Limitations of the special and general relativities and their isotopic generalizations

The scientific scene of this century has been dominated by the special and general relativities. In this paper we first recall that these relativities were not conceived for unlimited physical conditions, but solely for exterior problems (motion of point-like test bodies in the homogeneous and isotropic vacuum). We then show that the relativities are inapplicable (rather than violated) for the more general interior problems (motion of extended test bodies within inhomogeneous and anisotropic physical media) on numerous, independent, topological, geometric, analytic and other grounds. We also outline the rather numerous problematic aspects of general relativity for exterior problems in vacuum, while the problematic aspects of the special relativity in vacuum are treated elsewhere in this volume. We also point our rather serious insufficiencies of the special and general relativities for an effective representation of antimatter, beginning at a classical-astrophysical level and then continuing at the operator-particle level. The paper ends with a brief outline of the so-called isotopic generalization of the special and general relativities initiated by this author back in 1978 when at Harvard University under support from the U. S. Department of Energy, and subsequently studied by a number of mathematicians, theoreticians and experimentalists. These isotopic studies are presented as an indication of the true scientific renaissance in mathematics, physics, superconductivity and other fields which has been stimulated by the limitations and problematic aspects of the special and general relativities. These studies are coordinated by the Istituto per la Ricerca di Base in Italy. All scholars interested in truly fundamental advances in mathematics, physics, superconductivity and other disciplines are encouraged to participate in this collegial effort.