Linking Direction and Rotation
Posted: Mon Nov 26, 2007 8:49 pm
When programming a ratio and cross-ratio class, I discovered that the cross-ratio needs to have a geometric component to it, a type of "directional association" between the two ratios.
The basic ratio of a:b (or space:time) does not appear to have any type of relationship between the two aspects save the reciprocal (inverse) relationship. Additive and negation do not apply, being a concept of displacement requiring a zero datum, and multiplication just increases the value of a single magnitude by a repeat count. The only choice of a direction relationship in a unit-datum ratio is greater or less than unity.
However, when two of these ratios are brought into proportion, a geometry can exist between them. Consider the two ratios of a cross-ratio like two lines interacting, the ratio determining the slope of the lines. When dealing with scalars, the concept of "angles" does not yet exist; the only function is "incidence" (same or different slope).The same slopes make the lines parallel to each other. For lack of a better term, we could consider different slopes to have an "orthogonal" relationship.
This adds something interesting to the cross-ratio concept. Picture the two ratios of a cross-ratio as simple, planar rotations, the ratio indicating their rotational speed and direction (we can call clockwise as 'greater-than unity' and CCW as 'less-than unity'). Four possible orientations result:
(CW,CW), (CW,CCW), (CCW,CW), (CCW,CCW)
As Nehru described in his article on the "Conservation of Direction", to an observer, there only appear to be TWO rotations, either "same" or "opposite" (not same). Without a common reference point, the actual direction cannot be determined.
Now take those rotations and consider the geometry: if the two rotational planes are parallel, the opposite rotations go through a dimensional reduction to produce a cosine wave. If they are in the same direction, one gets a rotating disc.
The other possibility is that the two rotational planes are not parallel, say "orthogonal" to each other. The same 4 directional orientations still exist, but all appear as the SAME rotation -- a spherical "double" or "solid" rotation. (No matter which way you intersect two rotating discs, you can always find the point where both rotations are rotation away from the same intersection point).
It becomes apparent that the concept of the parallel cross-ratio is Nehru's concept of bi-rotation, the basis of the photon. The orthogonal cross-ratio is then the solid or "magnetic" rotation that forms the building block of the neutrinos (Larson's 1/2-1/2-0 particle).
So it becomes a simple matter of the geometry with a cross-ratio (a bi-direction) that determines whether or not we have an "electric" (1d, parallel) or "magnetic" (2d, orthogonal) rotational system. This may explain the mechanism as to why Larson says an electric displacement can be converted to a magnetic displacement in the atomic building process, and vice-versa.
We know that certain optic effects can change the polarization of photons from linear to circular, in essence changing the orientation of one of the ratios in the cross-ratio to its inverse. It may also be possible to change the geometric relationship between the ratios, thus turning the photon into a neutrino.
Curious if anyone has ever run across anything along the lines of photon/neutrino transmutation?
The basic ratio of a:b (or space:time) does not appear to have any type of relationship between the two aspects save the reciprocal (inverse) relationship. Additive and negation do not apply, being a concept of displacement requiring a zero datum, and multiplication just increases the value of a single magnitude by a repeat count. The only choice of a direction relationship in a unit-datum ratio is greater or less than unity.
However, when two of these ratios are brought into proportion, a geometry can exist between them. Consider the two ratios of a cross-ratio like two lines interacting, the ratio determining the slope of the lines. When dealing with scalars, the concept of "angles" does not yet exist; the only function is "incidence" (same or different slope).The same slopes make the lines parallel to each other. For lack of a better term, we could consider different slopes to have an "orthogonal" relationship.
This adds something interesting to the cross-ratio concept. Picture the two ratios of a cross-ratio as simple, planar rotations, the ratio indicating their rotational speed and direction (we can call clockwise as 'greater-than unity' and CCW as 'less-than unity'). Four possible orientations result:
(CW,CW), (CW,CCW), (CCW,CW), (CCW,CCW)
As Nehru described in his article on the "Conservation of Direction", to an observer, there only appear to be TWO rotations, either "same" or "opposite" (not same). Without a common reference point, the actual direction cannot be determined.
Now take those rotations and consider the geometry: if the two rotational planes are parallel, the opposite rotations go through a dimensional reduction to produce a cosine wave. If they are in the same direction, one gets a rotating disc.
The other possibility is that the two rotational planes are not parallel, say "orthogonal" to each other. The same 4 directional orientations still exist, but all appear as the SAME rotation -- a spherical "double" or "solid" rotation. (No matter which way you intersect two rotating discs, you can always find the point where both rotations are rotation away from the same intersection point).
It becomes apparent that the concept of the parallel cross-ratio is Nehru's concept of bi-rotation, the basis of the photon. The orthogonal cross-ratio is then the solid or "magnetic" rotation that forms the building block of the neutrinos (Larson's 1/2-1/2-0 particle).
So it becomes a simple matter of the geometry with a cross-ratio (a bi-direction) that determines whether or not we have an "electric" (1d, parallel) or "magnetic" (2d, orthogonal) rotational system. This may explain the mechanism as to why Larson says an electric displacement can be converted to a magnetic displacement in the atomic building process, and vice-versa.
We know that certain optic effects can change the polarization of photons from linear to circular, in essence changing the orientation of one of the ratios in the cross-ratio to its inverse. It may also be possible to change the geometric relationship between the ratios, thus turning the photon into a neutrino.
Curious if anyone has ever run across anything along the lines of photon/neutrino transmutation?