Around the Physical Church-Turing Thesis: Cellular Automata, Formal Languages, and the Principles of Quantum Theory

The physical Church-Turing thesis explains the Galileo thesis, but also suggests an evolution of the language used to describe nature. It can be proved from more basic principle of physics, but it also questions these principles, putting the emphasis on the principle of a bounded density of information. This principle itself questions our formulation of quantum theory, in particular the choice of a field for the scalars and the origin of the infinite dimension of the vector spaces used as state spaces. 1 The Church-Turing Thesis and Its Various Forms