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
Physical theories modified by general relativity Physical theories modified by general relativity "This article will use the Einstein summation convention." The theory of general relativity required the adaptation of existing theories of physical, electromagnetic, and quantum effects to account for non-Euclidean geometries. These physical theories modified by general relativity are described below. Classical mechanics and special relativity are lumped together here because special relativity is in many ways intermediate between general relativity and classical mechanics, and shares many attributes with classical mechanics. In the following discussion, the mathematics of general relativity is used heavily. Also, under the principle of minimal coupling, the physical equations of special