Relativistic Locality from Electromagnetism to Quantum Field Theory

Electromagnetism is the paradigm case of a theory that satisfies relativistic locality. This can be proven by demonstrating that, once the theory's laws are imposed, the state of a region fixes what happens in a certain portion of the future: the converging light-cone with that region as its base. The Klein-Gordon and Dirac equations meet the same standard. We show that this standard can also be applied to quantum field theory (without collapse), examining two different ways of assigning states (reduced density matrices) to regions of space. Our preferred method begins from field wave functionals and judges quantum field theory to be local. Another method begins from particle wave functions (states in Fock space) and leads to either non-locality or an inability to assign states to regions, depending on the choice of creation operators. We take this analysis of Everettian (no collapse) quantum field theory to show that the many-worlds interpretation of quantum physics is local at the fundamental level. We argue that this fundamental locality is compatible with either local or global (non-local) accounts of the non-fundamental branching of worlds, countering an objection that has been raised to the Sebens-Carroll derivation of the Born Rule from self-locating uncertainty.