THE ESSENCE OF SPACE-TIME RELATIONSHIPS
It is now clear, that if we consider the relative unit of distance applicable to any two points of interest, and then define the unit of time as that time associated with possible merger of the two points, assuming current rate of relative motion remained unchanged, then the modern concept of variable values of velocity and acceleration (both linear and centripetal) become fixed constants equal simply to 1.0. Further more, as a result of that relationship, the modern concept of "mass" is shown to be nothing more than a reflection of "force".
We can begin to think of nature in terms of the face of a giant clock which rotates around a common center at a constant rate of one radian per unit of time. Every "fixed" point within the face of the clock rotates at an angular rate of one radian per unit of relative time. The relative unit of distance applicable to every point is based on the specific radial distance of that point. It must follow that the tangential velocity, (based on relative units of measurement) is identical for every point in that clock.
This model can be applied in either two or three dimensions. The two dimensional (planar) version can be expanded to the third by simply extending the center point of the two dimensional clock into a central axis of rotation for a three dimensional sphere. Actually, the three dimensional version may take any shape, but it is easier to visualize the arrangement if we visualize it as a sphere - such as our own Earth.
SPACE-TIME FRAMES
The obvious question which must immediately arise is what is the nature of that central axis of rotation, and is there more than one "clock". If so, then what determines which parts of the universe are associated with which clocks.
The ultimate answer may well be that there is one master clock which encompasses all parts of all clocks. But there are also an infinite number of smaller clocks, and each of the smaller clocks become only one specific "point" within a sequence of increasingly larger clocks. This is analogous to an electron being part of a clock which science refers to as an atom, an atom being a single "part" of a larger clock referred to as a physical object, the object being a single point on the Earth, the Earth a part of the solar system clock, the solar system part off the galaxy, etc, until eventually all parts of the universe are combined into the ultimate single "universal" clock.
What then determines which clock is of primary concern to an observer? The answer is so simple and so obvious that it is actually amusing. Every individual point within the universe is one center of rotation of one such clock. To aid the discussion, we shall consider the "center of consciousness" (whatever that may be) of one specific person as one "point" within the universe. We shall place that "point" on the surface of one celestial body (such as Earth). As that person observes his surroundings he perceives many other objects. If those objects are at equal "elevation" to himself, and there is no relative motion between himself and the observed object, then the person and that object share a common "clock", or "space-time frame". That means that the man and the object must be moving in unison around some third, common center of rotation (or clock). The man and the "fixed" object are in essence two "points" which share a location on the same "clock", and they therefore share a common space-time frame of relativity.
DIFFERENCES IN "ELEVATION" (RADIAL DISTANCES)
If there is no relative motion between man and object, but the object is at a different elevation then the man, then a "potential velocity difference exists" between the man and the object. That difference in elevation (or potential velocity difference) is an indication that the man and object share a common axis of rotation, but that their radial distances from the common axis are different. If the object "falls" so that it then is at equal "elevation" as the man, then the potential velocity difference would be converted into an actual (perceivable) velocity difference. During that fall, the original unit of length applicable to the object (equal to the original radial distance from the common center) is reduced to a final unit of length (equal to the final radial distance). That change is described by current science as a change in "velocity". However, in terms of our relative units of measurement, it was not "velocity" which changed, but only the associated unit of relative length applicable to the object. The factor of time, simply does not enter into the situation.
However, the significance of the word "elevation" (or radius) is important because it is critical to the concept of the word "fall". A difference in "elevation" exists because the man and the object are both attracted to a common third point. In this example, that point of mutual attraction is simply the center of the Earth. That attraction is of course the factor which Newton associated with "gravity" and "mass attraction". (We will come back to these terms again.) If objects (in our example, the man and the object) are mutually attracted to any third point, then the objects share a mutual center of rotation which forms the center point of a common clock.
RELATIVE MOTION WHEN ELEVATION IS CONSTANT
If the man perceives relative motion of an object which is at equal elevation as himself, that is an indication that there is a "potential" difference in elevation between the man and the object. If the man considers himself as being at rest, and that all of the perceived motion is due to the object, then the amount of that current motion could be reduced to zero if the object were elevated to a level where the ratio of the radial distances from the common center of attraction was changed in direct proportion to the inverse ratio of the perceived tangential velocities. This is exactly what Kepler’s first law revealed, when that law is presented in the form RV=K. And, as has already been shown, since the relative value of both R and V must always be simply, one, it follows that the value of K must be 1.0. In which case, that which science has defined as "velocity" is simply a reciprocal relationship of that which science has defined as "radius".
Relative motion and relative elevation are therefore simply mirror values of one common state of relativity. When man perceives a difference in elevation, or perceives relative motion, those differences do indeed exist. But the associated (imaginary) mathematics between those two perceptions is not a reality. The mathematical difference exists only as a result of the words which man created in an effort to communicate about the actual perception. A difference in elevation is identical to a potential difference in motion, and visa versa.
MUTUAL ATTRACTION TO A COMMON CENTER
In the second installment of this document, "Evolution of Science, " the imaginative genius of Isaac Newton was praised, but the logic underlying his choice of mathematics was challenged. It is now time for the writer to "fish or cut bait" in regard to that challenge.
While Newton’s mathematics may be incorrect, he was obviously correct in his recognition that some form of attractive force must exist between the objects within our physical universe. While his choice of words to explain a related repulsive force was poor, he was obviously correct in his recognition that some form of repulsive force must also exist between the objects within our physical universe.
