Techniques for programming Simulation Universe models at the Planck level

Programming Simulation Hypothesis

Genesis 1:2 presents an initial condition of creation - namely, that it is tohu wa-bohu; without form and void.

Techniques for programming a Universe Simulation (Simulation Hypothesis) at the Planck level

The simulation hypothesis (which proposes that all of reality is an artificial simulation, analogous to a computer simulation) has received popular attention yet there is little discussion as to how this might be achieved in practical terms given the immense computational requirements. The Simulation Hypothesis approach described here operates at the Planck level and uses geometrical objects where possible to replace laws of physics (orbits naturally emerge from geometrical imperatives rather than following pre-encoded functions). Being geometry based the simulation is independent of any numbering system and also of any set of units. The model is constructed around a black-hole electron. 

The model is divided into 2 parts;
(1) Planck units; programming mass, length, time, charge from a dimensionless mathematical electron 
(2) Planck universe scaffolding, relativity as the mathematics of perspective and momentum orbitals instead of forces 

Mathematical electron

Part 1: theory - mathematical electron) is based on a geometrical (dimensionless, units = 1) formula for an electron fe constructed from 2 mathematical (dimensionless physical) constants, the fine structure constant alpha and an assigned constant Omega.
From this formula we can extract geometrical objects for mass, length, time, charge MLTA. The SI units (kg, m, s, A, K) are replaced by numerical relationships. By adding 2 dimensioned scalars we may then convert from the dimensionless geometrical MLTA objects to their dimensioned SI Planck unit equivalents ... thereby resolving the problem of how to construct a physical universe from a mathematical universe, the Mathematical Universe Hypothesis conundrum (see video). 

By using 2 scalars (from c and permeability of vacuum mu0), the 2 fixed constants (alpha and Omega), and this numerical unit relationship we may solve the SI physical constants with CODATA 2014 precision, see table below. 

*Note: from the 2018 BIPM special revision of the SI units there are now 4 constants with values fixed by committee. In this model the Planck units are not independent of each other and so cannot have values arbitrarily imposed. Once 2 units are fixed in value then the remaining dimensioned constants are fixed by default, which is why only 2 scalars are required. This means for example that we might now have 2 numerical values for the elementary charge.

Part 2: theory - sqrt of Planck momentum) The model assigns the square root of momentum as an independent constant which is used to link the mass domain with the charge domain. By assigning this sqrt of Planck momentum (as an SI unit) the above geometrical model can be replicated using the SI constants, this gives a cross-reference by which to compare formulas and limits the possible MLTA geometries to the above.

Hyper-sphere Planck universe

In this section we look at gravity, relativity and time. A Planck unit simulation approach has the advantage in having available a discrete time (via the simulation clock-rate) where Planck time is assigned as the smallest unit of incremental time. Mass is measured in discrete units of Planck mass and length in discrete units of Planck length. By using discrete time all particles can experience a common time frame which is not possible in an analog (continuous) real-time, i.e.:
FOR age = 1 TO the_end                       'in units of Planck time, big bang = 1         
        FOR n = 1 TO all_particles             'all the particles in the simulation
        IF particle(n, age) = mass THEN GOSUB gravity ELSE GOSUB electric         
        NEXT n
NEXT age
... such that time as a dimension is replaced by increments to the variable age.

Part 1: theory: time and the black-hole universe) An expanding Planck unit universe:
A discrete micro Planck unit black-hole (as a unit of Planck time, Planck mass, Planck length ...)  is defined. The universe expands in micro black hole increments giving a Planck unit scaffolding. This permits select parameters for a cosmic microwave background to be calculated, the only variable required is the universe age as measured in units of Planck time.

Part 2: theory - black-hole universe and relativity) Relativity in a virtual hyper-sphere: 
Virtual particles are embedded within an incrementally expanding hypersphere (see part 1) and oscillate between an electric wave-state and a Planck mass point-state (see mathematical electron), driven by this hypersphere expansion. All objects and particles travel at and only at the speed of light in hyper-sphere co-ordinates (time and velocity are thus constants) but as photons (the means of information exchange) can only travel laterally along the hyper-sphere surface, a relativistic 3-D space effect is achieved.  Lorentz formulas are used to translate between the hyper-sphere and this 3-D space, relativity becoming the mathematics of perspective.

Part 3) Gravitational orbitals as gravitons:
The notion of the orbital as a probability region where the electron may be found in the atom is replaced by physical orbitals (physical units of momentum). As the proton and electron are thus physically linked there is no requirement for an electric force. Atomic spectra evolves from the geometry of the particles and the incompressibility of particle momentum and thus theoretically could emerge naturally. The same formulas are applied to gravitational orbitals (gravitons), the gravitational orbit as the sum of these orbitals, thus no gravitational force is required. As with the atom, summing the angular momentum of each individual orbital gives the angular momentum of each orbit, thus the angular momentum of planetary orbits is a function of these gravitational angular momentum orbitals.

The above describes an approach where a universe could emerge according to initial geometrical conditions rather than an abstract set of physical laws. It is a virtual universe in the sense that all components  (the total universe) sums to zero and all units sum to one, the universe therefore does not exist in any material sense, particles are a means of data storage and photons as data exchange. Digital time can best be explained by reference to an external clock source, suggesting a programmed approach, hence a philosophical argument for a Programmer.

Note: This model should be freely open for debate, but it is self-funded and takes much of my time, so I have added a donation button for those who can afford to and would like to contribute to this (and future work for there is still much to be done).