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May 9, 2026Open Access

The Helix Wave: Spin, Pair Production, and Sphere Covering from One Geometric Principle

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Authors

MSMandeep Singh

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Overview

Derives multiple theoretical results on photon behavior and particle properties through geometric principles, suggesting implications for fundamental physics.

Key Points

  • The study aims to explore the geometric principles underlying photonic and particle behaviors through a singular equation and geometry.
  • Derived 25 results from the equation v²(rot) + v²(fwd) = c² and the geometry of sphere volume (4/3)πR³.
  • Investigated properties like the helix radius, mass-size rule, pair production thresholds, and dispersion relations.
  • Included 10 chapters with detailed theoretical outcomes and verification scripts available online.
  • Photon has a finite helix radius R = (2/3)λ, and mass-size rule m×R = (4/3)π×ℏ/c holds for all particles, yielding mp/me = Re/Rp = 1836.
  • The photon spin ℏ and electron spin ℏ/2 are derived from geometric considerations of helix turns and topology respectively.
  • The dispersion relation matches BK7 glass to <0.5% accuracy with one calibration point.

Cite This Study

Mandeep Singh (2026) studied this question.

synapsesocial.com/papers/69fed17eb9154b0b82878dffhttps://doi.org/10.5281/zenodo.20074020
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Spherical Light: Wavelength as Sphere Size, Redshift as Dilution, and the Universal Rule m × R = n × ħc2026 · 2 citations
  2. 2From Energy to Helical Photon Geometry2026
  3. 3Geometric Origin of the Weak Equivalence Principle in the 0-Sphere Model: Force Classification and the λC Cancellation Theorem in the Helical Geometry2026
  4. 4Photon-Sphere Fragmentation as a Gravitational Mediator: Radiation-Gradient Ejection in the π-Cycle of the 0-Sphere model2026
  5. 5Emergent Minkowski geometry from helical curves in 4D Euclidean space: geometric consequences of the Zitterbewegung ansatz2026