# Simulation argument (coding relativity)

**Programming relativity for use in deep universe (Planck scale) Simulation Hypothesis modeling**

The simulation hypothesis or **simulation argument** is the argument that proposes all current existence, including the Earth and the rest of the universe, could 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 ^{[1]}

At the Planck scale we can embed a universe of 'relative motion' within a fixed (albeit expanding) 4-axis hypersphere (Newtonian) background. This approach is suitable for simulation hypothesis modelling as it uses discrete time (in units of Planck time t_{p}) and discrete mass (in units of Planck mass m_{P}) and can be run in real time (from the perspective of the simulation) on a serial processor.

The universe increments in digital steps *age* (the simulation clock-rate) with each step generating a unit of Planck time. All particles within the simulation share this common time *age*. By replacing wave-particle duality at the Planck level with an electric wave-state to a Planck mass point-state oscillation ^{[2]}, where the point-state is a discrete state, particles in the mass point-state can be assigned defined hyper-sphere co-ordinates.

In hyper-sphere co-ordinate terms; time (via the simulation clock-rate), and velocity (the velocity of expansion) are constants, and as particle motion derives from this expansion, all particles and objects travel at, and only at, this speed of expansion (the origin of *c*) ^{[3]}.

Photons (the electromagnetic spectrum) however can only traverse the hyper-sphere laterally (because they have no mass point-state), and as photons are the mechanism of information exchange, the 4-axis hyper-sphere coordinates are projected onto a 3-D space, and so in 3-D space co-ordinate terms, time and motion will be relative to the observer. The mathematics of perspective can be used to translate between the 2 co-ordinate systems ^{[4]}.

### Simulation clock-rateEdit

The simulation clock-rate would be defined as the minimum 'time' increment to the simulation. As each unit of dimensionless increment variable *age* generates 1 unit of dimensioned Planck time *T*, for a 14 billion year old universe *age* = 10^{62} (number of units of Planck time).

'begin simulation FOR age = 1 TO the_end 'big bang = 1 generate 1 time object T 'T is a dimension-ed unit of time generate 1 mass object M 'M is a dimension-ed unit of mass generate 1 length object L 'L is a dimension-ed unit of length ........ conduct certain processes NEXT age

### HypersphereEdit

An expanding in Planck step increments (variable *age*) 4-axis hyper-sphere is used as the scaffolding for particles. The mathematical electron model is suitable for mapping digital events at Planck time as it replaces wave-particle duality at the Planck level with an oscillation between an electric wave-state (the particle frequency as measured in units of *age*) and a discrete unit of Planck mass m_{P} (for 1 unit of *age*) point-state. While in this mass point-state, particles are assigned a location in hyper-sphere co-ordinates.

We take 2 particles *A* (*v = 0*) and *B* (*v = 0.866c*) which both have a frequency = 6; 5t_{p} (5 increments to **age**) in the wave-state followed by 1t_{p} in the point-state (the point-state is represented by a black dot, diagram right). The hyper-sphere expands radially (the origin of the dimensioned speed of light). Both particles begin at origin *O*, after 1sec, *B* will have traveled 299792458*0.866 = 259620km from *A* in 3-D space (horizontal-axis) and 299792458m from *O* (radial axis). From the perspective of the *A* time-line axis, *B* will have reached the point-state after 3t_{p} and so will have twice the (relativistic) mass of *A*. However the hypersphere expands radially from origin *O*, and so *A* will also have traveled the equivalent of 299792458m from *O* (radial axis *OA* = *OB*, *v = c*) and so from the perspective of the hypersphere, *B* can equally claim that *A* has traveled 259620km from *B* in 3-D space terms.

The time-line axis maps 1t_{p} steps (only the particle point-state can have defined co-ordinates), and so on this graph there can be only 6 possible velocity divisions (if including *v = 0*).

As the minimum step is 1 unit of Planck time, this means that *B* can attain Planck mass (m_{B} = m_{P}/1) when at maximum velocity v_{max} (relative to the *A* time-line axis), but *B* can never attain the horizontal axis = velocity *c* and so for particles, v_{max} can never attain *c*. However a small particle such as an electron has more time divisions and so can travel faster in 3-D space than can a larger particle (with a shorter wavelength).

### Particle motionEdit

Depicted is particle *B* at some arbitrary universe time *t = 1*. *B* begins at origin *O* and is pulled (stretched) by the hyper-sphere (pilot wave) expansion in the wave-state. At *t = 6*, *B* collapses back into the mass point state and now has defined co-ordinates within the hypersphere, these co-ordinates become the new origin *O’*.

In hypersphere coordinates everything travels at, and only at, the speed of expansion = *c*, this is the origin of all motion, particles (and planets) do not have any inherent motion of their own, they are pulled along by this expansion as particles oscillate from (electric) wave-state to (mass) point-state ... ad-infinitum.

### Particle N-S axisEdit

Particles are assigned an N-S spin axis. The co-ordinates of the point-state are determined by the orientation of the N-S axis. Of all the possible solutions, it is the particle N-S axis which determines where the point-state will occur.

*A*, *B* and *C* begin together, if we can then change the N-S axis angle of *A* and *C* compared to *B*, then as the universe expands the *A* wave-state and the *C* wave-state will be stretched as with *B*, but the point state co-ordinates of *A* (and *C*) will now reflect the new N-S axis angles.

