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arXiv:2511.12403

Nonlocal action in Everettian Quantum Mechanics

Mordecai Waegell, Kelvin J. McQueen

quant-phSubmitted Nov 16, 2025• Announced Nov 18, 2025• 0 citations
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Abstract

According to a common view, Everettian quantum mechanics (EQM) is a local theory because it avoids nonlocal action at a distance, and this is an important point in EQM's favor. Unlike collapse theories, EQM does not allow an action on one system to change the reduced density matrix (RDM) of a remote entangled system - a clear case of nonlocal action. However, EQM does allow an action on one system to change the global state of the system and its remote entangled partners. We argue that such changes should also count as nonlocal actions, meaning EQM is not local after all. First, we consider an argument to the contrary, which deems such global changes to be mere extrinsic changes, whereas nonlocal action requires intrinsic changes to the remote system. We respond that the intrinsic-extrinsic distinction is problematic and cannot hold the weight of this argument. We then try to clarify when actions that change global states count as nonlocal actions. We argue that it is when the global states are essential explanatory mechanisms of the theory. In EQM, the global state is needed to explain why, in an anti-correlated Bell state, Alice's measuring spin-up ensures that she encounters only the branch where Bob measures spin-down.

Comments
19 pages, 1 figure

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According to a common view, Everettian quantum mechanics (EQM) is a local theory because it avoids nonlocal action at a distance, and this is an important point in EQM's favor. Unlike collapse theories, EQM does not allow an action on one system to change the reduced density matrix (RDM) of a remote entangled system - a clear case of nonlocal action. However, EQM does allow an action on one system to change the global state of the system and its remote entangled partners. We argue that such changes should also count as nonlocal actions, meaning EQM is not local after all. First, we consider an argument to the contrary, which deems such global changes to be mere extrinsic changes, whereas nonlocal action requires intrinsic changes to the remote system. We respond that the intrinsic-extrinsic distinction is problematic and cannot hold the weight of this argument. We then try to clarify when actions that change global states count as nonlocal actions. We argue that it is when the global states are essential explanatory mechanisms of the theory. In EQM, the global state is needed to explain why, in an anti-correlated Bell state, Alice's measuring spin-up ensures that she encounters only the branch where Bob measures spin-down.
It is sometimes said that a reason to prefer Everettian quantum mechanics is that it allows one to avoid the kind of spooky action at a distance that is a consequence of quantum entanglement according to other approaches. There is a straightforward argument to show EQM has this virtue, however some advocates argue that this requires we see branching as a local causal process. I explain this reasoning and then show why, given the way Everettians standardly conceive of worlds and branching as emergent phenomena, branching need not be viewed as a causal process for EQM to be relativistically local. Forthcoming in Local Quantum Mechanics, OUP 2026.
An apparently emerging consensus holds that Everettian Quantum Mechanics (EQM), in the Spacetime State Realism (SSR) version of Wallace and Timpson, involves ontological non-locality (i.e., non-separability) but is fully compatible with the dynamical notion of locality usually taken to be required by relativity. The claim of dynamical locality is based on the fact that the local beables postulated by the theory (namely, Reduced Density Matrices, RDMs, associated with localized regions) are not affected by interventions outside their past light cones. However, the theory's non-separability means that it posits non-local beables (namely RDMs for non-localized regions) in addition to the local ones. We argue here that the involvement of non-local beables introduces complications for extant formulations of dynamical locality and at least suggests, contrary to the emerging consensus, that SSR EQM should perhaps not be considered compatible with relativistic causality after all.
It is shown that when properly analyzed using principles consistent with the use of a Hilbert space to describe microscopic properties, quantum mechanics is a local theory: one system cannot influence another system with which it does not interact. Claims to the contrary based on quantum violations of Bell inequalities are shown to be incorrect. A specific example traces a violation of the CHSH Bell inequality in the case of a spin-3/2 particle to the noncommutation of certain quantum operators in a situation where (non)locality is not an issue. A consistent histories analysis of what quantum measurements measure, in terms of quantum properties, is used to identify the basic problem with derivations of Bell inequalities: the use of classical concepts (hidden variables) rather than a probabilistic structure appropriate to the quantum domain. A difficulty with the original Einstein-Podolsky-Rosen (EPR) argument for the incompleteness of quantum mechanics is the use of a counterfactual argument which is not valid if one assumes that Hilbert-space quantum mechanics is complete; locality is not an issue. The quantum correlations that violate Bell inequalities can be understood using local quantum common causes. Wavefunction collapse and Schr\odinger steering are calculational procedures, not physical processes. A general Principle of Einstein Locality rules out nonlocal influences between noninteracting quantum systems. Some suggestions are made for changes in terminology that could clarify discussions of quantum foundations and be less confusing to students.
