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

Tien D Kieu
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Abstract

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 $Ω$ number, which is a representation of the Gödel's Incompletness theorem. Some interesting connection to Quantum Field Theory is pointed out.

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Tien D Kieu. 2001-11-21. Hilbert's Incompleteness, Chaitin's $Ω$ number and Quantum Physics. https://arxiv.org/abs/quant-ph/0111062

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