Planck scale

The Planck scale refers to the magnitudes of space, time, energy and other units, below which (or beyond which) the predictions of the Standard Model, quantum field theory and general relativity are no longer reconcilable, and quantum effects of gravity are expected to dominate (quantum gravitational effects only appear at length scales near the Planck scale). Consequently simulation hypothesis models that include these effects must consider (if not begin with) the Planck scale ^[8].

SI units

The SI units is the only system of measurement with an official status in nearly every country in the world. The SI mksa units are; meter (length), kilogram (mass), second (time), ampere (electric current). The corresponding Planck units are Planck length, Planck mass, Planck time, Planck charge. These units measure and so define the parameters of a physical universe.

Physical constants

A fundamental physical constant is a physical quantity that is generally believed to be both universal in nature and have a constant value in time. These can be divided into dimension-ed (with units; speed of light c, gravitational constant G, Planck constant h, elementary charge e, electron mass m_e, Boltzmann constant k_B ...) and dimension-less (units = 1; fine structure constant α). There are also dimension-less mathematical constants such as pi.

Numbering systems

As well as the decimal system, present computers use binary and hexadecimal numbering systems. In particular the decimal and hexadecimal are of terrestrial origin and may not be considered 'universal'. Furthermore numbering systems measure only the frequency of an event and contain no information as to the event itself. The number 299 792 458 could refer to the speed of light (299 792 458 m/s) or could equally be referring to the number of apples in a container (299 792 458 apples). As such numbers require a 'descriptive', whether m/s or apples. Numbers also do not include their history, did the number 42 come from 50-8? 30+12? ...

Our universe simulations require the laws of physics and the physical constants built in, however both these laws and the physical constants are known only to a limited precision. Also even with 64-bit processing, a simulation with 10⁶² iterations (the present age of the universe in units of Planck time) will accumulate round-up errors. Number based computing may be sufficient for ancestor-simulations but has inherent limitations for Programmer God simulations.

Geometrical objects

A mathematical constant such as π refers to a geometrical construct rather than any numbering system and so may be considered universal and defined as a constant. Likewise, by assigning geometrical objects instead of numbers to the Planck units, the problems with a numbering system could be resolved. These objects would have to fulfill the following conditions, for example the object for length must;

1. include the function of length such that a descriptive is not required

2. be able to combine Lego-style with the objects for mass, time .. to form more complex objects (events) such as particles and planets whilst still retaining the underlying information (the Planck objects that combined to form that event)

Electron wavelength must then be measurable in terms of the length object, as such the length object must be embedded within the electron. Although the mass object would incorporate the function mass, the time object the function time ..., it is not necessary that there be an individual physical mass or physical length or physical time ..., but only that in relation to the other units, that object must express that function. The electron would then be a complex event constructed by combining the objects for mass, length, time and charge into 1 event, and thus electron charge, wavelength, frequency and mass would be different aspects of that 1 geometry (the electron event) and not independent parameters (independent of each other).

The units mass, length, time and charge must therefore be

1. interrelated (overlapping) whereby there be a relationship between them (so that they may combine)

2. combine in such a ratio that they cancel and the sum universe itself (being a mathematical universe) is unit-less.

If everything is the same temperature, there would be no unit temperature. What this means is that we have noted different temperatures and chosen a base temperature 0C or 32F and measured all temperatures against these. We are measuring temperature gradients against a base-line, likewise with 1kg, 1m, 1s ... we are taking a base unit and measuring the gradient against that 1 unit. In writing the simulation code, the parameters (dimensions) to be used would be chosen and assigned a geometrical object such as 1M, 1L, 1T ... and the information of that universe (the dimensions of that universe) would then be expressed by the gradients of these objects, although given that we are beginning with base units quantity may be more accurate.

Not only must these objects be able to form complex events such as particles, but these events themselves must function (i.e.: electrons orbiting protons in an atom) according to their underlying geometries, orbits for example would be the result of geometrical imperatives and not due to any built-in laws of physics. The computational problem can thus be resolved by instituting a geometrically autonomous universe. The electron orbits the nucleus due to the respective geometries, as this orbit follows a regular and repeating pattern, it can be described using mathematical formulas. As the events grow in complexity (from atoms to molecules to planets), so too will the patterns (and the formulas then used to describe them). Consequently the laws of physics become mathematical descriptions of geometrically imposed patterns.

