# Electron (mathematical)

Coding the electron for deep universe (Programmer God) Simulation Hypothesis models

The deep universe simulation hypothesis or simulation argument is the argument that the physical universe (to the Planck scale and perhaps below) could resemble a computer simulation, coded by a Programmer God (in the creator of the universe context).

In the mathematical electron model , the electron is a mathematical function fe that embeds the Planck units, there is no 'physical' electron. The dimension-ed electron parameters (mass, wavelength, frequency ...) are derivatives of these Planck units, the function fe dictating the application of the Planck units. All information is encoded into geometrical objects.

## Geometrical objects

Base units for mass $M$ , length $L$ , time $T$ , and ampere $A$  are constructed as geometrical objects in terms of 2 dimensionless physical constants, the fine structure constant α and Omega Ω

Being independent of any numerical system and of any system of units, these MLTA units qualify as "natural units";

...ihre Bedeutung für alle Zeiten und für alle, auch außerirdische und außermenschliche Kulturen notwendig behalten und welche daher als »natürliche Maßeinheiten« bezeichnet werden können...

...These necessarily retain their meaning for all times and for all civilizations, even extraterrestrial and non-human ones, and can therefore be designated as "natural units"... -Max Planck 
$M=(1)$
$T=(2\pi )$
$L=(2\pi ^{2}\Omega ^{2})$
$A=({\frac {2^{6}\pi ^{3}\Omega ^{3}}{\alpha }})$

### Relation

A mathematical relationship between the objects;

$(A)\;u^{3}\;$
$(L)\;u^{-13}\;$
$(M)\;u^{15}\;$
$(T)\;u^{-30}\;$

### Attribute

Each object is assigned a unit (for example object L is 'length')

Geometrical units
Attribute Geometrical object Relation
mass $M=1$  $unit=u^{15}$
time $T=2\pi$  $unit=u^{-30}$
length $L=2\pi ^{2}\Omega ^{2}$  $unit=u^{-13}$
ampere $A={\frac {2^{6}\pi ^{3}\Omega ^{3}}{\alpha }}$  $unit=u^{3}$

The following un groups cancel

${\frac {u^{3*3}u^{-13*3}}{u^{-30}}}={\frac {u^{-13*15}}{u^{15*9}u^{-30*11}}}=\;...\;=1$

## Mathematical electron

The electron function incorporates these geometrical base units yet itself is unit-less; units = 1.

$f_{e}=4\pi ^{2}(2^{6}3\pi ^{2}\alpha \Omega ^{5})^{3}=.23895453...x10^{23},\;units=1$

For example, fe can be defined in terms of σe, AL as an ampere-meter (ampere-length) are the units for a magnetic monopole.

$T=2\pi ,\;u^{-30}$
$\sigma _{e}={\frac {3\alpha ^{2}AL}{\pi ^{2}}}={2^{7}3\pi ^{3}\alpha \Omega ^{5}},\;u^{-10}$
$f_{e}={\frac {\sigma _{e}^{3}}{T}}={\frac {(2^{7}3\pi ^{3}\alpha \Omega ^{5})^{3}}{2\pi }},\;units={\frac {(u^{-10})^{3}}{u^{-30}}}=1$

##### Electron parameters

The electron has dimension-ed parameters, the dimensions deriving from the base units, fe is a mathematical function that dictates how these units are applied, it does not have dimension units of its own, consequently there is no physical electron, only these electron parameters. By setting MLTA to their Planck unit equivalents;

electron mass $m_{e}={\frac {M}{f_{e}}}$  (M = Planck mass)

electron wavelength $\lambda _{e}=2\pi Lf_{e}$  (L = Planck length)

elementary charge $e=A.T$

We may interpret this formula for fe whereby for the duration of the electron frequency (0.2389 x 1023 units of T) the electron is represented by AL magnetic monopoles, these then intersect with time T, the units then collapse (units (A*L)3/T = 1), exposing a unit of M (Planck mass) for 1 unit of T, which we could define as the mass point-state. Wave-particle duality at the Planck level can then be simulated as an oscillation between an electric (magnetic monopole) wave-state (the duration dictated by the particle formula) to this unitary mass point-state. The magnetic monopoles are analogous to quarks (by adding the exponents of u) but due to the symmetry and so stability of the geometrical fe this may not be observed (as the monopoles are equivalent there is no fracture point).

By this artifice, although the physical universe is constructed from particles (particle matter), particles themselves are not physical, they are mathematical.

Note: Using this approach, at the Planck scale quantum effects do not apply, rather quantum events such as the electron are a measure of discrete Planck events spread over time (the duration of a particle wave-state to point-state oscillation). The quantum world (of probabilities) thereby emerges from the discrete Planck world.

##### Electron Mass

If the particle point-state is a unit of (Planck) mass then we have a model for a black-hole electron (an electron centered around a Planck size black-hole). When the wave-state (A*L)3/T units collapse, this black-hole center is exposed (for 1 unit of T). The electron now is mass M. Mass would not then be a constant property of the particle, rather the measured particle mass me would be the average mass, the average occurrence of the mass point-state as measured over time. As for each wave-state then is a corresponding point-state, and as E = hv is a measure of the frequency of the wave-state and m a measure of the frequency of the point-state, then E = hv = mc2.

If the scaffolding of the universe includes units of (Planck) mass M then it is not necessary for the particle to have any mass, instead the point state becomes the absence of particle