Examples of Applications of an Invariant Statistical Theory of Field to Cosmology, Astrophysics, Hydrodynamics, Electrodynamics, and Photonics

Some examples of application of a scale-invariant statistical theory of fields to cosmology, astrophysics, hydrodynamics, electrodynamics, and photonics are described. The nature of quantum cosmology and the existence of multiverse based on definition of Planck temperature are examined. The origin of compressibility factor $${\text{Z}}:{\text{cVDW}} = 3/8$$ of Van der Waals fluid is identified. The definitions of dark energy, dark matter, and anti-matter and their role in density of universe are presented. Matter/anti-matter are identified as states of compression/rarefaction of Casimir vacuum. New perspectives concerning the nature of physical space quanta and non-Euclidean geometry are described. It is shown that physical space or Casimir vacuum is composed of a spectrum of volume elements containing a corresponding spectrum of atomic volumes in harmony with modern theories of quantum gravity. The universal constants of chaos theory $$(\updelta,\upalpha )$$ are related to universal gas constant and Avogadro-Loschmidt number of thermodynamics and to the number π of mathematics. Newton law of gravitational force is described in terms of the gradient of zero-point pressure of Casimir vacuum. Quantum mechanical foundation of turbulence is stablished and predicted velocity profiles for statistical fields of LED, LCD, LMD, and LAD covering spatial range of $${10}^{8}$$ are compared with experimental data available in the literature. Finally, transition and matching of solutions of statistical fields of different scales are examined.