Appendix C Tertiary Concepts

The Seven 3D Fundamental Relationships

The Seven Relationships of Mass, Distance and Time

In this appendix, the concepts that involve all three of the primary units of distance, time, and mass that when combined in seven simple relationships, form concepts, new and old revisited, that will become the basis of even more complex concepts.

Present Reality of Existence = Mass x Distance x Time

Potential Reality is the concept of three unit vectors that form a composite 1D Vector edge of a 2D surface element of Tangible Existence. It is the nature of surface within our universe that gives us the concept of reality. The Reality of Existence in terms of physicality is another property of the Point. Most physicists consider particles as solid inelastic points. Particles and points are actually a co-linear view of structural vectors of Present Reality of Existence. Consider for a moment that the current thinking in Q. E. D. is that virtually any sub-nucleon type particle can form in the vacuum of space, a.k.a. ‘Quark Foam’. This ‘Quark Foam’ is actually Vectors of Present Reality of Existence. How long will a line of Present Reality of Existence will last is a matter of its Potential. We exist in a linear fashion. We are dynamic volumes of space-time, filled with organized matter, that exist for a short amount of time.

Present Reality of Existence can also be viewed as a ‘Hot Time’ or ‘Massive Displacement’.

Together, the unit vectors of mass, time, and distance are all rolled into one composite vector package of Present Reality of Existence. Matter, Space-Time, Energy, Gravity are each a concept of higher linear dimension. Also, they are all concepts that require three or more degrees of freedom to form. All the unit vectors are pointing in some direction. Each rotating in some plane, to form and become the basis of all things material, propelling, impelling and cosmological.

Future Reality of Existence = 1/(Mass x Distance x Time)

To Be determined. A future-present dynamic vector that would make Heisenberg proud.

Momentum = Mass x Distance / Time

Momentum is the concept of three unit vectors that form a composite 1D Vector edge of said 2D surface element of Tangible Existence, adjacent to Potential Reality. Isaac Newton’s second law, or rather the second half of his statement about the motion of objects, namely that “…Every body perseveres in its … uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon...” is the statement from which the concept of Momentum is derived. An object that is in motion and traveling at a constant rate of velocity is considered to have Momentum. Mass x Distance / Time = Momentum, which is constant change of an objects distance or direction, through the action of motion. Einstein has taught us that everything is relative. Said object is considered to be in motion, in some ‘right’ direction relative to any other object not in apparent motion.

From ‘HyperPhysics – Momentum’, Momentum is defined as:

Momentum:

The momentum of a particle is defined as the product of its mass times its velocity. It is a vector quantity. The momentum of a system is the vector sum of the momenta of the objects, which make up the system. If the system is an isolated system, then the momentum of the system is a constant of the motion and subject to the principle of conservation of momentum.

The basic definition of momentum applies even at relativistic velocities, but then, the mass is taken to be the relativistic mass.  The most common symbol for momentum is p. The SI unit for momentum is kg m/s.  Momentum is in the motion of objects. Relative motion means just you as the observer and your frame of reference, and what it is that you the observer is observing and its frame of reference and the difference if any between the two. Momentum is the relative motion between two objects of differing volumes and densities and the distance between them. Momentum is matter’s resistance to change in direction while in motion.  Momentum can also be viewed as ‘Fast Mass’, or since mass x distance is the mechanical equivalent of Heat, then it can also be viewed as ‘Frequent Heat’.

Inertia = Mass x Time / Distance

Inertia is the concept of three unit vectors that form a composite 1D Vector edge of said 2D surface element of Tangible Existence, adjacent to Momentum and adjacent to Potential Reality, i.e. perpendicular to both. Isaac Newton first law of motion, or the first half of a statement about motion of object, namely, “Every body perseveres in its state of rest… unless it is compelled to change that state by forces impressed thereon.” Inertia is the concept of Mass x Inertial Friction, thus it is matter’s resistance to change in direction while at ‘rest’. The concept of being at ‘rest’ is in fact incorrect, since everything in the universe is in some kind of motion relative to something else, and certainly away from the center of the ‘Big Bang’ as it appears that the Universe is still expanding. It would be more correct to say, to paraphrase Einstein, that the concept of Inertia, is the Mass of a volume of Matter, being at ‘relative rest’ in relationship to its nearest large companion comparison mass against which it is ‘resting’.