The standard interpretation of quantum measurement on entangled systems holds that measuring one particle nonlocally collapses the wavefunction of its spacelike-separated partner. We argue that this conclusion rests on a false presupposition: that subsystems of entangled systems possess independent ontic states. If the global wavefunction is the sole ontic object (ψ-ontic holism), then for entangled systems, there is no "state of B" to be affected by measurement at A. Measurement is a local dynamical process-concretely modeled by continuous spontaneous localization-that destroys one local wavefunction component at the measurement site; the global state factorizes as a consequence, and subsystem ontology emerges for the first time. The transition of the distant particle's reduced density matrix from mixed to pure reflects this emergence of separability, not a physical change at the distant location. The framework satisfies no-signaling and embraces the contextuality required by the Kochen-Specker and GHZ theorems. We are explicit about its relation to Bell's theorem: Bell local causality (factorizability) fails, as it must in any empirically adequate theory, but the failure is confined to outcome independence and is identified with the nonseparability of the global ontic state, while parameter independence-and with it the locality of the dynamics-holds exactly. Decoherence provides the mechanism by which the global wavefunction factorizes and classical separability emerges. The apparent nonlocality of quantum mechanics is thus reinterpreted as nonseparability: the fundamental ontology is holistic, but the dynamics are local.
Introduction Fifty years after the publication of Bell's theorem, there remains some controversy regarding what the theorem is telling us about quantum mechanics, and what the experimental violations of Bell inequalities are telling us about the world. This chapter represents my best attempt to be clear about what I think the lessons are. In brief: There is some sort of nonlocality inherent in any quantum theory, and, moreover, in any theory that reproduces, even approximately, the quantum probabilities for the outcomes of experiments. But not all forms of nonlocality are the same; there is a distinction to be made between action at a distance and other forms of nonlocality, and I will argue that the nonlocality needed to violate the Bell inequalities need not involve action at a distance. Furthermore, the distinction between forms of nonlocality makes a difference when it comes to compatibility with relativistic causal structure. The Bell locality condition is a condition which, if satisfied, renders possible a completely local account of the correlations between outcomes of spatially separated experiments. Bell's theorem tells us that the probabilities that we compute from quantum mechanics do not admit of such an account. Modulo auxiliary assumptions that, in my opinion, should be noncontroversial, this yields the conclusion that there must be something nonlocal about any theory that yields the quantum mechanical probabilities or anything close to them. One way to violate the Bell locality condition – and this is the way that any deterministic theory must do it – is via straightforward action at a distance. However, we should also consider the possibility of a stochastic theorywith probabilistic laws that involve irreducible correlations. The sort of nonlocality inherent in such a theory involves relations between events that are significantly different from causal relations as usually conceived. Perhaps surprisingly, such a theory, unlike its deterministic cousins, need not invoke a distinguished relation of distant simultaneity. This makes a difference for the situation of the two sorts of theories vis-a-vis relativity. Though a deterministic theory can achieve the appearance of being relativistic, at the level of observable phenomena, it can do so only by introducing a preferred foliation and with it a causal structure at odds with relativistic causal structures. Things are otherwise with dynamical collapse theories.
It is shown that when properly analyzed using principles consistent with the use of a Hilbert space to describe microscopic properties, quantum mechanics is a local theory: one system cannot influence another system with which it does not interact. Claims to the contrary based on quantum violations of Bell inequalities are argued to be incorrect. A specific example traces a violation of the CHSH Bell inequality in the case of a spin-3/2 particle to the noncommutation of certain quantum operators in a situation where (non)locality is not an issue. A consistent histories analysis of what quantum measurements measure, in terms of quantum properties, is used to identify the basic problem with derivations of Bell inequalities: the use of classical concepts (hidden variables) rather than a probabilistic structure appropriate to the quantum domain. A difficulty with the original Einstein-Podolsky-Rosen (EPR) argument for the incompleteness of quantum mechanics is the use of a counterfactual argument which is not valid if one assumes that Hilbert-space quantum mechanics is complete; locality is not an issue. The quantum correlations that violate Bell inequalities can be understood using local quantum common causes. Wave-function collapse and Schr\"odinger steering are calculational procedures, not physical processes. A general Principle of Einstein Locality rules out nonlocal influences between noninteracting quantum systems. Some suggestions are made for changes in terminology that could clarify discussions of quantum foundations and be less confusing to students.