**Appendix B**

**The Nine 2D Fundamental Relationships**

**The Three Relationships of Distance and Time**

Time and distance, that when combined in the three simple relationships, form some interesting concepts.

**Displacement = Distance x Time**

Displacement is the concept of a 1D Structural Vector formed from two co-linear unit vectors, one of a directed distance and one of directed time. Any distance that is traveled is also traveled in time for one cannot travel a distance without also traveling in time. Since distance and time are not traversed separately then what occurs is displacement. Displacement, it is what occurs when we move, or when energy and matter moves, from place to place.

(x1 - x0) * (t1 - t0) = (dx * dt) = Displacement

The Structural Vector of Displacement is the 1D edge of 2D Structural surface elements. It is the contiguous-ness between two points forming a primary vector. Normal surface is formed by Hypersurface geometry that forms a closed contiguous perimeter to create an area. The Structural Vector is that which helps to form the surface that forms the volume. Many Displacement vectors acting together form ‘infinite planes’.

**Velocity = Distance / Time**

Velocity is the concept notion of relative motion. When we move through space and time, we do it at some velocity. When what we do involves motion, we do it at some linear velocity. All things are in motion. All things usually travel in a linear fashion. The velocity of an object is relative to the observer. When you increase your velocity, you are able to cover more distance in less time. The slower one goes the longer it takes to cross a specific distance. If this fundamental relationship did not exist between distance and time, there would be no movement available for matter or energy.

From “HyperPhysics - Velocity”, Velocity is defined as:

The average speed of an object is defined as the distance traveled divided by the time elapsed. Velocity is a vector quantity, and average velocity can be defined as the displacement divided by the time. For the special case of straight-line motion in the x direction, the average velocity takes the form:

Velocity is a 1D Dynamic vector relationship between distance and time. Relativity exists between two points, and when the two points have time dependant vectors, the time concept and its relationships, is critical.You can approach an expression for the instantaneous velocity at any point on the path by taking the limit as the time interval gets smaller and smaller. Such a limiting process is called a derivative and the instantaneous velocity can be defined as:

**Inertial Friction = Time / Distance**

Inertial friction is a 1D “anti-dynamic” hypervector, and is inverse to that of velocity. Inertial Friction and is the same as the concept of ‘resistance’ in units. The speed limit of the photon is the result of the Inertial Friction relationship. Inertial Friction is the opposite of the concept for motion, which is that of velocity. It can be seen that as the time factor becomes large, while the distance factor remains constant, that the value of the frictional resistance increases.

Physicists have shown that various kinds of matter allow photons to pass through, with ease or difficulty, depending on the matter. This ‘resistance’ to an photon’s passage is the result of the photon’s mass vector reaction to Inertial Friction vector of a particular volume of material. The amount of ‘drag resistance’ over a given distance that an photon is to travel, after energy has been applied to put the photon into motion, is similar to aerodynamic drag. In the case of the photon traveling through space-time, in a vacuum, one could believe that there would be no resistance to its passage, yet there is as such a resistance. It comes from the 2D ‘t/d’ unit vector relationship. Using the example of the electron, instead of the photon, passing through some medium, where it is easier to understand such a concept, Inertial Friction is at cause for the electron’s speed –limit of travel through any kind of matter or just space-time.

The geometry of Hypersurfaces plays a significant role in the expression of Inertial Friction when it comes to matter, energy, gravity and space-time.

**The Three Relationships of Primary’s Mass and Distance**

Distance and mass, that when combined in the three different simple relationships, form some ‘massive’ concepts.

**Linear Matter = Mass x Distance**

Linear Matter is the concept of 1D Vector of Matter, the edge of a matter element. It is the base vector part of matter just as Linear Displacement is the base vector part of space-time. Geometrical Structure is made from three points with stable vectors between points. When mass is a component of a structural vector, matter is a formed. Mobile differentiation of space, by a Hypersurface that creates “movable space-time”, using a relationship vector such as Linear Matter is what forms matter. Mass needs Distance to have reality. Matter is what matters, for without it space and time are meaningless and there is no differentiation.

