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 within general relativity. However, as pointed out by Willem de Sitter in 1916, Mach's principle is not completely fulfilled in general relativity because there exist matter-free solutions of the field equations. This means that the "inertio-gravitational field", which describes both gravity and inertia, can exist in the absence of gravitating matter. However, as pointed out by Einstein, there is one fundamental difference between this concept and absolute space of Newton: the inertio-gravitational field of general relativity is determined by matter, thus it is not absolute. In the "Bad Nauheim Debate" (1920) between Einstein and (among others) Philipp Lenard, the latter