If several physical theories are consistent with the same experimental data, which theory should we choose? Physicists often choose the simplest theory; this principle (explicitly formulated by Occam) is one of the basic principles of physical reasoning. However, until recently, this principle was mainly a heuristic because it uses the informal notion of simplicity.
With the explicit notion of simplicity coming from the Algorithmic Information theory, it is possible not only to formalize this principle in a way that is consistent with its traditional usage in physics, but also to prove this principle, or, to be more precise, deduce it from the fundamentals of mathematical statistics as the choice corresponding to the least informative prior measure. Potential physical applications of this formalization (due to Li and Vitanyi) are presented.
In particular, we show that, on the qualitative level, most fundamental ideas of physics can be re-formulated as natural steps towards choosing a theory that is the simplest in the above precise sense (although on the intuitive level, it may seem that, e.g., classical physics is easier than quantum physics): in particular, we show that such ideas as Big Bang cosmology,atomism, uncertainty principle, Special Relativity, quark confinement, quantization, symmetry, supersymmetry, etc. can all be justified by this (Bayesian justified) preference for formalized simplicity.