Towards Relational Foundations for Spacetime Quantum Physics ^†

Rovelli’s relational interpretation of quantum mechanics tells us that the description of a system in the formalism of quantum mechanics is not an absolute but is relative to the observer itself. The interpretation goes further and proposes a set of axioms. In standard non-relational language, one of them states that an observer can only retrieve a finite amount information from a system by means of measurement. Our contribution starts with the observation that quantum mechanics, i.e., quantum field theory (QFT) in dimension 1, radically differs from QFT in higher dimensions. In higher dimensions, boundary data (or initial data) cannot be characterized by finitely many measurements. This calls for a notion of measuring scale, which we provide. At a given measuring scale, the observer has partial information about the system. Our notion of measuring scale generalizes the one implicitly used in Wilsonian QFT. At each measuring scale, there are effective theories, which may be corrected, and if the theory turns out to be renormalizable, the mentioned corrections converge to determine a completely corrected (or renormalized) theory at the given measuring scale. The notion of a measuring scale is the cornerstone of Wilsonian QFT; this notion tells us that we are not describing a system from an absolute perspective. An effective theory at that scale describes the system with respect to the observer, which may retrieve information from the system by means of measurement in a specific way determined by our notion of measuring scale. We claim that a relational interpretation of quantum physics for spacetimes of dimensions greater than 1 is Wilsonian.