According to it the fine-structure constant is (and the other (mass) constants tend to also include √(3/8)):
julia> @interval 1/(9/1024 * exp((1/3 - √(3/8)) * 2/3)) [137.04, 137.041]
Regular Article Quantum gravity effects in the infrared: a theoretical derivation of the low-energy fine structure constant and mass ratios of elementary particles | SpringerLink
Published: 05 June 2022
We have recently proposed a pre-quantum, pre-spacetime theory as a matrix-valued Lagrangian dynamics on an octonionic spacetime. This theory offers the prospect of unifying internal symmetries of the standard model with pre-gravitation. We explain why such a quantum gravitational dynamics is in principle essential even at energies much smaller than Planck scale. […] We use the octonionic representation of fermions to compute the eigenvalues of the characteristic equation of this algebra and compare the resulting eigenvalues with known mass ratios for quarks and leptons. We show that the ratios of the eigenvalues correctly reproduce the [square root of the] known mass ratios. In conjunction with the trace dynamics Lagrangian, these eigenvalues also yield a theoretical derivation of the low-energy fine structure constant.
There ought to exist a reformulation of quantum theory, even at energy scales much lower than
Planck scale, which does not depend on classical time
We construct an action principle in which the only free parameters are Planck length, Planck time and Planck’s constant. Every other physical constant, dimensional as well as dimensionless, is intended to be derived in terms of these three parameters. Note that in comparison with the usual studies of quantum gravity, we have traded Planck mass for Planck’s constant ̄h. This enables us to treat both UV and IR quantum gravity in the same analysis. Constants such as Newton’s gravitational constant G, speed of light c, and Planck mass mP are all now regarded as derivative quantities.
To construct the aforesaid desired reformulation of quantum theory, we must propose a new
physical space [which replaces 4D Minkowski space-time] on which fermionic spinors are to be
defined. We must then propose a dynamics on this new physical space, and work out the conse-
quences of the new space and the new dynamics, and compare them with known but unexplained
data. Finally we must show how classical spacetime geometry, and quantum (field) theory as we
know it, are recovered from this new formulation.
An E8 ⊗ E8 unification of the standard model with pre-gravitation, on an octonion-valued twistor space
We identify the Left-Right symmetry breaking with electroweak symmetry breaking, which also results in
separation of emergent four-dimensional Minkowski spacetime from the internal symmetries which
describe the standard model. This ‘compactification without compactification’ is achieved through
the Ghirardi-Rimini-Weber mechanism of dynamical wave function collapse, which arises naturally
in our theory, because the underlying fundamental Hamiltonian is necessarily non-self-adjoint.
Only classical systems live in four dimensions; quantum systems always live in eight octonionic
(equivalently ten Minkowski) dimensions. We explain how our theory overcomes the puzzle of
quantum non-locality, while maintaining consistency with special relativity. We speculate on the
possible connection of our work with twistor spaces and spinorial space-time, and with Modified
Newtonian Dynamics (MOND).
Note, GRW spontaneous collapse theory, resolves Schödinger’s cat (i.e. is an alternative to Everettian multi-verse QM interpretation):