Relativistic Locality from Electromagnetism to Quantum Field Theory

Abstract 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, what is happening within a region fixes what will happen in the contracting lightcone with that region as its base. The Klein–Gordon and Dirac equations meet the same standard. The chapter shows that this standard can also be applied to quantum field theory (without collapse), examining two different ways of assigning reduced density matrix states to regions of space. The 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 nonlocality or an inability to assign states to regions, depending on the choice of creation operators. The chapter takes this analysis of quantum field theory (without collapse) to show that the many-worlds interpretation of quantum physics is local at the fundamental level. Debates about measurement and the branching of worlds do not challenge this fundamental locality.