Using nottales theory of scale relativity relying on a fractal spacetime, we derive a generalized schr\odinger equation taking into account the interaction of the system with the external. Then there is a return to a non fractal path in the ballistic regime. In physics, spacetime is any mathematical model which fuses the three dimensions of space and the one dimension of time into a single fourdimensional manifold. This is the first detailed account of a new approach to microphysics based on two leading ideas. A new approach to unifying relativity and quantum mechanics find, read and cite all the research you.
Cantorian fractal spacetime fluctuations characterize quantumlike chaos in atmospheric flows. Dec 05, 2017 starting at the largest sampling time, there is a transition from fractal drift regime to the non fractal diffusion regime. The theory of scale relativity is an attempt to study the consequences of giving up the hypothesis of spacetime differentiability. Read or download pdf online here scale relativity and fractal spacetime. Introduced by laurent nottale, it claims to extend the concept of relativity to physical scales of time, length, energy, or momentum. Even if you find yourself struggling, you should still be able to see and appreciate much that is new. Fractal dimension of quantum paths zooming on scale relativity.
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. Everyday low prices and free delivery on eligible orders. Mar 25, 2009 spacetime may have fractal properties on a quantum scale. 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. However, nottale works in 4 spacetime dimensions only and he has never claimed that his scale relativity is exact. The idea of a fractal spacetime theory was first introduced by garnet ord, and by laurent nottale in a paper with. 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. A new approach to unifying relativity and quantum mechanics in pdf or epub format and read it directly on. Whatever your feelings regarding the math, it is my hope that people will be drawn to the sheer wonder of this book.
A new approach to unifying relativity and quantum mechanics by laurent nottale isbn. Time and space are two separate spaces and the movement in one space. That we always pick the same scale and this is a problem somehow. Finally, we can anticipate a return to a fractal regime when the sampling is so fine as to reveal the quantum nature of the dynamics. Scale relativity scale relativity is a geometrical and fractal spacetime theory. Introduction and background information we start the present analysis of determining the dark energy density of the cosmos 112 in a reverse order to the heading of the paper at hand by recalling an important result of nottales scale relativity, namely that 11. Spacetime may have fractal properties on a quantum scale. The first postulate assumes absolute uniform scale cannot be detected. Hi all, i was wondering if anyone of you has read the book of laurent nottale fractal spacetime and microphysics. 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. The golden ratio is at the core of our fractal universe of infinite dimensions that looks and feels 4dimensional. This includes predictions in physics and cosmology value of the qcd coupling and of. Keck science center, the claremont colleges a spacetime diagram shows the history of objects moving through space usually in just one dimension. With gr, you can say that spacetime is curved and this explains why different masses follow the same paths, and that assuming spacetime is flat is an assumption not based on a principle.
Fractal spacetime, nondi erentiable geometry and scale relativity l. We have shown in the preceding chapter how the principle of scale. 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. A fractal matrix for organization in nature laurent nottale. In the framework of such a newlygeneralized relativity theory including position, orientation, motion and now scale transformations, the fundamental laws of.
Fractal spacetime and microphysics towards a theory of scale. Scale relativity and nondifferentiable fractal spacetime. Naschie, a rindlerkam spacetime geometry and scaling the planck scale solves quantum relativity and explains dark energy, international journal of astronomy and astrophysics, vol. One can show that a continuous but nondifferentiable spacetime is necessarily fractal here the word fractal is taken in a general meaning, as defining a set, object or space that shows structures at all scales, or on a wide range of scales. Fractal spacetime and microphysics towards a theory of scale relativity l. A new approach to unifying relativity and quantum mechanics at. Download the ebook scale relativity and fractal spacetime. New results in fractal spacetime theory are established. This book provides a comprehensive survey of the d. Spacetime diagrams can be used to visualize relativistic effects, such as why different observers perceive where and when events occur differently. Fractal dimension of a brownian path zooming on scale. This book provides a comprehensive survey of the development of the theory of scale relativity and fractal spacetime.
Scale relativity and fractal spacetime world scientific. Pdf cantorian fractal spacetime, quantumlike chaos and. Scale relativity is a proposal for a theory of physics based on fractal spacetime. 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. From chernsimon, holography and scale relativity to dark energy. One of the best recommended books to begin learning the subject. He is the author and inventor of the theory of scale relativity, which aims to unify quantum physics and relativity. A rindlerkam spacetime geometry and scaling the planck scale.
A horizontal line parallel to the position axis xaxis is a line of simultaneity. Scale relativity and fractal spacetime is not an easy read, yet if you aced advanced calculus, you can keep up with it. In a remarkable essay 1 the cofounding fa ther of heterotic superstring theory and strong interaction. Applications to quantum physics, cosmology and chaotic systems l. 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. A speci c point on a spacetime diagram is called an \event. Jan 22, 2016 scale relativity scale relativity is a geometrical and fractal spacetime theory. 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. Cantorian fractal spacetime, quantumlike chaos and scale. In this paper, we approach the problem of dm from the viewpoint of nottales theory of scale relativity 101 relying on a fractal spacetime. Spacetime physics introduction to special relativity taylor. Malinowski basf dispersions and resins monaca, pennsylvania usa abstract this first article, in a series of five, introduces fractal physics theory, which is founded on extending the two special relativity postulates to scale. Special relativityspacetime wikibooks, open books for an. Independently, french astrophysicist laurent nottale proposed a scalerelativity theory of fractal spacetime 5.
May 16, 2004 related threads on fractal spacetime and microphysics. It will be seen that the line of simultaneity differs between galilean and special. Fractal lqg spacetime and renormalization of the immirzi parameter. Cantorian fractal spacetime, quantumlike chaos and scale relativity in atmospheric flows. Apr 16, 2017 thus, a world line is really a line in spacetime, while an event is a point in spacetime. Golden geometry of einfinity fractal spacetime story of phi part 5. 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.
Pdf scale relativity, fractal spacetime and gravitational. Spacetime diagrams, spacetime, geometry introducing spacetime classically we have an absolute time, which can be viewed as a onedimensional euclidean space, r, plus an absolute threedimensional space, r3. Fractal spacetime, nondi erentiable geometry and scale. Scale relativity, fractal spacetime and quantum mechanics. The second idea is that of scaling the planck scale and working with topological quantities. Laurent nottale born 29 july 1952 is an astrophysicist, a retired director of research at cnrs, and a researcher at the paris observatory. Feb 11, 2011 scale relativity and fractal spacetime book.
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