In space, there appears to be no friction, but there is the “inertia” of matter. All known matter has some inherent “inertia”. One has no real way of knowing exactly how much Inertia an object has until you try to move it. One can use a horizontal spring balance to measure an objects mass as defined by SI. The object’s mass that is being inspected has to be moving and changing directions of travel at a frequent rate. The distance of travel and time of travel are the same in both directions, and cancel each other out by the use of math. The spring has to overcome both the inertia and the momentum to give the proper functional result of an objects mass as measured by SI. Most educated individuals will tell you that mass, is simply just the numerical measure of inertia. For Newton’s more complete statement we have:

Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.

Projectiles continue in their motions, as far as they are not retarded by the resistance of the air, or impelled downwards by the force of gravity. A top, whose parts by their cohesion are continually drawn aside from rectilinear motions, does not cease its rotations, otherwise than it is retarded by the air. The greater bodies of the planets and comets, meeting with less resistance in freer spaces, persevere in their motions both progressive and circular for a much longer time.

That is a pretty big ‘or’. Potential Linearity, (mass x time) / distance, if one can get the feel for word problems and the mathematical relationships that are formed in the process, as a dynamic construct of Hypersurface geometry, one can see how as a radius gets longer, mass and time held constant, the sense of ‘density’ and ‘inertia’ decrease because of volume increase. If the radial distance is decreased, and the mass and time value are held constant, then the volume decrease increases the sense of ‘density’ and ‘inertia’. This behavior is seen evident in the four common forms of matter. Mass multiplied by Inertial Friction is closer to describing the concept of Inertia than just plain mass. Both momentum and inertia involve the concepts of time and distance, in Momentum’s case, its Mass x Velocity, for the case of Inertia, Mass x Inertial Friction. Mass is the constant in both cases. Inertia is matter’s resistance to change in direction while at rest. An object that appears at rest, wants to stay at rest.

Gravity = Mass / Distance x Time

Gravity is the concept of three unit vectors that form a composite 1D Vector edge of a 2D surface element of Tangible Existence. Gravity is the concept of ‘In’, or towards center, parallel to the fourth axis of rotation. Gravity also represents ‘Applied Linear Density’, or how matter gets made denser. Displacement Mass is one form of the Gravity concept. Pushing Linearity is another form of the concept. It is a matter of application of the mass. All points in the universe have the same capacity to act. The affect of a unit vector of mass expresses itself on one axis or another. Gravity creates large massive objects, such as galaxies, stars and planets. Gravity is what pushes against matter, causing it to accelerate toward a larger clump of matter.

Time of Heat = Time / Mass x Distance

Potential Reality is the concept of three unit vectors that form a composite 1D Vector edge of a 2D surface element of Tangible Existence. Time of Heat is the concept of Specific Inertial Friction, or that of which specifically impedes. The Time of Heat is the length of time it takes to generate or use a unit of Heat, while Charge per unit of distance may have more meaning in terms of how the physical relationship between the different primary physical concepts may actually behave. The relationship, for the Time of Heat, is the inverse of the relationship concept of momentum, and can be thought of as inverse momentum, which implies ease in the ability of an object to change direction while in motion, but more at that Heat is what causes time to flow. Where one object’s momentum can be transferred to another, usually increasing the K.E. of the second object, SIF removes K.E. from the second object to be lost as ‘radiated heat’. Inertia is the concept of resistance to change in direction of an object at rest.

The fastest object that we are aware of is the photon, a unit of light. Light, which supposedly has no mass, has a speed limit. Even in the vacuum of space, with seemingly nothing to slow the photon down, the photon cannot exceed its limit. Specific Inertial Resistance is the relationship responsible for this fact.

The length of time that mass can be effective through some distance, is a concept that is much harder to fathom. If the mass term, or the distance term, increases, then the Specific Inertial Resistance decreases.

Linear Potential = Distance / Mass x Time

Linear Potential is the concept of a unit of distance per unit of Potential. Sounds a little like the MPG of gasoline. The distance is dynamically created, is structurally developmental, and is the resultant vector from the mass and time product vector, and this is what creates ‘space’.

Specific Velocity is velocity per unit of mass, or speed per unit of mass, and is the inverse relationship of Inertia. The application of a specific amount of mass will yield a certain velocity after the mass is applied. Mass is responsible for the photon’s achievement to its given velocity. It is mass that supplies the oomph that gives the velocity to the photon which sends it on its journey into Pure Space to be absorbed later by another object with mass. The mass vector in the photon is near perpendicular or is perpendicular to the distance vector, so that its scalar mass value is small or zero when compared to the distance vector, yielding a large velocity vector. This relationship yields the speed limit of light.

The Frequency of Specific Linearity lends its relationship to matter and its unique elemental forms. The variety of the elements that are available is evidence of this relationship.

