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.  

3D Field Model

Continuous or Discrete? 

A 3D Field Model

Consider several basic questions:

1. Is the nature of space, and time, continuous or discrete?
   

• 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?
    
• 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?
  
• Does Spacetime interact with photons?
  
  • Via particle (discrete point methodology)
    
  • Via wave (2D planar methodology)
    
  • Via field (3D structural methodology)
    

2. 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?
  

3. What are the interactions between Spacetime and matter in its different forms?
   

4. 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?
   

To really start afresh, in this Physics treatise, meta-anything will not be considered. Discrete methodology implies particles of all kinds, however we will limit ourselves for brevity, to the standard set of reasonably stable known ones of photon, electron, proton, neutron, and neutrino. They have their mirrored forms, but don't want to confuse them here with their so-call anti-forms, as there is disagreement about how the anti- is to be considered and represented. Clarity will be made further in this treatise. They can further be combined into various kinds and forms of matter.

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.  A 3D Field that is described via the Continous methodology implies wave-like functions. Waveforms can be viewed in several different ways. The areas of bright light, that are visible on the dorsal surface of the 'mermaids', that are playing in the '3D field', in the video, are cross-sections of 3D waves of light that were intercepted by a more opaque interface.

The continuous methodology, as is applied in the time domain, can be viewed through the analysis of mathematical functions, physical signals or time series of physical dimensional data, with respect to time. In the time domain, the 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. An oscilloscope is a tool commonly used to visualize real-world signals in the time domain. In the time-domain graph below, it is being shown how a signal changes with time, whereas a frequency-domain graph shows how much of the signal lies within each given frequency band over a range of frequencies, and a spectrum analyzer is a better tool for showing the harmonics.

As is shown, waveforms can start to be seen in 3D, via Fourier analysis which then starts to show how a 3D continuous field can be imagined.

Axiom

An axiom, or postulate, is a premise or starting point of reasoning. As classically conceived, an axiom is a premise so evident as to be accepted as true without the usual controversy. The word comes from the Greek ἀξίωμα (āxīoma) 'that which is thought worthy or fit' or 'that which commends itself as evident.'  As used in modern logic, an axiom is simply a premise or starting point for reasoning. Axioms define and delimit the realm of analysis; the relative truth of an axiom is usually taken for granted within the particular domain of analysis, and serves as a starting point for deducing and inferring other relative truths. No explicit view regarding the absolute truth of axioms is ever taken in the context of modern mathematics, as such a thing is considered to be an irrelevant and impossible contradiction in terms.

In mathematics, the term axiom is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms". Logical axioms are usually statements that are taken to be true within the system of logic they define (e.g., (A and B) implies A), while non-logical axioms (e.g., a + b = b + a) are actually defining properties for the domain of a specific mathematical theory (such as arithmetic). When used in the latter sense, "axiom," "postulate", and "presumption" may be used interchangeably. In general, a non-logical axiom is not a self-evident truth, but rather a formal logical expression used in deduction to build a mathematical theory. As modern mathematics admits multiple, equally "true" systems of logic, precisely the same thing must be said for logical axioms - they both define and are specific to the particular system of logic that is being invoked. To axiomatize a system of knowledge is to show that its claims can be derived from a small, well-understood set of sentences (the axioms). There are typically multiple ways to axiomatize a given mathematical domain.

In both senses, an axiom is any mathematical statement that serves as a starting point from which other statements are logically derived. Within the system they define, axioms (unless redundant) cannot be derived by principles of deduction, nor are they demonstrable by mathematical proofs, simply because they are starting points; there is nothing else from which they logically follow otherwise they would be classified as theorems. However, an axiom in one system may be a theorem in another, with the reverse also being true.

Axiomatic Schema

It is understood that the use of axioms in an axiomatic based set theory, as are used in the branches of logic, mathematics, and computer science will be employed. The various axiom schema of specification, axiom schema of separation, subset axiom scheme and axiom schema of restricted comprehension are schema of axioms based in Zermelo–Fraenkel set theory, which essentially says that any definable subclass of a set is a set. The evolution of the implied mathematics will proceed from properly established mathematical axioms. The evolution of the physics proposed, proceeds from here, towards the establishment of more fundamental physical axioms.

