UNRECOGNIZED ASSOCIATIONS IN CURRENT SCIENCE
So the plan has been changed. I’ll simply point to some very interesting correlations, suggest possible conclusions, and then let the reader work through the math at his own leisure as desired. The following items are based on currently accepted mathematical equations, using the currently accepted concepts of dimensions and units of measurement. After the item is discussed in those currently accepted dimensions and units of measurement, the same effect is reconsidered in terms of the "relative" units of measurement suggested in the earlier sections of this document.
To simplify the documentation, and avoid graphics, the term "square root of" is shortened to simply "sqrt" in the following discussion.
COMPARISON OF FREE FALL AND SATELLITE VELOCITIES
An object allowed to free fall from the surface of the earth to the center of the earth will arrive at the center with a velocity of V = sqrt(gR), where g is the "gravitational constant at the surface of the earth, and R is the radius of the earth. That value of velocity "just happens" to be identical to the velocity that would result in weightlessness (orbital condition) if the velocity vector were oriented parallel to the surface of the earth.
The ratio of average velocity of the falling object compared to its final velocity is 0.64. If the object had maintained a constant "orbital velocity" along the surface of the earth for that same period of time, it would have traveled a distance of R/0.64. The ratio of the orbital arc length to earth radius is therefore mathematically equal to the ratio of the average to final velocity of the falling object.
In terms of man’s current dimensional values, the length of travel (R) is approximately 4,000 miles, the time of fall would be about 21 minutes, and the average velocity would be about 16,500 ft/sec. These values would all be subject to change for any other celestial body since "g" and "R" are dependent on the density and radius of the selected celestial body.
When we convert all of the above into terms of relative units of measurement, then the distance of fall and the arc length are both 1 unit of length, the relative time of travel is therefore one unit of time, and the relative value of tangential velocity and average radial velocity is 1.0. Working backwards to solve for "g", it’s value is also found to be simply 1.0. (While not a factor in this example, it should be noted that when the value of "g" is 1, then weight and "mass" are mathematical identities.)
These relative values of unity are all totally independent on the choice of celestial body, and are all therefore, "universal constants" of nature.
GUITUIRE STRINGS AND CENTRIFUGAL FORCES
When a stringed instrument is "plucked", the stretched string is displaced from it’s "at rest" position. The two ends of the string are "fixed" in place due to the attachment points, but the location of the displaced portion of the string travels back and forth both perpendicular to and along the length of the string. The motion of the displacement along the length of the string is called the "transverse velocity". At a few select combinations of vibration, referred to as "harmonic frequencies" the lateral and longitudinal motion of the string, results in fixed "standing waves" along the length of the string.
The equation for the transverse (longitudinal) wave velocity (Vt) has been found to be Vt = sqrt[ F/ (M/R) ] where F is the undisturbed tensional force along the length of the string, M is the total "mass" of the string, and R is the length of the string.
I have noticed an amazing "coincidence" when that same equation is applied to the motion of an orbiting celestial body. The imagined situation is that the tension force is assumed to be due to centrifugal force (MV^2/R), and the mass density (M/R) is assumed to be the mass of the body divided by the radial distance. For that imagined arrangement it turns out that the mathematical value of the transverse velocity (along the radial) must be identical to the mathematical value of the tangential velocity of the body. And it must then follow that the body would move through one radian of arc during the same time that the displacement wave along the imagined string of density traveled from the object to the center point.
If the frequency associated with this imagined string of mass is at one of the "harmonic modes", then the line of mass would remain stationary (a null point along the wave) at the locations of both the object, and the center of rotation. Another amazing "coincidence" perhaps? I believe that this is a very strong clue about some as yet unidentified, underlying significance between the scientific concepts of "mass density", distance and motion. I also believe that it is one more clue that the scientific concept of the vector "velocity" value, should be reconsidered in terms of a scalar concept of instantaneous "motion" which is applicable in an omni-directional fashion.
I have not yet found a current text which explains the velocity of the string in the lateral direction, but the lateral displacement will of course be variable, depending on the distance from the null points, how "hard" the string was plucked, the tensional force, and the material characteristics of the string.
When all of the above is evaluated in terms of relative units of measurement, then the mathematical value of velocity is one, when the length is one, and the equation reduces to Vt=V=1 = sqrt[ F/M ] . Once again we have our old friend back whereby F=M, which in reality is of course simply, Fa=Fn. Conversely, if we start with F=M, then the equation becomes Vt=V=sqrt(R), in which case it must follow that V=R=1.0.
A similar situation must exist in the direction perpendicular to the length of the string. When vibrating at a harmonic frequency, each point along the length of the string must cycle through one half of it’s total lateral displacement during the same time that the longitudinal wave travels through the length of the string. Using the length of that lateral motion as the relative unit of length for that point on the string, then the relative velocity in the lateral direction must also be equal to 1.0 relative unit divided by one unit of time. Each point along the length of the string is acting in the lateral direction in a manner which is mathematically identical (in relative terms) to the action which applies to the entire string along it’s longitudinal axis.
If we consider the lateral displacement of the string in terms of relativity units, we might expect that the lateral velocity of the string at any point along it’s length, would be mathematically equal to the distance of the string at that point, from the "at rest" position of the string. Which would lead us back to the concept of relative elevation for each point along the string, relative to the "at rest" central point (or axis) of the string. In which case a standing wave along the length of the string would be simply a reflection of the "potential velocity" of each part of the string relative to the center "axis" of the system. In essence, each point along the string is acting as a "space-time" frame with the axis of that space-time clock being the undisturbed line of the string. And the entire length of the string is acting in unison within a different space-time frame which is centered around either of the (symmetric) end-points of the string
The implications of this train of thought will "connect" with another thought soon to be presented in the subsequent sections of this document.
There are many equally fascinating "coincidences" of nature waiting to be discovered once the concept of relative units of measurements is recognized as a reality of nature, and it is recognized that all of the "dimensions" are simply different mathematical representations of a single underlying factor of existence. In the interests of time and current document length, we will limit the current discussion.
CENTRIPETAL AND LINEAR ACCELERATION
One more quick point however. The mathematical term "centripetal acceleration" can be shown to be mathematical related to linear acceleration. If the tangential velocity is V, based on any real time duration, then during that time duration the object will undergo deceleration equal to V*cos(angle) in the initial direction of the tangent, and acceleration equal to V*sin(angle) in the direction perpendicular to the initial tangent. By vector addition the resultant value of linear acceleration reduces simply to V, regardless of the radius or length of the arc (or at least up to an arc length associated with a central angle of PI radians).
If we again apply our relative units of measurement then we choose the central angle of one radian when T is one, and then we find the same relationship of acceleration = V times angle/time = V*1/1 or simply 1.0. The same value would apply when we think in terms of a linear acceleration involving the relocation of the orbital object in linear fashion from the tangent point to the center duriing the same unit of time, in which case linear acceleration is (R/T)/T = (1/1)/1 = 1.0. This is just another example of the equal affect of "elevation" as a form of potential velocity, as preveiously discussed.
We are ready to move into the "modern science" realm of history, where the concepts of electro-magnetics, space contraction, and quantum physics and red shift, black holes, and dark matter have been recently introduced.
