... THE MATHEMATICAL ELECTRON ...
a Programmer-God Simulation-Hypothesis model

Physical units from Mathematical structures

The biggest problem with any mathematical universe approach is constructing a physical reality (the physical dimensions of mass, space and time) from mathematical structures. Our computer games may be able to simulate our physical world, but they are still simulations of a physical reality. The 1999 film The Matrix and the ancestor simulation both still begin with a physical level (a base reality), the planet earth.

In this Programmer God model (based on a mathematical electron), the dimensions of our universe (mass, length, time, charge) are geometrical objects MLTA at the Planck scale, furthermore these objects do not simply represent these units (of mass, length, time, charge), they are these units, for what the Programmer has done is choose objects whereby the assigned function; of mass, length, time ... is built into the geometry of the object itself. 

We may also find that these objects are not independent, for example, M exhibits mass-ness in conjunction with L length-ness and T time-ness. This arrangement means that, for example, the length object L can combine with the time object T to form a complex object V which is velocity (V = L/T), while still maintaining the underlying attributes of length and time, and so we can construct a universe Lego-style by combining these simple geometrical objects to form more complex geometrical objects (such as electrons and planets).

This however necessitates that the object for length L be able to interact with the objects for time T and mass M and charge A ..., which infers that there must be some relationship between their respective geometries, and indeed it is the evidence of a unit relationship upon which the credibility of this model depends, for this relationship is incompatible with modern physics.

Physics has a set of parameters used to define the universe; such as the speed of light, the strength of gravity ..., these are often referred to as fundamental constants as they cannot be reduced to more fundamental structures.

The 26th General Conference on Weights and Measures (2019 redefinition of SI base units) assigned exact numerical values to 4 physical constants (h, c, e, k_B) independently of each other (and thereby confirming these as fundamental constants), and as they are measured in units (kg, m, s, C, ...) these units must also be independent of each other (i.e.: fundamental units).

However, if these constants are interrelated via this unit number relationship, then they cannot all be fundamental constants, and so science cannot independently assign them numerical values. 

Scalars

The numerical value of mass object M = 1, the SI equivalent is Planck mass = 2.18 x10^-8 kg. Therefore to convert from M to Planck mass we can use a scalar k = 2.18 x10^-8 kg where M*k = Planck mass.
M * k = 1 * 2.18 x10^-8 kg = 2.18 x10^-8 kg

We can assign to each object a scalar; mass k, time t, length l, velocity v, ampere a. The scalars have both the numerical conversion factor (for k = 2.18 x10^-8) and the units (for k = kg). The unit number is denoted by θ.

The speed of light c = 299792458 m/s or c = 186200 miles/s ... i.e.: the numerical value of the speed of light depends on the units we use, kilometers or miles.

Likewise, if we were to meet aliens, they would write the speed of light in terms of their units, according to their numbering system, and so the numbering system and units are simply measurement systems, light continues to travel at the same velocity regardless of how we, and the aliens, measure it.

It is proposed that these geometrical MLTVA objects are used by the universe itself, they are built into the simulation source code, and so are 'universal' and independent of any numbering system or units. As example, the reason we can use c = 299792458 m/s or  c = 186200 miles/s to measure the speed of light is because embedded within our c is this geometrical object V, which is the real speed of light. Because this V is the geometry of Omega, and Omega has a numerical solution, Omega = 2.007134949, we can assign a numerical value to V = 2πΩ² = 25.312....

To this V, we then add scalar v;

v = 11843707.905 m/s such that 

c = V*v = 299792458 m/s

or scalar v = 7356.08 miles/s such that
c = V*v = 186200 miles/s.

Aliens will also have a value for the speed of light but in alien units, and so their scalar v will not resemble our v (in miles or meters). But for aliens and humans alike, object V will be the same.

The premise is that these MLTVA geometrical objects are used by the universe itself, they are the constructs of mass, space and time. The V term doesn't measure the speed of light, it is that quantity that bestows what we measure as the speed of light, the scalar v is just a conversion factor that we (and aliens) can use. We need a conversion factor because objects such as L or T are too small for daily use, the units that we use, such as seconds or feet or meters, are much more practical than these MLTA units (i.e.: 1 meter, a human size unit, = 6200000000000000000000000000000000 units of this geometrical length L).

If we set our scalar v = 11843707.905m/s then our c = V*11843707.905 = 299792458m/s. If the aliens set their scalar v = @#$/^%, then their c = V*@#$/^%.

If all we are doing is adding scalars then we are achieving little of any practical value, we have just exchanged 1 system of units for another, however, if we could eliminate the scalars, i.e.: if we eliminate scalar v, then for both us and the aliens c = V, and we would now have a common language. To do this, we use this unit number relationship.

* L is a geometrical object, to convert to our unit the meter, first we solve to a numerical value (L = 79.521193...), we are now using the numerical information encoded within these objects, the universe uses geometry, we use numbers. In the process, the geometrical information of L is lost.

** If we must combine mass and length (volume) and time to balance our equations so that the sum universe remains dimensionless (units = 1), then in order for the universe to create time T, the time to read this sentence for example, the universe must concurrently create mass M and space L (the universe has to get bigger and more massive). If time were to reverse, the universe must shrink accordingly.

We only need 2 scalars

Arrival is a 2016 American science fiction film in which extraterrestrials communicate using patterns.

Speed of light c = object V * scalar v. Planck mass = object M * scalar k ... and so on. If we simply add scalars to each of our MLTA objects then we have achieved nothing of value. However each scalar is not just a numerical value, but also includes a unit (v has units m/s or miles/s), and so they follow that unit number relationship, i.e.: the scalar v unit number θ = 17, k unit number θ = 15 ...

This then permits us, via this unit relationship, to define each scalar in terms of other scalars, and then we find that we need only 2 scalars to define all the other scalars. For example, the unit number for a = 3, l = -13 and t = -30, and so 3*3 + -13*3 = -30 = t, this then means that if I know the numerical values for scalar a and scalar l then I know the numerical value for scalar t, and if I know t and l then I know the value for k etc.

This then means that we need only 4 numbers (α, Ω and any 2 scalars) to solve our (or the aliens) physical constants. In this table we define scalars k, t, l, a in terms of scalars r and v, and so if we know the numerical values for r and v (α, Ω have fixed values), then we can solve the constants G, h, c, e, m_e, k_B for any chosen set of units, alien or terrestrial (see calculator below).

We can go 1 step further, and find combinations of the constants where the scalars (r, v) cancel. This would then leave us with only the 2 dimensionless constants α and Ω, which means that these combinations are also dimensionless f_X structures, and so solving these combinations will return the same numerical values whether we are using terrestrial units or alien units, because of course, sans scalars, we are simply combining the MLTVA object equivalents, without scalars the MLTVA objects are the system of units we, the aliens, and the universe itself, are all using. The electron, a dimensionless combination of MLTA objects, is an example.

This then can be applied as a test of our MLTA objects, if they are in fact the units used by the universe itself then the numerical values will be the same whether we are using our constants, alien constants, or the MLTVA equivalents.

We can use this calculator. The inputs are scalars for the speed of light v and Planck mass k; 2 fundamental units. It then solves the fundamental physical constants based on those 2 scalars. If we input the alien scalars for (v, k), then the calculator will return the alien values for those constants. Hopefully they will be impressed and not zap us.