## Abstract

A scale invariant model of statistical mechanics is applied to describe a modified statistical theory of turbulence and its quantum mechanical foundations. Hierarchies of statistical fields from cosmic to Planck scales are described. Energy spectrum of equilibrium isotropic turbulence is shown to follow Planck law. Predicted velocity profiles of turbulent boundary layer over a flat plate at four consecutive scales of LED, LCD, LMD, and LAD are shown to be in close agreement with the experimental observations in the literature. The physical and quantum nature of time is described and a scale-invariant definition of time is presented and its relativistic behavior is examined. New paradigms for physical foundations of quantum mechanics as well as derivation of Dirac relativistic wave equation are introduced.

Original language | English (US) |
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Pages (from-to) | 734-756 |

Number of pages | 23 |

Journal | WSEAS Transactions on Mathematics |

Volume | 9 |

Issue number | 9 |

State | Published - Sep 2010 |

## Keywords

- Dirac and schrödinger equations
- Quantum mechanics
- Relativity
- TOE
- Theory of turbulence

## ASJC Scopus subject areas

- Algebra and Number Theory
- Endocrinology, Diabetes and Metabolism
- Statistics and Probability
- Discrete Mathematics and Combinatorics
- Control and Optimization
- Management Science and Operations Research
- Computational Mathematics
- Applied Mathematics