Fundamental Physical Constants Spreadsheet Calculator

version 3 08NOV2025 Added geometric derivation of Planck’s constant (hₚₐₑd = 2 π² ΔI λ² τ) and updated Compton and Rydberg calculations to use the Swarm-derived h..

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ABSTRACT:  The Swarm Field Equations Calculator implements the Swarm Theory framework for deriving and validating physical constants from first principles. This Excel-based tool encodes the core lattice parameters (λ, κ, N, Φ, C) and calculates derived values including Planck units, electromagnetic constants, the fine-structure constant, and the gravitational constant. The calculator allows users to toggle correction factors on or off, compare uncorrected vs. corrected predictions, and examine the coherence between theory and CODATA reference values. It serves as a reproducible reference for the Swarm Field Theory appendices and provides a transparent platform for testing the theory’s predictive accuracy.

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]

Θ_geom (Route B)
Corrected gravitational closure term [–]

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]