The Mathematical Principles of Scale Relativity Physics The Concept of Interpretation

The Mathematical Principles of Scale Relativity Physics: The Concept of Interpretation explores and builds upon the principles of Laurent Nottale’s scale relativity. The authors address a variety of problems encountered by researchers studying the dynamics of physical systems. It explores Madelung fluid from a wave mechanics point of view, showing that confinement and asymptotic freedom are the fundamental laws of modern natural philosophy. It then probes Nottale’s scale transition description, offering a sound mathematical principle based on continuous group theory. The book provides a comprehensive overview of the matter to the reader via a generalization of relativity, a theory of colors, and classical electrodynamics. Key Features: Develops the concept of scale relativity interpreted according to its initial definition enticed by the birth of wave and quantum mechanics Provides the fundamental equations necessary for interpretation of matter, describing the ensembles of free particles according to the concepts of confinement and asymptotic freedom Establishes a natural connection between the Newtonian forces and the Planck’s law from the point of view of space and time scale transition: both are expressions of invariance to scale transition The work will be of great interest to graduate students, doctoral candidates, and academic researchers working in mathematics and physics.

Chapter 1. Introduction Chapter 2. Madelung Fluid Dynamics Chapter 3. De Broglie’s Interpretation of Wave Function Chapter 4. The Planetary Model as a Dynamical Kepler Problem Chapter 5. The Light in a Schrödinger Apprenticeship Chapter 6. The Wave Theory of Geometric Phase Chapter 7. The Physical Point of View in the Theory of Surfaces Chapter 8. Nonconstant Curvature Chapter 9. The Nonstationary Description of Matter Chapter 10. The Idea of Continuity in Fluid Dynamics Chapter 11. A Hertz-type Labelling in a Madelung Fluid Chapter 12. Theory of Nikolai Alexandrovich Chernikov Conclusions: Concept of Interpretation and Necessary Further Elaborations References Subject index

Nicolae Mazilu is a researcher at the Institute of Nuclear Research, Romania, an associate researcher at the University of Akron, USA, and recently retired as a Senior Project Engineer at Bridgestone/Firestone, Inc., USA; Maricel Agop is an associate researcher at the Technical University Gheorghe Asachi and Al.I.Cuza University, Romania: Ioan Merches is Professor Emeritus, at Al.I.Cuza” University, Iasi, Romania.