The Discrete Methodology:

We will view what we see and experience as a set of particles combined together as the optimum set of discrete 'points' as defined above. We will include in the context of particles the ones mentioned above and again here for reference: photon, electron, proton, neutron, and neutrino, which are classified and referred to in 'the standard model' as such:

Photon

The Photon is an elementary particle, is the quantum of light and all other forms of electromagnetic radiation, and the force carrier for the electromagnetic force, even when static via virtual photons. The effects of this force are easily observable at both the microscopic and macroscopic level, because the photon has zero rest mass; this allows long distance interactions. Like all elementary particles, photons are currently best explained by quantum mechanics and exhibit wave–particle duality, exhibiting properties of both waves and particles (however, for this particular methodology we will stick to the particle definition). For example, a single photon may be refracted by a lens or exhibit wave interference with itself, but also act as a particle giving a definite result when its position is measured (and also as a mechanism for the transfer of momentum).

Electron

The electron (symbol: e−) is a subatomic particle with a negative elementary electric charge, and belongs to the lepton particle family, and is generally thought to be an elementary particle because it has no known components or substructure and have a mass that is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum (spin) of a half-integer value in units of ħ, which means that it is a fermion. Being a fermion, it has been shown that no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle. The electron also has properties of both particle and wave, and so can collide with other particles and can be diffracted like light. Experiments with electrons have demonstrated this duality.

Hadron

Hadrons are categorized into two families: baryons (such as protons and neutrons, made of three quarks) and mesons (such as pions, made of one quark and one antiquark). Other types of hadron may exist. Of the hadrons, protons and neutrons bound to atomic nuclei are stable, whereas others are unstable under ordinary conditions; free neutrons decay in 15 minutes. Experimentally, hadron physics is studied by colliding protons or nuclei of heavy elements such as lead, and detecting the debris in the produced particle showers.

Neutrino

The Neutrino (/njuːˈtriːnoʊ/) is an electrically neutral, weakly interacting elementary subatomic particle with half-integer spin. The neutrino (meaning "small neutral one" in Italian) is denoted by the Greek letter ν (nu). All evidence suggests that neutrinos have mass but that their mass is tiny even by the standards of subatomic particles. Their mass has never been measured accurately. Neutrinos do not carry electric charge, which means that they are not affected by the electromagnetic forces that act on charged particles such as electrons and protons. A typical neutrino passes through normal matter unimpeded.

Measurements of the interaction between energetic photons and hadrons show that the interaction is much more intense than expected by the interaction of merely photons with the hadron's electric charge. Furthermore, the interaction of energetic photons with protons is similar to the interaction of photons with neutrons in spite of the fact that the electric charge structures of protons and neutrons are substantially different. This is because the magnetic aspects of the neutron and proton are greater than the electron, and as will be shown later as being part the polarization of a photon.

If experimentally probed at very short distances, the intrinsic structure of the photon is recognized as a flux of quark and gluon components, quasi-free according to asymptotic freedom in QCD and described by the photon hyper-structure function. In the Standard Model of particle physics, photons are described as a necessary consequence of physical laws having a certain symmetry at every point in space-time. The intrinsic properties of photons, such as charge, mass and spin, are determined by the geometric shape properties of this gauge-type symmetry.

Plasma

Plasma (from Greek πλάσμα, "anything formed") is one of the four fundamental states of matter (the others being solid, liquid, and gas). It comprises the major component of the Sun. Heating a gas may ionize its molecules or atoms (reducing or increasing the number of electrons in them), thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions. Ionization can be induced by other means, such as strong electromagnetic field applied with a laser or microwave generator, and is accompanied by the dissociation of molecular bonds, if present. Plasma can also be created by the application of an electric field on a gas such as air. The presence of a non-negligible number of charge carriers makes the plasma electrically conductive so that it responds strongly to electromagnetic fields. Plasma, therefore, has properties quite unlike those of solids, liquids, or gases and is considered a distinct state of matter. Like gas, plasma does not have a definite shape or a definite volume unless enclosed in a container; unlike gas, under the influence of a magnetic field, it may form structures such as filaments, beams and double layers. Some common plasmas are found in stars. In the universe, plasma is the most common state of matter. Most of the matter in the universe, is in the form of the rarefied intergalactic plasma (particularly intracluster medium) and in stars.  Much of the understanding of plasmas has come from the pursuit of controlled nuclear fusion and fusion power, for which plasma physics provides the scientific basis. It is further postulated here, for the discrete methodology, that Spacetime itself, is generally to be thought of as a 'gelatin' of quantum elementary plasma-like particles, with similar qualities. Models like liquid or foam don't leave a history behind them.

