G\"odel's incompleteness theorem and universal physics theories

Abstract

An ultimate universal theory -- a complete theory that accounts, via few and simple first principles, for all the phenomena already observed and that will ever be observed -- has been, and still is, the aspiration of most physicists and scientists. Yet, a basic principle that is embodied in the results of G\"{o}del's incompleteness theorems is that self-referencing leads to logical conflict or failure, as in the liar paradox or Russell's paradox. In physics theories self-referencing necessarily occurs when it is realized that the observer is also a participant in the experienced phenomena -- we, humans, are part of the universe while observing it. Therefore self-referencing, and consequently logical conflicts, are unavoidable, and any theory pretending to be universal is bound to be incomplete.