Scale Relativity

Scale relativity is a theory of space-time initially developed by Laurent Nottale, working at the French observatory of Meudon, near Paris. It is an extension of the concept of relativity found in special relativity and general relativity to physical scales (time, length, energy, or momentum scales). If scales in nature are always relative, an absolute scale cannot exist. As a consequence, fundamental physical laws need to be scale invariant. While differential trajectories found in standard physics are automatically scale invariant, it is the main insight of the theory that also certain non-differential trajectories (which explicitly depend on the scale of the observer) can be scale invariant and new tools are developed to treat such trajectories. One of the claimed successes of the theory that the laws of quantum mechanics, like the Schroedinger equation, can be derived directly from the assumption that space-time itself is non-differential and scale invariant. Scale invariance is closely related to the self-similarity observed in fractals.