If discrete particles can group together and act continuously as a dielectric, gas, or plasma, for the purposes of photon transmission, using Fresnel's system of index of refraction as a function of the indexes, f(n), what are the effects on photon transmissions?

Plasma is found so effective in wave particle interaction it currently leads stealth technology, by using a boundary plasma layer to absorb radar waves. Changes in pressure affect amplitude of the incoming wave and not the frequency. Spectroscopy shows very low flux plasma can still change photon speed to it's own local c/n. Thus the photon speed is controlled by 'n' as within a dielectric medium, and thus bends the incoming photon at the interface of boundary plasma layers between arbitrary pressure regions of the plasma, within an arbitrary unit volume of space.

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 photons. 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.

However within a plasma cloud there are always stray magnetic fields, induced by random motion causing differentials between plasma particles, causing a random bunch of ionized particles to behave together, to form a 'plasma field' via magnetic interaction. The plasma does consist of both positively-charged and negatively-charged particles whose average kinetic energy is greater, or distance between particles is greater than the 'Debye' length, or greater than the level of kinetic energy of combining into non-ionized particle systems, or formation of neutral particles such as loose unbound neutrons. Loose bound neutrons are unstable and will change into three different particles, those being the Proton, the Electron, and the Neutrino. Thus a cloud of plasma tends to stay plasma-like, unless acted upon by other conditions.

Plasma is neither flat, nor planar, nor homogeneous. Thus calculations for the Reflection, and Refraction of photons depend on polarization of the incident photon, while the Absorption depends on inline changes in local kinetic energy between source particles in the presence of incident photons.

If the incident photon is polarized with its electric field parallel to the interface differential, and perpendicular to said plasma, containing the incident, reflected, and refracted photons, such a photon is described as p-polarized. The incident photon that is polarized with its electric field perpendicular to said plane, is said to be s-polarized, from the German 'senkrecht' (perpendicular). A-polarization is a photon's forward momentum, being affected by the passage through stray magnetic field interface lines which causes harmonics within the amplitudes of the incident photons. As a consequence of the conservation of energy, the transmission coefficients are given by:

P-Polarized

S-Polarized

A-Polarized

 These relationships hold only for power coefficients, not for amplitude coefficients. If the incident light is not polarized (containing an equal mix of a-, s- and p-polarization), the reflection coefficient is:

Photons can bounce back and forth a number of times between the interface differentials within an arbitrary volume of plasma. The combined reflection coefficient for this case is 3R/(1 + R). The discussion given here presumes that the permeability of plasma, is nearly equal to the vacuum permeability of space. This is approximately true for most dielectric materials, but not for all types of material. The completely general Fresnel equations are more complicated.

Amplitude equations for coefficients corresponding to ratios of the electric field complex-valued amplitudes of the s-polar and p-polar 'ballistic Hypervectors', (not necessarily real-valued magnitudes) are styled after "Fresnel equations", while the equations for the a-polar waves take on 3D Sonar like topology, using differentiated velocities integrated into a geometric shape that provides structuralism for the boundaries that form the interface differentials. These equations take several different forms, depending on the choice of formalism and sign convention used. The amplitude coefficients are usually represented by lower case r, t, and a.

For the following, it is presumed that any incident photon is normal to the Differential Interface, DI, and that any change in angle in the original path is the result of refraction, given by 'n' for single dielectric, and is also shown below as the ratio of n2/n1, and that any change in velocity within the path of the photon, is the effect of variable density regions and near relativistic differential Kinetic Energy levels within the structurally defined arbitrary volume of plasma, with all else in equilibrium outside said volume, gives a dynamic process to the redshift, between the photon source and photon receiver.

