Friday, November 7, 2008

QED, Feynman, and Me

Points with Geometry from the One Equation:


I went here: and watched all four of Feynman's lectures. It was most enlightening, particularly when he describes the Photon and the Electron, as vectors of "chance potential" of an event occuring. The probability was given as the square of the scalar value of the resultant vector, times Pi, giving the area of a circle. The Photon has zero mass, while the Electron has a very small mass.

Here I have worked out a model of how the universe works, quantum to cosmic, alone, with no help or incouragement, using Points and Dynamic Vectors, and only recently come to find that Feynman had used the nearly the same thing to describe the photon and the electron. Had I seen this earlier I could have saved some time.

Feynman used a flat 2D surface, drew 2 vectors, connected them with a resultant vector. The length of the resultant vector, was then squared and multiplied by Pi. He was able to describe complex particle formation, and most other observed phenomena using this method, except for gravity, radioactivity, and the source of 'mass'.

I have taken it to the next level. With four degrees of freedom of rotation, for any resultant vector, i.e. 'Dynamic Hypervector', added to the concept of mass as a vector, similar to that of time and distance, constrained to the dictates of the One equation, combines to form a theory that can easily describe all observed phenomenon, including radioactivity, gravity, blackholes, whiteholes, charged and neutral particles, and all the different kinds of forces. The 'strength' of any force, energy, or 'mass', is given by the curve of the surface. The 'tighter' the angle of the curvature, the greater the effect.


What Do They Form?
The Hypermass:

Before everything was made, there was a ‘Hypermass’ that is the Point of Origin, (0, 0) see Top View. All the Points that formed in the first phase of ‘The Big Bang’, in a 6D frame of reference, created a formless ‘sphere’ of rapidly expanding Hyperspace gelatin, all the same as the Point of Origin. The second phase of The Big Bang, was the creation of Dynamic Points with ‘Change, Push and Spin’, which put everything into ‘random’ motion, forming layers of expanding gelatin and the starting of expanding ‘relationships’ which then initiated the third phase of 4 dimensional Rapid Expansion. Here we have a large sphere, made up of a growing number of smaller spheres, all unified as to properties. This is ‘spacetime’ starting to form, as the concept of ‘spacetime’ doesn’t ‘exist’ as a matter of reference, but rather a ‘hypermass’, that from our 3D1T point of view would appear to be an infinitely small, infinitely dense singularity. Each Dynamic Point Hypersurface Element has a ‘mass’ component. All of the Points (the number of which continues to increase) have no direction, thus no relationships, thus no reference, thus there are no differences as everything is still just one thing with ‘layers’ of the same thing in a ‘linear’ 0D frame of reference.

In our 3D1T world, we have Distance with Direction. We can make 3 lines meet at one Point and have each be perpendicular to the other two lines. Now imagine being able to do the same thing with 4 lines. Extension, a ‘linear’ 1D frame of reference, is formed by the individual rotational expression between any two Points, forming Dynamic Hypervectors, with one degree of freedom of rotation. The first degree is about the longitudinal formation of a unit-vector, ‘r’, (r = Pd – Po). Having two Dynamic Points rotating in the same ‘direction’ create ‘distance’, (because of polarity) and differing rates of spin allows ‘r’ to vary in ‘distance’. This dynamic change in distance creates a form of oscillation that occurs between any two Dynamic Points, this ‘dynamic changing length’ forms ‘time’. Each Origin Point, acts in concert, with every other Origin Point, is the center of a Dynamic Point Hypersurface Element, with every other Point acting as the Dynamic Point. It takes ‘mass’ to move ‘mass’. It takes Mass to create 'distance' and 'time' between Points of Origin. Each Point ‘pushes’ against all of the others, this causes extension and expansion. Each Point finds its own ‘spin axis’, with Dynamic Points rotating around a Point of Origin. An Origin Point and a Dynamic Point, with the same ‘spin axis,’ dynamically form unit-vectors.

