Scale relativity and fractal space-time: theory and applications
In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads (i) to a generalization of possible physically relevant fractal laws, writt...
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ftciteseerx:oai:CiteSeerX.psu:10.1.1.329.1210 2023-05-15T15:06:42+02:00 Scale relativity and fractal space-time: theory and applications Laurent Nottale The Pennsylvania State University CiteSeerX Archives 2009 application/pdf http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.329.1210 http://luth2.obspm.fr/~luthier/nottale/arEDU08.pdf en eng http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.329.1210 http://luth2.obspm.fr/~luthier/nottale/arEDU08.pdf Metadata may be used without restrictions as long as the oai identifier remains attached to it. http://luth2.obspm.fr/~luthier/nottale/arEDU08.pdf text 2009 ftciteseerx 2016-09-04T00:35:23Z In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. 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. In the second part, we discuss some examples of application of the theory to various sciences, in particular in cases when the theoretical predictions have been validated by new or updated observational and experimental data. This includes predictions in physics and cosmology (value of the QCD coupling and of the cosmological constant), to astrophysics and gravitational structure formation (distances of extrasolar planets to their stars, of Kuiper belt objects, value of solar and solar-like star cycles), to sciences of life (log-periodic law for species punctuated evolution, human development and society evolution), to Earth sciences (log-periodic deceleration of the rate of California earthquakes and of Sichuan earthquake replicas, critical law for the arctic sea ice extent) and tentative applications to systems biology. 1 Text Arctic Sea ice Unknown Arctic |
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In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. 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. In the second part, we discuss some examples of application of the theory to various sciences, in particular in cases when the theoretical predictions have been validated by new or updated observational and experimental data. This includes predictions in physics and cosmology (value of the QCD coupling and of the cosmological constant), to astrophysics and gravitational structure formation (distances of extrasolar planets to their stars, of Kuiper belt objects, value of solar and solar-like star cycles), to sciences of life (log-periodic law for species punctuated evolution, human development and society evolution), to Earth sciences (log-periodic deceleration of the rate of California earthquakes and of Sichuan earthquake replicas, critical law for the arctic sea ice extent) and tentative applications to systems biology. 1 |
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The Pennsylvania State University CiteSeerX Archives |
format |
Text |
author |
Laurent Nottale |
spellingShingle |
Laurent Nottale Scale relativity and fractal space-time: theory and applications |
author_facet |
Laurent Nottale |
author_sort |
Laurent Nottale |
title |
Scale relativity and fractal space-time: theory and applications |
title_short |
Scale relativity and fractal space-time: theory and applications |
title_full |
Scale relativity and fractal space-time: theory and applications |
title_fullStr |
Scale relativity and fractal space-time: theory and applications |
title_full_unstemmed |
Scale relativity and fractal space-time: theory and applications |
title_sort |
scale relativity and fractal space-time: theory and applications |
publishDate |
2009 |
url |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.329.1210 http://luth2.obspm.fr/~luthier/nottale/arEDU08.pdf |
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Arctic |
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Arctic |
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Arctic Sea ice |
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Arctic Sea ice |
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http://luth2.obspm.fr/~luthier/nottale/arEDU08.pdf |
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http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.329.1210 http://luth2.obspm.fr/~luthier/nottale/arEDU08.pdf |
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Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
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1766338260031766528 |