Nottale entitled scale relativity and nondifferentiable fractal spacetime 7. This book provides a comprehensive survey of the d. Cantorian fractal spacetime, quantumlike chaos and scale relativity in atmospheric flows. A general systems theory for chaos, quantum mechanics and gravity for dynamical systems of all spacetime scales contents 1. The fundamental principle upon which we rely is that of scale relativity, which generalizes to scale transformations einsteins principle of relativity. Geometric theory of gauge fields in scale relativity. This varying fractal dimension remains however constrained by a loglorentz law.
Introduction the theory of scalerelativity is an attempt to extend todays theories of relativity, by applying the principle of relativity not only to motion transformations, but also to scale transformations of the reference system. Whatever your feelings regarding the math, it is my hope that people will be drawn to the sheer wonder of this book. Scale relativity and nondi erentiable fractal spacetime. Article pdf available in foundations of science 152 december 2008 with 187 reads. Pdf download scale relativity and fractal spacetime a new approach to unifying relativity and quantum pdf online. The notion of fractal spacetime has been also introduced by ord 5, who exhibited an explicit correspondence. He defines the term fractal as divergent with decreasing scale nottale 1993, 20 building on mandelbrots definition which highlights irregularity at all scales creating a density described by fractal dimensionality. Feb 11, 2011 scale relativity and fractal spacetime book.
The theory of scale relativity is an extension of the principle of relativity to scale transformations of the reference system, in a fractal geometry framework where coordinates become explicitly. Quadratic relativistic invariant and metric form in. Relativity sprang out from laurent nottales scale relativity 5. The idea that spacetime is fractal originated with canadian mathematician garnet ord 4 who coined the term fractal spacetime, using a model in which particles are confined to move on fractal trajectories. A fractal matrix for organization in nature laurent nottale. Indeed, fractal geometries allow to study such nondifferentiable paths. Then we recall that the principle of scale relativity leads one to generalize the standard galilean laws of scale transformation into a lorentzian form, in which the planck lengthscale becomes invariant under dilations, and so plays for scale laws the same role as played by the velocity of light. A new approach to unifying relativity and quantum mechanics find, read and cite all the research you. It suggests an original solution to the disunified nature of the classicalquantum transition in physical systems, enabling the basis of quantum mechanics on the principle of relativity, provided this principle is extended to scale transformations of the reference system.
Independently, french astrophysicist laurent nottale proposed a scalerelativity theory of fractal spacetime 5. This theory leads i to a generalization of possible physically relevant fractal laws, written as partial differential equation acting in the space of scales, and ii to a new geometric. In a remarkable essay 1 the cofounding fa ther of heterotic superstring theory and strong interaction. May 16, 2004 hi all, i was wondering if anyone of you has read the book of laurent nottale fractal spacetime and microphysics.
Scale relativity, fractal spacetime, and quantum mechanics. Cantorian fractal spacetime fluctuations characterize quantumlike chaos in atmospheric flows. A new approach to unifying relativity and quantum mechanics in pdf or epub format and read it directly on your mobile phone, computer or any device. This means that the laws satisfy a logarithmic version of the lorentz transformation. Application to quantum physics, cosmology and chaotic systems. 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 spacetime. Hi all, i was wondering if anyone of you has read the book of laurent nottale fractal spacetime and microphysics. May 14, 2008 taking only e8, you need at least 162 8 dimensions for spacetime embedding because its gossett is made of 8dimensional vectors called octonions, the wellknown generalization of complex number. The theory of scale relativity is a new approach to the. The more wrinkles the higher the fractal dimension. The geometrical framework for implementing einsteins general relativity is riemannian, curved spacetime. Proponents have made wideranging claims on its behalf, including applications to the existence of dark matter and the formation of planetary systems, as well as to biology. That way we derive an effective quantum gravity energymass relation and compute a dark energy density in complete agreement with all cosmological measurements, specifically wmap and type 1a supernova.
The hypothesis of fractal invariance is very similar to the socalled scale relativity principle pioneered by. Huge list of fractals in physics complete book fractals in physics fractal patterns seen in semiconductor magnetismscale relativity brownian motion, thus heatenergy is fractalcheck if true. Independently, french astrophysicist laurent nottale proposed a. Everyday low prices and free delivery on eligible orders. After having related the fractal and renormalization group. Fractal spacetime, nondi erentiable geometry and scale relativity l. We have demonstrated with scale relativity that going from scale invariance to scale covariance provides us with fundamental scales.
