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This preprint rigorously demonstrates that Quantum Field Theory satisfies relativistic locality when analyzed without wave function collapse, supporting a local interpretation of the Many-Worlds framework. By reconciling fundamental locality with non-fundamental world branching, the work addresses key objections regarding derivations of the Born Rule from self-locating uncertainty. The analysis bridges high-energy physics theory and foundational quantum mechanics, offering clarity on how relativistic constraints apply to modern interpretations of reality.
Relativistic Locality from Electromagnetism to Quantum Field Theory
arXiv:2412.11532v2 Announce Type: replace 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.
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.
June 12, 2026 preprint. Forthcoming in Local Quantum Mechanics: Everett, Many Worlds, and Reality (ed. Alyssa Ney), New York: Oxford University Press (2026)
Quantum Physics (quant-ph); High Energy Physics - Theory (hep-th); History and Philosophy of Physics (physics.hist-ph)
arXiv:2412.11532 [quant-ph]
(or arXiv:2412.11532v2 [quant-ph] for this version)
Full text under the publisher's open licence · 239 words
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