Infinite Hyperplanes:
Infinite Hyperplanes (±1, 0) are formed from unit vectors with 2DFR. The first degree is about the longitudinal formation of a unit-vector, ‘r’, while the second degree of freedom is the rotation of a Dynamic Point at the end of the longitudinal section, (r = Pd – Po) acting as the head of the arrow, about an Origin Point. Each Point, in concert, with every other Point, is the center of a Dynamic Hyperplane element, with every other Point acting as the Dynamic Point. All Points, in a 6D frame of reference, created a formless, motionless Hypermass. The Big Bang, i.e. the addition of Change using Push, put everything in motion. Hyperplanes are the basis of all dynamic surface elements, i.e. the stuff we can see, hear, taste, smell, touch and from which we are formed. The concepts of ‘Mass’, ‘Time’ and ‘Distance’ start to form. In our visible viable universe, we have Distance with Direction. The Hyperplanes, which form Hypersurfaces, are ‘normal’ in all directions to our point of view. No matter which direction one looks, our view of a Hypersurface will always be perpendicular to it. Our view, of such a thing, would be such that we would ‘see’ light, and the images that we see because of the light, becoming ‘Macro Hypervectors’ that flow as a curved surface made up of Dynamic Hypersurface Elements, and appear as thin bands of light alternating with bands of dark, in both directions on the Hypersurface of greatest curvature. The bands of light would be the light coming toward you, while the dark bands would be the light going away from you.

Infinite Hyperspacetime:
In our 4D1T1M universe, and being able to set R1 and R2 to (-1, -1) or (1, 1) says that there is a ‘nega-universe’ as well as our ‘posi-universe’. This corresponds to the concept of polarity, which is derived from the first degree of freedom of rotation, (see Top View), that gives a clockwise or counter clockwise direction to the first degree of freedom of rotation. The D-R vector that forms between 2 Points can also point in opposite ‘directions’ which then adds to the properties of any D-R vector, thus adding another level of complexity at the very beginning of things. When the unit-vectors all have the same freedoms rotation and are ‘Pointing’ together, they form a full unit-vector. Single full unit-vectors with 4DFR form the ‘Points of the Universe’ and are indistinguishable from each other. This Hypersurface function gives one the concept of ‘outside’ surface. It has one ‘active’ side, yet its geometry yields more functions than just that of ‘outside surface.’ The ‘hollow’ inside provides for the vacuum of ‘space’ while the outside 'active surface' provides for the gravity of ‘space.’

Neutral Matter-Antimatter:
Neutral Matter-Antimatter is formed by the Hypersurface configuration (0, ±1). This is what forms the bulk of the universe along with Hyperspacetime. This is the base form of matter, regardless of its level of ‘kinetic energy’. By the given understanding of the common four states of matter, (solid, liquid, gas, plasma), it appears that any common solid matter can attain the ‘higher’ states of matter by accumulating and exhibiting ‘kinetic energy’, as can matter in ‘higher’ states can be lowered by the removal of ‘kinetic energy’. This ability shows up in many different ways in a 4DFR universe. It can be seen that as long as R2 remains zero, varying R1 in either direction, plus or minus, yields a scaling function, the nature of which is dynamic, while the functional geometry remains the same, which allows for the smallest of structures to the largest of structures. This shape also fits nicely in the center of a Hyperspacetime function, and together they give the appearance of what has been termed “dark matter or dark energy” out there in ‘dark’ space.

Dynamic Change, or that which is Changing, that which has Continuous Change, has the function (±A, ±B), such that R1 is LessThan the absolute value of R2 or the absolute value of R1 LessThan R2 with the non-occurrence of R1 = |R2| or |R1| = R2, neither R1 nor R2 equal to zero, neither R1 nor R2 equal to ±1 at the same instance. This functional gives the ‘wrapped candy’ geometry of ‘Time-Flow’ and ‘Motion’. The formation of Hypervectors, of any kind, causes Change; the kind of ‘change’ is not so obvious. Time, as most people experience it, is a linear expression, which is a measure of Change, the measure of which our brains have become accustomed to taking on a regular basis, ‘frame’ by ‘frame’.