In this paper, we approach the problem of dm from the viewpoint of nottales theory of scale relativity 101 relying on a fractal spacetime. It suggests an original solution to the disunified nature of the classicalquantum transition in physical systems, enabling the basis of quantum mechanics on the principle of relativity, provided this principle is extended to. Fractal spacetime and microphysics world scientific. The resulting scale relativity theory is an extension of the concept of relativity found in special. A new approach to unifying relativity and quantum mechanics by laurent nottale isbn. Spacetime may have fractal properties on a quantum scale. So, both in the case of a brownian particle and in the case of a quantum particle, we see a transition in the fractal dimension of the dynamical path depending on the resolution scale with which it is considered. A general systems theory for chaos, quantum mechanics.
Taking only e8, you need at least 162 8 dimensions for spacetime embedding because its gossett is made of 8dimensional vectors called octonions, the wellknown generalization of complex number. Applications to quantum physics, cosmology and chaotic systems l. The macroscale atmospheric flow structure behaves as a unified whole quantum system, where the superimposition of a continuum of eddies results in the. Author links open overlay panel pierrehenri chavanis. A new approach to unifying relativity and quantum mechanics in pdf or epub format and read it directly on. The fundamental principle upon which we rely is that of scale relativity, which generalizes einsteins principle of relativity to scale transformations. A rindlerkam spacetime geometry and scaling the planck. Applications to quantum physics, cosmology and chaotic systems. Introduced by laurent nottale, it claims to extend the concept of relativity to physical scales of time, length, energy, or momentum. Mar 25, 2009 spacetime may have fractal properties on a quantum scale. A variation of the fractal dimension with scale is more difficult to represent graphically as it implies to visualize an object at different resolutions. Scale relativity is a proposal for a theory of physics based on fractal spacetime.
Fractal spacetime and microphysics towards a theory of scale relativity l. This is not only a mathematical game, since objects may look very different depending on the resolution with which we look at them. This fractal interpretation of quantum mechanics has been further specified by abbot and wise1981, showing that the paths have a fractal dimension 2. Fractal dimension of quantum paths zooming on scale relativity. Nottale offers fractal spacetime as a method for establishing a relativity of scale.
Scale relativity and fractal spacetime structures in atmospheric flows 171 4. From fractal spacetime to relativistic quantum mechanics. Scale relativity and fractal spacetime world scientific. We introduce an ultra high energy combined kamrindler fractal spacetime quantum manifold, which increasingly resembles einsteins smooth relativity spacetime, with decreasing energy. Introduction abandonment of the hypothesis of spacetime differentiability towards a fractal spacetime relativity and scale covariance scale differential equations quantumlike induced dynamics.
Scale relativity and fractal spacetime is not an easy read, yet if you aced advanced calculus, you can keep up with it. Garnet ords original work on fractal random walks 7. Time and space are two separate spaces and the movement in one space. Scale relativity is a geometrical and fractal spacetime theory. Download the ebook scale relativity and fractal spacetime. Similarly, scalerelativity may be given a geometric meaning, in terms of a nondifferentiable, fractal spacetime 1.
Pdf cantorian fractal spacetime, quantumlike chaos and. However, nottale works in 4 spacetime dimensions only and he has never claimed that his scale relativity is exact. Scale relativity, nondifferentiability and fractal spacetime. We have shown in the preceding chapter how the principle of scale. Scale relativity hypothesizes that quantum behavior comes from the fractal nature of spacetime. The second idea is that of scaling the planck scale and working with topological quantities. This book provides a comprehensive survey of the development of the theory of scale relativity and fractal spacetime. The theory of scale relativity is a new approach to the problem of the origin of fundamental scales and of scaling laws in physics, that consists of generalizing einsteins principle of relativity up to now applied to motion laws to scale transformations. In galilean scale relativity, spacetime was fractal with constant fractal dimensions. The idea of a fractal spacetime theory was first introduced by garnet ord, and by laurent nottale in a paper with jean schneider. Jan 08, 2016 read or download pdf online here scale relativity and fractal spacetime. Section 7 is devoted to the discussion and conclusion.