Physics:Simulation argument (Programmer God)

Is God a Programmer; a deep-universe simulation hypothesis at the Planck scale

The simulation hypothesis or simulation theory is the proposal that all of reality, including the Earth and the rest of the universe, could in fact be an artificial simulation, such as a computer simulation. Neil deGrasse Tyson put the odds at 50-50 that our entire existence is a program on someone else’s hard drive . David Chalmers noted “We in this universe can create simulated worlds and there’s nothing remotely spooky about that. Our creator isn’t especially spooky, it’s just some teenage hacker in the next universe up. Turn the tables, and we are essentially gods over our own computer creations .

The commonly postulated ancestor simulation approach, which Nick Bostrom called "the simulation argument", argues for "high-fidelity" simulations of ancestral life that would be indistinguishable from reality to the simulated ancestor. However this simulation variant can be traced back to an 'organic base reality' (the original programmer ancestors and their physical planet). The Programmer God hypothesis conversely states that the simulation began with the big bang (the deep universe simulation) and was programmed by an external intelligence (external to the physical universe), the Programmer by definition a God in the creator of the universe context. Our universe in its entirety, down to the smallest detail, is within the simulation .

Philosophy

Discussion

Philosophy of mathematics is that branch of philosophy which attempts to answer questions such as: ‘why is mathematics useful in describing nature?’, ‘in which sense, if any, do mathematical entities such as numbers exist?’ and ‘why and how are mathematical statements true?’ This reasoning comes about when we realize (through thought and experimentation) how the behavior of Nature follows mathematics to an extremely high degree of accuracy. The deeper we probe the laws of Nature, the more the physical world disappears and becomes a world of pure math. Mathematical realism holds that mathematical entities exist independently of the human mind. We do not invent mathematics, but rather discover it. Triangles, for example, are real entities that have an existence .

The Mathematical universe hypothesis states that Our external physical reality is a mathematical structure. That is, the physical universe is not merely described by mathematics, but is mathematics (specifically, a mathematical structure).

The principle constraints to any mathematical universe simulation hypothesis are;

1. the computational resources required. The ancestor simulation can resolve this by adapting from the virtual reality approach where only the observable region is simulated and only to the degree required, and

2. that any 'self-aware structures' (humans for example) within the simulation must "subjectively perceive themselves as existing in a physically 'real' world".. Succinctly, our computer games may be able to simulate our physical world, but they are still only simulations of a physical reality (regardless of how realistic they may seem) ... we are not yet able to program the physical dimensions of mass, space and time from mathematical structures.

Deep-universe simulation

As a deep-universe simulation is programmed by an external (external to the universe) intelligence (the Programmer God hypothesis), we cannot presume a priori knowledge regarding the simulation source code other than from this code the laws of physics could emerge, and so any deep-universe simulation model we emulate must be universal, i.e.: independent of any system of units, of the dimensioned physical constants (G, c, h, e .. ) and of any numbering systems. Furthermore, although a deep-universe simulation source code may use mathematical forms we are familiar with (a circle can appear on my screen because it was coded to do so), it will have been developed by a non-human intelligence and so we may have to develop new mathematical tools to decipher the underlying logic. By implication therefore, any theoretical basis for a source code that fits the above criteria (that uses techniques that we are not cognizance of) could be construed as our first tangible evidence of a non-human intelligence.

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). Although particles may not be cognizance of our 'laws of physics', they do know the 'laws of nature'. These laws of nature, in a simulation model, would describe the universe OS (operating system), and so below this OS, 'physics' as we know it must necessarily break down. At present the Planck scale is the lowest known level, consequently any attempt to detect evidence of an underlying simulation coding must consider (if not actually begin at) this, the Planck scale.

Further information: v:Planck units (geometrical)

Dimensioned quantities

A 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 1) dimension-ed (measured using physical units kg, m, s, A ...) such as the speed of light c, gravitational constant G, Planck constant h ... and 2) dimension-less (units = 1), such as the fine structure constant α.

