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, 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. The theory of scale relativity extends einsteins principle of relativity to scale. Another consequence is that clocks in different inertial frames will be observed to run at different rates. Spacetime physics introduction to special relativity taylor wheeler pdf. Read online and download pdf ebook scale relativity and fractal space time a new approach to unifying relativity and quantum mechanics. Scale relativity and fractal spacetime is not an easy read, yet if you aced advanced calculus, you can keep up with it. Pdf on jan 1, 1993, laurent nottale and others published fractal spacetime and microphysics. General relativity and the curvature of spacetime explained. Isbn 1848166508 fractal spacetime and microphysics, editions world scientific, may 1993 isbn 9810208782 the reference book about scale relativity theory. Spacetime physics introduction to special relativity taylor. Everyday low prices and free delivery on eligible orders. On the other hand, for a specialized and complicated subject like general relativity, the emphasis is i think not on being able to do something but on being able to understand something, and there, copying rote problems, like computing every.
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 foundation of quantum mechanics and gauge field theories and their possible generalisations. If scale relativity reproduces the lay person idea this makes the theory appealing to lay people and unappealing to physicists. A horizontal line parallel to the position axis xaxis is a line of simultaneity. On the other hand, for a specialized and complicated subject like general relativity, the emphasis is i think not on being able to do something but on being able to understand something, and there, copying rote problems, like computing every entry in some threedimensional tensor, is fine, whereas copying the much more difficult proofs.
A fractal matrix for organization in nature laurent nottale. 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. A new approach to unifying relativity and quantum mechanics.
It is free of quantum field theory anomalies and is inherently scale invariant because it is geometry without ordinary points. A third article is planned to present a profound and surprising extension of the language to incorporate general relativity. 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 and fractal spacetime world scientificimperial college press, 2011, 764 pp, gbp105.
In scalerelativity therefore, the underlying fractal geometry of spacetime plays the role. Cantorian fractal spacetime, quantumlike chaos and scale. Even if you find yourself struggling, you should still be able to see and appreciate much that is new. The largescale structure of spacetime cambridge, 1973. If youd like some information on the history and context of general relativity and the measurements weve made that tell us its true, check out these great articles by ethan siegal and brian koberlein. Fractality field in the theory of scale relativity. Cantorian fractal spacetime fluctuations characterize quantumlike chaos in atmospheric flows. World scientificimperial college press, 2011, 764 pp, gbp105.
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. Fractal spacetime and microphysics towards a theory of scale relativity l. It will be seen that the line of simultaneity differs between galilean and special. A new approach to unifying relativity and quantum mechanics by laurent nottale isbn. 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.
Euclidean alternative to minkowski spacetime diagram. Jan 22, 2016 scale relativity scale relativity is a geometrical and fractal spacetime theory. Get scale relativity and fractal space time a new approach to unifying relativity and quantum mechanics pdf file for free from our online library created date. Carroll institute for theoretical physics university of california. Applications to quantum physics, cosmology and chaotic systems, chaos. In the next article, we will see how such transition can be described in the context of resolution scale space relativity. May 14, 2008 the point is that a quantum particle in nottales fractal spacetime has a path with a hausdorff dimension equal two. The status and programs of the new relativity theory carlos castro. Spacetime may have fractal properties on a quantum scale. Applications to quantum physics, cosmology and chaotic systems l. Keck science center, the claremont colleges a spacetime diagram shows the history of objects moving through space usually in just one dimension. A second one is that some main predictions are known consequences of the renormalization group mathematics.
These include a straightforwardderivation of the black hole entropyarearelation and its. We have shown in the preceding chapter how the principle of scale. Independently, french astrophysicist laurent nottale proposed a. Spacetime physics introduction to special relativity. General relativity generalizes special relativity and refines newtons law of universal gravitation, providing a unified description of gravity as a geometric property of space and. Fractal spacetime and microphysics towards a theory of scale. Then there is a return to a nonfractal path in the ballistic regime. May 16, 2004 one, generic to fractal science, is vagueness. Mar 25, 2009 spacetime may have fractal properties on a quantum scale. In scalerelativity therefore, the underlying fractal geometry of spacetime plays the role of a universal structuring field.