The scalar measure of Change can be such as ‘distance’ in a linear system or of ‘time’ in a cyclic system. A spherical atom of “Cesium” vibrates at a constant rate. How does a sphere oscillate or vibrate? It shrinks, or grows, and then returns, back to its original size. The change in size can be measured as well as the rate of change in size and back. The change is linear and cyclic. This kind of behavior is the result of the first degree of freedom of rotation in action, i.e. that of ‘Push’ and ‘Spin’. Push creates ‘dynamic change’ along the direction Hypervector, while Spin creates ‘dynamic change’ perpendicular to the direction of the Hypervector. The tick-tock of clock is a repeatable event. The amount of each ‘time’ event is registered on the face of the clock by some kind of indicator. Analog or digital, change is measured, and indicated, never to be seen or felt again, except on the face of the clock as time having past, or the distance as having been traveled. No ‘do-overs’ during game play.

Blackholes and Whiteholes:
Many individuals have already written much on the concept of Blackholes. Since Schwarzschild’s solutions to Einstein’s equations in 1916, Blackholes, i.e. Schwarzschild’s radius, have been a topic of interest. There have been many mathematical attempts, using different geometries, to define and describe the cause and effect of Blackholes. Quasars are stellar Whiteholes that are represented by the bottom half of the function, where all light is emitted, while ‘blackholes’ are represented by the top half of the function, where all light is collected, and both halves ‘point’ to a Point.
In the above Equation, it is easy to see that as R1 = R2, or R1 = R2, the geometry of the formation creates the Blackhole / Whitehole function. The Blackhole / Whitehole (1, -1) or (-1, 1) function rotates all directions of spacetime, dynamic mass vectors included, towards or away from, what appears to be a single Point, thus it looks like a ‘singularity’ from a 3D1T point of view, no matter from which direction one approaches. The Blackhole half of the function rotates the axis of spin of the ‘mass’, ‘time’, and ‘distance’ components of all the ‘Points’, in a specific radius, towards the Point of Origin of the radius, while the opposite occurs with the Whitehole half of the function, as all is rotated away from the Point of Origin of the radius. The dense collections ‘particles’ that make up the planets and regular stars remain as individual particles, with each particle owning and maintaining its own volume of spacetime. However, greater is the number of particles that go into making a Blackhole/Whitehole function, as is the mass of the original star, which ‘collapsed’ to form the Blackhole/Whitehole function. The larger ‘cross-section,’ and the greater area density of that cross-section of matter, that the original star presented to the rest of the ‘universe’, the greater the chance for the Blackhole function to occur. As the ‘collapse’ progresses, the Dynamic Hypervectors of Push, which are aligned with the 1DFR, cause the Dynamic Hypervectors of Extension and Time-Flow to rotate to align with the 1DFR becoming no longer perpendicular to one another and further combine together to form a single contiguous Dynamic Point Hypersurface Element. Quasars emitting or Blackholes collecting, the same amount of photons or matter, will be equal in radius.

Many individuals have already written much on the concept of Wormholes. Since Schwarzschild’s solutions to Einstein’s equations in 1916, Wormholes have been a topic of interest. There have been many mathematical attempts, using different geometries, to define and describe the cause and effect of Wormholes. Wormholes are temporary structures, which serve to move photons and matter from one Point in ‘spacetime’ to another, different, Point in ‘spacetime’. The Wormhole is the structure that creates the shortest ‘distance’ between two Points in ‘spacetime’.

In the above Equation, it is easy to see that as along as if 0 <> R2, or if 0<> R2 the geometry yields the formation that creates the Wormhole function. Wormholes, allow for the passage of matter, energy, and light, in both directions, through the interface that is formed at the ‘zero-cross-over’ between the two ‘areas’ of spacetime. While the 6D Hypersurface geometry of (1,1) Hyperspacetime provides for ‘surface’ in our 3D1T world, it is a surface that is ‘outside’ and only outside. The Wormhole function provides the only ‘inside’ Dynamic Path Hypersurface Elements, and like anti-mater, it does not last long in our ‘spacetime’.

The Hyperplane interface at the ‘zero-cross-over’ cross-section of the Wormhole, is formed by Dynamic Hypervectors pointing in opposite directions parallel to gravity’s normality to a massive infinite surface and is the 2DF axis of rotation for R1. R2’s 2DF axis of rotation is perpendicular to that of R1. The edge view of the plane of rotation of R2 is parallel to the axis of rotation of R1 always. The zero in the ‘zero-cross-over’ term refers to the fact, that Time is zero, or appears non-existent at that point, in the rotation of the unit-vectors. It is also the point of greatest curvature of ‘spacetime’ along the Hypersurface.