There are also dimension-less mathematical constants such as pi. The mathematical constant is a number that can occur within the simulation, pi for example can emerge from the rotation of an object. The fundamental physical constant conversely is a parameter specifically chosen by the programmer and encoded into the simulation code directly and so whilst it may be inferable, it is not derived from mathematical constants (Richard Feynman on the fine structure constant). It should also be dimension-less otherwise the simulation itself becomes dimensioned, and so the dimensioned constants themselves must be derivable (from within the simulation).

Physicist Lev Okun noted "Theoretical equations describing the physical world deal with dimensionless quantities and their solutions depend on dimensionless fundamental parameters. But experiments, from which these theories are extracted and by which they could be tested, involve measurements, i.e. comparisons with standard dimension-ful scales. Without standard dimension-ful units and hence without certain conventions physics is unthinkable . The SI units for the dimension-ful 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.

Purpose

Any simulated universe, whether a simple computer game or NASA program, may presume a 'Purpose', that the simulation, being the result of an 'intelligent design', is intended for an 'intelligent reason' (intent). If ours is a simulated universe then we cannot judge the motives of the Programmer God, however in theological texts we do find a common thread and that is the battle between Good and Evil and so this may be taken as an example 'Purpose'.

Zoroastrianism is one of the world's oldest continuously practiced religions. It is a multi-faceted faith centered on a dualistic cosmology of good and evil and an eschatology predicting the ultimate conquest of evil. The opening chapters of the Book of Genesis provide a mythic history of the infiltration of evil into the world. God places the first man and woman (Adam and Eve) in his Garden of Eden, from whence they are expelled.

In the context of the above, this becomes a multi-layered Game in which Evil is given dominion over the physical 3-D world (Luke 4:5 And the devil, taking him (Jesus) up into an high mountain, shewed unto him all the kingdoms of the world in a moment of time. And the devil said unto him, All this power will I give thee, and the glory of them: for that is delivered unto me; and to whomsoever I will I give it) ... and Good is given dominion over the spiritual realm (Matthew 6:19 But lay up for yourselves treasures in heaven, where neither moth nor rust doth corrupt, and where thieves do not break through nor steal) ... the battle between these worlds played out within mankind as both an internal and external struggle . To account for suffering and misery as an integral construct to the Game, we could consider the earth as analogous to a meta-verse prison where, instead of incarceration in a physical prison, an avatar could be selected and tasked (unknowingly) with self-rehabilitation on earth as the means (for their 'real' self) to 'complete' their sentence, upon which their 'real' self is then set free in the 'real' world .

Avatars

Video games project our 3-D space onto a 2-D screen with the users manipulating the game as external observers. The VR helmet is an attempt to place the user within the simulation (within a 3-D space), but it is still a projection onto a 2-D screen and so is limited by the mobility of the operator (via a haptic suit), and thus not suitable for interactive games if the terrain of the game is limited by the terrain of the operator. An avatar could be placed within a 3-D simulation, however the problem of haptic suit mobility remains.

However, if the avatar is programmed to closely resemble the operator, then the avatar may autonomously represent the operator from within the game. For example, avatars could be programmed to play tennis with the skill level of their operators, realistic virtual tournaments can then be arranged within a 3-D simulation between operators via avatars. In a Game of Life scenario, the avatars could be programmed to achieve certain goals ('Purpose') via experience and learning.

Evidence of a simulation

“Science presumes the fundamental physical constants (G, h, c, e, me, kB, ...) are fundamental,
but this requires the dimensioned units (kg, m, s, A ... ) to be independent of each other,
the simulation hypothesis however requires that these units can overlap and cancel,
for the universe itself does not exist outside of the 'Computer'.
Evidence of a relationship between these units could therefore be construed as evidence of a simulation.” 

At our level, and at the quantum level, the dimensions of mass, length (distance), time and charge (amperes), represented by such units as kilograms, pounds, meters, miles, seconds … etc. are independent of each other (we cannot measure the distance from Tokyo to London using pounds or kilograms or amperes). The units appear to be distinct (mass cannot be confused with length or time), the independence of these units then becoming an inviolable rule, as every high school science student can attest (the units must always add up!). Indeed, what characterizes a physical universe as opposed to a simulated universe is the notion that there is a fundamental structure underneath, that in some sense mass 'is', time 'is' and space 'is' ... thus we cannot write kg or s in terms of m. To do so would totally render our concepts of a physical mass, space and time meaningless. A simulation universe however is required to be (in sum total) unit-less (units = 1), for the simulated universe does not 'exist' in any physical sense outside of the 'Computer'.

