Hilbert's Incompleteness, Chaitin's $\Omega$ number and Quantum Physics
Tien D. Kieu · arXiv (Cornell University) · 2001
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, but a direct generalisation of the quantum algorithms cannot satisfy, among others, the requirement of finite energy.