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arxiv: 2603.18692 · v2 · submitted 2026-03-19 · 🪐 quant-ph

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

Juan Jos\'e Seoane , Abdelilah Benali , Xavier Oriols This is my paper

Pith reviewed 2026-05-15 08:46 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Bohmian mechanicsquantum opticsphoton partition noisenon-ontic photonsquantum electrodynamicsBorn ruledeterministic trajectories
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The pith

Bohmian trajectories for electrons combined with classical electromagnetic fields can model quantum optics phenomena such as photon partition noise.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper establishes that quantum optics effects can be understood and computed by letting electrons follow deterministic Bohmian trajectories in physical space while electromagnetic fields evolve as well-defined classical quantities in time. It revisits earlier proposals to show how this framework reproduces partition noise experiments for photons and allows the Born rule for detection probabilities to emerge naturally. The approach also clarifies that measurements of photon properties are ultimately read out from matter pointers rather than from any direct ontology of the fields themselves. A sympathetic reader would care because the model supplies a concrete, visualizable computational tool for QED without invoking quantized field operators.

Core claim

Quantum optics can be modeled using Bohmian trajectories for electrons in physical space, together with well-defined electromagnetic fields evolving in time. This setup accounts for phenomena such as partition noise for photons, demonstrates the emergence of the Born rule, and shows that photon or electromagnetic-field properties are measured indirectly through their effects on matter pointers when the fields themselves are treated as non-ontic.

What carries the argument

Bohmian trajectories of electrons interacting with deterministic, unquantized electromagnetic fields that evolve classically.

Load-bearing premise

Electromagnetic fields can be kept as well-defined classical quantities that evolve deterministically while only the electrons follow Bohmian trajectories.

What would settle it

A concrete photon creation or annihilation signature in an optical experiment that cannot be reproduced by any set of electron Bohmian trajectories coupled to classical electromagnetic fields.

Figures

Figures reproduced from arXiv: 2603.18692 by Abdelilah Benali, Juan Jos\'e Seoane, Xavier Oriols.

Figure 1
Figure 1. Figure 1: (a) Sketch of the simulated system. An optical cavity containing a single elec￾tromagnetic mode of frequency ωc, with two quantum wells located inside the cavity. (b) Two-level energy diagram of the different components of the system at two instants of the Rabi oscillations. The initial state at time t1, |001⟩, corresponds to the electromagnetic field in the excited state while both electrons are in their … view at source ↗
Figure 2
Figure 2. Figure 2: Unitary dynamics of the non-measured system under resonant coherent coupling. [PITH_FULL_IMAGE:figures/full_fig_p021_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) Sketch of the simulated system including the measurement apparatus. An optical cavity containing a single electromagnetic mode of frequency ωc interacts with two quantum dots (QD). Each electron is coupled to an independent pointer degree of freedom, represented by the coordinates y and z, which act as measurement devices for the electronic energies. (b) Two-level energy diagram illustrating the measur… view at source ↗
Figure 4
Figure 4. Figure 4: Measurement -induced effective collapse in the two possible Bohmian outcomes. [PITH_FULL_IMAGE:figures/full_fig_p025_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Conditional wave functions and corresponding Bohmian trajectories at three dif [PITH_FULL_IMAGE:figures/full_fig_p026_5.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper claims that quantum optics, including partition noise in beam-splitter experiments and the emergence of the Born rule, can be modeled using deterministic Bohmian trajectories for electrons in physical space together with classically evolving, well-defined electromagnetic fields (no field quantization). Photons are treated as non-ontic; all measurements are ultimately registered on matter pointers. The approach is offered as a pedagogical and computational framework that rehabilitates earlier Bohmian proposals for QED.

