A Bayesian Foundation for Physical Theories

Abstract: Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also leads to a well-defined procedure to select one or more theories among a family of (well-defined) candidates by ranking them according to their posterior probability distributions, which result from Bayes's theorem by incorporating to an initial prior the information extracted from a dataset, ultimately defined by experimental evidence. Examples with different levels of complexity are given and three main applications to basic cosmological questions are analysed: (i) typicality of human observers, (ii) the multiverse hypothesis and, extremely briefly, some few observations about (iii) the anthropic principle. Finally, it is demonstrated that this formulation can address problems that were out of the scope of scientific research until now by presenting the isolated worlds problem and its resolution via the presented framework.