Loop Observables and the Gauge Structure of Interpretation: A Preliminary Discussion of Evaluation without an External Frame

Abstract

An assessment of a social arrangement is made from some interpretive frame, and no frame stands outside the history it assesses. The difficulty this creates is familiar and is usually met either by privileging one frame or by abandoning the possibility of frame-independent content. This paper proposes a third route, taken from the treatment of the same structural problem in gauge theory. Where a quantity defined at a point depends on a choice of local frame, the quantity carried around a closed loop does not, and the loop-carried quantity is the frame-independent content of a system that has no privileged frame anywhere. The paper develops the proposal in three steps. It fixes the signature of an assessment, arguing that the object evaluated is the transformation and never the transformed structure, and that the resulting type is recursive and coalgebraic: an assessment returns a restructured world together with a new assessor. It identifies the equivalence appropriate to such an object as bisimulation, from which it follows that no scalar quotient of the assessment relation exists. And it identifies interpretive frames with gauge, bisimilarity with gauge equivalence, and the frame-independent content with holonomy around closed circuits. Two results follow that the paper verifies numerically. Loop traces are invariant under every change of frame while edge-local quantities are not, and the failure of translations to compose to the identity around a cycle is a measurable anholonomy. The paper states the relation to generative justice in one line: where that programme locates a conserved quantity, this one locates a holonomy, and the two differ in precisely the way a local conservation law differs from a global obstruction.