Time still ‘exists’ it just doesn’t appear to flow. On the Dynamic Hypersurface itself, photons show up as lines or vectors of light that is brightly emitted alternating with lines or vectors of a total lack of light as the absorbed blackness of space.

The dark area in the above rendered image is medium gray (in low indirect light), short-loop pile carpet. The circular light area in the center of the image is sun-lit concrete sidewalk. The gray carpet was located on the inside of an apartment at 10:00 PM on Friday, April 12, 1996. The sun-lit concrete sidewalk was located outside of the apartment at 10:30 AM on Sunday, April 14, 1996. The diameter of the circle was approximately 3.65 inches. The circle, formed, remained, then un-formed in period of approximately 3.65 seconds. The distance between the two areas of space was approximately 3.65 yards, with the direction being due east going from entrance to exit, and the ‘height difference’ at the z-c-o was about 3 x 3.65 inches. The difference in time between entrance and exit was 36.5 hours.

Tuesday, October 7, 2008

Six Dimensional Geometrical Objects:

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

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

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

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

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

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

The Point (4DFR)

A Point is a concept in need of a definition. What are the properties of a point? For some, a point is the beginning, for others it is the end. A Point is the concept of how the universe began, as an origin, i.e. the concept of the Origin of the Universe and it’s beginning as a Point.

Concisely then, all the clear, cognizable concepts, were creatively conceived, concentrated, completely compressed, and confined to a coalesced object. All concepts were conceived and clearly created though an act of cohesive, coherent, concentric, cognizing by a considerable comprehensive consciousness, with but a compunction, did conceptualize and compact all concepts into one coalesced concurrent condensed Point of Origin.

'In The Beginning’, the first Point is the universe, and is the Origin of all Points. When the Big Bang went “BOOM,” The One Point became many. It was a geometrical exponential expansion: 1, 3, 27, 19683, 7625597484987, etc. The Big Bang, “The Origin of All Points” having occurred, we can now start to define more complex concepts now that we have more that one point with which to work.

Mathematically speaking, a point marks the beginning and the end of a line, or an intersection of two or more lines. A Point also has the same mathematical definition and includes the collinear dimensional view of a line (looking parallel along the line, i.e. an end view); otherwise, it is perceived as a ‘flat’ sphere that has the same perpendicular view, as viewed from all ‘sides’, within our universe. This sphere shaped Point has no dimension or volume in and of itself relative to our “4D Space-time”, yet it is there to define dimension. A sphere is the simplest of shapes and forms, for it has one point of origin, one single contiguous surface of the same shape as the center origin point, and one single continuous edge easily seen from all angles, which is also the same shape as the center point from which it is formed.


The point of The Point is that the concept of The Point, as a sphere is:
  • The sphere is the simplest of all geometrical concepts from which all other concepts arise.
  • Within each Sphere reside all the properties needed for higher dimensional constructs.
  • The universe naturally uses a spherical coordinate system.

Dynamic Point Laws
    • Each Point can act as an origin.
    • Each Point can act separately.
    • Each Point can act in concert with any other Point.
    • Each Point is tied to all other Points.
    • Each Point adds or transfers its properties to the next and in turn receives a property set from said next Point.
    • All Points can act together.
    • One Point can affect all the other Points.
    • All of the other Points can affect just one Point.

What we see as a point in our 4D environment is really a ‘cross-section’ of something that has more than four dimensions. To imagine as an example, we can talk about ‘Mr. 3D’. Mr. 3D has 2D in terms of extension, and 1D of time so that he knows motion. He knows about left and right and up and down, but not about forward or backward. He can’t see ‘In’ or ‘Out’. He can move around objects in his 3D environment, but all he sees is a dot, a line, or a line of dots or moving lines and dots. Concepts like ‘square’ and ‘circle’ are abstract and tough to visualize or prove. The only way he can determine a shape is to move around it. He can only rotate left or right about an axis that is normal to his plane of ‘reality’. He can move in any direction save for the direction of the axis of rotation that is ‘normal’ to his plane of existence. He cannot rotate ‘in’ and ‘out’ of his plane, only within it. Now we can introduce various objects into his plane of existence. Our objects are 4D in our ‘Hyperplane of Existence’. When we move our 4D objects to intersect his plane, he can only see their cross-section edge. If we were to put our finger through his plane, he would see only solid lines that were impassable, after awhile he might find that he could go around but just not through. As we move our finger into his plane he would notice that the line he sees is changing length. He is able to determine distance, angle, color, and his 2D position relative to the position of our finger. Mr. 3D has limited view and knowledge of anything beyond his 3D (2D plane, 1D time) environment.