Evidence therefore that the units do overlap and in certain combinations cancel, rendering our sum universe unit-less, could therefore be construed as evidence that we are in a deep-universe (Programmer God) simulation. There is a physical constants anomaly that appears to link the constants (G, h, c, e, m_e, k_B) via a mathematical relationship between the units (kg ⇔ 15, m ⇔ -13, s ⇔ -30, A ⇔ 3), and this has been offered as evidence that we are in a simulation .

Programming

“God vs. science debates tend to be restricted to the premise that a God does not rely on science and that science does not need a God. As science and God are thus seen as mutually exclusive there are few, if any, serious attempts to construct mathematical models of a universe whose principle axiom does require a God. However, if there is an Intelligence responsible for the 14 billion year old universe of modern physics, being the universe of Einstein and Dirac, and beginning with the big bang as the act of 'creation', then we must ask how it might be done? What construction technique could have been used to set the laws of physics in motion?” 

Numbering systems

As well as our decimal system, computers apply 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, is 299 792 458 for example a derivation of other base numbers?

Present universe simulations use the laws of physics and the physical constants are built in, however both these laws and the physical constants are known only to a limited precision, and so a simulation with 10⁶² iterations (the present age of the universe in units of Planck time) will accumulate errors. Number based computing may be sufficient for ancestor-simulation models where only the observed region needs to be calculated, but has inherent limitations for deep universe simulations where the entire universe is continuously updated. The actual computational requirements for a Planck scale universe simulation based on a numbering system with the laws of physics embedded would be an unknown and consequently lead to an 'non-testable' hypothesis. This is a commonly applied reasoning for rejecting the deep universe simulation.

Geometrical objects

A number such as pi refers to a geometrical construct (the ratio of circle circumference to circle radius) and so is not constrained by any particular numbering system (in the decimal system π = 3.14159...), and so may be considered both universal and eternal. Likewise, by assigning geometrical objects instead of numbers to the Planck units, the problems with a numbering system can be resolved. These objects would however have to fulfill the following conditions, for example the object for length must;

1. embed the function of length such that a descriptive (km, mile ... ) is not required.

Electron wavelength would then be measurable in terms of the length object, as such the length object must be embedded within the electron (the electron object). 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, the object must express that function (i.e.: the mass object has the function of mass when in the presence of the objects for space and time). The electron could then be a complex event (complex geometrical object) 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 objects for mass, length, time and charge must therefore

2. be able to combine with other objects (for mass, time, charge ...) to form more complex objects (events) such as electrons and apples whilst still retaining the underlying information (the individual objects that combined to form that event).

3. combine in such a ratio that they cancel whereby the sum universe, the simulation itself, being a mathematical universe, is unit-less. While internally the universe has measurable units, externally (seen from outside the simulation) the universe has no physical structure.

Not only must these objects be able to form complex events such as particles, but these events themselves are geometrical objects and so must likewise function according to their geometries. Electrons would orbit protons according to their respective electron and proton geometries, these orbits the result of geometrical imperatives and not due to any built-in laws of physics (the electron does not need to know physics, the orbital path is a consequence of all the underlying geometries). However, as orbits follow regular and repeating patterns, they can be described (by us) using mathematical formulas. As the events grow in complexity (from atoms to molecules to planets), so too will the patterns (and the formulas we use to describe them). Consequently the laws of physics would then become our mathematical descriptions of the underlying geometrically imposed patterns. The computational problem could thus be alleviated by instituting a geometrically autonomous universe.

Furthermore, as the sum universe is unit-less, there is no limit to the number of (mass, time, length ...) objects (aka the information content of the universe), other than the capacity of the celestial hard disk upon which the simulation resides. If the 'Programmer' can determine appropriate geometrical objects that satisfy the above and also include a mechanism for the addition of further objects, then a universe could '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, in our universe therefore, these mathematical objects would have to be indistinguishable from our observed physical reality.