To this purpose, covariant derivatives are constructed that implement the various e. A new approach to unifying relativity and quantum mechanics on. First, lets consider carefully how we compare the running of two clocks. Starting at the largest sampling time, there is a transition from fractal drift regime to the nonfractal diffusion regime.
Jan 26, 2020 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 mhd and gravity in a spatial scale dimension. Scale relativity and fractal spacetime cern document server. Scalerelativity and quantization of the universe luth. This book provides a comprehensive survey of the development of the theory of scale relativity and fractal spacetime. The idea of a fractal spacetime theory was first introduced by garnet ord, and by laurent nottale in a paper with. Since we havent observed a minimum length and dont expect to be able to soon it is so small and didnt actually think there was one, physicists arent excited by that prediction. Jan 10, 2018 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. Towards a theory of scale relativity find, read and cite all the research you need on researchgate. One writes the equations of motion in such a spacetime as geodesics equations, under the constraint of the principle of relativity of all scales in nature.
Spacetime physics introduction to special relativity taylor wheeler pdf by edwin taylor and john wheeler. Special relativity, general reletavity, spacetime, taylor, wheeler. Thus, a world line is really a line in spacetime, while an event is a point in spacetime. Minkowski spacetime, the relativity of simultaneity tells us that there are many ways to do this. 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 mhd and gravity in a spatial. To formulate the geometry we put forward the next postulate, postulate 2. This book provides a comprehensive survey of the stateoftheart in the development of the theory of scale relativity and fractal spacetime. In the next article, we will see how such transition can be described in the context of resolutionscalespace relativity. General relativity gr, also known as the general theory of relativity gtr, is the geometric theory of gravitation published by albert einstein in 1915 and the current description of gravitation in modern physics.
Spacetime may have fractal properties on a quantum scale by lisa zyga. The equation of geodesics in such a spacetime can be integrated. Time and space are two separate spaces and the movement in one space. February 14, 2008 the views of space and time which i wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. General relativity also predicts the existence of gravitational waves, which have since been observed directly by the physics collaboration ligo. Relative to an observer the velocity in spacetime of any inertial frame remains the same at c. 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. Fractal dimension of quantum paths zooming on scale relativity. Scale relativity, fractal spacetime and quantum mechanics.
In addition, general relativity is the basis of current cosmological models of a consistently expanding universe. 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. It suggests an original solution to the disunified nature of the classicalquantum transition in physical systems, enabling quantum mechanics to be based on the principle of relativity provided this. The status and programs of the new relativity theory. Fractal spacetime, nondi erentiable geometry and scale relativity l. 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. Finally, we can anticipate a return to a fractal regime when the sampling. Spacetime physics, chapter one 1965 first edition by edwin f. A new approach to unifying relativity and quantum mechanics find, read and cite all the research you. This book provides a comprehensive survey of the d. Fractal dimension of quantum paths zooming on scale. Special relativityspacetime wikibooks, open books for an. In this sense, space and time get fused together and this fusion is the real novelty of the spacetime approach in relativity theory.
A fractal is an infinitely intricate structure and only deceptively simple. The point is that a quantum particle in nottales fractal spacetime has a path with a hausdorff dimension equal two. Concerning scale relativity, the next step is now to include fields into the description. Scale relativity scale relativity is a geometrical and fractal spacetime theory. Fractal dimension of a brownian path zooming on scale. A speci c point on a spacetime diagram is called an \event. This post has been imported on physicsoverflow, see here the astrophysicist laurent nottale develops since 1984 the scale relativity, which aims to unify quantum physics and relativity theory, using a fractal spacetime i would like to understand why this theory, which seems have a good potential, is not taken seriously by the physics community, in the sense that it is not as developed as. Feb 11, 2011 scale relativity and fractal spacetime book. Dec 05, 2017 starting at the largest sampling time, there is a transition from fractal drift regime to the non fractal diffusion regime. Then there is a return to a non fractal path in the ballistic regime. Nottale offers fractal spacetime as a method for establishing a relativity of scale.
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