Physics:Fundamental Fractal Geometric Field Theory

Short description: Alternative physics theories

Fundamental Fractal Geometric Field Theory (FFGFT)

Fundamental Fractal Geometric Field Theory (FFGFT), also referred to as T0 Time-Mass Duality, is an independent theoretical framework developed by Johann Pascher (Oberösterreich, Austria) that derives Standard Model particle masses and fundamental constants from a single dimensionless geometric parameter.

Core Parameter

The framework is built on a single dimensionless parameter

$\xi =\frac{4}{3}\times 10^{-4}\approx 1.333\times 10^{-4}$

which emerges from the fractal packing deficit of three-dimensional Euclidean space, yielding a fractal spacetime dimension $D_f=3-\xi \approx 2.9999$. As an independent consistency check, $\xi$ can be related to Higgs sector quantities:

$\xi \approx \frac{{\lambda }_h^2{v}^2}{16{\pi }^3{m}_h^2}$

where $v=246.22$ GeV is the Higgs vacuum expectation value, $m_h=125.1$ GeV the Higgs mass, and ${\lambda }_h=m_h^2/(2v^2)\approx 0.129$ the Higgs self-coupling. This relation reproduces $\xi$ to within 2.5%, consistent with the experimental precision of the Higgs parameters.

Sub-Planck Geometry

FFGFT postulates a 4D toroidal geometry at a sub-Planck length scale:

$L_0=\xi \cdot {\ell }_P\approx 2.15\times 10^{-39}\text{ m}$

$t_0=L_0/c\approx 7.19\times 10^{-48}\text{ s}$

where ${\ell }_P$ is the Planck length. These scales are 7500 times smaller than the Planck length and Planck time respectively. The quantity $t_0$ represents the maximum system clock rate of the framework: ${\nu }_{\text{max}}=1/t_0$.

Particle Masses

Fermion masses follow a Yukawa-type formula with geometric coefficients:

$m_i=r_i\cdot {\xi }^{p_i}\cdot v$

where $r_i$ are exact rational coefficients and $p_i$ are rational exponents with step size $\mathrm{\Delta }p=1/3$.

Particle	$r_i$	$p_i$	Calculated [MeV]	Experimental [MeV]	Error
Electron	$4/3$	$3/2$	0.505	0.511	1.2%
Muon	$16/5$	$1$	104.96	105.66	0.7%
Tau	$25/9$	$2/3$	1783.4	1776.9	0.4%
Up	$6$	$3/2$	2.27	2.27	0.1%
Strange	$26/9$	$1$	94.8	93.4	1.5%
Charm	$2$	$2/3$	1284	1270	1.1%
Bottom	$3/2$	$1/2$	4261	4180	1.9%
Top	$1/28$	$-1/3$	171975	172760	0.5%

Neutrino masses carry a double suppression:

$m_{{\nu }_i}=r_i\cdot {\xi }^2\cdot m_e$

yielding $m_{{\nu }_e}\approx 9.1$ meV, consistent with the KATRIN upper limit of 45 meV.

Fundamental Constants

From $\xi$, ${\ell }_P$, and the characteristic energy $E_0=\xi \cdot v\approx 7.4$ MeV, the framework derives 47 physical constants. Selected results:

Constant	FFGFT value	Reference value	Error
Fine structure constant $\alpha$	$7.2974\times 10^{-3}$	$7.2974\times 10^{-3}$	0.0005%
Gravitational constant $G$	$6.6735\times 10^{-11}$ m³ kg⁻¹ s⁻²	$6.6743\times 10^{-11}$	0.013%
Bohr radius $a_0$	$5.2917\times 10^{-11}$ m	$5.2918\times 10^{-11}$	0.0005%
Rydberg constant $R_{\mathrm{\infty }}$	$1.0974\times 10^7$ m⁻¹	$1.0974\times 10^7$	0.0009%

Average error across all 47 constants: 0.033%.

Koide Relation

The Koide relation

$Q=\frac{m_e+m_{\mu }+m_{\tau }}{(\sqrt{m_e}+\sqrt{m_{\mu }}+\sqrt{m_{\tau }}{)}^2}=\frac{2}{3}$

emerges as a structural consequence of the rational exponent ladder ($\mathrm{\Delta }p=1/3$) rather than as an independent postulate. The framework reproduces $Q=2/3$ to within 0.001% of the experimental value.

No Singularities

The sub-Planck floor $t_0$ provides a fundamental lower bound that eliminates singularities. Mass concentrations cannot compress beyond $L_0$; what is conventionally described as a black hole singularity corresponds in FFGFT to a geometric saturation state at maximum packing density.

Status

FFGFT is an independent theoretical framework, not yet peer-reviewed. It is documented in an ongoing series of numbered papers (Documents 001–186 as of April 2026).

References and External Links

• Pascher, J. (2026). FFGFT — T0 Time-Mass Duality. Zenodo. DOI: 10.5281/zenodo.18834145
• Source documents and Python validation scripts: github.com/jpascher/T0-Time-Mass-Duality