**Update pending!!!! 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, solves physical constants in terms of c, μ_{0}, R, alpha

# Sqrt of Planck momentum:

A principal premise of this model is that the sqrt of Planck momentum is a link between 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}

As this sqrt of Planck momentum Q is common to both mass and charge, I use it 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 is constructed which then gives a solution for the electron frequency f_{e}.

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).

Formulas that incorporate Q^15, such as the electron function f_{e}, have the ratio of mass, time, length units M^9T^11/L^15 = 1, this ratio is dimensionless (the units for mass, space and time overlap and cancel) and thus f_{e} is a mathematical constant (without units).

By linking M^9T^11 = L^15 we can define L in terms of M and T and thus reduce the number of required units from 5 to 2. This then permits us to replace Q with the Rydberg constant R and thus redefine the dimensioned fundamental physical constants in terms of the 4 most precise constants c (exact), μ_{0} (exact), R (12-13 digits), alpha (the fine structure constant). Results are consistent with CODATA (see calculator below);

The following video summarises the above, it is taken from the article (below).

The model is described in the following article (See also black-hole electron);

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):

Comment:

Physics still debates the number of dimensioned units that are required, the present consensus being 3; MLT of the 5 SI units (kg, m, s, Ampere, kelvin), nevertheless the 6 principal physical constants G, h, c, e, m_{e}, k_{B} cannot be derived in terms of each other although they are defined using the SI units and are supposed to be independent of each other (physics has no model which may link them together). This model proposes a more fundamental system of (2) units that can be used to derive both the SI units and these physical constants in terms of each other. This requires that these units are not independent but rather overlap, as noted above we can for example define distance using mass and time.

An unexpected result from this model is the charged nature of (Planck) temperature = magnetic monopole/time. If we can construct a monopole from temperature then a new understanding of the nature of temperature is required.