On the Structure of Local Observables in String Field Theory

In 1993 Sorkin showed that extending textbook ideal measurements to relativistic quantum fields conflicts with locality as for generic observables, the state-update associated with an ideal measurement can transmit information faster than light, even when the intervening and readout regions are spacelike separated. We reformulate this tension in covariant string field theory, where the fundamental degrees of freedom are extended and the spacetime description involves operators with intrinsic string-scale nonlocality. We show that the paradox relies on the existence of sharply localized projectors and an exact Lüders reduction rule, neither of which is operationally realized in string field theory. This yields an operational notion of locality that resolves Sorkin’s signaling channel while recovering local quantum field theory in the limit of vanishing string length.