Simulation Time

The (dimensionless) simulation clock-rate would be defined as the minimum 'time variable' (age) increment to the simulation. It may be that Gods use analog computers, but as an example;

 'begin simulation
 FOR age = 1 TO the_end                       'big bang = 1                 
         conduct certain processes ........ 
 NEXT age 
 'end simulation

Quantum spacetime and Quantum gravity models refer to Planck time as the smallest discrete unit of time and so the incrementing variable age could be used to generate units of Planck time (and other Planck units, the physical scaffolding of the universe), for example;

 Initialize_physical_constants;
 FOR age = 1 TO the_end                        'age is a dimensionless variable                            
         generate 1 unit of (Planck) time;       '1 time 'object' T
         generate 1 unit of (Planck) mass;       '1 mass 'object' M
         generate 1 unit of (Planck) length;     '1 length 'object' L
         ........ 
 NEXT age 

The variable age is the simulation clock-rate (the universe age). If age is the origin of Planck time then age = 10⁶², the present age of the universe measured in units of Planck time.

For each age, certain operations are performed, only after they are finished does age increment (there is no 'time' interval between increments). As age is dimensionless, it is not the same as dimensioned Planck time (represented by the object T, which being dimensioned can only appear within the simulation). Although operations (between increments) may be extensive, self-aware structures from within the simulation would have no means to determine this, they could only perceive themselves as being in a real-time (for them the smallest unit of time is 1T). Their (those self-aware structures) dimension of time would then be a measure of relative motion (a change of state) and so although ultimately deriving from the variable age, their time would not be the same as age. If there were no motion, if all particles and photons were still (no change of state), then their time dimension could not update, age however would continue to increment. The analogy being pressing the pause button on a movie, this would not affect the computer clock-rate itself. Thus we have 3 time structures; the dimension-less simulation clock-rate variable age, the dimensioned time unit (Planck time represented as object T), and time as change of state (the observers time dimension).

The forward increment to age would constitute the arrow of time. Reversing this would reverse the arrow of time, the universe would likewise shrink in size and mass accordingly (just as a white hole is the (time) reversal of a black hole).

 FOR age = the_end TO 1 STEP -1                                 
         delete 1 unit of Planck time;
         delete 1 unit of Planck mass;
         delete 1 unit of Planck length;
         ........ 
 NEXT age 

Adding mass, length and time objects per increment to age would force the universe expansion (in size and mass), and as such an anti-gravitational dark energy would not be required, however as these objects are dimensioned, they exist (they are generated) within the simulation, and so must somehow combine such that they (the units for mass length, time, charge; kg, m, s, A) in sum total cancel each other, leaving the sum universe (the simulation itself) dimensionless. We could have a dimensionless (primary) geometrical object within which are embedded the dimensioned objects MLTA (mass, length, time, charge). A geometrical electron is an example.

 FOR age = 1 TO the_end                                                    
         add 1 primary geometrical object
               extract 1 unit of (Planck) time;       '1 time 'object' T
               extract 1 unit of (Planck) mass;       '1 mass 'object' M
               extract 1 unit of (Planck) length;     '1 length 'object' L
         ........ 
 NEXT age 

Thus no matter how small or large the physical universe is (when seen internally), in sum total (when seen externally) it is always dimensionless (without size or mass or age). There is no sum physical universe.

Universe time-line

As the universe expands and if the data storage capacity expands proportionately, then the 'past' could be retained. Because particles are pulled outwards by this expansion (of the universe in size, mass and time, which has the effect of increasing simulation data storage capacity accordingly), previous information (the past) will not be over-written by new information (the present). The analogy would be the storing of every keystroke, a Planck scale version of the Akashic records ... and if our deeds (the past) are both stored and cannot be over-written (if the present cannot access the past), then we have a candidate for the 'karmic heavens' (Matthew 6:19 But lay up for yourselves treasures in 'heaven', where neither moth nor rust doth corrupt, and where thieves do not break through nor steal).

This also forms a universe time-line against which previous information can be compared with new information (a 'memory' of events), without which we could not link cause with effect.

Singularity

In a simulation, the data (software) requires a storage device that is ultimately hardware (RAM, HD ...). 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 an electro-mechanical device, is not part of their 1's and 0's world, it is a part of the 'real world', the world of the Programmer. 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'. 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.

