Four Fundamental Forces as Successive Complex-Plane Rotations of a Single Algebraic Seed

We propose that the four fundamental forces (gravity, electromagnetism, weak, strong) correspond to four successive rotations by arctan(1/2) ≈ 26.57° in the complex plane, driven by the cascade seed z = 2+i. Each rotation adds one power of z, changing the argument by arctan(1/2) and scaling the norm by √5. The first rotation (n = 1) is gravity; the second (n = 2) produces the 3-4-5 Pythagorean triple governing electromagnetism; the third (n = 3) reaches the weak scale; the fourth (n = 4) crosses the real axis (polarity flip at J = −7+24i), identified with the strong force.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-31
DOI
https://doi.org/10.5281/zenodo.23842332
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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preprint

Four Fundamental Forces as Successive Complex-Plane Rotations of a Single Algebraic Seed

Robert A. Kenney
Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
preprint

Four Fundamental Forces as Successive Complex-Plane Rotations of a Single Algebraic Seed

Robert A. Kenney
preprint en

Abstract

We propose that the four fundamental forces (gravity, electromagnetism, weak, strong) correspond to four successive rotations by arctan(1/2) ≈ 26.57° in the complex plane, driven by the cascade seed z = 2+i. Each rotation adds one power of z, changing the argument by arctan(1/2) and scaling the norm by √5. The first rotation (n = 1) is gravity; the second (n = 2) produces the 3-4-5 Pythagorean triple governing electromagnetism; the third (n = 3) reaches the weak scale; the fourth (n = 4) crosses the real axis (polarity flip at J = −7+24i), identified with the strong force.

Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
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Four Fundamental Forces as Successive Complex-Plane Rotations of a Single Algebraic Seed — Robert A. Kenney · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS