bb69bc25d3abcca44f4397273d9bf312 entropy-28-00474-v2.pdf cadd203da90f97185b82f36437f38ae44549ea60 entropy-28-00474-v2.pdf ed4c9cec1ce665621c637acbc17f075ae2f05f4f2bdfe26f1ff22452d77ff401 entropy-28-00474-v2.pdf Title: A Simple Understanding of Quantum Electrodynamics Using Bohmian Trajectories: Detecting Non-Ontic Photons Subject: 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 experimental scenario demonstrating partition noise for photons, and to how the Born rule emerges in this context, the paper pursues two main goals. First, it validates the use of this simple Bohmian framework for pedagogical and computational purposes in understanding and visualizing 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. Keywords: Bohmian mechanics; quantum optics; Bohmian trajectories; Born rule; action-at-a-distance electrodynamics; quantum foundations Author: Juan José Seoane, Abdelilah Benali and Xavier Oriols Creator: LaTeX with hyperref Producer: pdfTeX-1.40.25; modified using OpenPDF 1.4.2 CreationDate: Fri Apr 24 11:33:33 2026 CEST ModDate: Fri Apr 24 11:36:37 2026 CEST Custom Metadata: yes Metadata Stream: no Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 38 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 11869182 bytes Optimized: no PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- GXPMOJ+URWPalladioL-Bold Type 1 Custom yes yes yes 185 0 WVQRVH+URWPalladioL-Roma Type 1 Custom yes yes yes 186 0 CJDQEX+URWPalladioL-Ital Type 1 Custom yes yes yes 187 0 WTMORE+PazoMath Type 1 Builtin yes yes yes 351 0 AUURTZ+PazoMath-Italic Type 1 Builtin yes yes yes 352 0 SOSTRQ+CMR10 Type 1 Builtin yes yes yes 353 0 NKULIZ+CMSY10 Type 1 Builtin yes yes yes 354 0 YERLIZ+CMEX10 Type 1 Builtin yes yes yes 394 0 OQQBOK+EUFM10 Type 1 Builtin yes yes yes 460 0 PWQHWD+MSBM10 Type 1 Builtin yes yes yes 461 0 GJXTFQ+ArialNarrow TrueType WinAnsi yes yes yes 674 0 YRBHXW+ArialMT CID TrueType Identity-H yes yes yes 675 0 TIIYPD+Verdana TrueType WinAnsi yes yes yes 676 0 ZAPSNM+Verdana CID TrueType Identity-H yes yes yes 677 0 HQDBQN+ArialMT TrueType WinAnsi yes yes yes 678 0 WHTTTZ+LucidaSansUnicode CID TrueType Identity-H yes yes yes 679 0 QZDURO+Cambria CID TrueType Identity-H yes yes yes 680 0 HQDBQN+ArialMT TrueType WinAnsi yes yes yes 681 0 HINBMY+ArialMT CID TrueType Identity-H yes yes yes 682 0 UBACJG+LMRoman10-Regular Type 1 Custom yes yes yes 886 0 QKEDQR+ArialMT CID TrueType Identity-H yes yes yes 887 0 FEQGGN+ArialMT TrueType WinAnsi yes yes yes 888 0 ZNNFTK+ArialMT CID TrueType Identity-H yes yes yes 889 0 GBKOXO+ArialNarrow TrueType WinAnsi yes yes yes 890 0 WHTTTZ+LucidaSansUnicode CID TrueType Identity-H yes yes yes 891 0 QZDURO+Cambria CID TrueType Identity-H yes yes yes 892 0 TIIYPD+Verdana TrueType WinAnsi yes yes yes 893 0 ZAPSNM+Verdana CID TrueType Identity-H yes yes yes 894 0 LAZQVP+ArialMT TrueType WinAnsi yes yes yes 979 0 KAOYLY+ArialMT CID TrueType Identity-H yes yes yes 980 0 Jhove (Rel. 1.28.0, 2023-05-18) Date: 2026-05-06 03:07:48 CEST RepresentationInformation: entropy-28-00474-v2.pdf ReportingModule: PDF-hul, Rel. 1.12.4 (2023-03-16) LastModified: 2026-05-05 14:01:14 CEST Size: 11869182 Format: PDF Version: 1.7 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 1428 FreeObjects: 1 IncrementalUpdates: 0 DocumentCatalog: ViewerPreferences: HideToolbar: false HideMenubar: false HideWindowUI: false FitWindow: true CenterWindow: false DisplayDocTitle: false NonFullScreenPageMode: UseNone Direction: L2R ViewArea: CropBox ViewClip: CropBox PrintArea: CropBox PageClip: CropBox PageLayout: SinglePage PageMode: UseNone Outlines: Item: Title: Introduction Children: Item: Title: What Are Electromagnetic Fields? Item: Title: What Are Photons? Item: Title: Measuring Photon and Light Properties Item: Title: Classical Light–Matter Hamiltonian Children: Item: Title: Matter Item: Title: Electromagnetic Field(s) Item: Title: Minimal Coupling Hamiltonian Item: Title: Mode Decomposition Children: Item: Title: Electromagnetic Energy Item: Title: Light–Matter Interaction Item: Title: Canonical Quantization Children: Item: Title: Quantization of Matter Item: Title: Quantization of the Electromagnetic Field Item: Title: The Schrödinger Equation Item: Title: Bohmianization Item: Title: Born Rule and Statistical Predictions Item: Title: Photon Partition Noise Children: Item: Title: Simulation of a Non-Measured Light–Matter System Children: Item: Title: Model Without Measuring Apparatus Item: Title: Numerical Results Without Measuring Apparatus Item: Title: Simulation of a Measured Light–Matter System Children: Item: Title: Model with Measuring Apparatus Item: Title: Numerical Results with Measuring Apparatus Item: Title: Conclusions Item: Title: Appendix A. Creation and Annihilation in Fock Space Item: Title: Appendix B. Schrödinger Equation for Two Electrons and One Electromagnetic Mode Item: Title: Appendix C. Schrödinger Equation for Two Electrons, One Electromagnetic Mode and Two Pointers Item: Title: Appendix D. Computation of the Bohmian Trajectories Item: Title: References Info: Title: A Simple Understanding of Quantum Electrodynamics Using Bohmian Trajectories: Detecting Non-Ontic Photons Author: Juan José Seoane, Abdelilah Benali and Xavier Oriols Subject: 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 experimental scenario demonstrating partition noise for photons, and to how the Born rule emerges in this context, the paper pursues two main goals. First, it validates the use of this simple Bohmian framework for pedagogical and computational purposes in understanding and visualizing 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. 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