For the black-hole electron, its center would then be analogous to a storage address on a hard disk, the interface between the simulation world and the real world. A massive (galactic) black-hole would be as an entire data sector.

The surface of the black-hole would then be of the simulation world, the size of the black hole surface reflecting the stored information, the interior of the black-hole however would be the interface between the data world and the 'hard disk' of the real world, and so would not exist in any 'physical' terms. It is external to the simulation. As analogy, we may discuss the 3-D surface area of a black-hole but not its volume (interior).

Laws of Physics

The scientific method is built upon testable hypothesis and reproducible results. Water always boils (in defined 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 repeating patterns, the more complex the orbits, the more complex the formulas required to describe them and so forth. However if there is a source code from which these geometrical conditions were programmed, then there may also be non-repeating events, back-doors built into the code (a common practice by terrestrial programmers), these by definition would lie outside the laws of physics and so be labelled as miracles, yet they would be no less valid.

Determinism

An animation of the figure-8 solution to the three-body problem over a single period T ≃ 6.3259.

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.. Simply put, this means that although a simulation using gravitational orbitals of similar mass may have a pre-determined outcome, it seems that for gods and men alike the only way to know what that outcome will be is to run the simulation itself.

Mathematical Universe

The mathematical universe refers to universe models whose underlying premise is that the physical universe has a mathematical origin, the physical (particle) universe is a construct of the mathematical universe, and as such physical reality is a perceived reality. It can be considered a form of Pythagoreanism or Platonism in that it proposes the existence of mathematical objects; and a form of mathematical monism in that it denies that anything exists except these mathematical objects.

Physicist Max Tegmark in his book "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality" proposed that Our external physical reality is a mathematical structure. That is, the physical universe is not merely described by mathematics, but is mathematics (specifically, a mathematical structure). Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well. Any "self-aware substructures will subjectively perceive themselves as existing in a physically 'real' world".

Physics

Physicist Eugene Wigner (The Unreasonable Effectiveness of Mathematics in the Natural Sciences)

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.

The following is adapted from the mathematical electron model , this model illustrates how a Planck scale deep universe simulation could be implemented using geometrical objects.

Mass, length, time, charge

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. Here we look at the theory behind constructing physical units from mathematical structures.

For a simulated universe to be unit-less, the units must be able to cancel within a certain ratio such that in sum total there is no physical universe (when seen from outside the simulation, the universe is merely a data set on a celestial hard-drive). In the following, geometrical objects are assigned to the base units; mass M, length L, time T, ampere A (see table 1.). These MTLA objects are the geometry of 2 dimensionless physical constants; the fine structure constant α and Omega Ω and so are themselves dimensionless. They do however encode the attribute of the units; object M encodes the function mass, L encodes the function length etc ... but as they are dimensionless objects, their respective functions occur only in relation to each other ... we cannot have mass M without length L and time T... however this also means that we can combine these base units Lego-style to build more complex units; we can combine object L with object T to form object V (velocity) ... and so on adding complexity up to electrons, atoms, planets to galaxies while still maintaining the underlying unit functions. The electron object for example includes the objects for MLTA and so the electron has the attributes of mass, wavelength, frequency, charge.

This however requires that there be a mathematical relationship between the base units which defines how they interact with each other, and so a unit number θ is assigned to each geometry whereby a relationship between them may be established . As such a mathematical relationship cannot occur in a 'physical' universe, evidence of a unit number can therefore be taken as evidence that we are in a simulation.

These objects correspond to the Planck units, and so by equating the unit number θ with its SI equivalent (i.e.: θ = 15 ⇔ kg), these geometrical mass, length, time and charge objects can be interchangeable with (and in a real simulation they will need to be indistinguishable from) the 'physical' Planck mass, length, time and charge units.