When thinking about objects, that appear to be singularity orientated, such as particles and Blackholes, the cross-sections that we see in our environment are actually 5D Hypersurfaces imposed on a '6D Hyperspace' structure / environment. Dimensions noted here, are always perpendicular to each other. All four 'linear' dimensions of Extension are perpendicular to each other. We can only see in 3D. The fourth is 'just around the corner,' out of view. A Point in 4D, is a line in 5D, is a curved surface on a 6D object. Time-Flow and Dynamic Mass are Hypervectors similar to that of Extension.

Points are the basis of everything. It is the properties that we can ascribe to any one Point that creates differences from any other Point and since we have laid out the concept groundwork of the Point, it is now easier to see that Dynamic Hypervectors are formed between any two Points. One Point acts as the Origin Point the other acts as the Dynamic Point. Hypersurfaces have designated scalar truth table values such as [±1, 0] which yields the structure for ‘Infinite Hyperplanes’. Dynamic Path Hypersurface Elements are formed by rotational (α, ß, (R1,Θ), (R2, φ)) Dynamic Hypervectors, with four degrees of freedom of rotation. The first degree is about the longitudinal direction of a unit-vector, ‘R’, and yields the ‘plus or minus’ Polarity value of the scalar, while the second, third, and fourth degrees of freedom is the rotation of a Dynamic Point at the end of the dynamic longitudinal section, (r = Pd – Po) acting as the head of the arrow, about an Origin Point. It should be noted that π equals one degree of freedom of rotation. In the One Equation, the first half of the equation uses 0 to 2π, this equals 2DFR, while the second half of the equation uses -π/2 to π/2, the range of which is equal to π, 1DFR, together they yield a 3DFR.

The ‘first’ degree half of the above equation yields a circular perimeter created by a 2DF Dynamic Point (2πr). The rotating D-R unit-vector will form in situ an ‘Infinite Hyperplane’ (πr^2), 2D1T. Any two Infinite Hyperplanes, acting in concert together, will always be perpendicular to each other, thus Infinite Hyperplanes exist in all directions, thanks in part to Heisenberg’s Principle. An Infinite Hyperplane is one of seven different Hypersurfaces. The ‘second’ degree half of the above equation describes a Dynamic Hypersurface Path Element, with limitations, that goes through ‘zero’, in a rotational plane that is perpendicular to the rotational plane of the ‘first’ degree half of the equation, (2D1T), that due to the rotation of the first plane, (2D1T), forms two of the 6D ‘linear’ dimensions. The 6D ‘linear’ dimensions are really 4D1T1M ‘not so linear’ dimensions.

The One Equation (4DFR)

The One Equation, with just 3 of the degrees of freedom of rotation described, given a Linear 6D frame of reference, will generate multiple Dynamic Hypersurface geometries. Just two Dynamic Relationship Vectors, comprised of one or more unit-vectors, head to tail, creating a third Dynamic Hypervector, with scalar values that constantly change, each DRV rotating in a plane perpendicular to the others, can create seven different Dynamic Hyperspace structures from three Points all by changing the scalar values of each D-R unit-vector that is between each Point. The scalar value of the Dynamic Hypervector is always in flux, subject to the strictures of Heisenberg's Principle of Uncertainty. One scalar can be 1/10th scale of the other. Each DRV  is comprised of Extension, Dynamic Mass, or Change vectors, as derived from the Primary, Secondary, and Tertiary concepts as laid out in Appendixes A, B, and C. It is briefly noted here that the value of Pi, 3.14159..., in radians, is equivalent to any 1DFR. Typically with 3D, one also has 3DFR.

