**Continuous or Discrete?**

**A 3D Field Model**

Consider
several basic questions:

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'.- 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)

- 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?

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

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

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 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:

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
*. 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:*__energy flux__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.

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