The Measurement Problem

Abstract

Every measurement inserts a probe into the field it measures, and the probe displacessome of that field. At the macroscopic scale the displacement is small relative to thequantity measured, it is computable, and it is subtracted; a dipstick in a fuel tank isthe ordinary case. This paper takes the ratio of probe recursion volume to targetrecursion volume as a single continuous variable and follows it from the tank to theelectron. Under the energy identity E = pr the displacement fraction of anymeasurement is the volume ratio itself, and the analysis shows three regimes: areading regime, in which the displacement is resolved and removed; a transitionalregime, in which the displacement is real but no smaller probe exists to resolve it;and a synchronization regime, in which the probe and target are of comparablerecursion volume and the measurement is not a reading of a prior value but a jointclosure of two structures, as the series has established for quantum measurement. Atthe electron end of the variable the framework already supplies the number: thecoupling between the photon recursion and the electron recursion, derived in theseries with no fitted parameters, is the fine-structure constant. What the standardaccount treats as intrinsic uncertainty is identified as unresolvable displacement at ascale ratio the framework computes. The mechanism is the published one; this papersupplies its scale variable.