Specific Displacement = Distance x Time / Mass

Specific Displacement is the concept of ‘Out’, or away from center, parallel to the forth axis of rotation. Specific Displacement can also be considered as Linear Charge, Charge x distance, or the Time Specific of matter. Specific Displacement is opposite of Gravity.

Displacement is any one event of change in distance and time. Displacement occurs from start to finish of the event, the result being a distance that was traversed, the time it took to transverse it, and the dynamic mass vector that was increased, decreased, moved or rotated.

A 3D Field Model cont.

Continuous or Discrete?

A 3D Field Model

Consider several basic questions:

1. Is the nature of space and time continuous or discrete?
2. Is the construction of Space, or Time, analog or digital, or both?

• If analog, do we use the current 2D wave model, or upgrade to 3D?
• If 3D wave analog model is used, do we use Plank's methodology?
• If digital, then is QED methodology needed, and referable and preferable?
• If quantifiable into particles, do they have shapes?

3. If Space and Time are not separate, but tied together in relationships, then what and how many relationships are there, and then are they each continuous or discrete?
4. Does Spacetime interact with photons?

• Via particle (discrete point methodology)
• Via wave (2D planar methodology)
• Via field (3D structural methodology)

5. Is the metric of the natural co-ordinate system, essential to the field paradigm, continuous or discrete?

• Are we in a linearized co-ordinate system, aka x, y, z, …?
• Are we in a rotational co-ordinate system, aka r, Θ, Φ, …?
• Are we in a co-ordinate system that is differential or integral?

6. What are the interactions between Spacetime and matter in its different forms?
7. How do the collections of ions and massive particles, at wide ranges of density, that are populating space, affect a photon pathway, as in a preferential manner of said transmission as through a continuous, or discrete, 3D field?

A 3D field of particles will be like being immersed deep in an ocean, with neutral buoyancy (no sense of gravity), and all the air you can breath. Going up, down, left, right, etc. all feels the same, and takes the same effort. All of the particles meld together, to form the field, and thereby a medium with various properties. So then lets look at a 3D Field that is described via the Continuous methodology implies wave-like functions. Waveforms can be viewed in several different ways. The continuous methodology, as is applied in the time domain, can be viewed through the analysis of mathematical functions, using the amplitude of physical signals or time series of physical dimensional data, with respect to time. In the time domain, the amplitude of a signal or function's value is known for all real numbers, for the case of continuous time, or at various separate instants in the case of discrete time. In addition to the time domain, there is also the frequency domain. A frequency-domain graph will show how much of the signal lies within each given frequency band over a range of frequencies, such as a spectrum. When looking at the spectrum of light from the sun, after passing a slit of it through a prism, we do not see widths of color in equal bands. Some colors have a broader spectrum than others, so measuring the width of each major color, to determine a 'bandwidth', gives a percentage of energy expended at those particular 'bandwidths'.

The Continuous Methodology:

We will view what we see and experience as a continuous process that is Time dependent, or Frequency dependent, which involves a medium as a precondition. Precondition you say, well just think about it. If we examine all that we can look at, we will find that all wave type activities are within some kind of medium. In a vacuum, the only 'waves' we can encounter, are those from 'Active Electromagnetic Waveform Producers', AEWP's for short. Active light sources are AEWPs. Light, as most are aware, is considered to be an Electromagnetic Waveform. So here I have been talking about waves, wave types, waveforms, mediums of conduction, continuous structures and the like, but have yet to really get down to the heart of the methodology, the wave.

