In scalerelativity therefore, the underlying fractal geometry of spacetime plays. 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 and nondifferentiable fractal spacetime. 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 di. Scale relativity and fractal spacetime, imperial college press, 2011. The theory of scale relativity 10 studies the consequences of giving up the hypothesis of spacetime di erentiability. The proposal to combine fractal spacetime theory with relativity principles was made by laurent nottale nottale 1989. Fractal transport phenomena through the scale relativity model. Scale relativity is a geometrical and fractal spacetime theory. Section 7 is devoted to the discussion and conclusion. Spacetime may have fractal properties on a quantum scale. Thermodynamics and scale relativity robert carroll university of illinois, urbana, il 61801.
A correspondence between nottales scale relativity model and cressons mathematical procedures is analyzed. This proposal, known as scale relativity, was originally formulated by one. Introduced by laurent nottale, it claims to extend the concept of relativity to physical scales of time, length, energy, or momentum. The theory of scale relativity and fractal spacetime accounts for a possibly nondifferentiable geometry of the spacetime continuum, based on an extension of the principle of relativity to scale transformations of the reference system. When measuring something that is fractal, the smaller the measuring stick or scale is, the longer the measured distance will be. Applications to quantum physics, cosmology and chaotic systems l. In addition, the obtained laws, which combine fractal and scaleindependent behaviours, are the equivalent for scales of what inertial laws are for. The scale relativity theory, by giving up the differentiability of spacetime coordinates at very large timescales, describes the solar system in terms of fractal trajectories governed by a. The theory of scale relativity is a new approach to the problem of the. Whatever your feelings regarding the math, it is my hope that people will be drawn to the sheer wonder of this book. Time and space are two separate spaces and the movement in one space. 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. The theory of scale relativity is an attempt to study the consequences of giving up the hypothesis of spacetime differentiability.
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. Pdf on jan 1, 1993, laurent nottale and others published fractal spacetime and microphysics. Scale relativity, fractal spacetime and quantum mechanics. Fractal spacetime and microphysics towards a theory of scale relativity l. Cantorian fractal spacetime fluctuations characterize quantumlike chaos in atmospheric flows. 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. This state of things has been cleverly used by nottale to develop a theory of fractal spacetime 1. By combining them we get our final expression for our complex scalecovariant. It has been suggested that this article be merged into laurent nottale.
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. We then investigate the hypothesis that the microstructure of spacetime is of fractal nature, and that the observed properties of the quantum world at a given resolution result from the smoothing of curvilinear coordinates of such a spacetime projected into classical spacetime. Towards a theory of scale relativity find, read and cite all. Scale is almost universally believed not to be a dimension.
Scale relativity is the proposal of a relativistic approach to account for the interplay between different scales at the most fundamental level in the formulations of the laws of nature. Scale relativity and fractal spacetime is not an easy read, yet if you aced advanced calculus, you can keep up with it. Applications to quantum physics, cosmology and chaotic systems. This book provides a comprehensive survey of the development of the theory of scale relativity and fractal spacetime. The golden ratio is at the core of our fractal universe of infinite dimensions that looks and feels 4dimensional. Let us now come to our first attempts to define fractals in an intrinsic. 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 spacetime of this model consists of a set of regions in spacetime, the metric tensors of which are connected by discrete scale transformations. This book provides a comprehensive survey of the d. While the latter always has four dimensions, independent of the scale, the number of dimensions in the quantum version decreases to three as a function of the scale. The resulting scale relativity theory is an extension of the.
The aim of the theory of scale relativity is to derive the physical behavior of a nondi erentiable and fractal spacetime and of its geodesics with which particles are identi ed, under the constraint of the principle of the relativity of scales. The aim of this theory is to derive the physical behavior of a nondi. In fact, the twofoldness appearing in stochastic mechanics is. 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. In both kminkowski spacetime and the quantum sphere, the dimensionality becomes nonintegral, which is a typical signature of fractal geometry. The theory of scale relativity extends einsteins principle of relativity to scale. We finally combine these three effects by constructing a new tool, the scalecovariant.
The theory of scale relativity extends einsteins principle of relativity to scale transformations of resolutions. In the same way as quantum physics differs from the classical at very small scales because of fractal effects, symmetrically, at very large scales, scale relativity also predicts that corrections from the fractality of spacetime must be taken into account see also fig. However, nottale works in 4 spacetime dimensions only and he has never claimed that his scale relativity is exact. In the late 19th century mathematicians such as du boisreymond, weierstrass. A second key fractal property, related to scale divergence, is nondifferentiability, meaning that a line is irregular or fragmented at all scales. Assimilating the physical spacetime with a fractal, a general theory is built. Golden geometry of einfinity fractal spacetime story of phi part 5. The idea of a fractal spacetime theory has been first introduced by garnet ord 1983, and bylaurent nottale in a paper with jean schneider1984. Scale relativity is a proposal for a theory of physics based on fractal spacetime. A new approach to unifying relativity and quantum mechanics discover the worlds research. Read or download pdf online here scale relativity and fractal spacetime. The fundamental principle upon which we rely is that of scale relativity, which generalizes.
The macroscale atmospheric flow structure behaves as a unified whole quantum system, where the superimposition of a continuum of eddies results in 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 relativity, nondifferentiability and fractal spacetime. Note, that in the fractal cosmological model, the simulation of the large scale structure of the galaxy distribution should require less computational time, because our need is to model the self.
Cantorian fractal spacetime, quantumlike chaos and scale relativity in atmospheric flows. Pdf cantorian fractal spacetime, quantumlike chaos and. Is this an indication that universe is non symetrical through 4d fractal spacetime. Do fractals confirm the general theory of relativity. Scale relativity, fractal spacetime, and quantum mechanics. Even if you find yourself struggling, you should still be able to see and appreciate much that is new. Fractal spacetime and microphysics towards a theory of. Subsequently, a geometric formulation of the gravitation theory on a fractal spacetime is given.
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