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.
- 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.
Table of Contents
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
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.