Ontological Fluctuating Lattice Cut Off
Holger Bech Nielsen
TL;DR
This work proposes that an ontological, fluctuating lattice with three copies of the Standard Model group can encode a straight-line relation between the logarithms of energy scales and the powers of a fluctuating link length $a$, unifying diverse scales such as string tension, fermion tip, and a Planck-like scale. It introduces a log-normal distribution for the lattice link lengths, arguing that multiplicative fluctuations naturally produce the observed linear trend and enabling predictions of a near-SU(5) unification scale. By constructing a diagonal-subgroup framework and incorporating quantum corrections multiplicatively across the three SMG copies, the paper derives expressions for the inverse finestructure constants that agree with experimental differences to within a few hundredths and provides precise estimates for the four best scales, including a predicted unification scale around $\mu_u \sim 10^{13.7}$ GeV. The results suggest that cutoff effects from the fluctuating lattice may appear in precision measurements of fundamental constants, offering a potential window into high-energy dynamics beyond conventional GUT frameworks.
Abstract
Remarkably accurate fine structure constants are calculated from assumptions further developed from two earlier publications. We have put together a series of energy scales related to various physical phenomena such as the Planck scale, a scale, which we call ``fermion tip'' being a certain extrapolation related to the heaviest Fermions in the Standard Model, an approximate SU(5) unification scale (without susy); and then we found, that as function of the power of an imagined lattice link length supposedly relevant for the scale in question, these powers are rather well linearly related to the logarithms of the associated energy scales. The coincidence of these scales fitting a straight line is remarkable and in some cases quite intriguing. It is evidence for Nature truly having a fluctuating lattice, meaning, that the size of the links say fluctuate quantum mechanically. We review a self-reference obtaining the three fine structure constants via three theoretically predictable quantities, among which is a scale on our straight line plot, namely for an approximate SU(5)-like unification (SU(5) coupling relations are only true in a classical approximation). Concentrating on the four energy scales, for which most precise numbers make sense (this is new in the present article), we interpolate to the approximate unification scale to such an accuracy, that it combined with the quantum corrections making the deviation from genuine SU(5) delivers the differences between the three inverse fine structure constants agreeing within errors being a few units on the second place after the comma! E.g. we predict the difference between the non-abelian inverse fine structure constants at the Z-mass MZ to be (1/alpha2 - 1/alpha3)(M_Z)predict=29.62-8.42 =21.20, while the experimental difference is 29.57-8.44=21.13 both with uncertainties of order +/- 0.05.