table 1. Geometrical units

Attribute	Geometrical object	Unit number θ	SI unit
mass	[math]\displaystyle{ M = 1 }[/math]	[math]\displaystyle{ 15 }[/math]	kg
time	[math]\displaystyle{ T = 2\pi }[/math]	[math]\displaystyle{ -30 }[/math]	s
length	[math]\displaystyle{ L = 2\pi^2\Omega^2 }[/math]	[math]\displaystyle{ -13 }[/math]	m
velocity	[math]\displaystyle{ V = 2\pi\Omega^2 }[/math]	[math]\displaystyle{ 17 }[/math]	m/s
ampere	[math]\displaystyle{ A = \frac{2^6 \pi^3 \Omega^3}{\alpha} }[/math]	[math]\displaystyle{ 3 }[/math]	A

The unit relationships show how these units interrelate to each other. In a particular ratio they can overlap and cancel, for example, here (amperes, length, time ALT: θ = 3*3 -13*3 +30 = 0) and (mass, length and time MLT: θ = -13*15 -15*9 +30*11 = 0).

[math]\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 }[/math]

Thus we may have dimensioned units from within (when seen from inside) the simulation, yet still maintain a dimensionless universe externally (external to the universe). We only need a 'master' geometrical object that is itself dimensionless but embeds the MLTA objects. For this we can use a mathematical electron.

Mathematical electron

If the electron is a mathematical particle, and the universe is constructed from mathematical particles, then the universe itself is a mathematical universe 

We can use the above ratio to construct our 'mathematical electron' formula; f_e (AL as an ampere-meter are the units for a magnetic monopole).

[math]\displaystyle{ T = (\pi),\; u^{-30} }[/math] (time object, θ = -30)

[math]\displaystyle{ \sigma_{e} = \frac{3 \alpha^2 A L}{2\pi^2} = ({2^7 3 \pi^3 \alpha \Omega^5}),\; u^{-10} }[/math] (magnetic monopole object, θ = -10)

[math]\displaystyle{ f_e = \frac{ \sigma_{e}^3}{2T} = \frac{(2^7 3 \pi^3 \alpha \Omega^5)^3}{2\pi},\; units = \frac{(u^3)^3 (u^{-13})^3}{u^{-30}} = 1 }[/math] (electron formula, θ = 0)

[math]\displaystyle{ f_e = 4\pi^2(2^6 3 \pi^2 \alpha \Omega^5)^3 = .23895453...x10^{23},\;unit = 1 }[/math] (unit-less)

In order that the electron may have dimensioned (measurable) parameters; electron mass, wavelength, frequency, charge ... the geometry of the mathematical electron (the electron 'event' [math]\displaystyle{ f_e }[/math]) includes (embeds) the geometrical MLTA (mass, length, time, charge) objects, this electron 'event' then dictating how those MLTA objects are arranged into dimensioned electron parameters. The electron itself can be considered as equivalent to a programming sub-routine, [math]\displaystyle{ f_e }[/math] does not have dimension units of its own (there is no physical electron), instead it is a geometrical formula that encodes the MLTA information required to implement those electron parameters.

electron mass [math]\displaystyle{ m_e = \frac{M}{f_e} }[/math] (M = Planck mass) units = kg, θ = 15

electron wavelength [math]\displaystyle{ \lambda_e = 2\pi L f_e }[/math] (L = Planck length), units = m, θ = -13

elementary charge [math]\displaystyle{ e = A.T }[/math] units = C, θ = 3

The AL magnetic monopoles confer the electric properties of the electron and also determine the duration of the electron frequency (0.2389 x 10²³ units of the simulation clock-rate variable age corresponding to 0.2389 x 10²³ units of Planck time). At the conclusion of this electric (magnetic monopole) 'wave-state' (duration 0.2389 x 10²³ units of age), the AL units intersect with time T, the units then collapse thereby exposing a unit of M (Planck mass) for 1 unit of age, which we could label the mass point-state. Unlike the 'wave-state' (which is spread over space and time), this 'mass point-state' can have defined co-ordinates (in space and time).

[math]\displaystyle{ \frac{({u^3})^3{(u^{-13}})^3}{(u^{-30})}\;(\frac{ampere^3 \;length^3}{time}) = 1 }[/math]

This mass 'point-state' would be the electron center (see singularity) and so during the 'point-state', the electron is mass M (M = 1), there is no longer charge A or length L or time T. It thus resolves the problem of the electron 'as a point'; (from ChatAI) in physics, the electron is considered to have no size or dimension, but instead is considered to be a point-like particle with a specific location in space ... and is treated as a mathematical point in mathematical models and theories. This is based on the idea that electrons are fundamental particles and do not have any substructure, and therefore, they can be considered as a single point-like object.

