Around the Physical Church-Turing Thesis: Cellular Automata, Formal Languages, and the Principles of Quantum Theory
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چکیده
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
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The Physical Church-Turing Thesis and the Principles of Quantum Theory
Notoriously, quantum computation shatters complexity theory, but is innocuous to computability theory [17]. Yet several works have shown how quantum theory as it stands could breach the physical Church-Turing thesis [26, 25] We draw a clear line as to when this is the case, in a way that is inspired by Gandy [20]. Gandy formulates postulates about physics, such as homogeneity of space and time,...
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