Wave

The following is mainly from Wikipedia with some minor edits:
In the scientific sense, waves on the surface of the ocean or lakes, are one ones that are generated by the 'energy' in the Wind. In physics, a wave is a disturbance or oscillation that travels through space and matter, accompanied by a transfer of energy. Wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass transport. They consist, instead, of oscillations or vibrations around almost fixed locations within the medium. Waves are described by an equation which sets out how the disturbance proceeds over time through the medium. The mathematical form of the equation varies depending on the type of wave. There are two main types of waves. Mechanical waves propagate through a medium, wherein the substance of this medium is temporarily deformed. The deformation reverses itself owing to restoring forces that put back that which was moved during the deformation, this is a property of materials, and in terms of a solid it is called elasticity. For example, sound waves propagate via air molecules colliding with their neighbors, in a kinetic process. When air molecules collide, they also bounce away from each other (a restoring force), with each molecule getting 1/2 of the total energy of the collision, think of an 'executive pendulum' that has five stainless steel ball in a row, each a pendulum touching the next. This keeps the molecules from continuing to travel in the direction of the wave. This restoring force is a result of the normal air pressure of the atmosphere, and the innate forces of equilibrium. There is research being done on sonic weapons, providing concussive force without shrapnel. Non-lethal ear shattering pressures, think 'Battleship' the movie, or 'Close Encounters of the 3^rd Kind', where the widows get blown out. What is actually occurring in respect to the air itself, is called compression - decompression. Within an arbitrary volume of air there are differentials of pressure that are created by the incoming sound pressure wave. Different frequencies and amplitudes generated by the original sound source modulate the air molecules, causing differential pressures within the arbitrary volume generating pitch and volume. Within the heights of the atmosphere and within the depths of ocean, there are 'currents' of flow of the medium within the medium, as well as 'layering'. There are waves on the surface of the Sun, made of plasma, that generate electromagnetic waves across the full spectrum of EM radiation. It is very apparent that the description of the wave is closely related to the physical origin for each specific instance of a wave.  The second main type of wave, electromagnetic waves (photons in the discrete methodology), do not seem to require a medium. Instead, they consist of periodic oscillations of electrical and magnetic fields generated by moving charged particles, as the particles travel through a vacuum. These types of waves vary in wavelength, and include radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. Further, the behavior of particles in quantum mechanics is described by waves and that the inherent angular momentum, or spin-dependent properties, are fundamental to the particular quantum, and are responsible for these 'waves'. So, here then, for the purpose of continuous methodology, the 'moving charged particles traveling through a vacuum' will be viewed as 'finite standing wave, moving at a finite speed, in the linear manner of a straight line, ('mass packets') rotating as such to cause the formation of EM wave ('momentum packets'), as it passes through the medium, that shoot off periodically as energy is being shed due to the inherent resistance of the 'mass packet' to the medium.

An EM wave oscillates in a 360 degree circle perpendicular to the path of travel. This 'circle' forms a wavy surface as the 'rotating mass packet' moves through space-time. These wavy surfaces occur as a disturbance within the medium, like bubbles in water, to the propagation (the direction of energy transfer). The EM wave, that is being emitted by a 'mass packet' as it moves through a medium, is formed perpendicular in two directions (electric field vs magnetic field) that are not in the direction of forward propagation. Longitudinal waves are parallel to the direction of propagation. While mechanical waves can be both transverse and longitudinal, it is most likely that EM waves are transverse, meaning they occur in directions perpendicular to the direction of travel of the particle, however as they travel though space-time their forward speed is not as limited as traveling through a plasma-like medium.
Can a EM wave exist without a charged particle moving to make it happen? In this part of the treatise I am attempting to describe a continuous 3D Field, not using particles. If everything is made of the 'same thing', just configured in an infinite fractal pattern of harmonics, using an infinite number of 'waves', with 'particles' as peaks of pressure as determined by the diffraction and interference patterns, with areas of addition, being density increases = matter, and areas of subtraction, being density decreases = vacuum. When the amplitudes of different waves are in the same direction, they add. When in opposite directions, they subtract. Much like vectors. So then, the term wave is often intuitively understood as referring to a transport of momentum via spatial disturbances that are generally not accompanied by a progressive finite linear motion of the medium occupying this space as a whole. A wave results from the energy outburst of an initial impulse, which will form a vibration if the impulse is repeated. The wavefront, with maximum amplitude, is moving away from the source in the form of a disturbance within the surrounding medium. In this 3D Field Model, a standing wave (for example, a wave on a string), is where the energy is moving in both directions equally, within the medium, of the medium, will generate a 'mass packet', and by applying certain harmonic frequencies of standing waves in place of atomic numbers, a new table of 'frequency' elements could be made. As for electromagnetic waves in a vacuum, where the concept of medium does not seem to apply, and where interaction with a target is the key to wave detection and to practical applications, it is in this part of the 3D Field Model, where continuous methodology is being applied to Spacetime itself, and where Spacetime itself is a medium as an active source of vacuum and momentum for the propagation of EM waves.

