Examines a suggestion by Bell (1984) that a deterministic model might be furnished by the continuum limit of an objective stochastic model which he has proposed for quantum field theory on a lattice. The virtues of models of Bell's type for general quantum systems are discussed, and it is shown that for a system of a fixed number of particles such a model does yield the deterministic de Broglie-Bohm model in an appropriate limit. It is argued, however, that a deterministic limit is unlikely to emerge from a quantum field theory capable of describing particle production and decay. An interpretation of quantum field theory is proposed which has the advantages of Bell's interpretation but is closer to conventional quantum mechanics.
Abstract We propose an extension of Bell-type Bohmian quantum field theories, called Contextual Bohmian Quantum Field Theory (CBQFT), which integrates micro-level dynamics and macro-level contextual structure within a unified, ontologically explicit formalism. CBQFT introduces classical variables
Λ that encode macroscopic contexts—such as detector configurations, thermal phases, or symmetry-breaking sectors—and allows these to modulate the underlying quantum dynamics in a lawlike way. We develop two versions of the model. CBQFT-1 treats context as a fixed but dynamically influential background, entering via a context-sensitive Hamiltonian and modified Bell-type jump rates on a single Fock space. CBQFT-2 upgrades context to a dynamical variable co-evolving with the particle (or field) configuration:
Λ(x,t) selects a (typically inequivalent) representation of the field algebra on a Hilbert space, wavefunctions are realised as global sections of the resulting Hilbert bundle, and Bohmian trajectories are guided by globally well-defined velocity fields constructed from local currents. Context transitions in CBQFT-2 are governed by a stochastic kernel informed by particle (or field) configurations and histories. This yields a Bohmian QFT with an explicit feedback loop between quantum events and macroscopic structure, offering a hylomorphic account of measurement, decoherence, and top–down causation.
Based partly on proving that algebraic relativistic quantum field theory (ARQFT) is a stochastic Einstein local (SEL) theory in the sense of SEL which was introduced by Hellman (1982b) and which is adapted in this paper to ARQFT, the recently proved maximal and typical violation of Bell's inequalities in ARQFT (Summers and Werner 1987a–c) is interpreted in this paper as showing that Bell's inequalities are, in a sense, irrelevant for the problem of Einstein local stochastic hidden variables, especially if this problem is raised in connection with ARQFT. This leads to the question of how to formulate the problem of local hidden variables in ARQFT. By giving a precise definition of hidden-variable theory within the operator algebraic framework of quantum mechanics, it will be argued that the aim of hidden-variable investigations is to determine those classes of quantum theories whose elements represent a statistical content that cannot be reduced in a given way. In some particular way to be stated, a proposition will be stated which distinguishes quantum field theories whose statistical content cannot be reduced without violating some relativistic locality principle.