Matter Currents Are the Pointer Observables of Quantum Field Theory

Abstract

Decoherence and einselection do not specify, among the field operators of the Standard Model, what realises the pointer basis for Born-rule probabilities on a physical observer. Since observers in relativistic quantum theory are themselves composite fermionic matter, we identify the physical Dirac matter current as the pointer observable on the class of composite detectors built from Standard Model fermions, defined by pure-dephasing environment coupling; strict-timelike smeared current; macroscopic record stability; and the pointer, macroscopicity, and einselection conditions. We read the matter-current expectation as physical-matter density rather than a probability average over outcomes. In this reading, we recover the Born form of pointer-outcome probabilities from non-contextual probability assignment on the joint projection lattice and the Born state-probability link identifying the density operator with the unitarily evolved preparation. Independent and identically distributed trials then recover the Born frequency law under the classical strong law. The branch-conditioned matter-current expectations serve as local beables in Bell’s sense once decoherence has selected the branch structure, and the wavefunction describes correlations in the matter current, with its independent physical status left open. The construction excludes antimatter-dominated, particle-producing, non-Markovian, and rotating or spinful regimes, and single-outcome selection across decoherent branches lies outside standard unitary dynamics and is not derived here.