Use of Mathematical Logical Concepts in Quantum Mechanics: An Example

Details Use of Mathematical Logical Concepts in Quantum Mechanics: An Example Use of Mathematical Logical Concepts in Quantum Mechanics: An Example

2001-06-27

arxiv.org/abs/quant-ph/0106153v3

J. Phys. A: Math. Gen. Vol 35, pp. 5843-5857, 2002.

Physics

Quantum Physics

18 pages, 1 figure, extensively revised and expanded; includes work on the basis dependence of validity and on the relation be

Scientific paper

10.1088/0305-4470/35/28/305

The representation of numbers by product states in quantum mechanics can be extended to the representation of words and word sequences in languages by product states. This can be used to study quantum systems that generate text that has meaning. A simple example of such a system, based on an example described by Smullyan, is studied here. Based on a path interpretation for some word states, definitions of truth, validity, consistency and completeness are given and their properties studied. It is also shown that the relation between the meaning, if any, of word states and the algorithmic complexity of the process generating the states must be quite complex or nonexistent.

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