- The paper introduces a precise local causality (LOC) principle that reframes Bell experiments by focusing on actions rather than events.
- It develops two models of objective probability, 2-MANY and 2-ONE, which reproduce the Born rule without invoking action-at-a-distance.
- The analysis shows that Everettian quantum mechanics explains Bell inequality violations via outcome non-uniqueness rather than nonlocal causation.
Physical Probability in the Everett Interpretation and Bell Inequalities: An Expert Analysis
Introduction
This paper presents a rigorous reformulation of the connection between physical probability in the Everett interpretation of quantum mechanics and the empirical violations of Bell inequalities. The core contributions are two-fold: (i) the introduction of a precise principle of local causality (LOC), which modifies Bell's definition to focus on actions rather than events, and (ii) the proposal of a theory of objective, "physical" probability for Everettian quantum mechanics that is consonant with the Born rule and fundamentally rejects action-at-a-distance. The analysis demonstrates that Everettian quantum theory is consistent with LOC even as it predicts and explains the observed quantum violations of Bell inequalities, and it explicates the logical consequences and loopholes involved.
LOC Principle and Its Implications
The LOC principle postulated in this work asserts that single-case probabilities for outcomes in spacetime region 1 are unaffected by causal changes in a spacelike-separated region 2, conditional on a full specification of the relevant past (region 3). The focus on actions rather than just event specifications tightens the intuitive correspondence to Einstein’s locality heuristics while avoiding epistemic entanglements. LOC formalizes the no-action-at-a-distance axiom with mathematical precision.
Violations of Bell inequalities, as historically demonstrated, imply a tension between quantum predictions and any local, realistic hidden-variable model under certain auxiliary assumptions—specifically, outcome independence, parameter independence, and measurement independence. LOC, as formulated, forces Bell inequalities but admits two distinct loopholes:
- Retrocausation: The possibility that choices made later can influence prior hidden variables or states, circumventing standard causality.
- Non-uniqueness of Remote Outcomes: Everettian quantum theory's many-worlds structure permits remote measurements to induce a superposition of outcomes rather than a unique event, invalidating the uniqueness premise necessary for Bell's deduction.
Notably, the second loophole is exploited only by LOC, not by Bell's original principle, and directly opens Everettian theory to compatibility with local causality.
Everettian Probability: Theories 2-MANY and 2-ONE
The paper advances a frequentist-inspired model of physical probability within Everettian quantum theory by defining probabilities through the ratio of microstates—orthogonal vector states of equal Hilbert-norm—adapted to measurement projectors. Two models are developed:
- 2-MANY: All microstates in the expansion of the quantum state contribute to defining probabilities for observables, consistent with the Born rule. This theory represents probabilities as objective features ("physical probabilities") of the superposition, unaffected by epistemic concerns about uncertainty, ignorance, or predictability.
- 2-ONE: A one-world, deterministic hidden-variable theory where, for each trial, a single microstate is randomly selected according to the microstate expansion. 2-ONE also reproduces the Born rule and Bell inequality violations but does so via retrocausality rather than non-uniqueness and is analogous in structure to pilot-wave theory (Bohmian mechanics).
The importance of 2-MANY is that Everettian quantum probability is objective and statistical in nature, rather than epistemic. Probability counts are defined via expansions of the wavefunction in adapted microstates, and the resulting theory aligns with both the empirical Born rule and with LOC.
Violation of Bell Inequalities and Consistency With LOC
Within the 2-MANY framework, parameter independence is satisfied—remote choices do not affect local probabilities. However, outcome independence is explicitly violated for entangled states, mirroring standard quantum theory, which leads to the empirical violation of Bell inequalities. The crucial difference highlighted is that, in Everettian theory, nonlocal correlations do not arise from action-at-a-distance but from the structure of entanglement and superposition, specifically the failure of outcome uniqueness.
For 2-ONE, parameter independence does not apply contextually, due to retrocausal modification of microstate assignment, yet the theory remains consistent with LOC. This demonstrates that within Everettian quantum mechanics, both permissible loopholes for Bell’s theorem are exploited: retrocausality in deterministic hidden-variable analogues, and outcome non-uniqueness in the many-worlds case.
Theoretical and Practical Implications
By demonstrating that Everettian quantum theory, via 2-MANY, is consistent with local causality yet predicts and explains Bell inequality violations, the paper provides a logical structure wherein many-worlds realism is not at odds with Einsteinian locality. The analysis leads to a deductive inference: if locality and forward causation are assumed, experimental violation of Bell inequalities is strong evidence that remote quantum measurements do not yield unique outcomes—an Everettian signature.
Strong numerical congruence to the Born rule is claimed for the microstate-counting approach, bolstering the physical probability framework. The principle of INVARIANCE proposed—that probabilities of a quantum event cannot be changed without a causal change to the event—justifies equiprobable microstate assignment and is used to derive the extended Born rule.
A major theoretical implication is the distinction between nonlocal explanation (entanglement and superposition) and nonlocal causation (action-at-a-distance): only the latter is excluded by LOC; the former is the actual source of Bell violations in Everettian quantum mechanics.
Future Research Directions
This work suggests multiple directions for future research. Investigating retrocausal models in quantum theory, constructing explicit relativistic hidden-variable models consistent with LOC, and further formalizing the notion of physical probability outside of the Everettian framework may yield additional insights. Extending the microstate-counting approach to dynamic (non-static) processes, generalized measurements (POVMs), and quantum field settings will deepen the understanding of probability in quantum theory.
The paper highlights the need for granular analysis of entanglement-induced nonlocality in other experimental regimes, and for more explicit models wherein the parameters of local causality, retrocausality, and outcome uniqueness can be tuned independently.
Conclusion
This paper rigorously recasts the logic of Bell inequalities in the context of Everettian quantum mechanics, introducing a formal notion of local causality and an objective theory of probability immune to action-at-a-distance. The results demonstrate that the empirically observed violation of Bell inequalities does not entail nonlocal causation but is fully explicable in terms of outcome non-uniqueness, as structurally captured in Everett’s many-worlds ontology. The work provides a deductive framework wherein the many-worlds interpretation not only withstands but is supported by Bell inequality violations, given the absence of retrocausality and superluminal action, and establishes that physical probability in quantum theory can be robustly grounded in its fundamental formalism.
