Levels of Physical Theories

Abstract

Many physicists view the most sublime task of physics in presenting some day a world formula or a simple Theory of Everything (T.O.E.) that accounts for all major physical theories and from which everything follows by pure deduction.¹ This striving for universality can look back on a long history, which contains the failed attempts to incorporate electrodynamics into universal mechanics, Einstein’s einheitliche Feldtheorie and Heisenberg’s explicit proposal of an Urgleichung. Those attempts were encouraged by the success of general relativity, which embraced classical mechanics and Newtonian gravity as well defined limits. A decade later quantum mechanics was given its final shape, which allowed the explanation of all atomic phenomena known up to then and contained classical mechanics as its macroscopic limit at least in the stochastic interpretation, i.e. comparing both as theories of measurement. After the success of gauge theories in elementary particle physics, the search for a fundamental simple equation was replaced by the search for a basic symmetry group that described all fundamental interactions apart from gravity. It resulted in the famous gauge group of the Standard Model SU (3) × SU (2) _L × U (1), which comprises the strong, the weak and the electromagnetic interaction. But the fact that the Standard Model contains 18 (21) parameters, which have to be introduced from outside, inspired the search for a larger unifying gauge group. These Grand Unified Theories (G.U.T.) tried to derive some of the parameters of the Standard Model from more fundamental gauge symmetries. With the rise of string theory, which intends to include gravity as well, a new term popped up to express the old claims: Theory of Everything (T.O.E.).

The ideas presented here initiated from a talk Walter Thirring gave at the symposium of the Pontificial Academy Understanding Reality: The Rôle of Culture and Science and led to a joint article in Naturwissenschaften [10].