What question did this study set out to answer?

To show that atomic spectra in hydrogen arise from constructive interference of hyperspace projections.

March 16, 2026Open Access

Atomic Spectra as Constructive Interference of Hyperspace Projections in the Unified Theory of Flor (TUF): From Orbital Quantization to Fine Structure

Q: What does this research mean for the field?

The discrete spectrum of the hydrogen atom, including Bohr radii, energy levels, electron spin, and fine structure, arises from the constructive interference of projection amplitudes from an atemporal hyperspace onto observable spacetime. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

Key Points

To show that atomic spectra in hydrogen arise from constructive interference of hyperspace projections.
Analyze the discrete spectrum of the hydrogen atom
Investigate the geometric implications of Sagnac holonomy
Derive the Schrödinger equation from Wick-rotation projections
All predictions match experimental data within 0.4% for fine structure.
The residual discrepancy is linked to the Lamb shift.
An independent formalism for vacuum fluctuations is planned for future work.

Abstract

We demonstrate that the discrete spectrum of the hydrogen atom — Bohr radii, energy levels, electron spin, and fine structure — all follow from a single principle: the constructive interference of projection amplitudes from the atemporal hyperspace Ξ onto observable spacetime M⁴×S¹. The de Broglie relation, orbital quantization, and spin ℏ/2 are not independent postulates but geometric consequences of the Sagnac holonomy of the compactified fifth dimension S¹. The Schrödinger equation emerges as the self-consistency condition of the Wick-rotation projection. All predictions agree with experiment to < 0.4% at the fine structure level. The residual is the Lamb shift at order α⁵, which requires the vacuum fluctuation formalism of TUF and will be derived separately. This paper is part of the TUF series:- Paper 0 (Ontological Foundation): https://doi.org/10.5281/zenodo.19024705- Paper 1 (Fermion masses): https://doi.org/10.5281/zenodo.18988060- Paper 2 (Three generations): https://doi.org/10.5281/zenodo.18991190- Paper 3 (Dark matter): https://doi.org/10.5281/zenodo.18991306- Paper 5 (Cosmological constant): https://doi.org/10.5281/zenodo.19024913- Paper 6 (Spectral fixed point): https://doi.org/10.5281/zenodo.19025379

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Cite This Study

Fabián Flor (Sun,) studied this question.

synapsesocial.com/papers/69b79ea18166e15b153ac397 https://doi.org/https://doi.org/10.5281/zenodo.19025651

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