Theoretical physics is presently at a very exciting time in the history of scientific discovery. For we are at a precipice facing two conflicting 20th century revolutionary movements in physics, each purporting to be basic truths of nature - the quantum theory and the theory of relativity. In the 20th century the mathematical expression of the quantum theory yielded correct predictions of a great deal of the data on the behavior of the molecular, atomic, nuelear and elementary partiele domains of matter. In the same period, the theory of relativity suc­ cessfully described new features of material systems. In special rela­ tivity, the relativistic Doppler effects (transverse and longitudinal) of electromagnetic radiation, and the mechanics of matter that moves at speeds elose to the speed of light, revealing, for example, the en­ 2 ergy mass relation, E = mc , revolutionized our thinking. In its form of general relativity, it has yielded a formalism that successfully pre­ dicted features of the phenomenon of gravity, also predicted by the elassical Newtonian theory, but in addition, features not predicted by the elassical theory, thereby superceding Newton's theory of universal gravitation. The problem we are now faced with, in these early decades of the 21st century, is that in their precise mathematical forms and their conceptual bases, the theory of relativity and the quantum theory are both logically and mathematically incompatible.