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The Quantum Mechanical Path Integral: Toward a Realistic Interpretation

Mark F. Sharlow

Published Dec 1, 2007• 8 citations
OpenAlex

Abstract

In this paper, I explore the feasibility of a realistic interpretation of the quantum mechanical path integral - that is, an interpretation according to which the particle actually follows the paths that contribute to the integral. I argue that an interpretation of this sort requires spacetime to have a branching structure similar to the structures of the branching spacetimes proposed by previous authors. I point out one possible way to construct branching spacetimes of the required sort, and I ask whether the resulting interpretation of quantum mechanics is empirically testable.

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In this paper, I explore the feasibility of a realistic interpretation of the quantum mechanical path integral - that is, an interpretation according to which the particle actually follows the paths that contribute to the integral. I argue that an interpretation of this sort requires spacetime to have a branching structure similar to the structures of the branching spacetimes proposed by previous authors. I point out one possible way to construct branching spacetimes of the required sort, and I ask whether the resulting interpretation of quantum mechanics is empirically testable.
The Feynman path integral does not allow a one real path interpretation, because the quantum amplitudes contribute to probabilities in a non-separable manner. The opposite extreme, all paths happen, is not a useful or informative account. In this paper it is shown that an intermediate parsing of the path integral, into realistic non-interfering possibilities, is always available. Each realistic possibility formally corresponds to numerous particle paths, but is arguably best interpreted as a spacetime-valued field. Notably, one actual field history can always be said to occur, although it will generally not have an extremized action. The most obvious concerns with this approach are addressed, indicating necessary follow-up research. But without obvious showstoppers, it seems plausible that the path integral might be reinterpreted to explain quantum phenomena in terms of Lorentz covariant field histories. Quanta 2016; 5: 1–11.
In this paper, I propose a realistic interpretation (RI) of quantum mechanics, that is, an interpretation according to which a particle follows a definite path in spacetime. The path is not deterministic but it is rather a random walk. However, the probability of each step of the walk is found to depend from some average properties of the particle that can be interpreted as its propensity to have a certain macroscopic momentum and energy. The proposed interpretation requires spacetime to be discrete. Prediction of standard quantum mechanics coincide with predictions of large ensembles of particles in the RI.
The Feynman path integral is an essential part of our mathematical description of fundamental nature at small scales. However, what it seems to say about the world is very much at odds with our classical intuitions, and exactly why nature requires us to describe her in this way is currently unknown. We will describe here a possibility according to which the path integral may be the spacetime manifestation of objects existing in a lower-dimensional analog of spacetime until they give rise to the emergence of spacetime objects under a process that is currently labeled a ‘Quantum Measurement’. This idea is based on a mathematical distinction which at present does not appear to be widely appreciated.
The Feynman path integral is an essential part of our mathematical description of fundamental nature at small scales. However, what it seems to say about the world is very much at odds with our classical intu-itions, and exactly why nature requires us to describe her in this way is currently unknown. We will describe here a possibility according to which the path integral may be the spacetime manifestation of objects existing in a lower-dimensional analog of spacetime until they give rise to the emergence of spacetime objects under a process that is currently labeled a ‘Quantum Measure-ment’. This idea is based on a mathematical distinction which at present does not appear to be widely appreci-ated.
Abstract We aim to understand the extent to which something resembling the EPS approach can be applied when the inputs are quantum mechanical rather than classical. That is, we consider versions of EPS with all classical light ray signals replaced by quantum light signals, and all particle signals replaced by quantum particles. In making these substitutions and applying the EPS approach, one ultimately derives a superposition of metric structures as the relevant kinematical structure for quantum spacetime; moreover, as we will see, there is a way of interpreting these outputs in terms of branching spacetime structures.
This article presents a conceptual interpretation of the double-slit experiment using Feynman's path integral formulation. Rather than treating a quantum particle as a point-like object following a single trajectory, the particle's propagation is viewed as a distributed structure in 4D spacetime. In the path-integral picture, this structure is represented by a coherent sum over possible paths between emission and detection. From this perspective, the observed interference pattern emerges from the phase relationships between these possible spacetime paths. The article distinguishes between propagation and interaction. Propagation is described as an extended 4D process, while measurement appears as a localized spacetime event within a 3D spatial slice, producing the point-like detections observed in the double-slit experiment. The aim is not to propose a new physical theory or to explain the mechanism of collapse, but to provide an intuitive geometric interpretation of the standard quantum formalism and its relationship between quantum propagation, interference, and localized measurement outcomes. This is a conceptual essay and interpretive synthesis, not a proposal of a new physical theory.