In space, where the vacuum exists, as an example, typically acoustics as is distinguished from optics, will not work without a 'plasma-like' medium in place, in that sound waves are related to a physically connected kinetic transfer of energy caused by vibration, rather than an electromagnetic wave transfer of momentum via heat transfer to the surrounding environment through radiation. Concepts such as mass, momentum, inertia, or elasticity, become therefore crucial in describing acoustic (as distinct from optic) wave processes. This difference in origin introduces certain wave characteristics particular to the properties of the medium involved such as what kind of medium makes up the 3D Field. Other properties, however, although usually described in terms of origin, may be generalized to all waves.
Thermal radiation is the emission of electromagnetic waves from all matter that has a temperature greater than absolute zero. It represents a conversion of thermal energy into electromagnetic energy. Thermal energy results in kinetic energy in the random movements of atoms and molecules in matter. All matter with a temperature by definition is composed of particles which have kinetic energy, and which interact with each other. These atoms and molecules are composed of charged particles, i.e., protons and electrons, and kinetic interactions among matter particles result in charge-acceleration and dipole-oscillation. This results in the Electro-dynamic generation of coupled electric and magnetic fields, resulting in the emission of photons, radiating energy away from the body through its surface boundary. Electromagnetic radiation does not seem to require the presence of a medium to propagate and travel in the vacuum of space, and will do so infinitely far if unobstructed by other matter.
For example, based on the mechanical origin of acoustic waves, a moving disturbance in space–time can exist if and only if the medium involved is neither infinitely stiff nor infinitely pliable. If all the parts making up a medium were rigidly bound, then they would all vibrate as one, with no delay in the transmission of the vibration and therefore no wave motion, and no apparent flow of time. On the other hand, if all the parts were independent, then there would not be any transmission of the vibration and again, no wave motion, thus here I will postulate that Spacetime will have to be more like a gelatin for EM wave propagation, for while it appears that there is a flow within our 'universe', currents if you will, there is still no evidence for wave-like action within the 'medium' that makes up Spacetime. Although the above statements may seem meaningless in the case of waves that do not require a medium, they reveal a characteristic that is relevant to all waves regardless of origin: within a wave, the phase of a vibration (that is, its position within the vibration cycle) is different for adjacent points in space because the vibration reaches these points at different times.
Interaction
By observing the current natural conditions of space and matter, and applying the concept of continuous methodology, as defined by real dynamic physical boundaries, one can expose a hard physical and logical reality underlying all we observe. When considering scattering and it's broader micro and macro implications, EM waves interact with particles causing increased action, and the reverse is true as well. EM waves propagate through a dielectric media such as glass or air by interacting with the particles of the transparent material. As an EM wave interacts with a particle, the EM wave can be said to be changing or be in the act of being 'polarized', as the EM wave's orientation, spin, and direction of travel get modified in the process, think of river water going around a large boulder. Then depending on Heisenberg, and the random roll of the dice, the EM wave may be fully absorbed, be re-emitted at a lower or higher wavelength, bounce off, or just pass through, which will show up as the 'scatter' of each photon.

The Fresnel equations (or Fresnel conditions), deduced by Augustine-Jean Fresnel, describe the behavior of light when moving between media of differing refractive indexes. The reflection of light that the equations predict is known as Fresnel reflection. When light moves from a medium of a given refractive index n1 into a second medium with refractive index n2, both reflection and refraction of the light may occur. The Fresnel equations describe, as a ratio, what fraction of the light is reflected and what fraction is refracted (i.e., transmitted). They also describe the angle of emission, and the phase shift (color change) of the reflected light. Plasma can also absorb the EM waves. The act of absorption is where amplitude modulation occurs, creating pressure differentials within the plasma volume. Most Fresnel equations presume that the interface is flat, planar, and homogeneous, and that the light is a plane wave. The fraction of the incident power that is reflected from the interface is given by the reflectance R and the fraction that is refracted is given by the transmittance T. The media is usually presumed to be non-magnetic.

The first, c/n, the refractive speed differences between media due to the change of index of refraction 'n', but secondly; to the relative velocity between the media. The reflected and incident waves propagate in the same medium and make the same angle with the normal to the interface, the amplitude reflection coefficient is related to the reflectance R = |r|². The transmittance T is generally not equal to |t|^2, since the light travels with different direction and speed in the two media. The transmittance is related to t by:

The factor of 'cos θt/cos θi' represents the change in area, resulting in magnification, 'm', of the cross-section of the photon stream, needed since T, the ratio of powers, is equal to the ratio of (intensity × area). In terms of the ratio of refractive indexes,

and where by multiple indexes, in a line of sight are included between original EM wave source and receiving target, and where the ratios of magnification 'm' of the incident EM wave at the cross section occurring at surface interfaces follows the standard rule of optics for magnification (depends on the contours of the incident interfaces), the Transmittance can be shown to be:

The rate of energy transfer (per unit volume) from a region of space equals the rate of work done on a charge distribution plus the energy flux leaving that region, this is the Poynting Vector. When used in conjunction with the Law of Refraction, as applied to co-moving media, it may be part of a solution in a proper consideration of the macro effects of EM wave scattering, within the inherent medium of Spacetime, where continuous EM waves may be considered, by focusing on yet more conceptual logic.

