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.