The Scale-Relativity Program∗

The theory of scale relativity is an attempt at developing the consequences of giving up the implicit hypothesis of space-time differentiability. One of these consequences is that space-time becomes fractal, i.e., explicitly resolution-dependent. The principle of relativity is extended in order to be also valid for scale transformations of space-time resolutions. In the present contribution, we mainly focus on the general structure of the theory and on its possible future goals. This description is completed by a development of three specific points: (i) a new demonstration of the Schrödinger equation in which all terms are kept; (ii) a method of entropy maximization allowing one to unveil the fractal geometry from the quantum behavior; (ii) a discussion of the metric forms in scale-relativity. c ©1999 Elsevier Science Ltd. All rights reserved