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 Kretschmann was mistaken (subsequent papers showed that such a theory would still be usable), another argument can be made in favor of general covariance: it is a natural way to express the equivalence principle, "i.e.", the equivalence in the description of a free-falling observer and an observer at rest, and thus it is more convenient to use general covariance together with general relativity, rather than with Newtonian mechanics. Connected with this, also the question of absolute motion was dealt with. Einstein argued that the general covariance of his theory of gravity supports Mach's principle, which would eliminate any "absolute motion"