Hilbert's Incompleteness, Chaitin's $Ω$ number and Quantum Physics

Details Hilbert's Incompleteness, Chaitin's $Ω$ number and Quantum Physics Hilbert's Incompleteness, Chaitin's $Ω$ number and Quantum Physics

2001-11-10

arxiv.org/abs/quant-ph/0111062v2

Physics

Quantum Physics

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Scientific paper

To explore the limitation of a class of quantum algorithms originally proposed for the Hilbert's tenth problem, we consider two further classes of mathematically non-decidable problems, those of a modified version of the Hilbert's tenth problem and of the computation of the Chaitin's $\Omega$ number, which is a representation of the G\"odel's Incompletness theorem. Some interesting connection to Quantum Field Theory is pointed out.

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