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.