The idea of a fractal space time theory was first introduced by garnet ord, and by laurent nottale in a paper with. A new approach to unifying relativity and quantum mechanics. This is the approach of physicist laurent nottale, who developed a fractal spacetime theory in the books fractal spacetime and microphysics. Fractal topology of spacetime theory part 2 youtube. Then, in spring 2000 i decided to type my lecture notes and distribute them to the class in order to provide more relevant reading materials. Golden geometry of einfinity fractal spacetime story of phi part 5. It is based on the giving up of the axiom of differentiability of the spacetime continuum. To view pdf you will need to install adobe acrobat reader if you. Feb 11, 2011 scale relativity and fractal spacetime book. Even before that a few basic definitions are in order. The fundamental principle upon which we rely is that of scale relativity. Lecture notes on special relativity macquarie university. 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. Read online and download pdf ebook scale relativity and fractal space time a new approach to unifying relativity and quantum mechanics.
Wu, general relativity for mathematicians springerverlag, 1977. Aug 22, 2012 scientists have long debated whether the universe is a fractal, or whether matter is distributed evenly within it. Special relativityspacetime wikibooks, open books for an. Time and space are two separate spaces and the movement in one space time is independent of movement through the other space. The sun for example, being heavy, bends space time enormously. Jan 22, 2016 scale relativity scale relativity is a geometrical and fractal space time theory. Pdf on jan 1, 1993, laurent nottale and others published fractal spacetime and microphysics. Geometry and cosmology, the fundamental laws of classical mechanics, the newtonian worldsystem, the fundamental laws of optics, the fundamental laws of electrodynamics and einsteins special principle of relativity. General relativity is the classical theory that describes the evolution of systems under the e ect of gravity. 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 relatively high abundance of fractal properties of complex systems on earth and in space is considered an argument in support of the general relativity of the geometric theory of gravity. A new approach to unifying relativity and quantum mechanics on.
We have shown in the preceding chapter how the principle of scale relativity, even in its special. Fractal spacetime, nondi erentiable geometry and scale. Even though time dilation is covered in any basic book on special relativity, we will spend some time on the basics here before we move on to spacetime finance. 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. Chaotic fractals at the root of relativistic quantum. Down in the fractal depths of quantum matter and spacetime. We have shown in the preceding chapter how the principle of scale. This book provides a comprehensive survey of the development of the theory of scale relativity and fractal spacetime.
Albert einstein 5 preface december, 1916 the present book is intended, as far as possible, to give an exact insight into the theory of relativity to those readers who, from a general scientific and philosophical point of view. This book provides a comprehensive survey of the d. Fractal spacetime relativity by alexander timmons youtube. 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. Applications to quantum physics, cosmology and chaotic systems. Nottale offers fractal spacetime as a method for establishing a relativity of scale.
Scale relativity and nondifferentiable fractal spacetime. Fractal space time, nondi erentiable geometry and scale relativity l. Keck science center, the claremont colleges a spacetime diagram shows the history of objects moving through space usually in just one dimension. Lecture notes on general relativity columbia university. 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. Space time of general relativity is supple and can be visualized as a rubber sheet, bent by massive bodies. Spacetime physics with geometric algebra 1 david hestenes department of physics and astronomy arizona state university, tempe, arizona 852871504 this is an introduction to spacetime algebrasta as a uni. More than being just an interesting idea, this phenomenon might provide insight. From 1975 to 1991 this included conventional topics, such as gravitational lenses, while from 1984 onwards he focused on developing his theory of scale relativity, a proposal for a theory of physics based on fractal spacetime. Scientific video dvd edited by the spacetime editions. The majority of this cos mic cotton candy is naturally voids containing nothing. However, most of the course content was conveyed directly through the lectures.
Special relativity, general reletavity, spacetime, taylor, wheeler. Towards a theory of scale relativity find, read and cite all the research you need on researchgate. How subjective duration varies, depending on the way we embed current content into contexts, is explained. Since space time is also omnipresent and the same for all physical systems, einstein was led to regard gravity not as a force but a manifestation of space time geometry. Einstein and inside relativity by mook and vargish as supplemental reading. This theory leads i to a generalization of possible physically relevant fractal laws, written as partial differential equation acting in the space of. Everyday low prices and free delivery on eligible orders. Besides that, only surprisingly few initial experimental facts are needed to develop the theory. The theory of scale relativity is an attempt to study the consequences of giving up the hypothesis of spacetime differentiability. Notes on relativity and cosmology for phy312 donald marolf physics department, syracuse university c january 2003.
Just what the title says, although the typically dry mathematics prose style. Scale relativity and fractal spacetime a new approach to unifying relativity and quantum mechanics by laurent nottale parismeudon observatory, france 764pp 9781848166509. Nottale offers fractal space time as a method for establishing a relativity of scale. In this the second part i want to show how a modification to the ideas put forwards by. First, lets consider carefully how we compare the running of two clocks. The first postulate assumes absolute uniform scale cannot be detected. 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. The principle of relativity assures that all three observers are equally good. Fractal time studies of nonlinear phenomena in life science. Cambridge core cosmology, relativity and gravitation the large scale structure of space time by s.
