electric forces in the charged syk model

The connection between gravitational force and operator growth, reported in earlier papers, is generalized to include electromagnetic forces. it is shown how in the u(1)-invariant syk system electric forces emerge through the same mechanisms---the momentum-size correspondence, and operator growth--- that give rise to gravitational force. the unit of electric charge implied by the u(1)-syk theory is consistent with a kaluza-klein radius inverse to the characteristic energy scale of the syk theory.