Programming a Virtual (Mathematical) Universe

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:

The sqrt of Planck momentum is used as a link between mass and charge. An electron formula is constructed from magnetic monopoles. From these the required number of dimension units can be reduced from 5 (kg, m, s, A, K) to 2. This then permits the dimensioned physical constants to be solved in terms of c, μ0, R (Rydberg), α (see calculator below). This section is continued on the next page (see black hole electron).

An introduction in an ebook format:

Because of the large number of formulas the e-book itself does not use free text. Note that the ebook uses flash and cannot be read on a tablet or smart phone. 

The formulas are listed in the following article;

Alpha* as input (0 = default)




Solutions (α, c, μ0, R) :

Planck constant*

h = 6.626 070 040(81)e-34


elementary charge*

e = 1.602 176 6208(98)e-19


electron mass*

me = 9.109 383 56(11)e-31


Boltzmann constant*

kB = 1.380 648 52(79)e-23


Gravitation constant*

G = 6.674 08(31)e-11

μ0 = 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, μ0, 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):