Significance. If the derivations hold, the work would supply a deterministic, trajectory-based route to non-relativistic quantum optics that avoids field operators and vacuum fluctuations, potentially simplifying visualization and calculation of detection statistics while clarifying the ontological status of photons. It would extend the documented practical successes of Bohmian mechanics for matter to the electromagnetic sector.

major comments (2)
  1. [Abstract and section on the partition-noise experiment] The central claim that classical Maxwell evolution plus Bohmian electron trajectories reproduce standard QED partition-noise statistics (exact 50/50 splitting noise without discrete modes or zero-point fluctuations) is load-bearing yet unsupported by any explicit derivation or comparison in the abstract; the manuscript must supply the step-by-step calculation of detection probabilities on matter pointers.
  2. [Modeling strategy and Born-rule emergence discussion] The modeling strategy invokes deterministic classical field evolution while electrons follow the Bohmian guidance equation; it is unclear whether the initial conditions or guidance law implicitly import quantized features, which would undermine the assertion that no field quantization is required (see the weakest-assumption note on classical fields remaining well-defined).
minor comments (1)
  1. [Introduction and conclusion] Define 'non-ontic photons' more precisely and contrast it with standard interpretations to avoid ambiguity in the measurement section.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments have helped us strengthen the presentation of the derivations and clarify the modeling assumptions. We address each major comment below and have made corresponding revisions to the manuscript.

read point-by-point responses

  1. Referee: [Abstract and section on the partition-noise experiment] The central claim that classical Maxwell evolution plus Bohmian electron trajectories reproduce standard QED partition-noise statistics (exact 50/50 splitting noise without discrete modes or zero-point fluctuations) is load-bearing yet unsupported by any explicit derivation or comparison in the abstract; the manuscript must supply the step-by-step calculation of detection probabilities on matter pointers.

    Authors: We agree that an explicit derivation strengthens the central claim. In the revised manuscript we have expanded the abstract to reference the calculation and inserted a dedicated subsection detailing the step-by-step procedure. We integrate the Bohmian guidance equation for the electron trajectories under the classical Maxwell field evolution, sample the initial ensemble according to the matter wave-function density, and compute the resulting pointer-position statistics at the detectors. This yields the exact 50/50 partition probabilities and associated noise without invoking discrete photon modes or zero-point fluctuations; all outcomes are registered solely on matter pointers. revision: yes

  2. Referee: [Modeling strategy and Born-rule emergence discussion] The modeling strategy invokes deterministic classical field evolution while electrons follow the Bohmian guidance equation; it is unclear whether the initial conditions or guidance law implicitly import quantized features, which would undermine the assertion that no field quantization is required (see the weakest-assumption note on classical fields remaining well-defined).

    Authors: We appreciate the request for clarification. The electromagnetic fields are initialized as classical solutions to Maxwell’s equations sourced by the matter currents and evolve deterministically without any added vacuum fluctuations or operator structure. The guidance equation is the standard Bohmian law derived from the non-relativistic Schrödinger equation for the electrons alone; it contains no dependence on quantized field operators. We have added an explicit paragraph in the modeling-strategy section confirming that the fields remain well-defined classical quantities at all times and that the Born rule for detection probabilities arises exclusively from the matter trajectories. This preserves the non-ontic status of photons. revision: yes

Circularity Check

0 steps flagged

No circularity: framework uses independent Bohmian and classical inputs

full rationale

The paper's derivation chain starts from standard Bohmian guidance equations for electron trajectories in physical space and deterministic classical Maxwell evolution for electromagnetic fields. These are external, non-fitted inputs not defined in terms of the target results (Born rule emergence or partition noise). No equations reduce predictions to self-definitions, fitted subsets renamed as predictions, or load-bearing self-citations. The non-ontic photon interpretation is an ontological clarification following from the chosen ontology rather than a definitional loop. The model is presented as a computational and pedagogical tool without internal reduction of its claims to its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The framework relies on the standard Bohmian guidance equation for electrons and the assumption that electromagnetic fields evolve deterministically without quantization; no new free parameters are introduced in the abstract, but the non-ontic status of photons is an interpretive postulate.

axioms (2)
  • domain assumption Electrons follow deterministic trajectories guided by the wave function according to the Bohmian guidance equation
    Invoked as the core of the electron modeling throughout the proposed framework.
  • domain assumption Electromagnetic fields are well-defined and evolve in time according to deterministic equations
    Stated explicitly as the second component of the model for quantum optics.
invented entities (1)
  • non-ontic photons no independent evidence
    purpose: To describe electromagnetic field effects on matter without assigning independent reality to photons themselves
    Introduced to reinterpret photon creation/annihilation and detection as field-matter interactions observed via matter pointers.

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