Furthermore, as the sum universe is unit-less, there is no limit to the number of objects (size, mass, age ... i.e.: the information content of the universe) that can be added. If the Programmer God can determine appropriate geometrical objects and a mechanism for the addition of further objects, then the universe will grow accordingly.

There is a caveat; self aware structures within the simulation will perceive a physical mass, space and time as forming their physical reality, these mathematical objects must therefore be indistinguishable from any observed physical reality.

Determinism

Particles form more complex structures such as atoms and molecules via a system of orbitals; nuclear, atomic and gravitational. The 3-body problem is the problem of taking the initial positions and velocities (or momenta |momentum|momenta) of three or more point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's law of universal gravitation.^[10]. Simply put, this means that although a simulation using gravitational orbitals of similar mass may have a pre-determined outcome, it seems that for god's and men alike the only way to know what that outcome will be is to run the simulation.

Mass, length, time, charge

Wave-particle duality at the Planck level is replaced with an electric wave-state (duration of particle frequency) to a Planck mass (for 1 discrete unit of Planck time) point-state. In the point-state the particle has defined co-ordinates and so all particles simultaneously in the point-state per unit of Planck time may be measured relative to each other.

The units for mass, length, time and charge are assigned geometrical objects MTLA.

The electron (f_e) is a mathematical structure, the geometry of 2 unit-less constants (α, Ω) and so is also unit-less (units = 1). The geometrical objects MTLA are embedded within the electron, consequently these units must overlap and cancel according to a particular ratio as defined by this electron f_e. In the following table are listed objects MTLA and the relationships uⁿ between them.

Geometrical units

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

For example, the following unit relationships cancel;

${\displaystyle {\frac {{u^{3}}^{3}{u^{-13}}^{3}}{u^{-30}}}\;({\frac {ampere^{3}\;length^{3}}{time}})={\frac {{u^{-13}}^{15}}{{u^{15}}^{9}{u^{-30}}^{11}}}({\frac {length^{15}}{mass^{9}\;time^{11}}})=1}$

and so;

${\displaystyle f_{e};\;units={\frac {(A\;m)^{3}}{s}}={\sqrt {\frac {m^{15}}{kg^{9}s^{11}}}}=1}$

The electron wave-state has the units (ampere*meter), the units for the magnetic-monopole. After .23895453... x10²³t_p (units of Planck time), the (A*L)³ units combine with a unit of time T, and cancel (units (A*L)³/T = 1) exposing a unit of Planck mass for a unit of Planck time (the point-state). As the electron is defined by this wave-state to point-state oscillation, it does not exist at any single unit of (Planck) time, rather time is 1 of the dimensions of the physical electron.

3-D space is traditionally measured in meters although what is actually being measured is the distance between 2 points irrespective of the medium (space or air or water ...). If we assign to 3-D space a physical component of ampere-meters (an aether) then electrons will not be moving through space, rather they will oscillate through space, the 3-D space and the electron wave-state both being composed of the same (AL)³ medium, there is no distinction (the particle is an oscillation of the aether).

As such the sum universe itself will also be unit-less. In essence this means that although we may quantify physical structures from within the boundaries of the universe, if we combine all the mass, space, charge etc (the measurable units of a universe) together, they would sum to 1 (regardless of the age of the universe). Thus in order for a universe to create time (the time required to read this page for example), an equivalent mass and space must also be created to balance this units = 1 ratio (found in the electron), the universe thereby growing larger and more massive as it ages. Should time reverse, the universe must likewise shrink in size and mass accordingly. However the units of the universe will always sum to 1 regardless of the universe age. Seen from the outside (the world of the Programmer God), the universe is only data.

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 micro Planck black-hole). When the wave-state (A*L)³/T units collapse this black-hole center is exposed (for 1 unit of Planck time). The electron now is mass. Mass is not a constant property of the particle, rather the measured particle mass is the average mass, the average occurrence of the point-state. If the scaffolding of the universe includes units of Planck mass then it is not necessary for the particle to have any mass, instead the point state becomes the absence of the particle ^[13].

Hyper-sphere universe

The simulation universe macro-structure uses an expanding (digital time) 4-axis hyper-sphere into which particles are embedded ^[14]. This hyper-sphere expands (giving the arrow of time) in discrete steps (the simulation clock-rate), these expansion steps in micro Planck black-hole increments measured in units of Planck time with the velocity of expansion as the speed of light. Particle motion is driven by the expansion of the hyper-sphere, all particles travel at, and only at, the speed of expansion (the speed of light) in hyper-sphere co-ordinate terms.