In electrodynamics, Poynting's theorem is a statement of conservation of energy for the electromagnetic field, in the form of a partial differential equation, due to the British physicist John Henry Poynting. Poynting's theorem is analogous to the work-energy theorem in classical mechanics, and mathematically similar to the continuity equation, because it relates the energy stored in the electromagnetic field to the work done on a charge distribution (plasma), through energy flux. The Poynting vector represents the directional energy flux density (the rate of energy transfer per unit area, in watts per square meter (W·m^−2)) of an electromagnetic field. It is named after its inventor John Henry Poynting. Oliver Heaviside and Nikolay Umov independently co-invented the Poynting vector. The Poynting vector represents the particular case of an energy flux vector for electromagnetic energy. However, any type of energy has its direction of movement in space, as well as its density, so energy flux vectors can be defined for other types of energy as well, e.g., for mechanical energy. The Umov-Poynting vector discovered by Nikolay Umov in 1874 describes energy flux in liquid and elastic media in a completely generalized view. In a propagating sinusoidal linearly polarized electromagnetic plane wave of a fixed frequency, the Poynting vector always points in the direction of propagation while the EM wave is oscillating in magnitude. The time-averaged magnitude of the Poynting vector is:

In its original form in his original paper, which is often called the Abraham form, where E is the electric field and H the magnetic field. Occasionally an alternative definition in terms of electric field E and the magnetic flux density B is used. It is even possible to combine the displacement field D with the magnetic flux density B to get the Minkowski form of the Poynting vector, or use D and H to construct another. The choice has been controversial, with Pfeifer to summarize the century-long dispute between proponents of the Abraham and Minkowski forms. It is possible to derive alternative versions of Poynting's theorem. Instead of the flux vector E × B as above, it is possible to follow the same style of derivation, but instead choose the Abraham form E × H, the Minkowski form D × B, or perhaps D × H. Each choice represents the response of the propagation medium in its own way. The E × B form above has the property that the response happens only due to electric currents, while the D × H form uses only (fictitious) magnetic monopole currents. The other two forms (Abraham and Minkowski) use complementary combinations of electric and magnetic currents to represent the polarization and magnetization responses of the medium. The above still presumes 2D vector fields, all the while here I am looking at a 3D field, so maybe I am looking to use E×H×D, as each is a field vector, as I am describing a 3D field model.

Geometrical optics, or ray optics, describes light propagation in terms of "rays". The "ray" in geometric optics is an abstraction, or "instrument", which can be used to approximately model how light will propagate. Light rays are defined to propagate in a rectilinear path as they travel in a homogeneous medium. Rays bend (and may split in two) at the interface between two dissimilar media, may curve in a medium where the refractive index changes, and may be absorbed and reflected. Geometrical optics provides rules, which may depend on the color (wavelength) of the ray, for propagating these rays through an optical system. This is a significant simplification of optics that fails to account for optical effects such as diffraction and interference, whereas the Law of Refraction does help to account for the effects of diffraction and interference. It is an excellent approximation, however, when the wavelength is very small compared with the size of structures with which the light interacts. However, since where are considering cosmological sized structures, Geometric optics can't be used to describe the geometrical aspects of imaging, including optical aberrations of the light as view in plasma clouds in space.

The co-moving plasma media in space, may affect the path of transmission of the EM wave. At the core of the solution is a proper consideration of the macro effects of scattering. The Medium is all, forms all, is all that is required to form 'mass packets' and 'momentum packets', are to be considered as particles and photons in the form of waves. By focusing on yet more conceptual logic and conceiving the plasma shock boundary interface as a 'moving finite volume of compressing-decompressing plasma', within a larger bulk flow of plasma, in relative terms, that is 'at rest', the rapidly propagating 'wavefront' is in terms of a massive system, moves via Electric-field screening, where there is the damping of electric fields caused by the presence of mobile charge carriers. It is an important part of the behavior of charge-carrying fluids, and plasmas. In a plasma each pair of particles interact through the Coulomb force, and it is this interaction that complicates the theoretical treatment of the plasma.

For example, a naive quantum mechanical calculation of the ground-state energy density yields infinity, which is unreasonable. The difficulty lies in the fact that even though the Coulomb force diminishes with distance as 1/r², the average number of particles at each increased distance r is proportional to r², assuming the plasma is fairly isotropic. As a result, a charge fluctuation at any one point has non-negligible effects at large distances. In reality, these long-range effects are suppressed by the flow of the plasma in response to electric fields. This flow reduces the effective interaction between particles to a short-range "screened" Coulomb interaction. Thus the colors we see, in the plasma clouds in space, are less affected by the speed of the flow of the plasma, and the speed of any wave-fronts formed by the explosive nature of the sources of plasma, than might be presumed. According to Coulomb's interaction, negative charges repel each other. Consequently, any electron will repel other electrons creating a small region around itself in which there are fewer electrons. This region can be treated as a positively-charged "screening hole". Viewed from a large distance, this screening hole has the effect of an overlaid positive charge which cancels the electric field produced by the electron. Only at short distances, inside the hole region, can the electron's field be detected.

