Ivancevic_Applied-Diff-Geom

Applied Bundle Geometry 703for deriving comprehensive univocal predictions about our world.In string theory, gravity is just one of the excitations of a string (orother extended object) living over some background metric space. Theexistence of such background metric space, over which the theory is defined,is needed for the formulation and for the interpretation of the theory, notonly in perturbative string theory, but in the recent attempts of a nonperturbativedefinition of the theory, such as M theory, as well, in myunderstanding. Thus, for a physicist with a high energy background, theproblem of quantum gravity is now reduced to an aspect of the problemof understanding what is the mysterious non–perturbative theory that hasperturbative string theory as its perturbation expansion, and how to extractinformation on Planck scale physics from it.For a relativist, on the other hand, the idea of a fundamental descriptionof gravity in terms of physical excitations over a background metric spacesounds physically very wrong. The key lesson learned from general relativityis that there is no background metric over which physics happens.The world is more complicated than that. Indeed, for a relativist, generalrelativity is much more than the field theory of a particular force. Rather,it is the discovery that certain classical notions about space and time areinadequate at the fundamental level; they require modifications which arepossibly as basics as the ones that quantum mechanics introduced. Oneof such inadequate notions is precisely the notion of a background metricspace (flat or curved), over which physics happens. This profound conceptualshift has led to the understanding of relativistic gravity, to the discoveryof black holes, to relativistic astrophysics and to modern cosmology.From Newton to the beginning of this Century, physics has had a solidfoundation in a small number of key notions such as space, time, causalityand matter. In spite of substantial evolution, these notions remained ratherstable and self-consistent. In the first quarter of this Century, quantum theoryand general relativity have modified this foundation in depth. The twotheories have obtained solid success and vast experimental corroboration,and can be now considered as established knowledge. Each of the two theoriesmodifies the conceptual foundation of classical physics in a (more orless) internally consistent manner, but we do not have a novel conceptualfoundation capable of supporting both theories. This is why we do not yethave a theory capable of predicting what happens in the physical regimein which both theories are relevant, the regime of Planck scale phenomena,10 −33 cm.General relativity has taught us not only that space and time share the