The coefficient r is the ratio of the reflected photon's complex electric field amplitude to that of the normal of the DI. The coefficient t is the ratio of the transmitted photon's electric field amplitude to that of the normal of the DI. The photon is split into s and p polarizations, whereby s-polarization is perpendicular, and p-polarization is parallel. The coefficient a is the ratio of attenuation via absorption by the plasma, resulting in heating, or or cooling, via a change in kinetic activity of the plasma through interactions with the incident photons, within the region of plasma, to that of the incident photon's original transmission and propagation vector, resulting in no attenuation of the momentum of the photon, just like a photon's passage through a void in the plasma, or the vacuum permeability of space, where we have postulated, using the discrete methodology, that Spacetime itself, is generally to be thought of as a 'gelatin' of quantum elementary plasma-like particles, with similar qualities, where the photon's velocity appears to be the fastest, 'c', and is considered to be 100% transparent to the passage of photons. Yet a photon's passage is not instantaneous, so there must be some kind of resistance, which is a 'time / distance' type relationship, in our '3D*1T' environment.

For s-polarization, a positive r or t means that the electric fields of the incoming and reflected or transmitted photon are parallel, while negative means perpendicular. The magnetic field of the photon interacts strongly with all particles, while the electric field of the photon interacts only strongly with the electron. For p-polarization, a positive r or t means that the magnetic fields of the photons are parallel, while negative means perpendicular. It is also presumed that the magnetic permeability, µ, of a plasma layer region is equal to the permeability of free space constant µ₀ The physical constant μ₀, commonly called the vacuum permeability, or permeability of free space, or magnetic constant is an ideal, (baseline) physical constant, which is the value of magnetic permeability in a classical vacuum. Vacuum permeability is derived from production of a magnetic field by an electric current or by a moving electric charge and in all other formulas for magnetic-field production in a vacuum. In the reference medium of classical vacuum, µ0 has an exact defined value: µ0 = 4π×10^−7 V·s/(A·m) ≈ 1.2566370614...×10^−6 H⋅m^−1 or N·A^−2 or T·m/A or Wb/(A·m), in the SI system of units. As a constant, it can also be defined as a fundamental invariant quantity, and is also one of three components that defines free space through Maxwell's equations. In classical physics, 'free space' is a concept of electromagnetic theory, corresponding to a theoretically perfect vacuum, and sometimes referred to as the vacuum of free space, or as classical vacuum, and is appropriately viewed as a reference medium.

Let's take a quick look at the multidimensional units of the vacuum permeability: V·s/(A·m), and see how it is that it can be called a 'medium'. If we look at the units the vacuum permeability, Volt second / Ampere meter, and look at 'time/distance' as the inverse of velocity, which is 'Inertial Resistance' which for the vacuum permeability gives (Volt / Ampere) * IR. The units for the Volt are: (mass x area) / (Ampere x second^3); the ampere, whose SI unit symbol is: A, and SI dimension symbol is: I, often shortened to amp, is the SI unit of electric current and is one of the seven SI base units. It is named after André-Marie Ampère (1775–1836), French mathematician and physicist, considered the father of electrodynamics. In practical terms, the ampere is a measure of the amount of electric charge passing a point in an electric circuit per unit time, with 6.241×10^18 electrons (or one coulomb) per second, constituting one ampere.  The Ohm, has units of kg·m²·s^-3·A^-2 but fortunately, it doesn't come into play in this calculation.  So now we have ((mass x area) / ( 6.241×10^18 electrons x second^4)) * (time/distance).  Using the appropriate math, we can rewrite the units as (mass x distance) / ( 6.241×10^18 electrons x second^3), which we can then rewrite as (one unit of Thrust / second) /(6.241×10^18 electrons).  So, now if we are considering empty space-time, the vacuum of free space, where we have postulated, using the discrete methodology, that Spacetime itself, is generally to be thought of as a 'gelatin' of quantum elementary plasma-like particles, such as the electron, positron, proton, neutron, and the neutrino, then here, we now have that basis for a medium. Then considering Gravity as being sourced from empty space-time, just like the vacuum, and whether the force it applies is a 'push' or a 'pull', (and here it is stipulated that all 'force' as applied to any surface, is by the action of 'push', as in to apply pressure which is opposite of vacuum) where the '4π * Thrust/second per 6.241×10^18 plasma particles', can be seen here as a constant spherical 'Thrust Frequency' type force just from the empty space-time, no 'dark matter' or 'dark energy' required. The vacuum would be 'push-in-towards' each space-time plasma particle, while gravity would be 'push-out-from' each space-time plasma particle.  We just need to know the density of plasma particles in free space.