Wave-particle duality at the Planck level can then be reduced to an oscillation between an electric (magnetic monopole) wave-state (the duration dictated by the particle formula, for the electron = 0.2389 x 10²³ units of Planck time) to this unitary mass point-state.

In the formula E = hv, h (Planck's constant) refers to the wave-state, with the v term referring to the frequency of occurrence of h (per second). Conversely E = mc2 refers to the point-state, and as there is 1 wave-state per 1 point-state (a particle is a single wave-point oscillation), hv = mc2. The m of modern physics however refers to mass as a constant property of the particle whereas here particle mass has a frequency component (it is a measure of the frequency of occurrence of the mass point-state over time) and so here particle mass becomes average particle mass (the average occurrence of the point mass per second). For example, if a particle has a frequency of 10, then it will have 10 electric wave-states and 10 mass point-states (10 wave-point oscillations) per second.

If we can apply a unit number relationship θ, then although the 'physical' mass, space, time universe is constructed from particles, particles themselves are not physical, they are mathematical, and when summed, the mass, length, time, charge units cancel. Thus we may construct a physical universe from within a mathematical framework .

Null universe

We next need to construct a scaffolding for our particles

If the universe can expand by adding a discrete dimensionless geometrical object (such as the electron) that encodes the base (Planck) units of mass, length, time and charge per increment of age, then the sum universe can remain unit-less externally but not internally (from within the simulation).

For example, from this primordial object we may extract the object time T, but simultaneously we are extracting the other objects MLA (so that the sum universe is always dimensionless). This means that to create time T, the time required to read this sentence for example, the universe has to grow larger (add space L³) and more massive (add mass M). Likewise, if time went backward the universe would have to shrink in size and mass. But regardless of the age of the universe, if we combine all the mass, space and time (i.e.: all the physical units) within, the universe would disappear (units = 1). Seen from the outside, there would be no universe. This also means that if we know the age of the universe (number of units of T), then we know the number of units of M (mass) generated and the number of units of L (size) generated.

Relativistic universe

The simulation clock can give us the expansion of the universe in size and mass via these Planck objects. A 14 billion year old universe would put age = 1062. This expansion can also be used to introduce motion (particle momentum) by pulling particles with it, the problem however is that this expansion occurs at the speed of light (c = 1 unit of Planck length per 1 unit of Planck time), and so we need to provide a reference for our surroundings (if everything is moving away from us at the speed of light then we have no means to detect anything). One solution is for an expanding 4-axis hyper-sphere universe to project onto a fixed 3-D (Newtonian) background using the mathematics of perspective. If we can perceive only this 3-D background, then we will perceive the motion of all objects as relative to our motion. The expansion of the universe at the speed of light will be 'invisible' to us. This can be achieved using the electromagnetic spectrum.

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), using the same approach here would implement a 4-axis expanding hypersphere super-structure in which 3-D space is the projection .

The expanding hyper-sphere can be used to replace independent particle motion (momentum) with motion as a function of the expansion itself, as the universe expands (adding units of mass, space and time in the process), it pulls all particles along with it. In the mass point-state, the particle can be assigned defined co-ordinates in the hyper-sphere, in technical terms it is assigned a data address within the (hyper-sphere) hard-disk. This is not the same as co-ordinates in 3-D space, for the electron-as-a-point has no size dimension, in the point state there is no length L; (ChatAI An object without size would therefore be an object that occupies no space and has no physical extent. While it is possible to imagine such an object in a purely theoretical sense, there is no evidence to suggest that objects without size actually exist in the physical world).

If all particles simultaneously in the point-state per unit of age have defined hypersphere co-ordinates, they may then be measured relative to each other. As photons (the electromagnetic spectrum) have no mass state, they cannot be pulled along by the universe expansion (consequently they are date stamped, as it takes 8 minutes for a photon to travel from the sun, that photon is 8 minutes old when it reaches us), and so photons would be restricted to a lateral motion within the hyper-sphere. As the electromagnetic spectrum is the principal source of information regarding the environment, a 3-D relative space would be observed (as a projected image from within the 4-axis hyper-sphere), the relativity formulas can then be used to translate between the hyper-sphere co-ordinates and our observable 3-D space co-ordinates .

