Relativistic Locality from Electromagnetism to Quantum Field Theory

TL;DR

This paper investigates the concept of relativistic locality in quantum field theory, showing that the many-worlds interpretation can be fundamentally local depending on the method of assigning states, challenging previous objections.

Contribution

It demonstrates that quantum field theory can be considered local without collapse, using different state assignment methods, and supports the locality of the many-worlds interpretation.

Findings

Field wave functional approach shows locality in quantum field theory.

Particle wave function approach indicates non-locality or state assignment issues.

Supports the fundamental locality of the many-worlds interpretation.

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 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 reduced density matrix states 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 quantum field theory (without collapse) 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 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.