Tuesday, October 7, 2008

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.

No comments: