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arXiv:2209.05345

Path integral and particle ontology

Jia, Ding

Published Jul 11, 2022• 0 citations
arXivHTMLPDF

Abstract

It is often said that in relativistic quantum physics, a fundamental particle ontology is not viable. However, previous works have shown that certain relativistic quantum field theories can be reformulated as path integrals over particle configurations. Drawing on these works, I argue that a fundamental particle ontology is actually viable in relativistic quantum physics.

DOI
10.48550/arxiv.2209.05345

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It is often said that in relativistic quantum physics, a fundamental particle ontology is not viable. However, previous works have shown that certain relativistic quantum field theories can be reformulated as path integrals over particle configurations. Drawing on these works, I argue that a fundamental particle ontology is actually viable in relativistic quantum physics.
Several recent arguments purport to show that there can be no relativistic, quantum-mechanical theory of localizable particles and, thus, that relativity and quantum mechanics can be reconciled only in the context of quantum field theory. We point out some loopholes in the existing arguments, and we provide two no-go theorems to close these loopholes. However, even with these loopholes closed, it does not yet follow that relativity plus quantum mechanics exclusively requires a field ontology, since relativistic quantum field theory itself might permit an ontology of localizable particles supervenient on the fundamental fields. Thus, we provide another no-go theorem to rule out this possibility. Finally, we allay potential worries about this conclusion by arguing that relativistic quantum field theory can nevertheless explain the possibility of "particle detections," as well as the pragmatic utility of "particle talk."
An important way in which quantum field theory (QFT) differs from non-relativistic quantum mechanics is that in QFT systems generically possess an infinite number of degrees of freedom. This chapter examines the proposals for non-fundamental roles that the particle concept plays in particle physics. The fields which feature in the QFT formalism are mathematical expressions; work needs to be done to determine the ontological properties of the entities that are represented by the mathematical field formalism. One difficulty for the quanta interpretation of QFT is that the analysis in terms of quanta offered in the preceding paragraphs is restricted to free systems. The no-go results for interacting systems inspire a different approach to regarding particles as non-fundamental entities. The fields which feature in the QFT formalism are mathematical expressions; work needs to be done to determine the ontological properties of the entities that are represented by the mathematical field formalism.
The existence of ontologically different but empirically indistinguishable versions of non-relativistic quantum mechanics is one of the most serious and widely discussed cases of metaphysical underdetermination. I argue that this problem is unlikely to disappear when we turn to the next more fundamental theory, namely relativistic quantum field theory. The problem is merely overshadowed by yet another interpretational controversy, but it persists regardless of the outcome of this latter debate. I further argue that one should not be too optimistic about transferring ontological lessons learned in the context of one physical theory to the context of a more fundamental theory.
This article probes the question of what interpretations of quantum mechanics actually accomplish. In other domains, which are briefly considered, interpretations serve to make alien systematizations intelligible to us. This often involves clarifying the status of their implicit ontology. A survey of interpretations of non-relativistic quantum mechanics supports the evaluation that these interpretations make a contribution to philosophy, but not to physics. Interpretations of quantum field theory are polarized by the divergence between the Lagrangian field theory that led to the Standard Model of Particle physics and the Algebraic quantum field theory, that discounts an ontology of particles. Ruetsche's interpretation, it is argued, offers a potential for loosening the sharp polarization that presently obtains. A brief evaluation focuses on the functional ontology of quantum field theory considered as an effective theory.
The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple relativistic action proportional to its proper time. This propagator is nonvanishing outside the light cone, implying that spacelike trajectories must be included in the path integral. The propagator matches the WKB approximation to the corresponding configuration-space path integral far from the light cone; outside the light cone that approximation consists of the contribution from a single spacelike geodesic. This propagator also has the unusual property that its short-time limit does not coincide with the WKB approximation, making the construction of a concrete skeletonized version of the path integral more complicated than in nonrelativistic theory.