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?

What Is "Space", And What I Mean When I Use the Term 'Space'

"Space", What is it?


We are born, we live, we die.  That is our human condition.  As a human, we are typically a, self-mobilized, self-organized pile, of a mixture of various kinds of matter.  Growing in the womb, we were in a liquid 'space', where we floated, effortlessly, and without a care, in a state of perfect peace.  The neutral buoyancy that we experienced for that period of gestation, gave us our first experience of life.  It creates within each of us, the gestation period of neutral buoyancy, an innate genetically integrated feeling of sensual containment, with freedom, that of total love and total peace combined.  It also gives us our first physical concept of boundaries, for as we grew, we found that the 'space' we had come into was getting cramped, and we were literally bouncing off the walls.  Towards the end of the gestation, were are more aware of being confined, and less aware of any feeling of floating, with a building need for that feeling of comfort of floating free, in neutral buoyancy, that we had initially found coming into this 'space'.  Then we are born.  This can happen one of two ways.  The natural method, we come out the way we came in, or the oven is ripped open, and we are pulled out, the oven is fixed afterwards, and the procedure is named after some guy who survived the same procedure first (Cesarean). 


So the concept of 'space' is out first realization, we just didn't know it as an intellectual concept that can be measured, and be used in many ways, including that as topic of understanding, knowledge, conversation, and what we Blog into.


There are many concepts out there, and that their immediateness is based upon the basic concept of 'space', is more a subjective, than objective, trait that we are more prone to employ as a deterministic format of how we want to perceive our environment, from our organic  perspective, that of a 'natural' viewpoint. 


The Physical Nature of things, objects that are real and are repeatably measurable, i.e., objects of mobile solid 'space', that have a measurable distance, and a measurable existence of time, or the Physics of the Natural, is the study of Nature, the natural viewpoint, through the discipline of the Philosophy of Physical Science, aka, Physics.   

From Wikipedia, the free encyclopedia:   "Space":

This article is about the general framework of distance and direction. 

For the space beyond Earth's atmosphere, see Outer space. For all other uses, see Space (disambiguation). 

Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction.^[1] Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. In mathematics one examines "spaces" with different numbers of dimensions and with different underlying structures. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework.

 From the above definition in Wikipedia, 'Space', is a rather complex subject to tackle in just one or two Kilobytes of text.

Once, we as humans, grow and live long enough to learn, then survive to tell about it, and then grow again, a cyclical process, we often get a better, more refined, and a more well defined, concept of 'Space', that of  'my space!' and then have to learn about the 'other's space!' as in other humans, and shared common space, and so on.  We are all made very aware of how much useless space we take up, including that space between the ears.  These all use the basic concept of  'Space' where "Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction."  It is our common inborn 'natural' viewpoint of the cold environment in which we live.  All of these kinds of 'space' concepts can be contained in a category called "Subjective Space".

So, What is it I mean when I use the 'Space'?
If you got this far e-mail me and I'll do the next segment sooner than later.
 

The Theories and Math's that have led to BIGTOE

An overt statement was made to say: "The boson is a natural outcrop of the Higgs mechanism . Why is it so difficult to corner the cagey Higgs Boson?"  To which I replied:

How is the Boson, a natural outcrop of the Higgs mechanism? You may ask better,

"It appears that, the Boson, is a natural outcrop of the Higgs mechanism, how is it that it is so difficult to corner the cagey Higgs boson?"

Otherwise I am going to have to ask you for your math proof for your statement, or reference to whom has proved the boson to be, ..."a natural outcrop of the Higgs mechanism".

It is simple, Bosons, by definition, are slippery. They carry no effective electrically charged surface differential providers, which makes them slippery. Having an effective electrically charged surface differential provider, that's created dynamically, what we view as a spiny constant mono static field of charged electric potential, that is perpendicular to the surface, with the magnetic field counterpart, that is in concentric spheroidal shells, parallel to the electrically charged surface differential provider, is a fermion, like an electron, or Proton.

Neutral particles are Bosons, and are not easily affected by magnets, except for very, very strong magnets that will align the axis of the magnetic moment, that is bipolar in nature and results from the singular average spin axis, and the triangular spinning and rotating structure of the 3, point shaped quarks, that form the triangle, the spinning and rotation of said triangle structure, forms the larger neutral particle.

