Scale relativity new principle of relativity. Mathematically, this can be expressed through the principle of covariance applied to scales, that is, the invariance of the form of physics equations under transformations of resolutions (dilations and contractions). Galileo introduced explicitly velocity parameters in the observational referential. Then, Einstein introduced explicitly acceleration parameters. In a similar way, Nottale introduces scale parameters explicitly in the observational referential. The core idea of scale-relativity is thus to include resolutions explicitly in coordinate systems, thereby integrating measure theory in the formulation of physical laws. An important consequence is that coordinates are not numbers anymore, but "functions", which depend
Criticism of the theory of relativity impossible, since this would violate the Poincaré-Einstein synchronization, and the causality principle. Following an old argument by Pierre-Simon Laplace, Poincaré (1904) alluded to the fact that Newton's law of universal gravitation is founded on an infinitely great speed of gravity. So the clock-synchronization by light signals could in principle be replaced by a clock-synchronization by instantaneous gravitational signals. In 1905, Poincaré himself solved this problem by showing that in a relativistic theory of gravity the speed of gravity is equal to the speed of light. Although much more complicated, this is also the case in Einstein's theory of general relativity.