Fractal Space-Time and Microphysics : Towards a Theory of Scale Relativity

Towards a Theory of Scale Relativity

By: Laurent Nottale

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Hardcover | 1 December 1992

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Hardcover
348 Pages

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22.86 x 15.24 x 2.54

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This is the first detailed account of a new approach to microphysics based on two leading ideas: that the explicit dependence of physical laws on scale encountered in quantum physics, is the manifestation of a fundamental principle of nature, namely, scale relativity (this generalizes Einstein's principle of (motion) relativity to scale transformations); and that the mathematical achievement of this principle needs the introduction of a nondifferentiable space-time varying with resolution, i.e. characterized by its fractal properties. The author discusses in detail reactualization of the principle of relativity and its application to scale transformations, physical laws which are explicitly scale dependent, and fractals as a new geometric description of space-time.

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Non-Fiction Science Physics Relativity Physics Quantum Physics & Quantum Mechanics & Quantum Field Theory Mathematics Geometry Fractal Geometry Applied Mathematics Chaos Theory Booktopia Publisher Services World Scientific Publishing

Preface
General Introduction	p. 1
Relativity and Quantum Physics	p. 6
On the Present State of Fundamental Physics	p. 6
The Need for a New Extension of Principle of Relativity	p. 16
Relativity of Scales	p. 21
On the Nature of Quantum Space-Time	p. 26
From Fractal Objects to Fractal Spaces	p. 33
Basics of Fractals	p. 33
Where Do Fractals Come from?	p. 39
Fractal Curves in a Plane	p. 49
Non-Standard Analysis and Fractals	p. 55
Fractal Curves in Space	p. 61
Fractal Surfaces	p. 64
Fractal Derivative	p. 69
Fractal Functions	p. 75
Variable Fractal Dimension	p. 80
Towards the Definition of a Fractal Space-Time	p. 81
Fractal Dimension of a Quantum Path	p. 89
Fractal Dimension of a Nonrelativistic Quantum Path	p. 93
Fractal Dimension of a Quantum Relativistic Path	p. 98
Fractal Dimension of Time	p. 103
The Fractal Structure of Quantum Space-Time	p. 110
On Quantum Properties of Fractals	p. 110
Derivation of Heisenberg's Relations in Fractal Space-Time	p. 112
Classical Quantities as Fractal Structures	p. 118
Emergence of Spin from Fractalization	p. 124
Geodesical Interpretation of Wave-Particle Duality	p. 127
Non-differentiable Space and Stochastic Quantum Mechanics	p. 135
Classical-Quantum Transformation	p. 153
Microscopic Reversibility of Fractal Time	p. 162
Fractals and Quantum Electrodynamics	p. 164
Possible Observable Implications	p. 171
Link to General Relativity	p. 182
Towards a Special Theory of Scale Relativity	p. 194
Principle of Scale Relativity	p. 194
Masses, Charges and Renormalization Group	p. 198
Galilean Scale Relativity	p. 220
A New Derivation of Lorentz Transformation	p. 224
Lorentzian Scale Transformation	p. 229
Breaking of Scale Relativity	p. 232
On the Nature of Planck Scale	p. 235
The New Scale-Relativistic Transformation	p. 237
Scale-Relativistic Mechanics	p. 240
Implications for High Energy Physics	p. 252
On the Nature of Charges and Masses	p. 262
Prospects	p. 283
Scale Relativity and Cosmology	p. 283
Beyond Chaos	p. 307
Index	p. 331
Table of Contents provided by Blackwell. All Rights Reserved.

Fractal Space-Time and Microphysics : Towards a Theory of Scale Relativity

Towards a Theory of Scale Relativity

At a Glance

Hardcover

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How to return your order

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