Integrating momentum into orbital theory.

For many years there has been questions as to how particles could have stable orbits. At the same time, it has been long known that the product of mass times velocity known as momentum, "p," seems to be a constant for any given system. Recently it was noted that momentum, considered as a mathematical expression, could be considered as either an integration or a derivative, that is, speaking in the sense of differential and integral calculus. As an integral it is the integral of force over time, in other words it sums up the total effect of all forces that have ever operated against the object on question. As a differential, it can be considered as either the instantaneous rate of change of velocity with respect to time, with mass being considered constant; or it may be considered the instantaneous rate of change of mass if velocity is held constant. In mathematical terms the expression, mv, can be integrated as if it were, mv x dv/dt, to give the familiar Kinetic Energy expression. KE=1/2 mv^2. Alternatively, it can be integrated as if it were vm x dm/dt to give another expression of the same form--which apparently has been overlooked previously, E=1/2 vm^2. This expression we shall call by contrast to Kinetic Energy, "Static Energy." These appear to correspond respectively to the "vector characteristic" of "Energy," i.e., Kinetic Energy, and the association of motion centered on a point which is postulated in the Motion in a Matrix Model.*

Assuming that both integrations are valid, and knowing that Mass and Kinetic Energy have some sort of inter-convertibility, we can write, Total Energy ("TE"), equals Kinetic Energy plus Static Energy and assume that for a stable situation, "TE" is equal to some constant, "C." So, for a stable "orbit." of any kind we can write

TE=SE + KE, or C=1/2 vm^2 + 1/2 mv^2. We can discard the "1/2" and write something like "C= vm^2 + mv^2. We can see that this adds up to the equation, C = pv + pm , i.e. the total energy content of the system is equal to the momentum times the velocity plus the momentum times the mass, and for a stable system, this energy content is, presumably, a constant. If the velocity in a given direction goes up, the mass goes down. At the point of greatest velocity in a stable system the mass would be the least, at the point of least velocity, the mass would be the greatest. This prediction from the mathematics is being done here without checking any of the literature, but the writer is willing to bet that the measured mass of planets varies from perihelion to aphelion in exactly the way mentioned above.

This fits also with the idea of a "3-D pendulum" model for electron orbitals wherein the electrons would pass through and about the nuclei in a three-dimensional analog of a pendulum wherein they would have their greatest mass at the farthest extent of their motion and the greatest speed at the center of the atom. This could account, at least to some extent, to the "solid" feel of matter.

In a previous article dealing with Black Holes, q.v., this writer has discussed the situation wherein "v" reaches a directional limit and any interaction which would have increased the velocity in that direction goes instead to increase "mass." or more correctly and interaction which would have increased the Kinetic Energy increases the Static Energy instead. The idea is that a "Black Hole would occur at any time when some object reached the speed of light along any one vector. As any further acceleration along that vector could not be compensated for the mass would have to increase causing a condition of instability with radiation necessary until stable states were reached by the components of the interaction. In this view, a "Black Hole" is not some very mysterious gravitational sink, it is simply some object which has reached the speed of light along some vector.

[Although Einstein's Relativity limit of "No speed greater than light" cannot apply to relative velocities, there is, in the Motion in a Matrix model, q.v., a basic notation that the fastest transport speed in the matrix is "c" for either information or energy. This would also include "Matter" as matter is considered as an indication of involved motion in the matrix. Therefore, Einstein seems to have been intuitively correct that no body will accelerate beyond the speed of light. Attempted acceleration will simply increase the "Static Energy" which we measure as "Mass."]

An interesting situation develops if one equates the two energy expressions. One finds that "m" = "v" in this case. If instead of equating the two expressions, one assumes a constant of zero, then the logical result is that m= -v; i.e. if the mass were exactly equal to the velocity, the total energy content of the system would be zero Both of these conclusions lead to the idea that "mass, " which we consider as being point-centered, may be a measure of the vector component of the angular velocities of the spinning "points" which is directed in the opposite direction of the vector of travel of the entire "body."

While this article is talking about the integration of the momentum definition equation it may be noted that the same thing can be done to the Force equals mass times acceleration equation, F = ma, to obtain analogous expressions to those noted above, as the summation of force over time is known to be momentum, both 1/2 am^2 and 1/2 ma^2 have to be expressions of momentum and presumably can be summed as was energy, giving a similar conclusion to the one postulated above for energy, the guess being that for a stable system momentum summation and energy summation will both be constants.

All of this seems consistent with the idea implicit to the Motion in a Matrix Model that a stable system would most likely be one which involved a fixed number of units of the matrix, or at least a certain fixed amount of "action" in the system. It is to be noted that Planck's constant which relates Energy to Frequency has the dimensions of "Action" or "Angular Momentum" implying that the two terms are synonymous.

--*See: Motion in a matrix...." by this same writer on this web site.

Black Holes ala Motion in a Matrix

The Motion in a Matrix model* for the universe has a very simple explanation for "Black Holes." In the model, mass and energy can be considered as two manifestations of the degree of involvement of the matrix, with mass being associated with the point-centered involvement and energy with motion of that point-centered involvement along a vector. The speed with which this total involvement can move along any given vector is the speed of light. When this involvement, one may call it a vortex or vortex cluster, mass, object, or any other convenient name, reaches the maximum velocity of the speed of light along any given vector, interactions which would usually increase its velocity along that vector increase its "mass."

[This is, in a sense predicted by something which seems to have nothing to do with matrix/motion ideas. The momentum equation, p=mv , can be taken as defining the momentary change of either velocity with respect to time, or mass with respect to time, and "integrated" in either way to give an expression for energy, "E." The usual integration gives the familiar Kinetic Energy formula, KE=1/2 mv^2. The other solution gives an equally valid, "E"=1/2 vm^2, which apparently is unnamed, so we will call it by contrast, "Static Energy." We can say, "It appears that if Kinetic Energy reaches its limit, Static Energy will be increased instead." The would be the same as saying, "If velocity cannot increase, the mass will."]

A Black Hole, then, by the Motion in a Matrix view' is simply any object moving at the maximum velocity along any vector in the matrix. In collisions any interaction that would normally increase its velocity increases its mass. Disturbances related to this interaction are electromagnetic radiation. As the velocity along the vector is such that no light will pass through the object and the object will "flat line" all emissions that it emits behind it, it will be detectable to anything lying along its vector only by the slower disturbances that it causes.

In this view, the idea of an object that causes such a gravitational sink that even light is trapped is conceptually akin to the complex mathematics which can be developed if one insists on an Earth Centered Universe, i.e, the explanation is too complicated if there be a simpler explanation.

The writer in other papers, before the development of "Motion in a Matrix," has stated his opinion that faster than light travel might be possible if one accelerated an object to the speed of light along a vector from an external source and then "kicked in an internal engine." It appears from the above discussion that what would be created would not only be the expected "black hole" from light blockage but that the mass of the object we were trying to accelerate would simply increase while the velocity along the vector would remain "c."

*See Motion in a matrix... by this same writer.