*A, B, C* do not need to have an independent motion; they are being pulled by the universe expansion in different directions (relative to each other). We can thus simulate a transfer of physical momentum to a particle by changing the N-S axis. The radial hyper-sphere expansion does the rest.

In this example (diagram right), we continuously change the N-S axis of B (orange dot *f* = 6) across all 11 options after each point state. A sin wave forms around the A (purple dot *v* = 0) time-line axis with a period measured in time units;

### PhotonsEdit

Information between particles is exchanged by photons. Photons do not have a mass point-state, only a wave-state and so have no means to travel the radial expansion axis, instead they travel laterally across the hyper-sphere (they are `time-stamped', a photon reaching us from the sun is 8minutes old).

The period required for particles to emit and to absorb photons is proportional to photon wavelength as illustrated in the diagram (right), (*v* = 0) emits a photon (wavelength ) towards . The time taken (*h*) by to absorb the photon depends on the motion of relative to . The Doppler shift;

Photons cannot travel the radial expansion axis, and so instead of virtual co-ordinates *OA*, *OB* and *OC* and a constant time and velocity, and as the information between particles is exchanged via the electromagnetic spectrum, *ABC* will measure only the horizontal *AB*, *BC* and *AC* (x-y-z) co-ordinates, thus defining for the observer a relative 3-D space.

### Gravitational OrbitsEdit

All particles simultaneously in the point-state at any unit of **age** form gravitational orbital pairs with each other ^{[5]}. These orbital pairs then rotate by a specific angle depending on the radius of the orbital. These are then averaged giving new co-ordinates in the hypersphere. Furthermore the orbital plane also rotates. The observed gravitational orbits of planets are the sum of these individual orbital pairs averaged over time.

Orbits, being also driven by the universe expansion, occur at the speed of light, however the orbit along the expansion time-line is not noted by the observer and so the orbital period is measured using only 3D space co-ordinates.

#### Geometrical orbitalsEdit

Gravitational orbitals are divided in an 'alpha based pixel' sub-structure

(inverse) fine structure constant α = 137.03599...,

n_{p} = pixel number

= number of Planck mass point-states per unit of Planck time

Orbital geometry for 2 (rotating) mass points;

- (pixel to mass ratio)

- (pixel aggregate)

- (orbital length)

#### Hyper-sphere co-ordinatesEdit

While *B* (satellite) has a circular orbit period t_{o} on a 2-axis plane (horizontal axis as 3-D space) around *A* (planet), it also follows a cylindrical orbit (from B^{1} to B^{11}) around the *A* time-line (vertical) axis in hyper-sphere co-ordinates. *A* is moving with the universe expansion (along the time-line axis) at (v = c) but is stationary in 3-D space (v = 0). *B* is orbiting *A* at (v = c) but the time-line axis motion is equivalent (and so `invisible') to both *A* and *B* and so the orbital period and orbital velocity measure is limited to 3-D space co-ordinates.

We can simplify this cylinder by projecting it onto a 2-axis plane as the difference between 2 orbits.

#### Planck unitsEdit

In terms of Planck units

λ_{object} = Schwarzschild radius

m_{P} = Planck mass

l_{p} = Planck length

- (number of particles in the Planck mass point-state per unit of Planck time)

- (converting to Schwarschild radius)

- (gravitational orbit velocity)

- (standard gravitational orbit period)

#### Hyper-sphere orbitalEdit

Measuring a hypersphere orbital in 3-D space where

To project the hyper-sphere cylindrical orbit onto 3-D space at radius , we can divide the orbit into an inner and outer circle;

Example: A 1kg satellite *B* orbit at radius *r* = 42164.170 km from earth center

- m

- million km

- s

- m/s

- s

- s

- m (distance travelled by the orbital plane itself per orbit)

### External linksEdit

- Mathematical electron
- Programming the Planck units for mass, length, time and charge
- Programming gravity at the Planck level
- Programming the cosmic microwave background CMB at the Planck level
- Micro black hole
- Planck particle
- Simulation hypothesis
- the Source Code of God; a Programming approach -online resource
- Simulation Argument -Nick Bostrom's website
- [1] - A Planck unit universe according to a geometrical electron formula and the magnitude of the fine structure constant alpha (overview)
- Our Mathematical Universe: My Quest for the Ultimate Nature of Reality -Max Tegmark

### ReferencesEdit

- ↑ Are We Living in a Computer Simulation? https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/
- ↑ Macleod, Malcolm J. "Programming Planck units from a mathematical electron; a Simulation Hypothesis".
*Eur. Phys. J. Plus***113**: 278. 22 March 2018. doi:10.1140/epjp/i2018-12094-x. - ↑ Macleod, Malcolm J.; "Programming cosmic microwave background parameters for Planck scale Simulation Hypothesis modeling".
*RG*. Feb 2011. doi:10.13140/RG.2.2.31308.16004/7. - ↑ Macleod, Malcolm J.; "Programming relativity for Planck unit Simulation Hypothesis modeling".
*RG*. Feb 2011. doi:10.13140/RG.2.2.18574.00326/3. - ↑ Macleod, Malcolm J.; "Programming gravity for Planck unit Simulation Hypothesis modeling".
*RG*. Feb 2011. doi:10.13140/RG.2.2.11496.93445/8.