The physical constant ε₀, commonly called the vacuum permittivity, or permittivity of free space, or electric constant, is an ideal, (baseline) physical constant, which is the value of the absolute (not relative) dielectric permittivity of the classical vacuum. Its value is:
ε₀ ≈ 8.854187817620... × 10−12 F·m−1 (or A^2·s^4·kg^−1·m^−3 in SI base units. 
In the vacuum of classical electromagnetism, the polarization is zero, so the relative permittivity ε_r = 1, and ε = ε₀. What we want to work with here, is the SI units: A^2·s^4·kg^−1·m^−3, so we get (( 6.241×10^18 electrons / second)^2 x second^4 )/(mass x volume) = 38.95×10^36 electrons x (second^2/(mass x volume)), not quite as clean as the permeability, but it gives a 'sense' of density.  And we can now also ask, "Is 38.95×10^36 electrons = 1Kg?

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, is needed since T, the ratio of powers, is equal to the ratio of (intensity × area).  


In terms of the ratio of refractive indices, and of the magnification 'm' of the incident photon at cross section occurring at surface interface, the Transmittance can be shown to be:

Thereby we can infer as an establishing axiom: The velocity of a photon is controlled by 'n' within a 'single' dielectric medium, and controlled by the ratio of 'n2/n1' within a variable dielectric medium. It is then possible to say, if space itself is discrete, with each point, within any arbitrary volume of space-time, in a state of change, going from a virtual photon, to a virtual electron-positron pair, and possibly other structural functions, that it can also act as a dielectric medium.  

When light makes multiple reflections, instead of refracting, between two or more surfaces, the multiple beams of light generally interfere with one another, resulting in net transmission and reflection amplitudes that depend on the light's wavelength. Typically in plasma conditions, the energy of the individual photons of light may see the way of entropy, and diminish in energy. The interference, however, is seen only when the surfaces are at distances comparable to or smaller than the light's coherence length, which for ordinary white light is few micrometers, using coherent light it can be much larger. An example of interference between reflections is the iridescent colors seen in a soap bubble or in thin oil films on water. A quantitative analysis of these effects is based on the Fresnel equations, but with additional calculations to account for interference.  The scattering of the photons, via passage through plasma clouds, can be readily compared to the iridescent colors seen in a soap bubble as mentioned above and is seen below.

2. Interaction
By observing the current natural conditions of space and matter, and applying the concept of discrete, or 'distinct localities', as defined by real and 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, via photonic interactions that modulate particle actions, with the reverse being true as well. Photons propagate through dielectric media such as glass or air by interacting with the particles.  As a photon interacts with a particle, the photon can be said to be changing or be in the act of being 'polarized', as the photon's orientation, spin, and direction of travel get modified in the process, think billiards. Then depending on Heisenberg, and the random roll of the dice, the photon 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 standard QED analogy is that of electrons absorbing photons and re-emitting them at 'c' with respect to the electron. In reality, the electron will accept the momentum supplied by the photon, and the velocity of the electron increases. When the electron feels frame resistance from space due to its new increase of velocity, it emits a new photon, that is frequency-dependent upon the spin rate of the electron at emission time.

If the electron is moving near light speed, this means that whatever relative speed an photon arrives at they'll be re-emitted, or scattered, at the new speed-dependent ratio of the different indexes of refraction, as dictated by the pressure differential conditions within the local cloud of plasma. The newly-emitted photons, then will travel at 'c' again when moving through the voids in the plasma. This process changes photon speed and direction, as required, equivalent to photons entering or leaving moving water (n = 1.33) which, as Fizeau first showed, is with respect to the waters relative motion. Even after meeting the fine structure surface boundary of ions, the photon reaches the lens of an instrument, then our eye. As the photon passes through each medium, its speed changes at each interface. As there is more than one interface with a plasma like medium, there is more than one refractive index, thus a system of functional refractive index ratios is needed to better describe plasma interaction within this 3D Field Model of Spacetime.

