We propose a reformulation of quantum field theory (QFT) as a relativistic statistical field theory. This rewriting embeds a collapse model within an interacting QFT and thus provides a possible solution to the measurement problem. Additionally, it relaxes structural constraints on standard QFTs and hence might open the way to future mathematically rigorous constructions as well as new numerical methods. Finally, because it shows that collapse models can be hidden within QFTs, this article calls for a reconsideration of the dynamical program, as a possible underpinning rather than as a modification of quantum theory.
We propose a reformulation of quantum field theory (QFT) as a relativistic statistical field theory. This rewriting embeds a collapse model within an interacting QFT and thus provides a possible solution to the measurement problem. Additionally, it relaxes structural constraints on standard QFTs and hence might open the way to future mathematically rigorous constructions as well as new numerical methods. Finally, because it shows that collapse models can be hidden within QFTs, this article calls for a reconsideration of the dynamical program, as a possible underpinning rather than as a modification of quantum theory.
Spontaneous collapse models provide a possible, testable solution to the quantum measurement problem, but constructing a relativistic version applicable to quantum field theory remains an important open challenge. Challenges in constructing relativistic collapse models include avoiding superluminal signaling and foliation dependence, controlling energy production, and ensuring vacuum stability. Here, we present a relativistic collapse framework that addresses these problems at the cost of introducing a new space of physical states, whose complete characterization is left open. A modified, history-dependent Aharonov--Albert prescription describes instantaneous nonlocal state updates on arbitrary spacelike foliations while preserving foliation independence. To ensure vacuum stability, we modify the standard unitary evolution through a prescription that we name dynamical vacuum subtraction. The resulting dynamical map is linear and trace-preserving but not positive on the full set of standard density operators. We establish no-signaling by proving microscopic parameter independence, and identify conditions under which standard nonrelativistic collapse dynamics are recovered. Finally, we apply our framework to a free massive scalar field, obtaining finite particle-number and energy-increase rates at leading order in the long-time regime, together with further promising evidence for the consistency of the framework.
The topic of measurement in relativistic quantum field theory is addressed in this article. Some of the long standing problems of this subject are highlighted, including the incompatibility of an instantaneous ``collapse of the wavefunction'' with relativity of simultaneity, and the difficulty of maintaining causality in the rules for measurement highlighted by ``impossible measurement'' scenarios. Thereafter, the issue is considered from the perspective of mathematical physics. To this end, quantum field theory is described in a model-independent, operator algebraic setting, on generic Lorentzian spacetime manifolds. The process of measurement is modelled by a localized dynamical coupling between a quantum field called the ``system'', and another quantum field, called the ``probe''. The result of the dynamical coupling is a scattering map, whereby measurements carried out on the probe can be interpreted as measurements of induced observables on the system. The localization of the dynamical coupling allows it to derive causal relations for the induced observables. It will be discussed how this approach leads to the concept of selective or non-selective system state updates conditioned on the result of probe measurements, which in turn allows it to obtain conditional probabilities for consecutive probe measurements consistent with relativistic causality and general covariance, without the need for a physical collapse of the wavefunction. In particular, the problem of impossible measurements is resolved. Finally, there is a brief discussion of accelerated detectors and other related work.
Nonrelativistic quantum mechanics is conceptually and mathematically simpler, and does, after all, work very well in a low-energy regime. Any solution of the measurement problem, or any account of the ontology of quantum theory, must yield sensible results in this regime, and so nonrelativistic quantum mechanics can serve as a testing ground for the viability of interpretations. On any approach, empirical adequacy requires recovery of at least an approximation to the quantum probabilities for outcomes of experiments, insofar as these have been verified by experiment. A quantum-mechanical theory is what results when one subjects a classical theory of a system with finitely many degrees of freedom to quantization. The task of extending additional beables theories to the context of quantum field theories remains a work in progress. A dynamical collapse theory modifies the evolution of the quantum state. Standard quantum theory predicts correlations between outcomes of spacelike separated experiments that violate Bell inequalities.
Non-relativistic objective collapse theories have been remarkably successful in addressing the conceptual problems of standard quantum mechanics. Despite substantial efforts, the project of extending them to the relativistic domain remains burdened by significant conceptual objections and technical challenges, often taken to cast doubt on the viability of the program as a whole. On the conceptual side, relativistic collapse theories have been claimed to face challenges involving tension between instantaneous collapse and relativity, frame-dependence of property values and probabilities, the possibility of superluminal signaling and the failure of narratability. On the technical side, persistent infinities, difficulties in constructing fully covariant frameworks and the apparent need for non-standard fields have hindered the development of workable models. In this paper, we offer a systematic rebuttal of the conceptual objections and provide a structured account of the remaining technical challenges. We conclude that relativistic collapse theories do provide a promising route toward a fully relativistic quantum framework that overcomes the conceptual limitations of standard quantum theory.
A field-theoretic version of Wigner’s friend (1961) illustrates how the quantum measurement problem arises for field theory. Similarly, considering spacelike separate measurements of entangled fields by ob-servers akin to Wigner’s friend shows the sense in which relativistic constraints make the measurement problem particularly difficult to resolve in the context of a relativistic field theory. We will consider proposals by Wigner (1961), Bloch (1967), Helwig and Kraus (1970), and Bell (1984) for resolving the measurement problem for quantum field theory. We will conclude by considering the possibility of giving up rich dynamical explanation in the context of a many-maps formu-lation of relativistic quantum field theory. 1. Wigner’s Friend When Eugene Wigner wrote his now famous paper (1961) on the dynam-ical role of observers in quantum mechanics, quantum field theory was flour-
We show that QFT (as well as QM) is not a complete physical theory. We constructed a classical statistical model inducing quantum field averages. The phase space consists of square integrable functions, f(ϕ), of the classical bosonic field, ϕ(x). We call our model prequantum classical statistical field-functional theory -- PCSFFT. The correspondence between classical averages given by PCSFFT and quantum field averages given by QFT is asymptotic. The QFT-average gives the main term in the expansion of the PCSFFT-average with respect to the small parameter α -- dispersion of fluctuations of "vacuum field functionals.'' The Scrödinger equation of QFT is obtained as the Hamilton equation for functionals, F(f), of classical field functions, f(ϕ). The main experimental prediction of PCSFFT is that QFT gives only approximative statistical predictions that might be violated in future experiments.