In this writing, the 1DFR is considered to be the longintudinal rotation motion of the Dynamic Hypervector, in relationship to its direction and motion of Extension.  The direction of the angular momentum is perpendicular to the linear extension of the DH.  The scalar value of the DH is in constant Change, and is induced by Dynamic Mass. The DPHE that is dynamically formed, and follows the strictures of the One Equation. As each DVR changes scalar 'length,' so to does the shape and scale of the Dynamic Path Hypersurface Element. The 'P' can represent the dynamic 'Point', as well as the dynamic 'Path' it can follow during a Rotation. The Path Element is perpendicular to the Dynamic Hypervector that forms the Path Element. The DPHE is what we experience. Each DPHE can comprise any physical relationship that can form between 'distance', 'time', and 'mass'. It will be shown that DPHE's can form at any scale, thus from the scale of the 'quantum' to the scale of the 'cosmic', everything comes from the same geometry, and the One Equation.

The linear vector concepts of distance, time, and mass, employ the first degree of freedom of rotation during formation. Each random Point spins about an arbitrary longitudinal axis. When the spin axis any 2 Points are aligned, such that the 'spin' axis of each of the 2 Points is collinear to the spin axis of the other with their angular momentum also in the same direction between them, much like an arrow in flight with feathers that cause the shaft to spin about its long axis. This process causes the 'linear' vectors to form dynamically and the 'spin' provides for the concept of ‘Polarity’.

Dynamic Hypersurface Path Elements form in situ as the DRV's rotate about their ‘origin Points’. The Dynamic Hypersurfaces are well defined in six ‘linear’ dimensions as opposed to five. Each Dynamic Hypersurface Path Element represents, at a maximum, 4 linear, 4 temporal, and 4 specific dimensional constraints and at a minimum 1 linear, or 1 temporal, or 1 specific constraint.
To properly develop the concept of Dynamic Hypersurfaces, that form structures in a Dynamic Hyper-massive-spacetime, we will start with the most primary of concepts, the Point.

Tuesday, September 23, 2008

Four Degrees of Freedom (of Rotation) cont.

Introduction:Different solutions, to Einstein’s field equations, in pioneering works by Michael S. Morris[1] [40] [43] [61], Kip S. Thorne [1] [40] [43] [61], and Ulvi Yurtsever [1] [61], were found at the behest of a popular science fiction writer by the name of Carl Sagan. Carl wanted a method of moving a human character faster than light though not in a manner violating Relativity. However, there were others before Carl. The concept of Blackholes and wormholes were imagined almost as soon as Einstein published General Relativity. Schwarzschild, a mathematician, in the same year that they were published, found several solutions to Einstein’s equations.

In 1916, less than a year after Einstein had formulated his equations of the general theory,an Austrian, Ludwig Flamm, had realized that Schwarzschild's solution to Einstein's equations described a Blackhole connecting two regions of ‘flat’ spacetime, or two different points of the same universe. Einstein himself, working at Princeton with Nathan Rosen in the 1930s, had discovered that the equations seemed to actually represent a wormhole as a bridge between two regions of flat space-time a phenomenon known as an "Einstein-Rosen bridge".

Matt Visser [2] [4] [5] [36] [37] [41] [42] [54] [118] [119] [122] [123] [126] [128] [130] [131] has done much to add clarity to the subject of the variations of different methods that might produce wormholes and the various kinds of mathematics that go with them. As of this writing, [7], has come the closest to correctly describing a wormhole, without the advantage of actually seeing one form. Nor actually watch something disappear from their present spacetime point to a future/nearby spacetime point. Nor then watch the wormhole close. Only to find the object, that disappeared, a couple of days later, in a place they just looked at not more two hours before they left for breakfast, upon their return from said breakfast.There have been a number of tries using Euclidian [149] and Lorentzian [41] methods. There are others too numerous to detail here [3] [6] [8] [9] [10] [11 – 39] [44 – 53] [55 – 60] [62 – 117] [120] [121] [124] [125] [127] [129] [132 – 153].

