It is known that the Unified Field Theories of Weyl [14] and of Einstein [4] give no indication of how Relativity and Quantum Theories should be connected into a comprehensive field theory of physics. Indeed, the only determined attempt to establish such a theory, due to Eddington [3] and [6], failed through lack of contact with the contemporary developments, especially in quantum electrodynamics and elementary particles. Its author tried to explain curvature of the space-time in terms of statistical fluctuations partly of a physical origin defined within a mechanical system, and partly of a geometrical origin of coordinates superimposed on the latter. It is clear however that both the fluctuations of Eddington refer to purely mathematical frames. The probabilistic nature of his theory takes no account of physical objects, such as particles or energy distributions. It is the author's belief that this is the cause of difficulties associated with the otherwise admirable work of Eddington.