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Particles creation and annihilation: Bohmian approaches. A metaphysical inquiry on the Ontology of Quantum Field Theory

Andréa Oldofredi

Published Jan 1, 2016• 0 citations
OpenAlex

Abstract

In this PhD thesis, the candidate has performed a metaphysical inquiry on the ontological structure of quantum field theory. This analysis s required since it is the rnost advanced physical theory concerned with the inherent structures of our reality. Unfortunately, this theory relies on the ill-defîned structures (both conceptual and mathematical) of quantum mechanics. After having convincingly refuted the widespread belief that an ontology of localizable particles is incompatible with the basic tenets of quantum field theory, the thesis compared the metaphysical pros and cons of two proposais: the so-called "Bell type quantum field theories", which associate an ontology of particles to (more or less) any regularized quantum field theory; in such theories the particles are non persistent in time (they can be created and annihilated) and evolve according to a non deterministic law , and the so called "Dirac sea models", that allow for ail ontology of persisting particles that move on continuous trajectories following a deterministic law. These models are based on a ontologically/technically consistent approach, thus they represent two viable alternative to quantum field theory.

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In this PhD thesis, the candidate has performed a metaphysical inquiry on the ontological structure of quantum field theory. This analysis s required since it is the rnost advanced physical theory concerned with the inherent structures of our reality. Unfortunately, this theory relies on the ill-defîned structures (both conceptual and mathematical) of quantum mechanics. After having convincingly refuted the widespread belief that an ontology of localizable particles is incompatible with the basic tenets of quantum field theory, the thesis compared the metaphysical pros and cons of two proposais: the so-called "Bell type quantum field theories", which associate an ontology of particles to (more or less) any regularized quantum field theory; in such theories the particles are non persistent in time (they can be created and annihilated) and evolve according to a non deterministic law , and the so called "Dirac sea models", that allow for ail ontology of persisting particles that move on continuous trajectories following a deterministic law. These models are based on a ontologically/technically consistent approach, thus they represent two viable alternative to quantum field theory.
We show that the Bohmian approach in terms of persisting particles that move on continuous trajectories following a deterministic law can be literally applied to quantum field theory. By means of the Dirac sea model—exemplified in the electron sector of the standard model neglecting radiation—we explain how starting from persisting particles, one is led to standard QFT employing creation and annihilation operators when tracking the dynamics with respect to a reference state, the so-called vacuum. Since on the level of wave functions, both formalisms are mathematically equivalent, this proposal provides for an ontology of QFT that includes a dynamics of individual processes, solves the measurement problem, and explains the appearance of creation and annihilation events. 1. Bohmian Mechanics from Quantum Mechanics to Quantum Field Theory2. The Dirac Sea Model3. Equilibrium States and the Vacuum4. Excitations of the Vacuum and the Fock Space Formalism5. The Appearance of Particle Creations and Annihilations6. The Merits of the Bohmian Approach
This paper reviews and discusses two extensions of Bohmian Mechanics to the phenomena of particle creation and annihilation typically observed in Quantum Field Theory (QFT): the so-called Bell-type Quantum Field Theory and the Dirac Sea representation. These theories have a secure metaphysical basis as they postulate a particle ontology while satisfying the requirements imposed by the Primitive Ontology approach to quantum physics. Furthermore, their methodological perspective intentionally provides a set of rules to immunize physical theories to the conceptual and technical problems plaguing the standard formulation of Quantum Mechanics and QFT. A metaphysical analysis of both theories will be given, emphasizing the relevant features of each proposal. Finally, it will be acknowledged that, despite the metaphysical virtues and niceties of these frameworks, ultimately they do not provide definitive answers to other cogent foundational issues in QFT. Thus, these theories (as well as the other Bohmian extensions to QFT) should be considered as partial solutions to the problems raised by the quantum theory of fields. This situation can be considered incentive for further research.
We show that the Bohmian approach in terms of persisting particles that move on continuous trajectories following a deterministic law can be literally applied to QFT. By means of the Dirac sea model -- exemplified in the electron sector of the standard model neglecting radiation -- we explain how starting from persisting particles, one is led to standard QFT employing creation and annihilation operators when tracking the dynamics with respect to a reference state, the so-called vacuum. Since on the level of wave functions, both formalisms are mathematically equivalent, this proposal provides for an ontology of QFT that includes a dynamics of individual processes, solves the measurement problem and explains the appearance of creation and annihilation events.
This chapter shows that the Bohmian approach does the same service for quantum field theory (QFT) that it does for quantum mechanics. The mathematical problems left aside, when it comes to the ontology of QFT, one has to be concerned with what is going on in the world according to the theory. The chapter examines so-called Dirac sea model or hole theory, which was the one to predict the phenomenon of electron-positron pair-creation. In general, the Dirac sea model applies to any fermion sector and potentially any interaction between those fermions. One can emphasize the quasi-particles character of the excitations already in the mathematical formalism. The Bohmian approach vindicates the minimalist ontology of there being only matter points individuated by distance relations and the change of these relations also when it comes to our most advanced physical theory of matter—the standard model of QFT.
This thesis aims to contribute to the discussion of how to interpret the Bohmian ontology. Bohmian Mechanics is a quantum theory that describes the motion of particles, whose trajectories are determined by the quantum wave-function. This theory faces two key questions. The former concerns the metaphysical characterization of the particles; the latter relates to the ontological status of the wave-function. \nAfter briefly presenting two possible metaphysical characterizations of the particles, I dedicate the bulk of this work to investigating the status of the wave-function. In particular, I analyse the realist view (which regards the wave-function as a multi-dimensional field) and the nomological view (which considers the wave-function as a law-like entity). My investigation touches upon different levels of inquiry. First, I show that these two ontological interpretations depend on contrasting formulations of the law that dictates the particle motion. Second, I argue that both views defend very problematic ontologies that not only violate familiar metaphysical criteria but also fail to provide a satisfactory explanation of the relation between the particles and the wave-function. Third, I spell out the implicit methodologies that underlie the two views, arguing that they conflate three important categories that should rather be kept separate: the informationally-complete representation of the system, the ontologically-complete representation of the system, and the ontology itself. \nFinally, I present and advocate structural realism as the metaphysical framework for investigating and understanding the Bohmian ontology. According to the structuralist interpretation, the wave-function represents a network of modal relations whose relata are the particles. I argue that this third view provides the best account of the Bohmian system for three reasons. First of all, it offers a parsimonious ontology that does not create any issue of metaphysical underdetermination. Secondly, it supplies an explanatorily powerful ontology. Thirdly, it relies on a sound methodological program. I conclude with an interesting insight: this structuralist interpretation can be regarded as reconciling the realist view and the nomological view given that it takes on aspects of both views and is compatible with both formulations of the law of motion for the particles. \n
Many attempts have been made to provide Quantum Field Theory with conceptually clear and mathematically rigorous foundations; remarkable examples are the Bohmian and the algebraic perspectives respectively. In this essay we introduce the dissipative approach to QFT, a new alternative formulation of the theory explaining the phenomena of particle creation and annihilation starting from nonequilibrium thermodynamics. It is shown that DQFT presents a rigorous mathematical structure, and a clear particle ontology, taking the best from the mentioned perspectives. Finally, after the discussion of its principal implications and consequences, we compare it with the main Bohmian QFTs implementing a particle ontology.