In the preceding section (this page) reference was made to two objects being mutually attracted to a common center of rotation. That certainly sounds like Newton’s thought of "mass attraction". And indeed it is similar. However, there was no need to create the word "mass", for the attraction is attributable solely to the word "radius". Similarly, the thought of "repulsion" bears resemblance to the word "centripetal force". However, there was no need to create the word centripetal force, for the repulsion is attributable solely to the words "tangential velocity" (or simply motion).
Attraction and repulsion are not opposites. They are reciprocal values of a single state of relativity. When we begin to think in terms of relative units of measurement, then that condition of reciprocal characteristics is perhaps most easily recognized to modern man by relating the two in the form of angular rate of rotation. The mathematical value of angular rate of rotation is equal to tangential velocity divided by radius. In that form we can recognize that the value of angular rotation will increase in direct proportion to the value of tangential velocity and inversely in proportion to the value of radius of rotation. Conversely, the value of angular rotation will decrease in direct proportion to to radius, and inversely in proportion to the radius of rotation. If we associate angular rotational rate with attraction, then it becomes clear that repulsion is simply the reciprocal value of attraction.
But when the concept of angular rotation is considered in terms of the relative units of measure, then by the definition of the unit of time the mathematical value of velocity (or relative motion) must always be identical to the mathematical value of radius. And it then becomes clear that value of the ratio of the two is 1.0. The attraction and repulsion forces must always be in balance. We are back once again to the correct interpretation of Newton’s "rolling ball" experiment that Fa/Fn=1, or simply that Fa = Fn. A strong point in Newton’s favor here is that this realty was initially introduced by Newton in his statement that "for every action there is an opposite and equal reaction". Which again is an obvious statement that it is impossible to push on any object (stationary or moving) unless that object resists with an equal and opposite force. Modern science normally attributes the resistance force in terms of the "structural strength" of an object which resists motion, and "mass" of an object which yields to the applied force. However, both terms are identical in that they represent equal and opposite forces to an applied force. The only difference is that in one case the object refuses to change its current state of motion, while in the other case the object does change its current state of motion as a result of the applied force.
WHAT ABOUT THAT UNIVERSAL CONSTANT OF "G"
We are aware that a celestial orbital condition involves the mutual rotation of the two bodies around a common center of rotation (or center of gravity if you insist) with equal angular velocity. We are also aware that the ratio of the radii must be mathematically identical to the ratio of the tangential velocity, and inversely proportional to the ratio of the "mass" values: That is R1:R2 = V1:V2= M2:M1.
Now let us apply that knowledge. We will assign a fixed mathematical value of 1 to the "mass", tangential velocity, and radius of rotation to the first of two celestial bodies. Then we shall assume a range of possible mathematical values for the "mass" of the second body. Let the range of "mass" of the second body vary from M1 to many, many times M1.
When the two bodies have equal mass (M2=M1) then M2:M1=1 and it must follow that R2:R1=1. We have a condition analogous to two equal weight children playing on a see-saw. At this condition, we shall "freeze the postion of the mutual center of rotation relative to M1.
Now let the value of M2 begin to increase, while M1, R1, and the location of the center of rotation remain fixed. As M2 increases, the value of R2 must decrease. This is analogous to a heavy child moving inward (toward the pivot point) on a playground see-saw board to offset the effect of his excess weight over that of the lighter child.
The geometric situation is depicted in the figure below for three different possible of values of M2:M1:
Now apply the current scientific concept that the centripetal force exerted by the celestial bodies (MV^2/R) is the cause of the "mass attraction" between the two bodies which causes them to remain in orbit. Mathematically, Fc = Fg = GM1M2/(R1+R2)^2.
We are aware that the mathematical value of the centripetal force exerted on both bodies must be identical. Then the mathematical equation of equality is M1V1^2/R1 = M2V2^2/R2 = GM1M2/(R1+R2)^2. To simplify, we know that the centripetal force must be simply M1V1^2/R1= 1*1^2/1 = 1. It must follow that GM1M2/(R1+R2)^2 = 1.0, and since M1 and R1 are 1.0, this reduces to 1.0=G*M2/(1+R2)^2.
Substitute M2=M1*(R1/R2) = 1*(1/R2) = 1/R2 in the preceding equation to get G=1/M2+2/M2^2+1/M2^3. Let M2 then vary from 1 (when M2=M1), to infinity (when M2 >>M1). The conclusion is that the mathematical value of that "universal constant" of G must actually be a variable. For example, when M2 = 1, then the value of G is 4.0. When the value of M2 is 2, then the value of G is 1.125. When the value of M2 is 10 the value of G must be 0.121.
As we continue to increase the value of M2, the value of "G" must continue to decrease, until eventually it approaches simply 1/M2. (Due to the predominance of the 1/M2 term in the equation in relation to the other terms.)
We are forced to the one of two conclusions. Either the currently accepted concept which forms the basis of "mass attraction" is false, or else "G" is not a "universal constant". If both those "accepted" concepts are valid, then the distance between every pair of mutually rotating celestial bodies throughout the universe would have be be identical. For example, the distance between Earth and moon would have to be identical to the distance between Earth and Sun.
We have come far in our journey. Time for another break to reflect on the thought which has hopefully been transferred up to this point.
