Planck's Constant as the Field Norm, and the Family Units

In IDWT every particle is a stationary solution of one field law, and every property worked out for a particle so far is proportional to one number, the solution's total size or norm N: its spin is N/2, its charge is a fixed multiple of N, and its energy is its frequency times N, up to a small binding correction. Physics states the same three facts with Planck's constant in place of N. If every particle carries the same norm, Planck's constant is that norm. This paper shows how the norm depends on the solution's frequency at each depth: near threshold N = c_d (m₀ − ω)^(9 − d/2), with one constant c_d per depth. A universal norm therefore fixes one frequency for each depth. The paper then gives the family units, the mass per portion of each particle family, with their frequencies and wavelengths. The lepton unit is the hartree to 1.16%: the electron's count times the square of the fine-structure constant is 0.989. The boson unit is a million times the lepton unit to 0.26%.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-11
DOI
https://doi.org/10.5281/zenodo.24121354
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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preprint

Planck's Constant as the Field Norm, and the Family Units

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Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
preprint

Planck's Constant as the Field Norm, and the Family Units

Fedge No
preprint en

Abstract

In IDWT every particle is a stationary solution of one field law, and every property worked out for a particle so far is proportional to one number, the solution's total size or norm N: its spin is N/2, its charge is a fixed multiple of N, and its energy is its frequency times N, up to a small binding correction. Physics states the same three facts with Planck's constant in place of N. If every particle carries the same norm, Planck's constant is that norm. This paper shows how the norm depends on the solution's frequency at each depth: near threshold N = c_d (m₀ − ω)^(9 − d/2), with one constant c_d per depth. A universal norm therefore fixes one frequency for each depth. The paper then gives the family units, the mass per portion of each particle family, with their frequencies and wavelengths. The lepton unit is the hartree to 1.16%: the electron's count times the square of the fine-structure constant is 0.989. The boson unit is a million times the lepton unit to 0.26%.

Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
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