In plasmas and electrolytes the Debye length, named after the Dutch physicist and physical chemist Peter Debye, is the measure of a charge carrier's net electrostatic effect and how far those electrostatic effects persist. A Debye sphere is a volume whose radius is the Debye length, which is the sphere of influence, and outside of which charges are electrically screened, and plays an important role in plasma physics.

The Debye length arises naturally in the thermodynamic description of large systems of mobile charges. In a system of a number of different species of charges, the j^th species carries charge q_j and has concentration n_j(r) at position r. According to the so-called "primitive model", these charges are distributed in a continuous medium that is characterized only by its relative static permittivity, ε_r. This distribution of charges within this medium gives rise to an electric potential Φ(r) that satisfies Poisson's equation. The mobile charges not only establish electric potential, but also move in response to the associated Coulomb force. If we further presume the system to be in thermodynamic equilibrium, at an equilibrium in temperature, then the concentrations of discrete charges, may be considered to be a thermodynamic average and the associated electric potential to be a thermodynamic mean field. With these presumptions, the concentration of the charge species is described by the Boltzmann distribution. Identifying the instantaneous concentrations and potential in the Poisson equation with their mean-field counterparts in Boltzmann's distribution yields the Poisson-Boltzmann equation. Solutions to this nonlinear equation are known for some simple systems. Solutions for more general systems may be obtained in the high-temperature (weak coupling) limit, by the Taylor expansion of the exponential. This approximation yields the linearized Poisson-Boltzmann equation which also is known as the Debye-Hückel equation. The term has the units of an inverse length squared and by dimensional analysis leads to the definition of the characteristic length scale that is commonly referred to as the Debye-Hückel length.

In space plasmas where the electron density is relatively low, the Debye length may reach macroscopic values, such as in the magnetosphere, solar wind, interstellar medium and intergalactic medium. In 'The Particle Kinetics of Plasma', Hannes Alfvén pointed out that, "In a low density plasma, localized space charge regions may build up large potential drops over distances of the order of some tens of the Debye lengths. Such regions have been called electric double layers. An electric double layer is the simplest space charge distribution that gives a potential drop in the layer and a vanishing electric field on each side of the layer. In the laboratory, double layers have been studied for half a century, but their importance in cosmic plasmas has not been generally recognized …" until now.

Perceptions of Reality

The perception of the realities we learned as children, is very different from the perception of the realities that we faced as teenagers, then again as adults, and then again as aging adults. One's views of reality are shaped by religion, mom, dad, teachers, peers, co-workers, neighbors, TV, news, government, media and friends. What is tangible, is the most definitively real experience we get from this world and universe. If it hurts, it is real, that is why corporal punishment brings a sense of reality to those who seem to need to reminded of what reality can be, and to choose their future actions more wisely and with care, unless they wish for more pain, which then is easily applied.

Fiction and fact in today's world, and the lines in between, are getting blurrier and blurrier. That which is real, can grab you by the top of your head, lift you up, give you a shake, put you back down on the ground. If malevolent, a bloody mess. If benevolent, then be healed, and walk with spine aligned. The lines between, the illusion of reality, and the virtual reality of illusion are defined by our perceptions of one's experience.

When what was theory, illusion, unreal, a non-fact, someone else's hypothetical science, small in possibility and non-existent probability, become just the opposite, how does one respond, how would you respond?

Degrees of Freedom, come in two flavors, any good modeling program will demonstrate these to you:  Linear Translational Motion and  Frequency Rotational Motion.  The number of degrees of freedom is determined by how many lines, through the same point, and all be perpendicular to each other.  In our visible world the 'space' in which we live, we get only 3, thus 3D.  In time, we only get one degree of freedom, and only in the same direction, forward, 1T.  Together they form 3D+1T.

The only 'fundamental flat' structure in my proposition is the simple triangle, which just happens to have available to it 4 actual degrees of freedom of motion as I have described above.  It also follows one equation to form all seven of the different geometries.  It is form by Hypervectors.

