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arXiv:2603.18692 · Entropy

A simple understanding of quantum electrodynamics using Bohmian trajectories: detecting non-ontic photons

Juan José Seoane, Abdelilah Benali, Xavier Oriols

quant-phSubmitted Mar 19, 2026• Announced Mar 20, 2026• 1 citation• Revised Apr 27, 2026 (v2)
v1 · Mar 19, 2026v2 · Apr 27, 2026
arXivHTMLPDF

Abstract

The use of Bohmian mechanics as a practical tool for modeling non-relativistic quantum phenomena of matter provides clear evidence of its success, not only as a way to interpret the foundations of quantum mechanics, but also as a computational framework. In the literature, it is frequently argued that such a realistic view-based on deterministic trajectories cannot account for phenomena involving the "creation" and "annihilation" of photons. In this paper, by revisiting and rehabilitating earlier proposals, we show how quantum optics can be modeled using Bohmian trajectories for electrons in physical space, together with well-defined electromagnetic fields evolving in time. By paying special attention to an experiment demonstrating partition noise for photons, and to how the Born rule emerges in this context, the paper pursues two main goals. First, it vindicates the pedagogical use of this simple Bohmian framework to compute, understand, and visualize quantum electrodynamics phenomena. Second, given that measurements are ultimately indicated on matter pointers, it clarifies what it means to measure photon or electromagnetic-field properties, even when they are considered non-ontic elements.

Journal reference
Entropy 2026, 28(4), 474
DOI
10.3390/e28040474
Comments
35 pages, 5 figures

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The predictions of quantum mechanics are probabilistic. Quantum probabilities are extracted using a postulate of the theory called the Born rule, the status of which is central to the problem of quantum mechanics. Efforts to justify the Born rule from other physical principles, and thus elucidate the measurement process, have involved lengthy statistical or information-theoretic arguments. Here we show that Bohm's deterministic formulation of quantum mechanics allows the Born rule for measurements on a single system to be derived, without any statistical assumptions. We solve a simple example where the creation of an ensemble of identical quantum states, together with position measurements on those states, are described by Bohm's quantum dynamics. The calculated measurement outcomes agree with the Born-rule probabilities, which are thus a consequence of deterministic evolution. Our results demonstrate that quantum probabilities can emerge from simple dynamical laws alone, and they support the view that there is no underlying indeterminism in quantum phenomena.
We formulate Bohmian mechanics (BM) such that the main objects of concern are macroscopic phenomena, while microscopic particle trajectories only play an auxiliary role. Such a formulation makes it easy to understand why BM always makes the same measurable predictions as standard quantum mechanics (QM), irrespective of the details of microscopic trajectories. Relativistic quantum field theory (QFT) is interpreted as an effective long-distance theory that at smaller distances must be replaced by some more fundamental theory. Analogy with condensed-matter physics suggests that this more fundamental theory could have a form of nonrelativistic QM, offering a simple generic resolution of an apparent conflict between BM and relativistic QFT.