# Simulation argument (coding relativity)

Relativity as the mathematics of perspective
Programming relativity 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.
A deep-universe simulation model operates at the Planck scale and uses the Planck units as the scaffolding upon which particles are embedded. The simplest variation embeds a space-time universe of 'relative motion' within a fixed (albeit expanding) 4-axis hypersphere (absolute 'Newtonian') background. Relativity then becomes the mathematics of perspective, projecting hyper-sphere co-ordinates onto a 3-D space.

#### Simulation clock-rate

At the Planck scale, simulation hypothesis modelling can use discrete time (which can be measured in units of Planck time t$_p$) and discrete mass (in units of Planck mass m$_P$). The universe increments in digital steps t$_{age}$ (the simulation clock-rate) with each step generating a dimensioned unit of Planck time. All particles within the simulation share this common time t$_{age}$.

#### Wave-particle duality

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 t$_{age}$) and a discrete unit of Planck mass m$_P$ (for 1 unit of t$_{age}$) point-state. While in this mass point-state, particles can be assigned a location in hyper-sphere co-ordinates.

#### Hypersphere

A 4-axis Planck black hole hyper-sphere expanding in increments (see t$_{age}$), is used as the scaffolding for particles. In hyper-sphere co-ordinate terms; time (via the simulation clock-rate), and velocity (the velocity of expansion v = c) are constants, and as particle motion derives from this expansion, all particles and objects travel at, and only at, this speed of expansion.
We take 2 particles A (v = 0) and B (v = 0.866c) which both have a frequency = 6; 5t$_p$ (5 increments to t$_{age}$) 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 at the 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 motion

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 axis

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 wave forms around the A (purple dot v = 0) time-line axis with a period $4(4f^{2}-f)$ measured in time units;

#### Photons

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 8 minutes old).
The period required for particles to emit and to absorb photons is proportional to photon wavelength as illustrated in the diagram (right), $A$ (v = 0) emits a photon (wavelength $\lambda$) towards $B$. The time taken (h) by $B$ to absorb the photon depends on the motion of $B$ relative to $A$. The Doppler shift;
    $v_{observed}=v_{source}.{\frac {\sqrt {1-{\frac {v^{2}}{c^{2}}}}}{1-{\frac {v}{c}}}}=v_{source}.{\frac {h}{\lambda -z}}$
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 relativistic 3-D space. Relativity translates between the hyper-sphere and 3-D space co-ordinate systems.

#### Gravitational Orbits

All particles simultaneously in the point-state at any unit of t$_{age}$ form orbital pairs with each other. 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 3D space co-ordinates.
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 for an observer the orbital period and orbital velocity measure is limited to 3-D space co-ordinates.

#### External links

* Programming Planck units as geometrical objects
* The mathematical electron
* 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
* The Simulation hypothesis
* The Source Code of God; Programming the Planck scale -online resource
* Simulation Argument -Nick Bostrom's website
* Our Mathematical Universe: My Quest for the Ultimate Nature of Reality -Max Tegmark

#### References

* ↑ Are We Living in a Computer Simulation? https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/
* ↑ https://codingthecosmos.com/planck-scale.html
* ↑ 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 scale Simulation Hypothesis modeling". RG. Feb 2011. doi:10.13140/RG.2.2.18574.00326/3.
* ↑ 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 gravity for Planck unit Simulation Hypothesis modeling". RG. Feb 2011. doi:10.13140/RG.2.2.11496.93445/12.