The theory of scale relativity extends einsteins principle of relativity to scale. This proposal, known as scale relativity, was originally formulated by one. Cantorian fractal spacetime fluctuations characterize quantumlike chaos in atmospheric flows. In addition, the obtained laws, which combine fractal and scaleindependent behaviours, are the equivalent for scales of what inertial laws are for. 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. Even if you find yourself struggling, you should still be able to see and appreciate much that is new. In scalerelativity therefore, the underlying fractal geometry of spacetime plays.
Scale relativity and fractal spacetime, imperial college press, 2011. Scale relativity scale relativity is a geometrical and fractal spacetime theory. In fact, the twofoldness appearing in stochastic mechanics is. Is this an indication that universe is non symetrical through 4d fractal spacetime. Time and space are two separate spaces and the movement in one space. Fractal spacetime and microphysics towards a theory of. A correspondence between nottales scale relativity model and cressons mathematical procedures is analyzed. This book provides a comprehensive survey of the development of the theory of scale relativity and fractal spacetime. Scale relativity and nondifferentiable fractal spacetime. Pdf cantorian fractal spacetime, quantumlike chaos and. 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.
Introduced by laurent nottale, it claims to extend the concept of relativity to physical scales of time, length, energy, or momentum. 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. Scale relativity is a proposal for a theory of physics based on fractal spacetime. The macroscale atmospheric flow structure behaves as a unified whole quantum system, where the superimposition of a continuum of eddies results in the. Section 7 is devoted to the discussion and conclusion. We finally combine these three effects by constructing a new tool, the scalecovariant. 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. 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.
Applications to quantum physics, cosmology and chaotic systems l. Fractal spacetime and microphysics towards a theory of scale relativity l. 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. Cantorian fractal spacetime, quantumlike chaos and scale relativity in atmospheric flows. The theory of scale relativity is a new approach to the problem of the. Golden geometry of einfinity fractal spacetime story of phi part 5. 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. 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. Scale relativity, fractal spacetime and quantum mechanics.
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. Scale is almost universally believed not to be a dimension. However, nottale works in 4 spacetime dimensions only and he has never claimed that his scale relativity is exact. The golden ratio is at the core of our fractal universe of infinite dimensions that looks and feels 4dimensional. It has been suggested that this article be merged into laurent nottale. It is based on the giving up of the axiom of differentiability of the spacetime continuum. The resulting scale relativity theory is an extension of the.
Towards a theory of scale relativity find, read and cite all. Scale relativity, nondifferentiability and fractal spacetime. Pdf on jan 1, 1993, laurent nottale and others published fractal spacetime and microphysics. The fundamental principle upon which we rely is that of scale relativity, which generalizes. Read or download pdf online here scale relativity and fractal spacetime. Scale relativity and fractal spacetime is not an easy read, yet if you aced advanced calculus, you can keep up with it. In the late 19th century mathematicians such as du boisreymond, weierstrass. Applications to quantum physics, cosmology and chaotic systems. Its framework was revealed to be particularly well adapted to a. This book provides a comprehensive survey of the d. Fractal transport phenomena through the scale relativity model.
Let us now come to our first attempts to define fractals in an intrinsic. 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 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. One can show 10 12 3 that a continuous but nondi erentiable spacetime is necessarily fractal.
The theory of scale relativity is an attempt to study the consequences of giving up the hypothesis of spacetime differentiability. Do fractals confirm the general theory of relativity. 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. A second key fractal property, related to scale divergence, is nondifferentiability, meaning that a line is irregular or fragmented at all scales. Whatever your feelings regarding the math, it is my hope that people will be drawn to the sheer wonder of this book. The idea of a fractal spacetime theory was first introduced by garnet ord, and by laurent nottale in a paper with. 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. This theory leads i to a generalization of possible physically relevant fractal laws, written as partial di. Thermodynamics and scale relativity robert carroll university of illinois, urbana, il 61801. The aim of this theory is to derive the physical behavior of a nondi. This implies that the universe is non relative through scale. The first postulate assumes absolute uniform scale cannot be detected. The theory of scale relativity 10 studies the consequences of giving up the hypothesis of spacetime di erentiability. Scale relativity is a geometrical and fractal spacetime theory.
A new approach to unifying relativity and quantum mechanics discover the worlds research. The theory of scale relativity extends einsteins principle of relativity to scale transformations of resolutions. The spacetime of this model consists of a set of regions in spacetime, the metric tensors of which are connected by discrete scale transformations. 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. Theory and applications article pdf available in foundations of science 152 december 2008 with 179 reads how we measure reads. 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. Spacetime may have fractal properties on a quantum scale. When measuring something that is fractal, the smaller the measuring stick or scale is, the longer the measured distance will be. Scale relativity, fractal spacetime, and quantum mechanics.
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