Missing - My Hyphen-Underline Key

The Above is my rendered 3D model of my missing Hyphen-Underline key from my current keyboard that I use to do my work.  The image above shows the key sitting upon a solid oak plywood desk, just like the desktop that the key had bounced twice upon, and then went quiet.   In the image you can see me looking back, waiting for the return of the lost key.  Seeing how as it seems yet once again that my insanity has return, I intend to take a wait and see approach.  After all, the longer the time it takes to come back, the closer it will be in distance when it returns.

It officially left @ 11:30 PM PDT Thursday on  September 26, 2013, and it is currently 7:41 PM PDT October 4, 2013, so a week has gone by, and no key yet.  Presumably, based upon previous observations, it will have the numbers '365', in the measurement.  The 3rd wormhole that took a small plastic nasal spray bottle, just guessing here, took 36.5 months in time to move through a distance of  3.65 in through space.  So we will see what transpires this decade.

Oh if anyone finds my black plastic one one their desk, please make a note of the date, time, and place of it discovery location, and then post it here someplace.  Thanks for you time and effort in this insanity of mine.

The Insanity has Returned ...

It's official, I have gone stark raving insane!  The cosmological implications are ,,,,  !??
[1:37:51 AM] donald.p.hutchins: @11:30pm PDT, California: (please note that any '-' used in this post comes from using the minus key on the numeric key pad)

I had been at my computer typing up physics piece on 'A 3D Field Model, Continuous or Discrete?' that was inspired by another paper, 'The Discrete Field Model ...' by Peter A. Jackson of the UK, et all.  I had just finished my work for the store at 10:PM PDT, I had eaten earlier at 7:PM and had returned to the premises, wherein I got myself squared away, and set to my daily routine tasks of answering E-mail.  I had gotten hungry again and ordered pizza at about 10:30 PM.  It arrived just after 11:PM.  I had sat down to eat at the desk, the one wherein my computer sits.  I had moved things mostly out of the way, and been sitting and eating, when a fly comes and finds me and starts bugging me.  So I close my food container, move the things out of the way that I don't want to hit with the fly swatter.  It's 11:25 PM and I have cleared the desk, turned off the lights so the fly would be attracted to the lit monitor.  Works like a charm.  I swat the fly as it sits on the monitor.  The swatter came down so hard onto my keyboard it popped off a key, the underscore hyphen key.  Well I heard the black square of plastic bounce a couple of times off the desk top and some other cardboard item and then go silent, as I thought it had to have landed on the desk top somewhere.  OK, so no real problem.  Just clean the wooden desk top off, inspect, clean and recheck each and every item, very carefully with my reading glasses, so as to not miss finding the Key, I said to myself out loud, thinking the worst.  Boy, I had not seen so much dust collected in one location since the last fall cleaning.   Such is the desk, that my computer is sitting upon, that is to say, upon the solid oak plywood desk top that is flush installed to the wall so that nothing can fall behind it ... obsessive person that I have become, I know I must have cleaned and gone through everything, recleaning with paper towels and spray cleaner, on this near 30 square foot desk, twice, but to no avail, for I did NOT find the innocent little square bit of plastic with a couple of little lines on it.  And here I am typing on the very same keyboard, without the key, 2+ hours later, and still no black plastic key to be found.  I am now sure I have truly lost it ... again ...again ...again ...again ...only this time, I believe that I, yours truly, some how may have caused it to happen ... again ...again ...again ... yes it seems that I can be a Wormhole Activator via Cranial Kinetic Output, that's right, you heard it here first, from the horse's mouth, I can be, or rather I am, a WACKO! 

Further Explorations

In the dictionary there is an entry about Vector Space, 3D.  Most mathematicians understand the concept of a vector.  In my case I am talking about a Hypervector Space 4D.  So, if then, I'm really talking about a hyper-vector space, depending on parameters, the parameters being in a manifold, as described by my One Equation, and the Kinetic Information Structure Simulation design system that provides the dynamic drive force behind the One Equation which describes and forms such manifolds, which is then expressed as the expansion rate of  "all that we can see" = the universe, which appears to be accelerating, because we exist within a 'surface', formed over a 'volume' object, the radius of said object, that for all intents and purposes, hypothetically, is expanding at a constant velocity, while said surface increases exponentially, i.e. radius vs. area-dependent-upon-radius, is one way to correctly state cause and affect / effect, for said "Problem of Accelerating Expansion Rate of the Universe"?

