**Our external physical reality is a mathematical structure. That is, the physical universe is mathematics in a well-defined sense, and in those [worlds] complex enough to contain self-aware substructures SAS [they] will subjectively perceive themselves as existing in a physically 'real' world (- Max Tegmark's MUH).**

Summary: Sqrt of Planck momentum as link between mass and charge, electron formula as magnetic monopole, reduces required number of dimension units to 2, solves physical constants in terms of c, μ_{0}, R, alpha

# Sqrt of Planck momentum:

1. A premise of this model is that the sqrt of Planck momentum can be used to link the mass domain (the mass constants) and the charge domain (the charge constants). I have defined (see article) the sqrt of Planck momentum as Q with its associated unit as q such that Planck momentum = 2piQ^2 = 6.524 kg.m/s (q^2 = kg.m/s).

The 5 principal SI units; kg, m, s, A(mpere), k(elvin).

The 6 principal dimensioned constants; G, h, c, e, m_{e}, k_{B}

I use this sqrt of Planck momentum Q to derive formulas for elementary charge e and for vacuum of permeability μ_{0}. From these, a formula for a magnetic monopole as an ampere-meter can be constructed which then gives a solution for the electron frequency function f_{e} in terms of magnetic monopoles and time.

Mass formulas use Q^2 and thus exhibit integer dimensions (q^2 = kg.m/s).

Charge formulas use Q^3, Q^5, Q^15 and thus exhibit non-integer dimensions (q^3 = q.kg.m/s).

2. From analysis of the electron formula f_{e}, I premise that the units for mass, space and time overlap and cancel in this ratio; units M^9T^11/L^15 = 1, this ratio is found in f_{e}, thus the electron formula, although constructed from magnetic monopoles and time, is a dimensionless mathematical constant units (AL)^3/T = M^9T^11/L^15 = 1.

By linking M^9T^11 = L^15 we can for example define L in terms of M and T and thus reduce the number of required units from 5 (the 5 SI units) to 2 (for example mass and time).

With a reduced unit set we can replace Q with the Rydberg constant R and then redefine the dimensioned fundamental constants (G, h, e, me, kB) in terms of the 4 most precise physical constants c (exact), μ_{0} (exact), R (12-13 digits), alpha (the fine structure constant). Results are consistent with CODATA (see calculator below);

The model is described in the following article (continued on black-hole electron, next page);

μ_{0} = permeability of vacuum = 4π/10000000 (fixed)

Rydberg = 10973731.568508 (CODATA 2014 mean)

alpha α = 137.035999139 (CODATA 2014 mean)

Maple code

pi:=3.14159265358979323846:

c:=299792458:

R:=10973731.568508:

mu0:=pi/2500000:

Constants in terms of c, μ_{0}, R, α

h:=(2*pi^10*mu0^3/(3^6*c^5*a^13*R^2))^(1./3):

e:=(4*pi^5/(3^3*c^4*a^8*R))^(1./3):

kB:=(pi^5*mu0^3/(2*3^3*a^5*c^4*R))^(1./3):

G:=(pi^3*mu0/(2^20*3^6*a^11*R^2))^(1./5):

Tp:=(2^10*3^3*c^15*a^3*R/(pi^4*mu0^3))^(1./5):

me:=(16*pi^10*R*mu0^3/(3^6*a^7*c^8))^(1./3):

Bm:=(pi^2/(2^7*3^3*c*a^14*R^4))^(1./3):

lp:=(pi^22*mu0^9/(2^35*3^24*a^49*c^35*R^8))^(1./15):

tp:=(pi^22*mu0^9/(2^20*3^24*a^49*c^50*R^8))^(1./15):

mP:=(2^25*pi^13*mu0^6/(3^6*c^5*a^16*R^2))^(1./15):

A:=(2^10*pi*3^3*c^10*a^3*R/mu0^3)^(1./5):