Another consequence is that clocks in different inertial frames will be observed to run at different rates. Scale relativity, fractal spacetime, and quantum mechanics. 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. The author discusses in detail reactualization of the principle of relativity and its application to scale transformations, physical laws which are explicitly. Spacetime may have fractal properties on a quantum scale 25 march 2009, by lisa zyga as scale decreases, the number of dimensions of kminkowski spacetime red. Download fractal spacetime and microphysics towards a theory. Even if you find yourself struggling, you should still be able to see and appreciate much that is new. 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 resolutionscale with which it is considered. 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. Fractal spacetime and microphysics towards a theory of scale relativity l. Scale relativity, fractal geometry, fractal matrix, quantization of the scalespace, biophysics, complex system. A new approach to unifying relativity and quantum mechanics. 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. As scale decreases, the number of dimensions of kminkowski spacetime red line, which is an example of a space with quantum group symmetry, decreases from four to three.
Is spacetime fractal and quantum coherent in the golden. That way we derive a rescaled energymass special relativity equation which includes quantum effects. In the next article, we will see how such transition can be described in the context of resolutionscalespace relativity. The idea of a fractal spacetime theory was first introduced by garnet ord, and by laurent nottale in a paper with jean schneider. In galilean scale relativity, spacetime was fractal with constant fractal dimensions. Time and space are two separate spaces and the movement in one space. The idea of a fractal spacetime theory was first introduced by.
Applications to quantum physics, cosmology and chaotic systems l. Spacetime physics introduction to special relativity taylor wheeler pdf by edwin taylor and john wheeler. Fractal spacetime, nondi erentiable geometry and scale. Theres also this paper, which seems to support my claims regarding frequency of cycles and volumesize fractal dimensions of time sequences fractal dimensions of time sequences i need also to mention about couple ineresting papers and articles, which although are referencing the notalle model of scale relativity, still seem to fit nicely to my claims regarding. Scale relativity scale relativity is a geometrical and fractal spacetime theory. Fractal spacetime, nondi erentiable geometry and scale relativity l. Pdf the theory of scale relativity 14 is an attempt to study the consequences of giving up the hypothesis of spacetime differentiability. Then the account of a new twovaluedness of the velocity allows one to suggest a geometric origin for the spin and to obtain the dirac equation 17. Spacetime may have fractal properties on a quantum scale. 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. For that purpose we fuse the large structure as well as the quantum scale of spacetime together and model it using certain calabiyau manifold. Everyday low prices and free delivery on eligible orders. This book provides a comprehensive survey of the development of the theory of scale relativity and fractal spacetime.
Scale relativity is a geometrical and fractal spacetime theory. First, lets consider carefully how we compare the running of two clocks. This theory leads i to a generalization of possible physically relevant fractal laws, written as partial differential equation acting in the space of. The geometrical framework for implementing einsteins general relativity is riemannian, curved spacetime. Nottale offers fractal spacetime as a method for establishing a relativity of scale. The applicability of fractal geometry to further understanding of diverse phenomena has proliferated since benoit mandelbrots seminal work in the 1970s 1. Pdf scale relativity and nondifferentiable fractal. Special relativity postulates generalized to scale are the basis of the two postulates of fractal physics theory.
A second one is that some main predictions are known consequences of the renormalization group mathematics. The point is that a quantum particle in nottales fractal spacetime has a path with a hausdorff dimension equal two. Spacetime physics introduction to special relativity. Fractal spacetime and noncommutative geometry in quantum. The resulting scale relativity theory is an extension of the concept of relativity found in special. Cantorian fractal spacetime fluctuations characterize quantumlike chaos in atmospheric flows. Scale relativity hypothesizes that quantum behavior comes from the fractal nature of spacetime. This varying fractal dimension remains however constrained by a loglorentz law. A new approach to unifying relativity and quantum mechanics on. This book provides a comprehensive survey of the d. Spacetime physics introduction to special relativity taylor wheeler pdf. Pdf download scale relativity and fractal spacetime a new approach to unifying relativity and quantum pdf online. Applications to quantum physics, cosmology and chaotic systems.
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. Spacetime diagrams can be used to visualize relativistic effects, such as why different observers perceive where and when events occur differently until the 20th century, it was assumed that the threedimensional. 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. Scale relativity and fractal spacetime is not an easy read, yet if you aced advanced calculus, you can keep up with it.
Fractal universe free physics help physics help forum. A more elaborate scalerelativity theory of fractal spacetime was proposed by laurent nottale, who was motivated by the failure of a large number of attempts to understand the quantum behavior in terms of standard differentiable geometry to look for a possible quantum geometry, i. Fractal dimension of quantum paths zooming on scale. Indeed, fractal geometries allow to study such nondifferentiable paths.
This is the first detailed account of a new approach to microphysics based on two leading ideas. A fractal is an infinitely intricate structure and only deceptively simple. This fractal interpretation of quantum mechanics has been further specified by abbot and wise1981, showing that the paths have a fractal dimension 2. A new approach to unifying relativity and quantum mechanics by laurent nottale isbn. Quadratic relativistic invariant and metric form in. In the subsequent section 5, the equations obtained in our first development of a theory of scale relativity are recalled. Independently, french astrophysicist laurent nottale proposed a scalerelativity theory of fractal spacetime 5. 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. 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. The notion of fractal spacetime has been also introduced by ord 5, who exhibited an explicit correspondence. Whatever your feelings regarding the math, it is my hope that people will be drawn to the sheer wonder of this book. The proposal to combine fractal spacetime theory with relativity principles was made by nottale. Similarly, scalerelativity may be given a geometric meaning, in terms of a nondifferentiable, fractal spacetime 1. We have shown in the preceding chapter how the principle of scale.
Download fractal spacetime and microphysics towards a theory of scale relativity ebook free. This means that the laws satisfy a logarithmic version of the lorentz transformation. We approach the problem of the mysteriously missing hypothetical dark energy of the universe from first principles. As scale decreases, the number of dimensions of kminkowski spacetime red line, which is an example of a space with quantum group symmetry, decreases from four to. 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. The last step in our construction consists in writing the field equations, i.
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