Locally covariant algebraic quantum field theory (LCQFT) satisfies Einstein causality through microcausality and operational no-signalling, yet Bell-type correlations persist in entangled field states across spacelike regions. We demonstrate that this apparent tension reflects a fundamental covariance obstruction: no assignment of classical past variables can simultaneously be covariant under spacetime embeddings, screen off quantum correlations, and reproduce AQFT statistics. This obstruction is distinct from dynamical nonlocality or signalling violations. We formalize this as a no-go theorem in the category-theoretic framework of LCQFT, showing that Bell's notion of local causality -- requiring factorization conditioned on a common past -- is structurally incompatible with diffeomorphism covariance. The failure of Bell locality thus reflects not a breakdown of relativistic causality but the impossibility of embedding quantum correlations into a classical causal framework without introducing preferred foliations or non-covariant beables. This clarifies the conceptual status of nonlocality in relativistic quantum theory.
Locally covariant algebraic quantum field theory (LCQFT) satisfies Einstein causality through microcausality and operational no-signalling, yet Bell-type correlations persist in entangled field states across spacelike regions. We demonstrate that this apparent tension reflects a fundamental covariance obstruction: no assignment of classical past variables can simultaneously be covariant under spacetime embeddings, screen off quantum correlations, and reproduce AQFT statistics. This obstruction is distinct from dynamical nonlocality or signalling violations. We formalize this as a no-go theorem in the category-theoretic framework of LCQFT, showing that Bell's notion of local causality -- requiring factorization conditioned on a common past -- is structurally incompatible with diffeomorphism covariance. The failure of Bell locality thus reflects not a breakdown of relativistic causality but the impossibility of embedding quantum correlations into a classical causal framework without introducing preferred foliations or non-covariant beables. This clarifies the conceptual status of nonlocality in relativistic quantum theory.
This paper surveys the issue of relativistic causality within the framework of algebraic quantum field theory (AQFT). In doing so, we distinguish various notions of causality formulated in the literature and study their relationships, and thereby we offer what we hope to be a useful taxonomy. We propose that the most direct expression of relativistic causality in AQFT is captured not (as has sometimes been claimed) by the spectrum condition but rather by the axiom of local primitive causality, in that it entails a form of local determinism for quantum fields which generalizes the constraint of no superluminal propagation of classical field theories to relativistic quantum field theory. We discuss the status of the axiom of micro-causality by locating its place within a large family of separability/independence/locality conditions developed for AQFT and also by relating it to so-called no-signalling theorems. And we also provide a critical survey of attempts to understand the implications for relativistic causality of the distant correlations endemic to the states in models of AQFT satisfying the standard axioms, and we provide an assessment of attempts to employ Reichenbach's common cause principle in AQFT to defuse worries that these distant correlations implicate direct causal connections between relatively spacelike events.
Between 1964 and 1990, the notion of nonlocality in Bell's papers underwent a profound change as his nonlocality theorem gradually became detached from quantum mechanics, and referred to wider probabilistic theories involving correlations between separated beables. The proposition that standard quantum mechanics is itself nonlocal (more precisely, that it violates ‘local causality’) became divorced from the Bell theorem per se from 1976 on, although this important point is widely overlooked in the literature. In 1990, the year of his death, Bell would express serious misgivings about themathematical form of the local causality condition and leave ill-defined the issue of the consistency between special relativity and violation of the Bell-type inequality. In our view, the significance of the Bell theorem, in both its deterministic and stochastic forms, can only be fully understood by taking into account the fact that a fully Lorentz covariant version of quantum theory, free of action at a distance, can be articulated in the Everett interpretation. Introduction John S. Bell's last word on his celebrated nonlocality theorem and its interpretation appeared in his 1990 paper ‘La nouvelle cuisine’, first published in the year of his untimely death. Bell was careful here to distinguish between the issue of ‘no superluminal signalling’ in quantum theory (both quantum field theory and quantum mechanics) and a principle he first introduced explicitly in 1976 and called ‘local causality’ [1]. In relation to the former, Bell expressed concerns that amplify doubts he had already expressed in 1976. These concerns touch on what is now widely known as the no-signalling theorem in quantum mechanics, and ultimately have to do with Bell's distaste for what he saw as an anthropocentric element in orthodox quantum thinking. In relation to local causality, Bell emphasised that his famous factorizability (no-correlations) condition is not to be seen ‘as the formulation of local causality, but as a consequence thereof’ and stressed how difficult he found it to articulate this consequence. He left the question of any strict inconsistency between violation of factorizability and special relativity theory unresolved, a not insignificant shift from his thinking up to the early 1980s.
Algebraic quantum field theory (AQFT) enforces relativistic locality at the level of observable algebras while allowing globally entangled states, but it does not explain why physically realized states are typically entangled, how entanglement propagates, or how measurement reduces entanglement without enabling superluminal signaling. We present an AQFT-compatible framework in which physically admissible states are restricted to those induced by coherent-sector dynamics in Modal Triplet Theory (MTT), characterized by bounded geometry, a uniform spectral gap, bounded coherent projectors, and disturbance–damping stability. Within this restricted state class, entanglement is interpreted as a global coherence constraint in configuration space, while microcausality, isotony, and the time-slice property remain exact on spacetime. Measurement is modeled as localized disturbance followed by stabilization into admissible basins, yielding partial disentanglement. Standard Bell/CHSH and temporal Bell (Leggett–Garg) violations are recovered without nonlocal influence, and entanglement spreading via mediated interactions is explained as causal propagation through common ancestors subject to finite-speed bounds. The framework unifies AQFT locality with the MTT analyses of measurement and Bell phenomena without modifying quantum field theory axioms.
Bell appealed to the theory of relativity in formulating his principle of local causality. But he maintained that quantum field theories do not conform to that principle, even when their field equations are relativistically covariant and their observable algebras satisfy a relativistically motivated microcausality condition. A pragmatist view of quantum theory and an interventionist approach to causation prompt the reevaluation of local causality and microcausality. Local causality cannot be understood as a reasonable requirement on relativistic quantum field theories: it is unmotivated even if applicable to them. But microcausality emerges as a sufficient condition for the consistent application of a relativistic quantum field theory.
This preprint clarifies a persistent category error in the interpretation of quantum mechanics and relativity by explicitly distinguishing propagation from correlation. Relativistic constraints, including the finite speed of light, apply to the transmission of energy, matter, and information through spacetime. Quantum mechanics, by contrast, permits nonlocal correlations between entangled systems that do not involve transmission, motion, or signal propagation. The apparent instantaneity of quantum effects therefore reflects the revelation of pre-existing correlation structure rather than superluminal dynamics. By maintaining this separation, the preprint shows that the finite speed of light and quantum nonlocality are not in conflict. Light is limited in speed because it propagates; quantum correlations have no speed because nothing propagates. This framing resolves common misconceptions surrounding entanglement, nonlocality, and causality without introducing hidden structures, preferred frames, or violations of relativistic invariance. The work is intended as a conceptual clarification and falsifiable interpretive framework, not a modification of quantum theory or relativity. Keywords quantum correlation nonlocality entanglement speed of light relativity causality non-signaling propagation vs correlation foundations of quantum mechanics conceptual clarification
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.