Universal Scaling Law
Creators: name: Sowersby, Scott
Publisher: name: Zenodo
Year: 2025
Subjects: subject: Universal Design
subject: Universal Design/economics
subject: Universal Design/standards
subject: Universal
subject: Particle physics
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description: . 

 

 This model derives from first principles and introduces a solitonic-based energy scaling framework that encompasses:

Nonlinear wave dynamics and solitonic field configurations,

 Resonance-corrected scaling relations,

  Cross-sector coupling and synchronization terms,

   Application to both microscopic (e.g., particle physics) and macroscopic (e.g., cosmological) domains.

 

 

 

The generalized universal scaling law is:

 

$E(\vec{n}, \vec{q}) = E_0 \prod_{X \in S} (F_X)^{n_X} \prod_{X<Y} \left( \frac{F_X F_Y}{F_{\text{cross}}} \right)^{q_{XY}} \cdot C_{\text{res}}(E) \cdot T(\nu_j, \phi_j$

 

where:

 

    $E_0$: reference energy scale (e.g., 1 GeV),

    $F_X$: sectoral solitonic scaling factors derived from amplitudes, wavenumbers, and coupling constants,

    $\vec{n}$: quantum number vector ($n_{\text{charge}}$, $n_{\text{isospin}}$, $n_{\text{spin}}$, $n_{\text{gen}}$, etc.),

    $q_{XY}$: cross-sector coupling exponents,

    $C_{\text{res}}(E)$: Lorentzian resonance correction factor,

    $T(\nu_j, \phi_j)$: frequency-phase synchronization term,

    $S$: expanded sector set $\{Q, I, S, G, B, T, M, C\}$ for Charge, Isospin, Spin, Generation, Biophysical, Thermal, Magnetohydrodynamic, Cosmological domains.

 

{Resonance Correction}

 

$C_{\text{res}}(E)$$ =1+ \sum_{j=1}^{N} \frac{A_{\text{sol},j}}{1+\left( \frac{E - E_j}{\Gamma_j/2} \right)^2$

 

with $E_j = \hbar \omega_j$, $\Gamma_j$: resonance widths, and $A_{\text{sol},j}$: normalized amplitudes from spectral decomposition.

{Synchronization Term}

 

$T(\nu_j, \phi_j) = \exp \left[ \sum_{j=1}^{N} \frac{\nu_j}{\nu_j + f_{\text{dom}}} \cos\left( \frac{2\pi \nu_j t}{f_{\text{dom}}} + \phi_j \right) \right]$

 

where $f_{\text{dom}}$ is the dominant system frequency from FFT analysis.

{Validation and Applications}

    Predictive accuracy: hadron mass spectrum with $<0.2\%$ error.

    Nuclear binding energy curve reproduced, including shell effects.

   Cross-sector couplings reproduce hyperfine, isospin, and generation-dependent phenomena.

    Applications span QED/QCD, condensed matter, plasma physics, biophysics, and cosmology.