Photons are a strange case, because they lack a structure, such as that of a sphere that seems to hold for point particles, and larger, one that gives them a more 'solid feel', instead it is more of a 'solid rod'. Photons are more like a rod of a finite length, that spins and rotates through 4D hyperspace, that gives us up to 3 different ways, so far, to view the Photon, each dependant upon the measuring device used, and the relative position / direction of the rod, (photon), at impact / absorption, that gives us the concept of a particle, wave, or field.

Neutrinos are the strangest, in that they have next to zero interaction with anything the size of an atom and larger. They seem to be subnucleonic, and all matter is transparent to them, except to very slow moving ones, that will hit an electron, kicking out a photon out of the electron cloud, to be detected by very sensitive instruments. More at, IMHO, these neutrinos, with a dense flux streaming in from the Sun and elsewhere, actively work with the neutrons, to produce the electron and proton "pairs" that form the nuclei of atoms with the electron clouds around them, leaving an average of one neutron to one proton in all stable atoms, and a few extra neutrons in the not so stable isotopes.          

From wikipedia:
In particle physics, the Higgs mechanism is the process in which gauge bosons in a gauge theory can acquire non-vanishing masses through absorption of Nambu-Goldstone bosons arising in spontaneous symmetry breaking.

The above leads to qualifying questions, "How is a gauge boson different from any other boson?"; "What, exactly, is a gauge boson?"; If mass can vanish, and then reappear, that would explain another 3 experiences I have had, if the mechanism is KNOWN in how the mass vanishes, then comes back, let alone be non-vanishing. Who are Nambu and Goldstone, how did they get their bosons, what makes them different from the standard boson, or the gauge boson, or the one I have discovered, an ⓒ"Intermediate Hypervector Boson"™ = IHB, and don't have it named after me as yet, that might be the affect that created an effect that I witnessed.

Hmm let's see ... Gauge Theory - In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under a **continuous group of local transformations**.

The term gauge refers to redundant degrees of freedom in the Lagrangian. The Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as Lagrangian mechanics. In classical mechanics, the Lagrangian is defined as the kinetic energy, T, of the system minus its potential energy, V:: L = T - V; 

Under conditions that are given in Lagrangian mechanics, if the Lagrangian of a system is known, then the equations of motion of the system may be obtained by a direct substitution of the expression for the Lagrangian into the Euler–Lagrange equation, a particular family of partial differential equations.

The transformations between possible gauges, called gauge transformations, form a Lie group which is referred to as the symmetry group or the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding vector field called the gauge field.

In mathematics, a Lie algebra ( /ˈliː/, not /ˈlaɪ/) is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" (after Sophus Lie) was introduced by Hermann Weyl in the 1930s. In older texts, the name "infinitesimal group" is used.

A Lie algebra is a vector space over some field F together with a binary operation [·, ·]
[*,*] : g x g -> g, called the Lie bracket, which satisfies the following axioms:

Bi-linearity:
[ax + by , z] = a[x , z] + b[y , z] , [z , ax + by] = a[z , x] + b[z , y]
for all scalars a, b in F and all elements x, y, z in g.

Alternating on g :
[x , x] = 0 for all x in g.

The Jacobi identity:
[x , [y , z]] + [y , [z , x]] + [z , [x , y]] = 0
for all x, y, z in g.

Note that the bi-linearity and alternating properties imply anticommutativity, i.e., [x , y] = -[y , x] for all elements x, y in g, while anticommutativity only implies the alternating property if the field's characteristic is not 2.[1]

For any associative algebra A with multiplication * , one can construct a Lie algebra L(A). As a vector space, L(A) is the same as A. The Lie bracket of two elements of L(A) is defined to be their commutator in A: [a , b] = a * b - b * a;  

Please see : xxx http://en.wikipedia.org/wiki/File:E8PetrieFull.svg xxx is a nice 2D spherical representation. Simple Lie groups include many classical Lie groups, which provide a group-theoretic underpinning for spherical geometry, projective geometry and related geometries in the sense of Felix Klein's Erlangen programme. It emerged in the course of classification of simple Lie groups that there exist also several exceptional possibilities not corresponding to any familiar geometry. These exceptional groups account for many special examples and configurations in other branches of mathematics, as well as contemporary theoretical physics. Secondly the Lie algebra only determines uniquely the simply connected (universal) cover G* of the component containing the identity of a Lie group G. It may well happen that G* isn't actually a simple group, for example having a non-trivial center. We have therefore to worry about the global topology, by computing the fundamental group of G (an abelian group: a Lie group is an H-space). This was done by Élie Cartan.            

