Updated: 31 October 2006

Scale Relativity

Warning:  these HTML pages are devoted to the concepts of Scale Relativity and Fractal Space-Time. For more detail, refer either to the book (Fractal Space-Time and Microphysics, World Scientific, 1993), or to a more recent (1996) review paper, or the popular books (in french) "La relativité dans tous ses états" (Hachette, 1998, Paris, 319 pp.) and "Les arbres de l'évolution" (L. Nottale, J. Chaline et P. Grou, Hachette Littératures, 2000). More generally, consult the bibliography published on the subject, the list of downloadable papers, or the author at the following e-mail address: laurent.nottale@obspm.fr. These pages have been developped from a first version achieved by E. Lefèvre.

The author:

This theory is proposed by Laurent Nottale, researcher at Paris-Meudon Observatory. He worked for a long time in parallel on cosmology and gravitational lenses, (see his book in French "l'Univers et la Lumière", Flammarion, Nouvelle Bibliothèque Scientifique 1994, Champs 1998, Prix du livre d'Astronomie Haute-Maurienne-Vanoise 1995). But he is now devoting most of his activity to the development of the theory of Scale Relativity (in french: Relativité d'Echelle) within LUTH department.

The origin

In this chapter, we first present the origin of the Scale Relativity (or ScR) theory: we will briefly evoke the reasons that led to its development.

The fundamental principle of ScR:

It is an extension of the principle of relativity. It can be stated as follows: The laws of nature must be valid in every coordinate systems, whatever their state of motion and of scale. The results obtained show once again the extraordinary efficiency of this principle at constraining and/or at constructing the laws of physics.

The method:

The formalism developed for ScR is already sufficiently settled to be used "as is" to deal with a particular problem in many situations. The procedure is outlined in this chapter. The most general version of the theory is still under construction.

The formalism and its consequences:

Some consequences:

The proofs/experimental and observational tests


The classification is only indicative since some problems belong to several categories. It is however not an arbitrary one because the 3 fields of microphysics, cosmology and chaotic systems correspond to privileged fields of application of ScR. Respectively: dx et dt tending towards zero, dx tending towards infinity and dt tending towards infinity. These are the three frontiers of today's physics: the infinitely small, the infinitely large and the infinity of complexity.

For a more complete list of the results and predictions of the scale-relativity theory, see Sec. 9 of the review paper: "Scale Relativity and Fractal Space-Time". A html completed version of this section can be found here.