Planck’s Constant as a Coherence Quantization from Phase Geometry
Internal ID: CGI-RSR-000020
Author(s): Barry L. Petersen
Document Type: Research Paper
Publication Date: May 2026
Original Creation Date: April 2025
Revised Document Date: December 9, 2025
Status: Public
Domains: Physics
Sub-Domain: Quantum Foundations
Research Topics: Planck’s Constant, Coherence Quantization, Phase Geometery
Abstract
Planck’s constant $h$ is traditionally introduced as an empirical constant. Here we show that a natural action scale $\Szero$ arises from phase-constrained coherence geometry: stable $\mu$-field structures must close phase cycles in integral multiples of $2\pi$, which quantizes the action as $S=2\pi n\,\Szero$. The standard quantum relations follow once $\Szero$ is calibrated to laboratory data (de Broglie/Planck–Einstein), yielding $\Szero=\hbar$. Thus quantization is not imposed but emerges from the geometry of phase closure.
Available Document
DOI: 10.5281/zenodo.20257619
Citation:
Petersen, B. L. (2026). Planck’s Constant as a Coherence Quantization from Phase Geometry. Zenodo. https://doi.org/10.5281/zenodo.20257619
Source Code and Supporting Materials
None.
Summary and Notes
Document role:
This paper presents a Coherence Geometry interpretation of Planck’s constant as a natural action scale arising from phase closure in structured coherence fields. Rather than introducing Planck’s constant as an unexplained empirical primitive, the paper argues that stable phase-constrained structures require closed phase cycles in integral multiples of (2\pi), producing quantized action increments of the form
S = 2π n S0.
The standard quantum relations follow once the natural coherence action scale S0 is calibrated to laboratory measurements, yielding S0 = hbar.
Scope:
This document should be read as a structural and geometric account of the role of Planck’s constant in Coherence Geometry. It does not claim to derive the numerical value of (h) without calibration. Instead, it identifies why an action scale of the Planck type appears naturally from phase closure, with the measured value fixed by comparison to physical units and laboratory data.
Framework context:
The paper uses the (\mu)-number / multi-phase framework of Coherence Geometry to explain quantization as a consequence of stable phase closure. Later Coherence Geometry Foundations materials provide broader algebraic and projection context for shared-amplitude, multi-phase structures.
Related Work
Petersen, B. L. (2026). Coherence Geometry Foundations, Part I: Orientation,
Closure, and Algebraic Foundations (Version 0.1). Zenodo.
https://doi.org/10.5281/zenodo.20156532
Petersen, B. L. (2026). Coherence Geometry Foundations, Part II: Physical
Projections (Version 0.1). Zenodo.
https://doi.org/10.5281/zenodo.20156997