A Mathematical Analysis Reveals Some Structural Features of the Theory of Everything

Abstract

Physicists have pursued the Theory of Everything (TOE) for centuries. Not much credible progress has been made towards the final theory so far. By extending the computability theory in mathematics, this paper proves a fundamental theorem of theoretical physics, which implies 21 structural features that TOE should have. The main result of this paper is that existing quantum gravity theories are not TOE; a unification theory of physics and social sciences/humanities, called “Choice Axiomatic System”, can be established even when the problem of unifying general relativity and quantum mechanics still remains unsolved; a prototype of TOE, which covers all existing human knowledge about the observable universe, can be created by the unification of physics and social science/humanities with a potential quantum gravity theory as an important component; unlike quantum gravity theories, Choice Axiomatic System has many important practical applications and its predictions can be tested with empirical data; Choice Axiomatic System can substantially narrow down the search for potential quantum gravity theories. This paper should be interesting to researchers working on the foundation of physics, social science, and humanities.