The various branches of chemistry and mechanical physics have well defined matter in its various forms. The table of elements is an excellent example of the repeatable information about the different kinds of matter from a nucleus and electrons point of view. Particle physicists have tried to crack the proton and electron with some success, and have tried to map out the nature of particles, from a particle point of view, as to what goes into the makeup of any one particle that they have been able to make and detect in colliders. Astronomical observations have also added information to both chemistry and particle physics, and provides a ‘cosmological’ point of view and services Einstein’s GR.  String theorists have given us more ‘linear’ dimensions.

Wednesday, September 17, 2008

Four Degrees of Freedom (of Rotation)

The concepts under consideration: Space, Time, Mass, Energy, Gravity, Polarity, Charge, Matter, Photons, Infinite Hyperplanes, Higher Linear Dimensions, Blackholes, and Wormholes are the space-like, energy-like, matter-like and time-like sections of the products of real-existing unit-vectors with consequential Dynamic Path Hypersurface Elements (D-P-H-E) is such that they all derive from a common metric. It is shown that scalar values of 0, ±1, provide the geometry, forming a D-P-H-E of constant curvature with three degrees of freedom of rotation, (3DFR), which forms a single origin, single edge, single surface topological metric (a sphere) as one of seven given Hypersurfaces. It is shown, that the one common metric admits to a class of seven geometries. One or more of the geometries can be applied to create all the concept cases when Four Degrees of Freedom of rotation, (4DFR), as combined with the scalar values of the unit-vectors that form them, is used, producing a 6D ‘linear’ object/environment, when properly viewed in terms of the common spatial Energy and Matter Densities. The Four Degrees of Freedom of Rotation is in the metric. It is in the boundaries of the integral, in the scalar values of the Dynamic-Relationship unit-vectors, in the ratio between the scalar values, and in the ‘polaric’ value of each scalar in the pair, which determines the D-P-H-E, and allows for the existence of the seven geometries responsible for forming the bulk of the Universe. For a negative boundary constant, the metric is such that it is the lower limit of the integral, and is considered to be coming from the future, which is neither arbitrary, nor fixed, as the solution describes a 6D horizon geometry, which inherits its metric from the D-P-H-E. If the scalar values of the unit-vectors, that form the D-P-H-E, are negative and/or positive respective to each other, Polarities for each kind of D-P-H-E are obtained. There is a case, for which the D-P-H-E is of constant curvature, and due to degeneration of the R2 scalar value, reaching a fractional negative value, relative to the first, that the metric admits a time-shift function and the formation of a Wormhole. Wormholes, (1, <-.05 to -.95>), of macro-size, and the other spacetime geometries, have gravity parallel to their R1 axis of rotation, which is normal to a Massive Infinite Plane, such as the surface of the Earth. The ‘interface area’ of the Wormhole is normal and transparent to gravitational forces, light, and matter, while at the Dynamic Hypersurface all will follow and point in the same direction as the D-P-H-E. All these concepts: Space-Time, Mass, Energy, Gravity, Polarity, Charge, Matter, Photons, Infinite Hyperplanes, Higher Linear Dimensions, Blackholes, and Wormholes, have a common metric, have finite Euclidean action from our 3D1T1M point of view, the free energy available in the case of Blackholes reduces to zero at the horizon, and is transverse or balanced in the other cases. Distance, Mass and Time are contained in the R1 and R2 scalar values within the metric of a D-P-H-E. The R1 and R2 scalar values are each determined by their first degree of rotation. The 1DFR in a 6D non-linear frame of reference is a composite of the geometrical three degrees of freedom of rotation within our 3D1T1M spacetime with mass properties, and its axis of rotation is normal (perpendicular) to any Point on the Hypersurface. The second, third and fourth DFR are the same as the three common ones of spherical geometry, with each axis of rotation perpendicular to the others, however they are in a 6D non-linear frame of reference. All forms of the D-P-H-E can be described by utilizing four degrees of freedom of rotation of unitized Dynamic Relationship Hypervectors of ‘Extension’, ‘Time-Flow’, and ‘Dynamic-Mass’. Linear Extension, Linear Time, and Linear Mass are Dynamic Hypervectors each with one to four degrees of freedom of rotation available to it. The common metric, from a 6D viewpoint where R1 and R2 represent the scalar values of their unitized vector relationships, form all of the geometries and metrics needed to create the above mentioned concepts as existing dynamic realities.