A Quantum Gate as a Physical Model of an Universal Arithmetical Algorithm without Church's Undecidability and Godel's Incompleteness

Pankovic, Vladan; Predojevic, Milan

A Quantum Gate as a Physical Model of an Universal Arithmetical Algorithm without Church's Undecidability and Godel's Incompleteness

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Description

In this work we define an universal arithmetical algorithm, by means of the standard quantum mechanical formalism, called universal qm-arithmetical algorithm. By universal qm-arithmetical algorithm any decidable arithmetical formula (operation) can be decided (realized, calculated. Arithmetic defined by universal qm-arithmetical algorithm called qm-arithmetic one-to-one corresponds to decidable part of the usual arithmetic. We prove that in the qm-arithmetic the undecidable arithmetical formulas (operations) cannot exist (cannot be consistently defined). Or, we prove that qm-arithmetic has no undecidable parts. In this way we show that qm-arithmetic, that holds neither Church's undecidability nor Godel's incompleteness, is decidable and complete. Finally, we suggest that problems of the foundation of the arithmetic, can be solved by qm-arithmetic.
13 pages, no figures