Fundamental Physical Constants Spreadsheet Calculator

version 4 16MAR2026 

Publication List

https://orcid.org/0009-0008-2011-5602 

email me at:  [e-mail]

ABSTRACT:  

This dataset provides the Swarm Field Equations Calculator, a transparent computational tool used to evaluate relationships between fundamental physical constants derived within the Swarm Field framework.

The calculator is implemented as a spreadsheet that reproduces a series of physical constants using a consistent set of underlying geometric and coherence parameters. The purpose of the calculator is not to perform curve fitting but to demonstrate how derived relationships propagate through the constant system and to allow independent verification of the calculation chain.

The spreadsheet computes and compares predicted values for multiple constants with the recommended values published by CODATA. Core quantities include the fine structure constant, vacuum permittivity, vacuum permeability, Planck constant, and the gravitational constant. Additional derived quantities such as Planck units, Coulomb constant, vacuum impedance, Stefan Boltzmann constant, Bohr radius, and related parameters are also evaluated.

All equations are implemented explicitly within the spreadsheet so that each intermediate value and dependency can be inspected directly. This structure allows users to verify dimensional consistency, inspect propagation of constants, and identify any implementation errors.

The calculator functions as a validation and exploration tool accompanying the Swarm Field derivation papers. It allows readers to reproduce numerical results and to experiment with the relationships between the constants under the assumptions of the model.

No fitting parameters are used in the spreadsheet, and all inputs are documented within the workbook.

Swarm Field Equations Calculator – Parameters

Parameter
Definition / Units

Parameter
Definition / Units

λ
Coherence aperture – smallest stable closure length [m]

ε₀, μ₀
Vacuum permittivity, permeability [F/m], [H/m]

κ
Helical projection (Arthur’s Constant) – projection ratio [–]

t_P
Planck time [s]

N
Rotations per wavelength – helical rotations per λ [–]

l_P
Planck length [m]

Φ
Junction packing factor – lattice packing density [–]

m_P
Planck mass [kg]

C
Discrete Gauss normalization – gravitational closure correction [–]

E_P
Planck energy [J]

τ
Lattice reaction time; τ = κλ / c [s]

q_P
Planck charge [C]

ΔI
Coherence membrane tension; ΔI = ħ / (π λ² τ) [J/m²]

k_e
Coulomb constant [N·m²·C⁻²]

ξ_base
Base suppression factor; κ / (2√(πN)) [–]

Z₀
Vacuum impedance [Ω]

ξ_geom
Geometric suppression factor; ξ_base · Φ [–]

σ
Stefan–Boltzmann constant [W·m⁻²·K⁻⁴]

α_pred
Predicted fine-structure constant [–]

a₀
Bohr radius [m]

ε₀_pred
Predicted vacuum permittivity [F/m]

r_e
Classical electron radius [m]

μ₀_pred
Predicted vacuum permeability [H/m]

λ_C(e), λ̄_C(e)
Electron Compton & reduced Compton wavelength [m]

Θ_geom_base
Base gravitational closure term [–]

R_∞
Rydberg constant [m⁻¹]

E_h
Hartree energy [J]

G
Gravitational constant (uncorrected / corrected) [m³·kg⁻¹·s⁻²]

μ_B
Bohr magneton [J/T]

h, ħ
Planck’s constant; reduced Planck constant [J·s]

μ_N
Nuclear magneton [J/T]

c
Speed of light [m/s]

λ_C(p), λ̄_C(p)
Proton Compton & reduced Compton wavelength [m]

e
Elementary charge [C]

μ_red(e–p)
Reduced electron–proton mass [kg]

k_B
Boltzmann constant [J/K]

a₀_H
Hydrogen Bohr radius [m]

α
Fine-structure constant [–]

R_H
Hydrogen Rydberg constant [m⁻¹]

Version 4 – What Changed

Version 2 includes several structural improvements and corrections to the original calculator.

• The gravitational constant derivation was updated to reflect the revised formulation presented in the 2026 gravity derivation paper.• Incorrect spreadsheet cell references introduced during the initial implementation of the updated gravity route were identified and corrected.• The calculator now reproduces the correct gravitational constant and propagates the value consistently through all Planck scale quantities.• Derived constants dependent on gravity, including Planck length, Planck time, Planck mass, and Planck energy, were recalculated using the corrected implementation.• The legacy "Closure Route B" gravity pathway was removed from the working calculator to simplify the dependency structure. The earlier implementation remains available in previous archived versions of the spreadsheet.• Documentation within the workbook was expanded to clarify the updated gravity derivation and to improve transparency of the calculation chain.

These changes improve the reliability and clarity of the spreadsheet while preserving the transparency of the underlying equations.