Linear Matter, the ‘solid’ equivalent of heat, in terms of SI physical primary units, is “kg-m”. Typically the kg-m is used as a conversion tool in a relationship equation, much like c2 converts mass into energy. Matter, whatever its current density and current composition, has its own mobile local space-time. Since before space-time and matter, before energy, before structure, it all was undifferentiated ‘Mass-Space-Time’. The real creation was mobile differentiation.

The path of a typical end-point of a vector is a curve. A 2D plane is necessary to describe a vector as a curve. The vector line element itself is a 1D vector between a Point and the next immediate Point tip on the path object, in a 2D environment. We can see that from a 3D perspective, perpendicular to the 2D surface, the veracity of this claim. Enthalpy is a progression from chaotic relationships to ordered relationships. Enthalpy follows a ‘path’ of progression. The Sun, and all other massive stars that still shine by the fusing of hydrogen into helium, is the main producer of enthalpy occurrences. Creating matter with larger nucleon counts is a process of enthalpy. Entropy, by contrast, is change from an ordered state, such as ice, to a more disordered state of chaos, such as water, which will lead to a form of equilibrium that is determined by available heat within a finite volume.

**Linear Density = Mass / Distance**

Linear Density is a 1D density vector, and is a precursor of the 3D ‘regular’ volumetric density measurement scalar in kg/m3. Linear Density is the concept of mass per unit length. If a given Linear Matter vector has a certain mass, it said to have an average mass for that distance, this is a form of density. When one weighs two identical cylindrical volumes, one made out of Aluminum and the other made out of Gold, on a weight scale, one will find that the gold cylinder weighs more than the aluminum cylinder. What this means is that there is more mass squeezed in to the same sized volume for the gold. This applies to the number of atoms of each element with identical volumes. If the number of atoms is the same in each cylinder, the gold one would still weigh more. If the mass of a cross-sectional disc is constant, then the total mass of the cylinder can be determined by measuring its total length.

The same is true of Linear Density. If, for equal distance vectors, gold has a unit mass vector that is longer or rotated at an angle that is smaller in relationship to the unit distance vector, it can be said to be denser. When a Linear Density vector is allowed to rotate with 3 degrees of freedom, a more familiar form of volumetric density is apparent to the observer.

The universe has its own natural ‘coordinate’ system. In physics, there is taught, within the mechanical branch, two types of systems when it comes to the motion of physical objects: linear and rotational. Linear uses the familiar x, y, z, while rotational uses two perpendicular angles and a variable scalar, which is known as the spherical coordinate system. This spherical coordinate system is similar to the natural one of the universe.

**Specific Linearity = Distance / Mass**

Specific Linearity is the concept of a 1D vector of specific length, which leads one to the Quantifiable. The concept of Specific Linearity of Matter, leads one to the quantitative and qualitative concepts in chemistry. Each nucleus of an atom of some element has a specific radius that makes it distinctive. The number of electrons, that form the ‘cloud’ about each nucleus, also conform to some specific radius for that element, and adds distinctiveness to the element. The Proton, Neutron, and the Electron each has its own specific radius and mass. If the Dynamic Mass hypervector truly is a constant unit, then it is plain to see that the radius of a particle determines its mass, this is given evidence by the size and mass of each, with the electron being the smallest in both size and mass, and the neutron the largest in both size and mass.

When looking at matter from the point of view of a unit mass vector, what is the radius distance, of a gram of it? The answer depends on the element that the gram of mass is made. The Specific Linearity of matter is specific to the differentiation of the element or particle system that it is specifically describing.

**The Three Relationships of Primary’s Mass and Time**

Time and mass, that when combined in the three simple relationships, form some ‘energetic’ concepts.

**Potential = Mass x Time**

Potential is the concept of a 1D Vector of Availability. What is Potential? Mass has no meaning or existence without time. Mass needs time to exist. The matter and energy that are here today can be gone tomorrow. For Matter and Energy to exist, both require the concepts of time and mass. The availability of mass or time is required for the formation of either matter or energy. There exists the requirement that there be a Potential to form either one.

