# Hilbert Book Model Project/Zigzag

HansVanLeunen respectfully asks that people use the discussion page, their talk page or email them, rather than contribute to this page at this time. This page might be under construction, controversial, used currently as part of a brick and mortar class by a teacher, or document an ongoing research project. Please RESPECT their wishes by not editing this page.

# Zigzag

## Chronological zigzag of elementary modules

### Mixed views

The Hilbert Book Model offers two views, the creator's view and the observer's view[1]. Sometimes it has sense, to mix both views. The zigzag of elementary modules is an example of such a situation. This zigzag cannot be observed. It only exists in the creator's view. The Hilbert Book Model impersonates the creator. We use the initials HBM to name the creator. At the instant of the creation the creator stored all essential dynamic geometric data of his creatures in a read-only repository. After that instant, HBM left his creatures untouched. For that reason the creator's view is also a storage view. All observable objects in the universe are modules or they are information messengers. All modules are potential observers. All modules can figure in an observed event. All modules are embedded in a continuum. This continuum transfers information from the containers that store the observed event to the containers that store the observer.

#### Elementary modules

A set of pointlike elementary modules exist that together configure all other modules and the existing modular systems. Private stochastic mechanisms provide the locations of the elementary modules. Consequently, the elementary modules hop around in a stochastic hopping path. The hop landing locations form a hop landing location swarm. The stochastic mechanism applies a stochastic process that owns a characteristic function that acts as a displacement generator for the swarm. Consequently, the swarm moves as a single coherent object.

### The zigzag reflection events

The elementary module can zigzag in the direction of progression. At the reflection instants some of the properties of the elementary module change sign. The reflection event emits information messengers that contain information about the refection event.

The hop landing locations trigger clamps. Clamps are spherical shock fronts that temporarily deform the embedding continuum. Clamps integrate in the Green's function of the embedding continuum. For that reason clamps carry a standard bit of mass.

Strings of equidistant warps constitute the information messengers. Warps are one-dimensional shock fronts. Each warp carries a standard bit of energy.

At the reflection event warps convert into clamps and clamps convert into warps. In the process elementary particles convert into their antiparticle. The procedure takes the complete regeneration cycle of the elementary module.

Due to the zigzag travel, at a single instant, the same elementary module possesses multiple realizations. For that reason these realizations are entangled.

In the creator's view the probability that an elementary module creates from the conversion of a warp string to a clamp swarm depends on the possibility of such conversion.

The fact that at reflection events two warp strings appear in a perpendicular direction suggests that the involved quaternions convert into complex numbers or vice versa.

Each quaternion ${\displaystyle c}$ can be written as a product of two complex numbers ${\displaystyle a}$ and ${\displaystyle b}$ of which the imaginary base vectors are perpendicular

${\displaystyle c=(a_{0}+a_{1}{\vec {i}})(b_{0}+b_{1}{\vec {j}})=c_{0}+c_{1}{\vec {i}}+c_{2}{\vec {j}}+c_{3}{\vec {k}}=a_{0}b_{0}+a_{1}b_{0}{\vec {i}}+a_{0}b_{1}{\vec {j}}\pm a_{1}b_{1}{\vec {k}};\ {\vec {i}}{\vec {j}}=\pm {\vec {k}}}$

Rotating ${\displaystyle c}$ with a pair of ${\displaystyle {\vec {k}}}$ vectors will invert quaternion ${\displaystyle c}$ in the direction of ${\displaystyle {\vec {k}}}$.

${\displaystyle {\vec {k}}\ c/{\vec {k}}=c_{0}-c_{1}{\vec {i}}-c_{2}{\vec {j}}+c_{3}{\vec {k}}}$

The HBM suggests that the complex numbers ${\displaystyle a}$ and ${\displaystyle b}$ describe the involved warps and the quaternions ${\displaystyle c}$ describe the involved clamp triggers.

In the generated hop landing location swarm each element must be treated. Seeː Hilbert Book Model Project/Information Messengers#The absorption dilemma

### What observers perceive

Observers cannot perceive reflection and they cannot perceive the conversion of an elementary particle in its antiparticle. Instead, observers see creation and annihilation events and they see emission or absorption of information messengers.

At the annihilation event of an elementary module observers perceive the annihilation of the elementary particle and the emission of two information messengers that leave the scene in opposite directions. The information messengers carry the energy equivalent of the mass of the annihilated particle.

During the same procedure, an antiparticle is created. The creation event goes together with the absorption of two information messengers that meet with incredible precision from opposite directions, such that the energy of the messengers convert into the mass of the created antiparticle.

Observers cannot perceive that elementary modules exist multiple times. They cannot see an antiparticle as a module that travels back in time.