Hypervectors are multi-'dimensional'.  They are self-forming Hypervectors of 'Extension', 'Change', and 'Push', and it is the differing combinations within each triangle, following the one formula, that creates the dynamic path drawn by the 3rd Point, created at the end of the dynamic Hypervector.  Then one uses the 4 Degrees of Freedom to form contiguous Hypersurfaces into functional shapes by applying the formula.

Every Point is capable of being any, or all, of the seven structures, at any instant, with each point being in equilibrium, this is called a medium.  This is the Quantum Mechanical Zero Point Particle Equilibrium, from which everything is made.  

Six Dimensional Geometrical Objects:

On the scale of the very small, one has QED. On the macro scale there is us, at the mesoscale there is everything that is on the surface of this planet. On the cosmological scale, one has stars, star systems, galaxies, globular clusters of galaxies, and even larger structures. Then there is GR. It takes a lot of the very small to create a small portion of the very large. It takes a star to create slightly bigger chunks of the very small. What is in common: A spherical coordinate system.
The universe is made up of photons, protons, electrons, and neutrinos plus space, time, and gravity. The neutrons are composed of an electron and a proton, and they convert between neutron to an electron and a proton, can then recombine to reform a neutron. Each conversion process is assisted by the interaction of a neutrino, so the neutron is not unique, however it appears that the neutrino acts as the ‘catalyst particle’ within the nucleons of a nucleus. Neutrinos are possibly, wholly responsible for the reaction.

Spherical Geometry, it seems, is the common link. Here, Time is considered to be a dimension and a vector. We live in a universe that has more than just four dimensions. Space has three dimensions that give us our volumetric portions of length, width, and depth. Vectors of unique unit type, and their inverse, opposites go to form each linear dimension, yet everything that we have been taught is in terms of linearity, instead of terms of spherical rotation.

A Dynamic Hypersurface, is based on spherical coordinates, and is viewed as a linearly mobile, rotating, point sized structural object composed of one or more Relationship unit-vectors, in a 4 degrees of freedom of rotation (4DFR) Multi-vectored Space-Time-Mass environment. Each Hypersurface type represents a configuration of a 4D Point Structure, and as viewed in the diagram, from our environmental view they all tend to look the same:

In string theory, the extra dimensions are small and wrapped up into tiny little strings or M-Branes and P-Branes. Here, they’re just the same as the other dimensions. The extra dimension of extension is just ninety degrees away from everything we know and see. What we gain with just one extra degree of freedom in rotation is one more dimension of extension. Having one more degree of freedom, allows us to imagine a view of our 4D environment collapsed to a curved surface on a 6D Hyper-object from more than just the parallel or end view. Four degrees of freedom apply to Dynamic Hypervectors of Extension, Time-Flow and Dynamic Mass.

This is our 3D+t view of any of these seven 6D structures, no matter where we looked, or what direction we were looking, and should one come across one of these, try to remember it, however, typically one won’t even see the above views as the individual Dynamic Hypersurfaces are too small to see, unless somehow they are combined to form a macro-sized structure viewable to the naked eye. Each structure has the same two D-R unit-vectors; each is a 2DF Hypervector rotating in one plane perpendicular to the other. Our view of any of the structures, rotated 90 degrees left, right, up, or down typically would look the same. Because of the circular nature of the structures, trying to visualize the structures, in linear 2D or 3D, or 4D, or 5D just by math has not been the best approach mainly because of the lack of any real experience to base the math. It is like giving Mr. 3D a choice of another axis’ to rotate about but all he can see is an infinite number of directions to turn (a full circle of them) to but can’t fathom how to physically turn about any one of them. However, maybe he can rotate himself and a section of his ‘Plane of Reference’ through the higher dimensional gelatin to gain a better perspective of his gelatin.

These are the 5D and 6D side views of the 6D rotational geometrical structures that form everything from the smallest of structures to the largest of structures. The curved ‘fabric’ spacetime Einstein had imagined exists in six dimensions as curved spacetime, with each dynamic surface element (dx, dy) being ‘flat’, just like any 2D surface in our 3D1T world, as our current correct observation tells us that spacetime is ‘flat’ in 4D. Both cases are true. The Dynamic Hypersurface (see cross-sections above) is exactly a ‘surface’…over a six dimensional object that supports a flattened 3D1T (4D) ‘volumetric’ structure within the Hypersurface. This condition is exactly similar to that of Mr. 3D in his 2D1T world. Yet, these same structures are in evidence in our world, we just can’t see them from a side view like they are shown above because we are linear 3D1T and they are 6D. Surface of a sphere is calculated from 4πr^2, and by integration to get the volume of the sphere, 4/3πr^3, by further integration we can achieve a formula of calculation for a Hypersurface as 1/3πr^4.