# Relativity (Planck)

Programming relativity using the mathematics of perspective at the Planck scale

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. A deep-universe simulation model [1] operates at the Planck scale and uses the Planck units as the scaffolding upon which particles are embedded [2]. One variation of a deep-universe simulation 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 [3].

#### Simulation clock-rate

The simulation universe (simulation clock-rate) increments in discrete steps (tage). Each increment is equivalent to 1 unit of Planck time, thus all particles within the simulation share a common time, this tage.

 FOR tage = 1 TO the_end         //1 = big bang
perform all processes
........
NEXT tage                       //tage is a dimensionless incrementing variable


#### Wave to point oscillation

For particles in the simulation, wave-particle duality is represented as an oscillation between an electric wave-state (the duration dictated by the particle frequency as measured in Planck time units), to a discrete (for 1 unit of Planck time) mass point-state[4]. The particle has (is) mass (1 unit of Planck mass mP) only at the point-state, likewise at this state the particle has no electric properties. The particle at the Planck scale is defined as an event (1 complete wave-point oscillation), and thus 1 of the dimensions of the particle is time, the particle per se does not exist at any 1 unit of (Planck) time.

#### Hypersphere

A 4-axis (black hole) hyper-sphere expanding in increments (see tage), is used as the scaffolding for particles. With every increment to (tage) the hypersphere axis also increment 1 step. In Planck unit terms, for every unit of Planck time, the universe expands by 1 unit of Planck length. Thus in hyper-sphere co-ordinates, time (via the simulation clock-rate), and velocity v (the velocity of expansion) are constants, and as the universe increments 1 Planck length per 1 Planck time, then v = 1lp/1tp = c. All motion derives from this expansion (as the universe expands it pulls particles along with it), and so in hyper-sphere co-ordinates all particles and objects travel at, and only at, the speed of light, this speed of expansion [5]. Consequently the speed of light is a defined limit.

During the mass point-state the particle, as a point, has defined co-ordinates within the hypersphere, and so all particles simultaneously in the point-state per any specified unit of (Planck) time can be defined relative to each other.

We take 2 particles A (v = 0 in 3D space) and B (v = 0.866c in 3D space) which both have a frequency = 6; 5tp (5 increments to tage) in the wave-state followed by 1tp 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 3tp 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 1tp steps (only the particle point-state has defined co-ordinates), and so on this graph there can be only 6 possible time-line divisions (if including v = 0). As the minimum step is 1 unit of Planck time, 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 attain the horizontal axis = velocity c, and so for particles, vmax can never attain c. However a small particle such as an electron has more time-line 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 (top left) and is pulled (stretched) by the hyper-sphere (pilot wave) expansion in the wave-state (top right). At t = 6, B collapses back into the mass point state (bottom left) and now has new co-ordinates within the hypersphere, these co-ordinates becoming 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 next occur.

A, B and C begin together at O, 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 their new N-S axis angles of orientation.

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 simply 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 ${\displaystyle 4(4f^{2}-f)}$ 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), ${\displaystyle A}$ (v = 0) emits a photon (wavelength ${\displaystyle \lambda }$) towards ${\displaystyle B}$. The time taken (h) by ${\displaystyle B}$ to absorb the photon depends on the motion of ${\displaystyle B}$ relative to ${\displaystyle A}$. The Doppler shift;

${\displaystyle v_{observed}=v_{source}.{\frac {\sqrt {1-{\frac {v^{2}}{c^{2}}}}}{1-{\frac {v}{c}}}}=v_{source}.{\frac {h}{\lambda -z}}}$

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 tage form orbital pairs with each other [6]. 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. 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 to on a 2-axis plane (horizontal axis as 3-D space) around A (planet), it also follows a cylindrical orbit (from B1 to B11) 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.