In the electric wave-state the particle is locally undefined, in the mass-gravity point-state the particle has defined hyper-sphere co-ordinates, each point can then be referenced against each other, consequently mass-gravity is the domain of the observable macro-world.

Particles are assigned N-S axis with motion in the hyper-sphere directed along that axis. Thus by changing the N-S axis (through a transfer of momentum), particles will appear to have motion relative to each other although still traveling at the speed of light in hyper-sphere co-ordinates.

As photons (the electromagnetic spectrum) do not have a point-state they have no mass and therefore do not have fixed co-ordinates in the hyper-sphere and so unlike particles they are not pulled by the hyper-sphere expansion and so can only travel laterally along the hyper-sphere. Consequently they are time-stamped, they do not age, a photon emitted from a distant galaxy a billion years ago is a billion years old. As the principal source of information regarding the observable universe comes predominately from the electromagnetic spectrum, and as this information can only transverse the hyper-sphere laterally, it is possible to infer the hyper-sphere expansion, but not directly measure it. It is akin to studying the movement of planes on/above an airport using 2-D satellite photos but without a knowledge of the height dimension.

Relativistic universe

The mathematics of perspective is a technique used to project a 3-D image onto a 2-D screen (i.e.: a photograph or a landscape painting). Because of the lateral motion of the electromagnetic spectrum within the hyper-sphere, visible 3-D space is a projected image from the 4-axis hyper-sphere, the relativity formulas are used to translate between the hyper-sphere co-ordinates and 3-D space co-ordinates ^[15]. Observed 3-D space is relative space (objects are determined relative to each other). The associated time dimension measures the change in state = change of information = change in relative position of particles in respect to each other and so derives from, but does not equate to, the universe clock-rate (digital time). If nothing moved relative to each other, there would be no means to measure a change of state and so for self-aware structures time would stand still, albeit the universe hyper-sphere would continue to expand at the speed of light.

Gravity

4 body gravitational orbit generated from 6 dimension-less orbital pairs

All particles that are simultaneously mass (in the point-state) at any given unit of time (digital time) are linked to all other particles also in the point-state by a gravitational orbital forming orbital pairs. Each orbital pair rotates by an increment defined by the orbital radius. The results are then summed and averaged and so the entire universe can be updated in real time (before the next increment of time). A gravitational orbit between objects (planets for example) then becomes the sum of all the underlying particle-particle orbital pairs (the particles that comprise those objects). Thus it is in principle not necessary to have direct information regarding the orbiting objects to calculate their respective orbits.

Black-holes

In a data world of 1's and 0's such as a computer game, characters within that game may analyze other parts of their 1's and 0's game, but they have no means to analyze the hard disk upon which they (and their game) are stored, for the hard disk is a mechanical device, is not part of their 1's and 0's world, it is a part of the 'real world'. Furthermore the rules programmed into their game would constitute for them the laws of physics (the laws by which their game operates), but these may or may not resemble the Laws that operate in the 'real world', assuming there even exist such laws. Thus any region where the laws of physics (the laws of the game world) break down would be significant. A singularity inside a black hole is such a region.

The particle point-state would then be analogous to a storage address on a hard disk, the interface between the (simulation) data world and the real world, a massive black-hole the sum of its individual particle Planck black-hole constituents.

The surface of the massive black-hole is of the particle world, the size of the black hole surface reflecting the stored information, the interior of the black-hole however, as the interface between the data world and the real world, does not exist in physical terms. Thus we may discuss the surface area of a spherical black-hole but not its volume.

Laws of Physics

The scientific method is built upon testable hypothesis and reproducible results. Water has always boiled, under identical conditions, at 100°C. In a geometrical universe particles behave according to geometrical imperatives, the geometry of the electron and proton ensuring that electrons will orbit nuclei in repeating and predictable patterns. The laws of physics would then be a set of mathematical formulas that describe these patterns, the more complex the orbits, the more complex the formulas required to describe them (and so forth). If there is a source code from which these geometrical conditions were programmed there there may be non-repeating events, back-doors etc built into the code, a common practice with our computer games, these by definition would lie outside the laws of physics yet would be no less valid.