A Helical Spacetime Ansatz Linking the Planck Scale and Electroweak Mixing

Xiaodan Wu

doi:10.5281/zenodo.22101000

Abstract

We examine a minimal helical ansatz for microscopic spatial structure in which a primitive transverse radius is calibrated from the measured gravitational constant and the helix shape is subsequently fixed by a one-cycle phase-closure condition. The construction originates in the broader Emergent Frame (TEF) proposal, which treats spacetime as an emergent physical entity rather than a structureless pre-existing background, but the present paper is deliberately restricted to one concrete geometry and its quantitative consequence. Inspired mathematically by Euler’s representation of planar rotation, a spatial line is modeled as a right-handed helix with radius $R$ , axial advance per radian $a$ , and dimensionless pitch ratio $q = a / R = tan β$ . A gravity-geometry calibration relation, using $G$ as an empirical input, gives $R_{G} = h G / (8 π c^{3}) = ℓ_{P} /2$ . The model then distinguishes the axial extension generated in one turn from the helical arc length traversed internally: the former sets the cycle energy through the gravitational line-tension scale $c^{4} / G$ , while the latter sets the cycle time. Requiring one complete primitive cycle to close its quantum phase, $E_{cyc} T_{cyc} /ℏ = 2 π$ , yields $q 1 + q^{2} = 2/ π$ , so that $q ≃ 0.556324$ , $β_{G} ≃ 29.08 8^{\circ}$ , and $sin^{2} β_{G} ≃ 0.236348$ . No electroweak observable enters this calculation. The resulting angle is therefore proposed only as a candidate primitive geometric reference for weak mixing, not as a completed derivation of the Weinberg angle. Its numerical proximity to the observed running weak-mixing parameter is presented as the reason this otherwise speculative spacetime ansatz merits further quantitative investigation.

Research Context

This manuscript investigates whether a minimal microscopic helical spacetime ansatz can connect a gravity-calibrated geometric scale with an intrinsic angular quantity numerically close to the electroweak weak-mixing parameter.

The result is presented as a candidate geometric correspondence rather than a completed derivation of electroweak physics. Its purpose is to test whether the proposed spacetime geometry produces nontrivial quantitative structure worthy of further investigation.

Version 5.1 states the one-cycle condition explicitly as quantum phase closure and includes diagnostic discussions of calibration sensitivity, covariance and isotropy, and the field-theoretic matching required for the weak-mixing correspondence.

Publication Status

Version 5.1 is publicly archived on Zenodo as a preprint under the Creative Commons Attribution 4.0 International license. Its version-specific DOI is 10.5281/zenodo.22101000; the concept DOI for the complete version history is 10.5281/zenodo.22100999. Source, verification materials, and release metadata are maintained in the public TEF research repository. The manuscript has not undergone peer review.

Citation

Zenodo citation

Wu, X. (2026). A Helical Spacetime Ansatz Linking the Planck Scale and Electroweak Mixing (Version 5.1). Zenodo. https://doi.org/10.5281/zenodo.22101000

@misc{wu2026helical,
  author = {Wu, Xiaodan},
  title = {A Helical Spacetime Ansatz Linking the Planck Scale and Electroweak Mixing},
  year = {2026},
  publisher = {Zenodo},
  version = {5.1},
  doi = {10.5281/zenodo.22101000},
  url = {https://doi.org/10.5281/zenodo.22101000}
}

From a Gravity-Calibrated Helix to a Conditional Fine-Structure Correspondence inherits the dimensionless helix parameter developed here and tests an explicitly conditional correspondence with the fine-structure constant.

The Emergent Frame Is Now Live is a first-person account of the project’s transition from private exploration to a public research program and the release of this preprint.

Version history

v5.1 — August 21, 2026

Public preprint release on Zenodo. Version DOI: 10.5281/zenodo.22101000.

v5 — August 20, 2026

Manuscript revision used as the basis for the archived v5.1 release.

v4 — August 16, 2026

Previous public working manuscript.

@unpublished{wu2026helical, author = {Xiaodan Wu}, title = {A Helical Spacetime Ansatz Linking the Planck Scale and Electroweak Mixing}, year = {2026}, note = {TEF-2026-001, version v5.1}, url = {https://theemergentframe.org/papers/helical-spacetime-weak-mixing/}, doi = {10.5281/zenodo.22101000}, }

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