Abstract :
Scale relativity is a new approach to the problem of the origin of fundamental scales and of scaling
laws in physics, which consists in generalizing Einstein’s principle of relativity to the case of scale
transformations of resolutions. We recall here how it leads one to the concept of tractal space-time, and to
introduce a new complex time derivative operator which allows to recover the Sclu%dinger equation, then to
generalize it, In high energy quantum physics, it leads to the introduction of a Lorentxian renormalixation group,
in which the Planck length is reinterpreted as a lowest, tmpassable scale, invariant under dilatations. These
methods are successively applied to two problems: in quantum mechanics, that of the mass spectrum of
elementary particles; in chaotic dynamics, that of the distribution of planets in the Solar System.
