Programming mass space and time in a computer simulated virtual 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 mathematical universe).

Summary:

(continued from sqrt of Planck momentum). The model uses a black-hole electron formula to separate the Planck units into a dimensionless geometrical component (alpha, Omega) and a dimensioned unit (u) where the SI units are stored in an array of the form un. To scale to the SI numerical values for the physical constants requires an additional 2 (Planck unit) scalars, thus 1 unit and 4 numbers; 2 fixed mathematical constants (alpha, Omega) and 2 variable dimensioned scalars are required to solve the 6 dimensioned physical constants; G, h, c, e, me, kB

There is a 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. It also does not work on the safari browser. 

The formulas referenced here are listed in the following article (see also sqrt of Planck momentum). Note eq 53 should read L=TV/2;


Cite: Macleod Malcolm, Programming Mass, Space and Time within a Computer Simulated Virtual Universe (November 24, 2014). Available at: https://ssrn.com/abstract=2531429

Alpha* as input (0 = default)



scalar p      
scalar v      
Omega       

Solutions (α Ω v, p) :

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


electron wavelength*

v = 2.4263102367(11)e-12


Boltzmann constant*

kB = 1.380 648 52(79)e-23


Proton mass*

mp = 1.672621777(74)e-27


Neutron mass*

mn = 1.674927351(74)e-27


Atomic mass unit*

mu = 1.660538921(73)e-27


von klitzing*

RK = 25 812.807 4555(59)


magnetic flux*

fx0 = 2.067 833 831(13)


Gravitation constant*

G = 6.674 08(31)e-11


electron gyro*

Ge = 1.760 859 644(11)e11


Planck mass*

mP = 2.176 470(51)e-8


Planck length*

lp = 1.616 229(38)e-35


Planck time*



Bohr magneton*

9.274 009 994(57) e-24


Bohr radius*

a0 = 0.52917721067(12) e-10


Gravitational coupling constant

aG = 1.7518e-45


Q (sqrt of Planck momentum)

The calculator (left) calculates Omega and the scalar units p and v. It then uses these 4 values; alpha, Omega, p, v to solve the constants as per the formulas below. The solutions are then compared with the CODATA 2014 equivalents for comparison.

The value for alpha changes with each codata update and so I have selected it as user input; the default value 0 = 137.035999139 (codata 2014 mean)

From MLTVPA, we can derive G, h, c, e, me, kB...:
Planck units from α, Ω, p, v (maple format);
P:=Omega*p:  
V:=2*pi*Omega^2*v:  

MTLA using p,v:
T:=2*pi*p^(9/2)/v^6: 
M:=(2*pi*P^2/V): 
L:=(T*V/2):  
A:=(8*V^3/(a*P^3)): 

Physical constants from MLTVPA
sigma:=(pi^2/(3*a^2*A*L)): (magnetic monopole)
fe:=(T*sigma^3): (electron function)
me=M*fe; (electron mass)
Tp=(A*V/pi); (Planck temperature)
mu0=pi*M*V^2/(a*L*A^2); (permeability of vacuum)
e=(A*T); (elementary charge)
h=(2*pi*L*M*V); (Planck constant)
kB=pi*M*V/A; (Boltzmann constant)
G=(V**2*L/M); (Gravitation constant)

Planck units as alpha, Omega, k (mass), t (time);
M:=1*k:
T:=2*pi*t:
P:=Omega*k^(4/5)/t^(2/15):
V:=2*pi*P^2/M:
L:=(T*V/2):
A:=(8*V^3/(a*P^3)):

Planck units as alpha, Omega, z^3 (ampere), l (length);
A:=(64*pi^3*Omega^3/a)*z^3:
L:=(2*pi^2*Omega^2)*l:
T:=(2*pi)*z^9*l^3:
V:=(2*L/T):
M:=(2^3*pi*V)/(a^(2/3)*A^(2/3)):

Notes:
- listed reference values from CODATA 2014
- proton mass from electron-proton ratio CODATA mean
- neutron mass from electron-neutron ratio CODATA mean

A rotating charged Dirac Kerr-Newman black-hole electron

A charged rotating black hole is a black hole that possesses angular momentum and charge. In particular, it rotates about one of its axes of symmetry. In physics, there is a speculative notion that if there were a black hole with the same mass and charge as an electron, it would share many of the properties of the electron including the magnetic moment and Compton wavelength. This idea is substantiated within a series of papers published by Albert Einstein between 1927 and 1949. In them, he showed that if elementary particles were treated as singularities in spacetime, it was unnecessary to postulate geodesic motion as part of general relativity. The Dirac–Kerr–Newman black-hole electron was introduced by Burinskii using geometrical arguments. The Dirac wave function plays the role of an order parameter that signals a broken symmetry and the electron acquires an extended space-time structure. Although speculative, this idea was corroborated by a detailed analysis and calculation.