Undecidability principle and the uncertainty principle even for classical systems

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Abstract
It is shown that for any physical system there is an infinite number of measurements which are related to one of the undecidable problems. The undecidability of the physical systems indicates that there is an infinite number of incomputable correlation functions for each physical system. These results show that there is an inherent and irreducible limitation on the knowledge of the nature of physical systems. This uncertainty principle is caused by the undecidability principle.