版本4，2026年3月16日

发表列表
https://orcid.org/0009-0008-2011-5602

请致邮至：[e-mail]

摘要：
本数据集提供群场方程计算器（Swarm Field Equations Calculator），一款可溯源的计算工具，用于评估基于群场框架（Swarm Field framework）推导得到的各类基本物理常数间的关联关系。

本计算器以电子表格形式实现，通过一组统一的底层几何与相干参数复现一系列物理常数。该工具的设计初衷并非进行曲线拟合，而是用于展示推导得到的关联关系如何在常数体系中传播，并支持对计算链路的独立验证。

本电子表格可计算并对比多个常数的预测值与CODATA发布的推荐值。核心物理量包括精细结构常数、真空介电常数、真空磁导率、普朗克常数以及引力常数。此外，还将评估普朗克单位制、库仑常数、真空阻抗、斯特藩-玻尔兹曼常数、玻尔半径等衍生物理量及相关参数。

所有方程均在电子表格中显式实现，因此可直接查看每一项中间值及其依赖关系。该结构允许使用者验证量纲一致性、追踪常数的传播路径，并排查任何实现错误。

本计算器作为配套工具，用于验证与探索群场推导论文中的相关内容，支持读者复现数值结果，并基于该模型的假设条件开展常数间关联关系的实验性研究。

本电子表格未使用任何拟合参数，且所有输入项均在工作簿中留有文档说明。

群场方程计算器——参数

参数 | 定义 / 单位 | 参数 | 定义 / 单位
--- | --- | --- | ---
λ | 相干孔径——最小稳定闭合长度 [m] | ε₀, μ₀ | 真空介电常数、真空磁导率 [F/m]、[H/m]
κ | 螺旋投影（亚瑟常数）——投影比 [–] | t_P | 普朗克时间 [s]
N | 每波长旋转数——λ 上的螺旋旋转次数 [–] | l_P | 普朗克长度 [m]
Φ | 结填充因子——晶格填充密度 [–] | m_P | 普朗克质量 [kg]
C | 离散高斯归一化——引力闭合修正项 [–] | E_P | 普朗克能量 [J]
τ | 晶格反应时间；τ = κλ / c [s] | q_P | 普朗克电荷 [C]
ΔI | 相干膜张力；ΔI = ħ / (π λ² τ) [J/m²] | k_e | 库仑常数 [N·m²·C⁻²]
ξ_base | 基础抑制因子；κ / (2√(πN)) [–] | Z₀ | 真空阻抗 [Ω]
ξ_geom | 几何抑制因子；ξ_base · Φ [–] | σ | 斯特藩-玻尔兹曼常数 [W·m⁻²·K⁻⁴]
α_pred | 预测精细结构常数 [–] | a₀ | 玻尔半径 [m]
ε₀_pred | 预测真空介电常数 [F/m] | r_e | 经典电子半径 [m]
μ₀_pred | 预测真空磁导率 [H/m] | λ_C(e), λ̄_C(e) | 电子康普顿波长与约化康普顿波长 [m]
Θ_geom_base | 基础引力闭合项 [–] | R_∞ | 里德伯常数 [m⁻¹]
| | E_h | 哈特里能量 [J]
G | 引力常数（未修正/已修正） [m³·kg⁻¹·s⁻²] | μ_B | 玻尔磁子 [J/T]
h, ħ | 普朗克常数；约化普朗克常数 [J·s] | μ_N | 核磁子 [J/T]
c | 光速 [m/s] | λ_C(p), λ̄_C(p) | 质子康普顿波长与约化康普顿波长 [m]
e | 元电荷 [C] | μ_red(e–p) | 电子-质子约化质量 [kg]
k_B | 玻尔兹曼常数 [J/K] | a₀_H | 氢玻尔半径 [m]
α | 精细结构常数 [–] | R_H | 氢里德伯常数 [m⁻¹]

版本4——更新说明

版本2相较于初始版本完成了多项结构优化与错误修正。
• 更新了引力常数的推导过程，以匹配2026年引力推导论文中提出的修正公式。
• 修正了更新后的引力路径初始实现阶段引入的错误电子表格单元格引用。
• 本计算器现已可复现正确的引力常数，并将该值一致传播至所有普朗克尺度物理量中。
• 基于引力的衍生常数（包括普朗克长度、普朗克时间、普朗克质量与普朗克能量）已通过修正后的实现方式重新计算。
• 移除了工作计算器中的旧版"Closure Route B"引力通路，以简化依赖结构；早期实现版本仍可在该电子表格的历史归档版本中获取。
• 扩展了工作簿内的文档说明，以澄清更新后的引力推导过程，并提升计算链路的透明度。

上述优化提升了本电子表格的可靠性与可读性，同时保留了底层方程的可溯源性。