# Relativity (Planck)

Programming relativity for use in Planck scale Simulation Hypothesis modeling

A Planck scale universe simulation (see Simulation Hypothesis) can be simplified by using discrete Planck unit time as the simulation clock-rate. This permits all particles within the simulation to have a common time t as measured in these units of Planck time. By replacing wave-particle duality at the Planck level with an electric wave-state to a Planck mass point-state oscillation [1], where the point-state is a digital (unit time) state, particles in the point-state can be assigned defined hyper-sphere co-ordinates.

In hyper-sphere co-ordinate terms; time (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 v = c [2].

Photons (the electromagnetic spectrum) 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 [3].

The time dimension of the observer is a measure of change of state (change of information) and thus derives from, but is not the same as, the simulation clock-rate.

## Hypersphere

An expanding, in Planck step increments, 4-axis hyper-sphere is used as the scaffolding for particles (events that dictate the frequency of the Planck units). 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 (particle frequency as measured in units of Planck time) and a unit of Planck mass mP (for 1 unit of Planck time 1tp) mass point-state. While in this point-state, particles are assigned a defined location in hyper-sphere co-ordinates.

A and B in hypersphere co-ordinates from origin O, (frequency 0A = 0B = 6)

We take 2 particles A (v = 0) and B (v = 0.866c) which both have a frequency = 6; 5tp in the wave-state followed by 1tp in the point-state. The hyper-sphere expands radially at the speed of light. Both particles begin at origin O, after 1sec, B will have traveled 259620km from A in 3-D space (x-axis). From the perspective of the A (hypersphere expansion) time-line axis, B will have reached the point-state after 3tp and so will have twice the (relativistic) mass of A. However the hypersphere expands radially from origin O, and so both A and B will have traveled the equivalent of 299792458m from O (radius OA = OB, v = c) and so B can equally claim that A has traveled 259620km from B in 3-D space terms.

The time-line axis maps 1tp steps (only the particle point-state can have defined co-ordinates), and so on this graph there can be only 6 possible velocity divisions (including v = 0), this means that B can attain Planck mass (mB = mP/1) when at maximum velocity vmax (relative to the A time-line axis), but B can never reach the horizontal axis = expansion velocity c and so vmax < c. A small particle such as an electron has more divisions and so can travel faster in 3-D space than can a larger particle (with shorter wavelength).

## Particle motion

particle wave to point oscillations in hyper-sphere expansion co-ordinates

Depicted is particle B at some arbitrary universe time t = 1. B begins at origin O and is pulled along 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 wave-state to point-state ... ad-infinitum.

## Particle N-S axis

particle N-S spin axis orientation mapped onto hyper-sphere

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

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.

## Photons

Doppler shift mapped onto hyper-sphere co-ordinates

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 (they are `time-stamped').

A emits a photon. B travels towards A, the period required for particles to emit and to absorb photons is proportional to wavelength, as such it will take B less time to absorb that photon than if B was parallel to or moving away from A. The Doppler shift;

${\displaystyle x_{axis}={\frac {v}{c}}}$
${\displaystyle h_{axis}={\sqrt {1^{2}-x^{2}}}}$
${\displaystyle v_{observed}=v_{source}.{\frac {\sqrt {1-{\frac {v^{2}}{c^{2}}}}}{1-{\frac {v}{c}}}}=v_{source}.{\frac {h}{1-x}}}$

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 by photons, ABC will measure only the horizontal AB, BC and AC (x-y-z) co-ordinates, thus defining a relative 3-D space (relative to the observer).

## Gravitational Orbits

B's orbit relative to A's time-line axis; mass B << A

Point-states orbit each other in orbital pairs, the observed gravitational orbits of planets as the sum of these individual orbital pairs and so a gravitational force is not required [4]. Orbits occur at the speed of light along the orbital plane t0 but also in incremental steps along the (unseen) time-line axis td thus giving the illusion of an orbital velocity in 3-D space. At the Planck level, Planck gravitational time dilation is a natural consequence of the cylindrical orbit.