Scale Relativity and Fractal Space-time: A New Approach to Unifying Relativity and Quantum Mechanics
World Scientific, 2011 - 742 psl.
This book provides a comprehensive survey of the state-of-the-art in the development of the theory of scale relativity and fractal space-time. It suggests an original solution to the disunified nature of the classical-quantum transition in physical systems, enabling quantum mechanics to be based on the principle of relativity provided this principle is extended to scale transformations of the reference system. In the framework of such a newly-generalized relativity theory (including position, orientation, motion and now scale transformations), the fundamental laws of physics may be given a general form that goes beyond and integrates the classical and the quantum regimes. A related concern of this book is the geometry of space-time, which is described as being fractal and nondifferentiable. It collects and organizes theoretical developments and applications in many fields, including physics, mathematics, astrophysics, cosmology and life sciences.
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applied behavior Chapter classical considered coordinates corresponds cosmological constant coupling covariant derivative defined described dilations Dirac Dirac equation distribution Einsteins electromagnetic electron energy equivalent Euler expected fluid fractal curve fractal dimension fractal fluctuation fractal space-time fundamental galaxies geodesic equation given gravitational integration invariant km/s length-scale log-periodic macroscopic mass metric momentum nondifferentiable obtained particle peaks physical Planck Planck scale planetary planets predicted principle of relativity probability density problem quantized quantum mechanics quantum potential quantum-like quaternionic ratio relation resolution result rotational scale dependence scale laws scale ratio scale relativistic scale relativity approach scale relativity framework scale relativity theory scale space scale transformations scale variables Schrödinger equation semi-major semi-major axis solar system solution space-time special scale relativity standard quantum mechanics stochastic structures tensor theoretical topological dimension transition velocity field wave function yields