What an interpretation of quantum mechanics should be?

Abstract

There are many so-called interpretations of quantum mechanics, but we presently do not have any clear-cut criteria to identify them. Usually, scientists do not distinguish the different interpretations of the standard quantum theory from its alternative or rival theories, although there is an established fact that there exist different – even non-empirically equivalent – quantum theories. In this article, I put forward some criteria to distinguish between formulations, interpretations, and alternatives to a given quantum theory. I then show that we have just some partial criteria to identify quantum theories and distinguish them from interpretations. According to such criteria, all interpretations of a given quantum theory must be empirically equivalent to it, otherwise, they are rival theories, and must not be logically equivalent to it, otherwise, they are different formulations of such theory. I conclude that interpreting a quantum theory cannot consist in providing a unique ontology for that theory because the same theory is compatible with many different ontologies.