In mathematics, an H-space is a topological space X (generally assumed to be connected) together with a continuous map μ : X × X → X with an identity element e so that μ(e, x) = μ(x, e) = x for all x in X. Alternatively, the maps μ(e, x) and μ(x, e) are sometimes only required to be homo-topic to the identity (in this case e is called homotopy identity), sometimes through base point preserving maps. These three definitions are in fact equivalent for H-spaces that are CW complexes. Every topological group is an H-space; however, in the general case, as compared to a topological group, and from what I have seen, H-spaces do not lack associativity and inverses.

In topology, a CW complex is a type of topological space introduced by J. H. C. Whitehead to meet the needs of homotopy theory. This class of spaces is broader and has some better categorical properties than simplicial complexes, but still retains a combinatorial nature that allows for computation. 

Roughly speaking, a CW-complex is made of basic building blocks called cells. The precise definition prescribes how the cells may be topologically glued together. The C stands for "closure-finite", and the W for "weak topology".

An n-dimensional closed cell is a topological space that is homeomorphic to an n-dimensional closed ball. For example, a simplex is a closed cell, and more generally, a convex polytope is a closed cell. An n-dimensional open cell is a topological space that is homeomorphic to the open ball. A 0-dimensional open (and closed) cell is a singleton space.
A CW complex is a Hausdorff space (H-space) X together with a partition of X into open cells (of perhaps varying dimension) that satisfies two additional properties:

• For each n-dimensional open cell C in the partition of X, there exists a continuous map f from the n-dimensional closed ball to X such that
  • the restriction of f to the interior of the closed ball is a homeomorphism onto the cell C, and
  • the image of the boundary of the closed ball is contained in the union of a finite number of elements of the partition, each having cell dimension less than n.
• A subset of X is closed if and only if it meets the closure of each cell in a closed set.

If the largest dimension of any of the cells is n, then the CW complex is said to have dimension n. If there is no bound to the cell dimensions then it is said to be infinite-dimensional. The n-skeleton of a CW complex is the union of the cells whose dimension is at most n. If the union of a set of cells is closed, then this union is itself a CW complex, called a sub-complex. Thus the n-skeleton is the largest sub-complex of dimension n or less.

A CW complex is often constructed by defining its skeleton inductively. Begin by taking the 0-skeleton to be a discrete space. Next, attach 1-cells to the 0-skeleton. Here, the 1-cells are attached to points of the 0-skeleton via some continuous map from unit 0-sphere, that is, S₀. Define the 1-skeleton to be the identification space obtained from the union of the 0-skeleton, 1-cells, and the identification of points of boundary of 1-cells by assigning an identification mapping from the boundary of the 1-cells into the 1-cells. In general, given the n-1-skeleton and a collection of (abstract) closed n-cells, as above, the n-cells are attached to the n-1-skeleton by some continuous mapping from S_{n − 1}, and making an identification (equivalence relation) by specifying maps from the boundary of each n-cell into the n-1-skeleton. The n-skeleton is the identification space obtained from the union of the n-1-skeleton and the closed n-cells by identifying each point in the boundary of an n-cell with its image.
Up to isomorphism every n-dimensional complex can be obtained from its n-1 skeleton in this sense, and thus every finite-dimensional CW complex can be built up by the process above. This is true even for infinite-dimensional complexes, with the understanding that the result of the infinite process is the direct limit of the skeleta: a set is closed in X if and only if it meets each skeleton in a closed set.

Singular homology and cohomology of CW-complexes is readily computable via cellular homology. Moreover, in the category of CW-complexes and cellular maps, cellular homology can be interpreted as a homology theory. To compute an extraordinary (co)homology theory for a CW-complex, the Atiyah-Hirzebruch spectral sequence is the analogue of cellular homology.  There is a technique, developed by Whitehead, for replacing a CW-complex with a homotopy-equivalent CW-complex which has a simpler CW-decomposition.  Consider, for example, an arbitrary CW-complex. Its 1-skeleton can be fairly complicated, being an arbitrary graph. Now consider a maximal forest F in this graph. Since it is a collection of trees, and trees are contractible, consider the space X / ∼ where the equivalence relation is generated by x∼y if they are contained in a common tree in the maximal forest F.
The quotient map is a homotopy equivalence. Moreover, X / ∼ naturally inherits a CW-structure, with cells corresponding to the cells of X which are not contained in F. In particular, the 1-skeleton of X / ∼ is a disjoint union of wedges of circles.  Another way of stating the above is that a connected CW-complex can be replaced by a homotopy-equivalent CW-complex whose 0-skeleton consists of a single Point. 

