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 includes the replacement of Euclidean geometry by non-Euclidean geometry, and the resultant curvature of the path of light led Einstein (1912) to the conclusion that (like in accelerated frames) the speed of light is not constant in extended gravitational fields. Therefore, Abraham (1912) argued that Einstein had given special relativity a coup de grâce. Einstein responded that within its area of application (in areas where gravitational influences can be neglected) special relativity is still applicable with high precision, so one cannot speak of a coup de grâce at all. In special relativity, the transfer of signals at superluminal speeds is