Energy, thanks to Einstein, equals mass times ‘the velocity of light in a vacuum’ squared, while Matter comes in four distinct forms. In the ancient days of yore, the four forms of matter were known as the ‘Four Elements’: Earth (solids), Water (liquids), Air (gases) and Fire (hot ionized gases i.e. Plasma or solar matter), and the once mythical 'fifth element' known as AEther (space-time and its drag / vacuum). Each form of matter, going from solid to liquid to gas to plasma, is less dense, displays more ‘kinetic energy’ and less ‘potential energy’ than the previous. However, there are many different types of each of the ‘four elements’, at least when it comes to the solids, liquids, and gases. One defines a ‘volume’ as ‘distance x distance x distance’ or d3, or aka ‘Space’, Matter comes from multiplying Potential x Space. Energy comes from multiplying Potiential / Inertial Resistance x Acceleration, which is a little different from matter. Energy goes to chaos, while matter creates order. Energy is time dependant and future orientated, while matter is distance dependant and past orientated. Vector direction in each Potential relationship in the formation of Hypersurface geometries goes to some differentiation to form some kind of matter or the transference of energy.

Matter is condensed Energy. Energy comes in several forms, as does Matter. Energy condenses to Matter. It’s all about DTM.

**Specific Time or Longevity = Time / Mass**

Longevity is the concept of a 1D vector edge of a 2D plane of specific time. It takes a specific amount of time to ‘change’. The process of changing moves mass, in some form, from one Point to the next Point. This relationship between time and mass is similar to the one in Inertial Resistance. It takes time to move mass. It takes time to build mass. This relationship between time and mass, a unit of time per unit of mass, if the mass term is kept constant as the 'change' occurs then it is the unit of time that is changing.

Longevity, Change and Time-flow with the addition of Hypersurface geometry, increase or decrease the strength of these concepts in normal space-time. Changing the mass vector can greatly affect the time component in this relationship.

The field (hypersurface) that develops in small particles of matter acts as an envelope surrounding the center origin point creating a spherical bubble that is able to slip through space-time yet acts like glue to create matter. Longevity or Change is one the differentiating components of matter. If there is a constant, such as ‘c’, for time/mass, that could be considered to be equal to 1, then as an object’s mass increases, it’s time of ‘existence’ decreases. Radioactive decay of elements with high nucleon counts is evidence for such a constant, as is the apparent longevity of the Proton.

**Push = Mass / Time**

Push is the concept of a 1D dynamic vector edge of a 2D surface element that impels. Any action to change the direction of any object requires Push. Mass and time in this form of a relationship leads to motion, action and change. Push is applied to matter through area. Push is equal in all directions in space-time. It takes mass and time to move other mass and time. Mass and time in this form of a relationship is the basis of “Gravity,” “Momentum,” “Force,” “Energy,” “Power,” and other concepts that will be defined later. Gravity is not a property of matter itself. It is a concept structure much like space and time that is a formed relationship around unit vectors of mass. Matter attenuates Push. Thrust, gravity, and Push: all cause matter to 'accelerate' and move.

When Sir Isaac Newton founded the laws of motion as they relate to gravity and the motion of the planets, he was not specific as to the direction of its application, nor whether it is a repulsive or attractive force. However, his laws of reaction are evident in the concept of Push. “For every action, there is an opposite reaction.” To pick up a rock, it takes Push. The fluid in the muscle cells Pushes against the flexible, but not so stretchable, cell walls during the contraction process. The contraction processes of the muscles in the arm allow the fingers to move. The action, of thumb and finger, against the rock is Push from opposite sides, causing sufficient pressure and friction to over come the inertia of the rock against gravity. With the rock in the palm of your hand, palm up, you use Push again to raise the rock from the ground to pocket level. This action has added ‘potential energy’ to the rock. To throw the rock, it takes Push. Once the rock has reached its maximum ‘potential energy’ and its initial ‘kinetic energy’, from the throw, has reached zero, then Gravity takes over and Pushes the rock back to the ground. There is no Pull, per say, just Push. Examine any action that takes place. Examine each component of the objects in the senario of the action. One will find Push rather than pull.