravity as a Dissipative deterministic system, Class. Quantum Grav. 16, 3263 (1999)