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Orbital quantization emerges from classical synchronization of proton-electron internal frequencies.

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Title: Orbital quantization emerges from classical synchronization of proton-electron internal frequencies.
Authors: Preston, John T. preston@mit.edu, Epstein, Harry Ian harryepstein@comcast.net
Source: Physics Essays. Mar2026, Vol. 39 Issue 1, p88-98. 11p.
Subjects: Synchronization, Quantization (Physics), Atomic models, Atomic spectra, Atomic orbitals, Fine-structure constant, Bohr, Niels, 1885-1962, Phase-locked loops
Abstract (English): This paper shows that atomic orbital quantization arises naturally from classical phase synchronization between the oscillatory electromagnetic fields of the proton, electron, and the electron's orbital motion. Stable atomic states emerge only at discrete phase-lock conditions, providing a classical analog that reproduces several atomic quantization formulas without invoking quantum wavefunctions. Additionally, the fine-structure constant acquires physical meaning as the coupling parameter governing phase coherence between internal and orbital oscillations. Phase locking also reproduces the absence of radiation in steady states, as synchronized fields cancel outgoing emission. When applied to Hydrogen, this framework reproduces the Bohr radius, Rydberg constant, and observed emission spectrum using only Coulombic dynamics and phase locking. Helium and Lithium spectra are also calculated. This work presents a deterministic, classical analog framework that reproduces selected atomic quantization results and may offer insight into synchronization-like mechanisms underlying quantum. [ABSTRACT FROM AUTHOR]
Abstract (French): Cet article montre que la quantification des orbitales atomiques émerge naturellement d'une synchronisation de phase classique entre les champs électromagnétiques oscillants du proton, de l'électron et du mouvement orbital de l'électron. Les états atomiques stables n'apparaissent que dans des conditions discrètes de verrouillage de phase, éliminant ainsi la nécessité de postulations quantiques probabilistes, et la constante de structure fine acquiert une signification physique en tant que paramètre de couplage régissant la cohérence de phase entre les oscillations internes et orbitales. Le verrouillage de phase explique également l'absence de rayonnement dans les états stationnaires, les champs synchronisés annulant l'émission sortante. Appliqué à l'hydrogène, ce cadre reproduit le rayon de Bohr, la constante de Rydberg et le spectre d'émission observé en utilisant uniquement la dynamique coulombienne et le verrouillage de phase. Les spectres de l'hélium et du lithium sont également calculés. Ce travail présente une base déterministe et classique de la structure atomique, dans laquelle les états quantifiés émergent d'une synchronisation électromagnétique harmonique plutôt que de règles quantiques imposées. [ABSTRACT FROM AUTHOR]
Copyright of Physics Essays is the property of Physics Essays Publication and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Orbital quantization emerges from classical synchronization of proton-electron internal frequencies.
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  Data: <searchLink fieldCode="AR" term="%22Preston%2C+John+T%2E%22">Preston, John T.</searchLink><i> preston@mit.edu</i><br /><searchLink fieldCode="AR" term="%22Epstein%2C+Harry+Ian%22">Epstein, Harry Ian</searchLink><i> harryepstein@comcast.net</i>
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  Data: <searchLink fieldCode="JN" term="%22Physics+Essays%22">Physics Essays</searchLink>. Mar2026, Vol. 39 Issue 1, p88-98. 11p.
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  Data: <searchLink fieldCode="DE" term="%22Synchronization%22">Synchronization</searchLink><br /><searchLink fieldCode="DE" term="%22Quantization+%28Physics%29%22">Quantization (Physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Atomic+models%22">Atomic models</searchLink><br /><searchLink fieldCode="DE" term="%22Atomic+spectra%22">Atomic spectra</searchLink><br /><searchLink fieldCode="DE" term="%22Atomic+orbitals%22">Atomic orbitals</searchLink><br /><searchLink fieldCode="DE" term="%22Fine-structure+constant%22">Fine-structure constant</searchLink><br /><searchLink fieldCode="DE" term="%22Bohr%2C+Niels%2C+1885-1962%22">Bohr, Niels, 1885-1962</searchLink><br /><searchLink fieldCode="DE" term="%22Phase-locked+loops%22">Phase-locked loops</searchLink>
– Name: Abstract
  Label: Abstract (English)
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  Data: This paper shows that atomic orbital quantization arises naturally from classical phase synchronization between the oscillatory electromagnetic fields of the proton, electron, and the electron's orbital motion. Stable atomic states emerge only at discrete phase-lock conditions, providing a classical analog that reproduces several atomic quantization formulas without invoking quantum wavefunctions. Additionally, the fine-structure constant acquires physical meaning as the coupling parameter governing phase coherence between internal and orbital oscillations. Phase locking also reproduces the absence of radiation in steady states, as synchronized fields cancel outgoing emission. When applied to Hydrogen, this framework reproduces the Bohr radius, Rydberg constant, and observed emission spectrum using only Coulombic dynamics and phase locking. Helium and Lithium spectra are also calculated. This work presents a deterministic, classical analog framework that reproduces selected atomic quantization results and may offer insight into synchronization-like mechanisms underlying quantum. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label: Abstract (French)
  Group: Ab
  Data: Cet article montre que la quantification des orbitales atomiques émerge naturellement d'une synchronisation de phase classique entre les champs électromagnétiques oscillants du proton, de l'électron et du mouvement orbital de l'électron. Les états atomiques stables n'apparaissent que dans des conditions discrètes de verrouillage de phase, éliminant ainsi la nécessité de postulations quantiques probabilistes, et la constante de structure fine acquiert une signification physique en tant que paramètre de couplage régissant la cohérence de phase entre les oscillations internes et orbitales. Le verrouillage de phase explique également l'absence de rayonnement dans les états stationnaires, les champs synchronisés annulant l'émission sortante. Appliqué à l'hydrogène, ce cadre reproduit le rayon de Bohr, la constante de Rydberg et le spectre d'émission observé en utilisant uniquement la dynamique coulombienne et le verrouillage de phase. Les spectres de l'hélium et du lithium sont également calculés. Ce travail présente une base déterministe et classique de la structure atomique, dans laquelle les états quantifiés émergent d'une synchronisation électromagnétique harmonique plutôt que de règles quantiques imposées. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Physics Essays is the property of Physics Essays Publication and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.4006/0836-1398-39.1.088
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        Text: English
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        PageCount: 11
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      – SubjectFull: Synchronization
        Type: general
      – SubjectFull: Quantization (Physics)
        Type: general
      – SubjectFull: Atomic models
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      – SubjectFull: Atomic spectra
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      – SubjectFull: Atomic orbitals
        Type: general
      – SubjectFull: Fine-structure constant
        Type: general
      – SubjectFull: Bohr, Niels, 1885-1962
        Type: general
      – SubjectFull: Phase-locked loops
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      – TitleFull: Orbital quantization emerges from classical synchronization of proton-electron internal frequencies.
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              Text: Mar2026
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