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Emergent quantization from a dynamic vacuum

Harold White ^*, Jerry Vera , Andre Sylvester, and Leonard Dudzinski

Casimir, Inc., 16441 Space Center Boulevard, Bldg. D-200, Houston, Texas 77058, USA

^*Contact author: sonny@casimirspace.com

Phys. Rev. Research 8, 013264 – Published 9 March, 2026

DOI: https://doi.org/10.1103/l8y7-r3rm

Abstract

We show that adding quadratic temporal dispersion to a dynamic-vacuum acoustic model yields a fully analytic, exactly isospectral mapping to the hydrogenic Coulomb problem. In the regime $ω = D q^{2}$ with $D = ℏ / (2 m_{eff})$ , a proton-imprinted constitutive profile produces an inverse sound speed $1 / c_{s}^{2} (r) = A (ω) + C (ω) / r$ and hence a time-harmonic operator $(\nabla^{2} + k_{eff}^{2})$ that is Coulombic at each bound eigenfrequency. Separation of variables yields the exact hydrogenic eigenfunctions $R_{n ℓ} (r) Y_{ℓ}^{m} (θ, ϕ)$ ; the angular labels $(ℓ, m)$ emerge naturally from the Laplace-Beltrami spectrum on $S^{2}$ via rotational symmetry and boundary conditions (as in standard quantum mechanics), while localization follows from $A (ω_{n}) < 0$ in a reactive stop band consistent with causal, passive dispersion. While angular-momentum quantization follows directly from rotational symmetry and boundary conditions in standard quantum mechanics (consistent with Noether's theorem), here it emerges within a classical-like dispersive acoustic framework without introducing additional wave-mechanical postulates beyond symmetry and self-adjointness. This highlights dispersion's role in bridging a hydrodynamic description to quantumlike spectral structure. Identifying $q_{n} \equiv κ_{n}$ maps spatial scale to frequency, giving $ω_{n} = D κ_{n}^{2} \propto 1 / n^{2}$ and reproducing the Rydberg ladder. Calibration to the reduced-mass Rydberg frequency ( $ω_{*} = 2 π c R_{H}$ ) fixes $D = ℏ / (2 μ)$ and $m_{eff} = μ$ , with no free parameters. We determine the frequency dependence of $A (ω_{n})$ and $C (ω_{n})$ consistent with the underlying dispersive physics and demonstrate agreement with hydrogenic mode shapes and transition lines. The framework also predicts isotope shifts $[μ \to μ (M)]$ and symmetry-respecting Stark/Zeeman analogues. Dispersion thus renders quantization an emergent consequence of symmetry, boundary conditions, and causal response in a dynamic vacuum.

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References (15)

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Phys. Rev. Research 8, 013264– Published 9 March, 2026

Vol. 8, Iss. 1 — March - May 2026

Received 24 October 2025
Accepted 18 February 2026

DOI: https://doi.org/10.1103/l8y7-r3rm

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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Emergent quantization from a dynamic vacuum

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