Abstract this paper describes the present state of an attempt at understanding the quantum behaviour of microphysics in terms of a nondifferentiable spacetime continuum having fractal i. May 14, 2008 well, scale relativity does make new predictions, particularly about the value of several fundamental constants, as well as the expected orbital formations of solar systems since one result of the theory is that solar system formation is, at least partially, governed by the schrodinger equation. Time and space are two separate spaces and the movement in one space. Although the special theory of relativity was first proposed by einstein in 1905, the modern approach to the theory depends upon the concept of a fourdimensional universe, that was first proposed by hermann minkowski in 1908. Citeseerx 1 scale relativity, fractal spacetime, and. The second solution that we will discuss is the freedmanrobertsonwalker frw metric which describes the. 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. 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 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. World scientificimperial college press, 2011, 764 pp, gbp105. Mar 25, 2009 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. 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.
Scale relativity, fractal spacetime, and quantum mechanics. It suggests an original solution to the disunified nature of the. 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. Well, scale relativity does make new predictions, particularly about the value of several fundamental constants, as well as the expected orbital formations of solar systems since one result of the theory is that solar system formation is, at least partially, governed by the schrodinger equation. 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. Fractal spacetime and microphysics towards a theory of scale relativity l. A new approach to unifying relativity and quantum mechanics by laurent nottale isbn. Fractal physics theory is based on fractal geometry with its scaling fractals all in golden ratios, i. Ellis, the largescale structure of spacetime cambridge, 1973. World scientific firm this book provides a comprehensive survey of the development of the theory of scale relativity and fractal spacetime. This video is a travel in the fractal spacetime in many scale of dimensions into the universes. An advanced book which emphasizes global techniques and singularity theorems. A new approach to unifying relativity and quantum mechanics find, read and cite all the research you. It was also almost entirely the work of one person, viz.
Whether it achieves what its originator seeks remains to be est. Space and time in special relativity essays on mathematics. May 16, 2004 one, generic to fractal science, is vagueness. 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. Isbn 1848166508 fractal space time and microphysics, editions world scientific, may 1993 isbn 9810208782 the reference book about scale relativity theory. Later, einstein was able to further develop this theory, leading to what is known as the general theory of relativity. Nottale cnrs, luth, paris observatory and parisdiderot university 92190 meudon, france laurent. A second one is that some main predictions are known consequences of the renormalization group mathematics. The fractality may be called the fractal symmetry of physical interactions providing selfsimilarities of complex systems.
It seems like if things on earth show fractal nature, then spacetime should have fractal nature toonot necessarily a continuous emptiness. Applications to quantum physics, cosmology and chaotic systems l. The aim of this theory is to derive the physical behavior of a nondi. Its history goes back to 1915 when einstein postulated that the laws of gravity can be expressed as a system of equations, the socalled einstein equations. The golden ratio is at the core of our fractal universe of infinite dimensions that looks and feels 4. The present note highlights some mathematical and formal connections between the theory of scale relativity and the cantorian spacetime approach to p. This theory leads i to a generalization of possible physically relevant fractal laws, written as partial di. Citeseerx document details isaac councill, lee giles, pradeep teregowda. The theory of scale relativity extends einsteins principle of relativity to scale transformations of resolutions. Scale relativity and fractal spacetime world scientific. Nov 24, 2015 asking is the geometry of space time fractal. This book provides an interdisciplinary introduction to the notion of fractal time, starting from scratch with a philosophical and perceptual puzzle. The judgments of simultaneity of any one is just as good a those of the other two and each of the figures is an equally good way of dividing the spacetime into sets of simultaneous events.
Spacetime may have fractal properties on a quantum scale. The reader is assumed to have but little mathematical knowledge. Einfinity theory is based on fractal geometry with the golden mean 0. A speci c point on a spacetime diagram is called an \event. Another consequence is that clocks in different inertial frames will be observed to run at different rates. Hawking please note, due to essential maintenance online purchasing will not be possible between 03. Fractal spacetime and microphysics towards a theory of scale. The idea of fractal space just popped into my mind just now, so i decided to come take a look who was discussing it online. Scale relativity claims to extend the concept of relativity to physical scales. These principles, and their consequences constitute the special theory of relativity. Although special relativity is a theory of physics, the chief ingredient in deriving its astonishing results about space and time is mere logical thinking. Reference frame in most of our examples we will use two reference frames.
Is there a geometry that describes spacetime as fractal. If spacetime itself is a real cantorian fractal then it resembles an unimaginably large cotton candy 5,7,11. Laurent nottale this book provides a comprehensive survey of the development of the theory of scale relativity and fractal spacetime. Spacetime physics introduction to special relativity taylor.
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