I was told on one occasion, "My fellow physicists throw mass around in such a way as to imply it is already well understood and even suppose it a property of vacuum without any explanation of what it is or its cause or how it can warp space and time and explain inertia only during acceleration and ....."

So my answer could only be, In my geometry model using 4DFR, Space-Time (Hyperspace) is shaped as the outside of a hyper-Torus, and is a curved Hypersurface, so space and time ARE warped but only in terms of 4DFR.  OK you say, so how does that work for vacuum and gravity?  Well, even though local space is a 'flat Euclidean space', as A.E. implied, it is curved, warped, in 4D, and any Hypersurface element(3D) on the hyper-Torus shaped Hyperspace object(4D), will appear, as observed, 'flat'.  The curve, and its direction, in 4D, is what is important here, in speaking about expansion, vacuum and gravity.

Since, then if we exist within the Dynamic Hypersurface, the convex and concave shapes of either side of the Dynamic Hypersurface, provide an action (acts as a 'mass' vector) that is 'normal to' the Hypersurface in the direction of the dimension that is perpendicular to the three dimensions in which we live, that appear as 'Gravity' and as 'Vacuum', and the same action parallel to the Hypersurface, as expansion or extension of the Hypersurface. Here, again we have a 3-is-1 situation of the action of Change.  The 3 actions: the Extension/Expansion of Spacetime, the action of Gravity is against any 2D surface on a 3D object, as in if it has surface it has 'mass', this action is OUT from all '3D+1T' Points, 'pushes' on all 2D surface, on a 3D object, acting to push it together, so surface wants to contract, (all 2D surface is 'outside'), and the third action that that of vacuum, which works in the opposite direction to that of gravity, this action is IN from all '3D+1T' Points, 'pulls' on all 2D surface, on a 3D object, acting to pull it apart, so surface wants to expand.

A Hypervector has, in this universe, 3 parts to one Hypervector of 'Existing-Reality'.  Yes, another 3-is-1 concept.  We use the concept of 'Distance' to define the concept of dimension, so we have '3D' or 'DxDxD' for Space.  So then Hyperspace is DxDxDxD, or 4D.  Yet we also experience Time, and it works equally, like distance, in all the same directions that 'distance' goes, in 3D, so maybe we really have 3T, and it just feels 'linear' and acts 'linear', just the same way Space acts 'linear' or feels 'flat'.  Then again, Time is really just a part of the concept we call Change, as is Distance.  We can measure both distance and time, in all directions.  So, if we use the concept of 'Extension' which includes the concepts of 'Distance' and 'Time', then we really have 'DT' in all directions, which then is 3E, where extension = distance * time, as the 'new' 6D.

We have Distance and Time, that is the first 2 parts.  Next is the "what causes action" part of the Hypervector.  We know that neither distance, area, nor volume can cause action.  Usually, an action such as motion, happens over a distance, across an area, or through a volume.  We know that time can not be at cause of action either.  We tend to experience time indirectly as we do things on a 'per second' basis.  We age, thus we accumulate experiences, our birthdays and the number of days we have been alive grow in number when counted.  This a direct use of time that is linear.  If one can run, someone may reach a speed of one pace per second, that's two steps (a left and a right) per pace which is 120 steps per minute is linear but an indirect use of time.

What is left, is the "what causes action", the third part of, what is now, the 'Dynamic Hypervector'?  I will call it 'dynamic mass'.  It is the 'unit' vector that arrears to be specifically in the axis of the 'linear' 4th dimension, the dimension perpendicular to all of the ones in which we live. So, if what we call vacuum and what we call gravity and what we call mass are all related this 4th dimension, and each of these three 'action type concepts', exist, yet we don't really know the 'source' of these dynamic expressions of our universe. Most

Then how might 'distance' and 'time' express themselves in the three dimensions?

"How is it that an electron has mass and neutrinos appear not to have mass and travel at the speed of light? Both are classed and half-spin leptons. To argue a lower speed for neutrinos in vacuum means some humanly-accessible inertial reference frame where they are at rest for us to examine their properties to the fullest extent possible." I say, "How does vacuum have mass? "


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 one's 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?