In algebraic topology, a branch of mathematics, singular homology refers to the study of a certain set of algebraic invariants of a topological space X, the so-called homology groups H_n(X). Intuitively spoken, singular homology counts, for each dimension n, the n-dimensional holes of a space. Singular homology is a particular example of a homology theory, which has now grown to be a rather broad collection of theories. Of the various theories, it is perhaps one of the simpler ones to understand, being built on fairly concrete constructions.

In brief, singular homology is constructed by taking maps of the standard n-simplex to a topological space, and composing them into formal sums, called singular chains. The boundary operation on a simplex induces a singular chain complex. The singular homology is then the homology of the chain complex. The resulting homology groups are the same for all homo-topically equivalent spaces, which is the reason for their study. These constructions can be applied to all topological spaces, and so singular homology can be expressed in terms of category theory, where the homology group becomes a functor from the category of topological spaces to the category of graded abelian groups.  By dualizing the homology chain complex (i.e. applying the functor Hom(-, R), R being any ring) we obtain a cochain complex with co-boundary map δ. The cohomology groups of X are defined as the cohomology groups of this complex; in a quip, "cohomology is the homology of the co- (dual complex)".  The cohomology groups have a richer, or at least more familiar, algebraic structure than the homology groups. Firstly, they form a differential graded algebra as follows:

• the graded set of groups form a graded R-module;
• this can be given the structure of a graded R-algebra using the cup product;
• the Bockstein homomorphism β gives a differential.

There are additional cohomology operations, and the cohomology algebra has addition structure mod p (as before, the mod p cohomology is the cohomology of the mod p cochain complex, not the mod p reduction of the cohomology), notably the Steenrod algebra structure. 

The multiplicative structure of an H-space adds structure to its homology and cohomology groups. For example, the cohomology ring of a path-connected H-space with finitely generated and free cohomology groups is a Hopf algebra. Also, one can define the Pontryagin product on the homology groups of an H-space.

The fundamental group of an H-space is abelian. To see this, let X be an H-space with identity e and let f and g be loops at e. Define a map F: [0,1]×[0,1] → X by F(a,b) = f(a)g(b). Then F(a,0) = F(a,1) = f(a)e is homotopic to f, and F(0,b) = F(1,b) = eg(b) is homotopic to g. It is clear how to define a homotopy from [f][g] to [g][f]. 

Adams theorem: S0, S1, S3, S7 are the only spheres that are H-spaces (e.g., using multiplication restricted from the reals, complexes, quaternions, and octonions, respectively). In fact, S0, S1, and S3 are groups (Lie groups) with these multiplications. But S7 is not a group in this way because octonion multiplication is not associative, nor can it be given any other continuous multiplication for which it is a group. However S7 is associative and has other continuous multiplication for which it is a group, when an actual spherical coordinate system, in conjunction with my One equation, is used in place of the octonions with their linearity of cubism restrictions.

Then with the continuous group of local transformations in mind, I came up with: xxx http://youtu.be/59157zE-u6s  xxx

So, I would say that: 'The Higgs mechanism is the natural outcrop of the Gauge Field Boson Theory, so why is the Higgs Boson so cagey?' if I thought the Higgs field Boson was even real or remotely possible, let alone findable, because it is like trying to create a particle of space. Space is an empty concept, while particle is a fully solid concept. In my theory, and the One Equation, they are related, but different structures. The primary vectors form dynamic relationship hypervectors that spin on 4 axis', which form into a surface element triangle that rotates with 4 degrees of freedom, that depending on the scalar values of the dynamic relationship hypervectors, with each hypervector perpendicular to the others, and the ratios of any 2 hypervectors that form dynamically a third hypervector, form S7, as there are 7 geometric functions in the group, a group that exhibits continuous local transformations between the 7 geometries within the group. 

Please note that in the above concepts: gauge theory, Lagrangian, Lie group and Lie algebra, H-space, CW complexes, were composited from information found on wikipedia, (don't forget to donate, no ads) to which I added what I know, and hopefully made a coherent contribution.  And on YouTube : http://youtu.be/1_HrQVhgbeo Higgs                              

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