In hyper-sphere co-ordinate terms; age (the simulation clock-rate), and velocity (the velocity of the universe expansion as the origin of c) would be constants and thus all particles and objects, as they are pulled along by this hypersphere expansion, would travel at, and only at, the speed of light c (the photon does not travel away from us at velocity c, it is we who travel away from the photon at c), however in 3-D space co-ordinate terms, time and motion would be relative to the observer.

The time dimension of the observer is a measure of the change in state = change of information = change in relative position of particles in respect to each other and thus derives from, but is not the same as, the expansion clock-rate age or object time T, for in the absence of motion there is no means for the observer to measure either, the dimensionless age variable however would continue to increment, the universe hyper-sphere would continue to expand at the speed of light.

Gravitational orbitals

Although we can accurately predict the motion of planetary bodies in space using our gravity models, these are not suitable when we have to include the influence of grains of sand blowing in the wind or waves crashing onto a rocky beach as a deep simulation must do in real time. A  solution is to form individual (dimensionless) rotating particle to particle orbital pairs at the Planck scale, each rotating according to the orbital radius, the planetary orbits emerging naturally as the averaging over time of these underlying rotating orbitals. Thus for the earth-moon orbit to be plotted in real (universe) time, down to the particle level, it would not be necessary to have any information regarding the earth and the moon, their relative masses, their (constantly changing) barycenter, or any dimensioned constants.

All particles simultaneously in the point-state at any unit of age form gravitational orbital pairs with each other . For each increment to age, these orbital pairs then rotate by a specific angle depending on the radius of the orbital to travel 1 unit of Planck length. The results are then summed and averaged and so the entire universe can be updated in real time (before the next increment to age). The observed gravitational orbits of planets are the sum of these (n-body) particle-particle orbital pairs averaged over time. Thus it is in principle not necessary to have direct information regarding the orbiting objects in order to derive their respective orbits.

 FOR age = 1 TO the_end                                 
         'gravitational orbits via orbitals
         FOR n = 1 TO total_number_of_particles
                IF particle{n}_is_in_the_point_state   
                       form_an_orbital_pair-with_all_other_point_state_particles
                       rotate_orbital_1_Planck_length
                END IF 
                sum_and_average_all_coordinates
         NEXT n
 NEXT age 

Orbits, being also driven by the universe expansion, occur at the speed of light, however if the orbit along the expansion time-line is not noted by the observer, who instead relies on the electromagnetic spectrum, then the orbital period will be measured in terms of 3D space co-ordinates.

Atomic orbitals

As atomic orbitals also involve 2 particles rotating, they can be treated as modified gravitational orbitals. If the orbital itself is a 'physical' unit of momentum, akin to a photon, albeit of inverse phase, then when the photon strikes the atom, it will impact the orbital, not the particle, resulting in a lengthening or shortening of the orbital radius in the process. Electron transition between orbitals can then be mapped as a modification of the orbital (change in orbital radius) in discrete steps according to the wavelength of the incoming photon (which is absorbed or ejected by the orbital), the electron itself is not directly involved .

External links

• Programming Planck units as geometrical objects
• The mathematical electron
• Anomalies of the physical constants
• Programming relativity at the Planck scale
• Programming gravity at the Planck level
• Programming the cosmic microwave background at the Planck level
• The sqrt of Planck momentum
• The Programmer God, Are We in a Computer Simulation (eBook)
• Programming at the Planck scale using geometrical objects -Malcolm Macleod's website
• Simulation Argument -Nick Bostrom's website
• Our Mathematical Universe: My Quest for the Ultimate Nature of Reality -Max Tegmark (Book)
• Dirac-Kerr-Newman black-hole electron -Alexander Burinskii (article)
• The Matrix, (1999)
• Pythagoras "all is number" - Stanford University
• Simulation Hypothesis
• Mathematical universe hypothesis
• Philosophy of mathematics
• Philosophy of physics
• Platonism