, Volume 33, Issue 10, pp 1985-2017

Logics and quantum gravity

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Abstract

We consider the logic needed for models of quantum gravity, taking as our starting point a simple pregeometric toy model based on graph theory. First a discussion of quantum logic seen in the light of canonical quantum gravity is given, then a simple toy model is proposed and the logical structure underlying it exposed. It is then shown that this logic is nonclassical and in fact contains quantum logics as special cases. We then go on to show how Yang-Mills theory and quantum mechanics fits in. A single mathematical structure is proposed capable of containing all these subjects in a natural and elegant way. Causality plays an important role. The mere presence of a causal relation almost inevitably yields this kind of logic.