Simple formal languages and the structure of spacetime

OSVALDO M. MORESCHI

La Falda, Argentina

Jornada; XI Jornadas de Epistemología e Historia de la Ciencia; 2000

The technique of assuming a smooth manifold to construct the framework for the description of physical systems, is so common that very rarely one stops to think whether is completely justified. But it is in the study of quantum gravity that this question acquires strong relevance. There exists many indications that make one to think that probably the structure of the spacetime is very different from the smooth one that has been assumed. For example, there are works in which the quantum operator associated to the area of a closed 2-surface has been calculated, and it was found that it has a discrete spectrum. This work has also been extended to the case of volume operator and length operator. If one accepts the idea that probably the quantum structure of the spacetime is discrete, one is faced with the question of which is the appropriate description of this structure. Our suggestion for this task is that if one studies a very small portion of the spacetime, then the description must necessarily be simple. In a previous work we have study the implications of the statement: It is possible to completely describe a finite system in terms of a finite sentence of a formal language. We are thus led to study simple formal languages.