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:

(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 mathematical constants (alpha, Omega) and 2 variable dimensioned scalars, are required to solve the 6 principal dimensioned SI 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. 

The formulas referenced here are listed in the following article (see also sqrt of Planck momentum);

The pdf has the maple code for the article formulas.

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.

A black-hole 2-state electron model

In this model the electron is envisaged as an oscillating-over-time 2-state event comprising an electric (magnetic monopole) state and a (Planck) mass micro black-hole state.

1. The electric state is constructed from magnetic monopoles. The units for a monopole are the ampere-meter (AL = ampere length), the electric state is a function of (AL)^3 and time T where the duration or period (frequency) of the electric state is determined by the electron function fe =  (AL)^3/T. In this model the dimensions of charge, mass, space and time are not independent but overlap and in this ratio they cancel, as such this electron function fe is a dimensionless mathematical constant (its numerical value is independent of the system of units used). As this electron function apparently encodes the physical parameters of the electron, it suggests that these parameters are both local and oscillatory (temporary constructs).

2. The mass state comprises a Planck size micro black-hole; Planck mass = 1, Planck time = 1.

Units for M^9T^11/L^15 = (AL)^3/T = 1
fe = (AL)^3/T = 0.12692 x 10^23; units = 1

It is surmised that after each rotation, the electric components (AL)^3 overlap and cancel (AL)^3/T; units = 1, leaving the electron as a Planck micro black hole (the mass-state) for the duration of 1 unit of Planck time. The electron continues to rotate and the electric-state dimensions re-emerge. The duration (period) of the electric-state = fe = 0.12692 x 10^23 units of Planck time. The electron thus oscillates between an electric-state and a mass-state.

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

Comment:

As referenced in the article, 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, me, kB  cannot be derived in terms of each other and they are still defined using the 5 SI units, and are supposed to be independent of each other (physics has no model which may link these physical constants together, hence the designation as fundamental constants).

This model suggests that the geometry of the constant confers the attributes of its units. There is an associated unit u which is the dimensional component of the constant, but as the information of unit u is embedded within the formula for the constant itself, u seems to have a descriptive rather than a physical role. Consequently I argue that it could be possible to construct our physical mass space time units within a virtual (mathematical) environment.