The Mathematical Principles of Scale Relativity Physics: The Concept of Interpretation, 1st Edition (Hardback) book cover

The Mathematical Principles of Scale Relativity Physics

The Concept of Interpretation, 1st Edition

By Nicolae Mazilu, Maricel Agop, Ioan Merches

CRC Press

252 pages

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Hardback: 9780367349349
pub: 2019-09-24
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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.

Table of Contents

Introduction. Madelung Fluid Dynamics. De Broglie’s Interpretation of Wave Function . The Planetary Model as a Dynamical Kepler Problem. The Light in a Schro¨dinger Apprenticeship. The Wave Theory of Geometric Phase. The Physical Point of View in the Theory of Surfaces. Nonconstant Curvature. The Nonstationary Description of Matter. The Idea of Continuity in Fluid Dynamics. A Hertz-type Labelling in a Madelung Fluid. Theory of Nikolai Alexandrovich Chernikov. Conclusions with a Briefing on Necessary Further Elaborations. References.

About the Authors

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.

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Arithmetic
SCIENCE / Chemistry / General
SCIENCE / Chemistry / Physical & Theoretical
SCIENCE / Mathematical Physics