THE UNRECOGNIZED DISCOVERY OF RELATIVITY
In the preceding sections, the concept of relative units of distance, motion, and time have been defined and discussed at some length. The underlying concept was that the units of measurement are based on the current existing state of existence between two specific points of interest within the mind of the observer at a specific instant of observation. The unit values are therefore simply 1.0 at every moment of observation. That relative unit value is totally independent of any other pre-defined (irrelevant) unit value, such as a foot of length, pound of force, or second of time, or miles per hour of velocity.
It is not difficult for us to mentally comprehend the concept of the unit of relative distance. However, the concept of relative motion and relative time are indeed difficult to comprehend. At the risk of being repetitious, the underlying thought of motion and relative time will be discussed once again in the following sub-section. Those readers who have already gained adequate understanding of the intended thought may wish to skip ahead to subsequent sub-sections.
A REVIEW OF THE DIFFERENCES BETWEEN RELATIVE MEASUREMENTS VERSUS CURRENT SCIENTIFIC CONCEPTS OF MEASUREMENT
Because the concept of "motion" is based on an infinitesimally short time lapse, the concept is absolute, rather than a variable value. Motion either exists or does not exist. If it does not exist then the concept of "time" is meaningless, because there is no associated change. If motion does exist, then by definition, the unit of "relative time" is that duration of time required for one unit of separation distance to be reduced to zero, based on a continuation of the current motion.
Motion differs from man’s current concept of "velocity" in that velocity can be "measured" only as the result of an actual physical relocation of an object from an initial to a final position during a corresponding lapse of time. Velocity is therefore defined as a "vector" factor having both magnitude and direction. "Motion" however, is an instantaneous state of existence which either is or is not currently occurring. If it is not occurring, "motion" is simply irrelevant. If it is occurring, then it is relevant, but because the associated duration of time is zero, physical movement does not actually occur. In mathematical terms, "motion" is the derivative of velocity as the value of time approaches zero. Because a change in location does not actually occur, motion is a scalar rather than vector factor. In less technical terms, motion is a dimensionless mathematical ratio equal to the average value of velocity when the associated values of distance traversed and duration of time are reduced to zero.
The concept of "motion" is a physically perceivable factor in the current real instant of "time". The concept of "velocity" is a purely imaginary mathematical value requiring mental projection into past (remembered) or future (imagined) states of both time and physical location.
The measurement of time, as used in modern science, is a pre-defined, absolute value which is independent of the current observation. The unit of "relative time" is dependent on the observation of current interest, and is defined as that duration of time required for the current "relative" separation distance between the specific objects of interest to be eliminated based on the current "relative motion". When relative units of measurements are applied to currently defined mathematical equations for "velocity", then the "relative" value of velocity is equal to the unit of relative distance (1.0) divided by the unit of relative time (1.0), and must therefore always have a mathematical value of simply 1.0. Similarly, the relative value of "acceleration" (distance/time squared) must always be simply 1.0
KEPLER’S FIRST LAW
Soon after Nicolaus Copernicus (1473-1543) announced that the Earth and other planets revolved around the Sun, Tycho Brahe (1546-1601) compiled a detailed history of observations about the patterns of motion of the planets. That history of observations was analyzed by Johannes Kepler (1571-1630). Kepler announced two very important observations about his analysis.
Kepler advised that an imaginary line drawn between the Sun and any specific planet would always sweep through a constant amount of area during any pre-defined period of time. In mathematical terms, that announcement advises that the swept area (which is equal to one half the product of tangential velocity of a planet times the radius of the orbit of that planet) is constant: VR/2= K, or VR=2*K=K’. The very interesting conclusion which apparently was overlooked is that if VR=K’, then it must follow that the mathematical value of V must be identical to the inverse value of R. This may have been mankind’s earliest clue about the (then unknown) concept of relativity. It was an obvious clue that the dimension man has defined by the word "distance" is mathematically related to the term man has defined as "tangential velocity".
Now let us apply the concepts of "relative" dimensional values to Kepler’s equation. The relative unit of distance for the Sun-planet system is simply 1.0. When we apply that relative value of length to the value of velocity, then the unit of length associated with the tangential velocity changes from V=L/dT to V=(L/R)/dT. But the relative unit of time is that time required for the dissipation of one unit of length (based on current motion). Hence the unit of time is that lapse of time associated with the motion of the planet through one unit of space (R). If follows that when (L/R) is equal to 1.0, then the value of dissipated time is also equal to 1.0, and the value of relative velocity under that condition reduces simply to 1.0/1.0 = 1.0. We conclude that when the value of L is equal to the value of R, then the value of T is equal to 1.0 Look now at the significance of the distance L. This value is the length of the arc through which the planet moved during it’s orbital path around the Sun. And with that recognition, we become aware then when L=R, then the angular rotation of the orbiting planet must , by definition of the term "radian" of angle, be exactly one radian.
What we have determined is that when the planet moves through one radian of rotation around the sun, the values of relative distance, relative time and the length of the arc all have identical mathematical values of 1.0. Which in turn, requires that the mathematical value of the modern words of tangential velocity, and centripetal acceleration also be equal to simply 1.0. That is R=L=T=Velocity=Acceleration= Angle =1.0.
That amazing "coincidence" of identical values must apply for all the orbiting planets. Again, it is very important to realize that these mathematical factors in no way affect the human observations of the motion of the planets around the sun. It is only the imaginary mathematics used to describe the observation that has been affected.
Even more interesting is the "coincidence" that the same relationships apply to a single spherical celestial body rotating around it own axis - such as the rotation of the Earth on its axis. When the radius associated with any point on the surface of the Earth is related to its center point (along the axis of rotation) is used as the relative unit of length, then the length of the arc traversed by that point will be equal to the radius when the relative unit of time is one, and the subtended arc angle is one radian. The associated mathematical values of relative distance, relative time, and relative velocity would all be simply 1.0. These relative mathematical values would remain for the point to center of rotation for every other point on, or inside the surface of the Earth.
In contrast, when we use our current system of (irrelevant) units of measurement, then the mathematical value of radius would vary as a function of latitude from zero to 4000 miles, and the mathematiical value of the time requried for the tangential arc length to equal the applicable length of the radius would be one day divided by 2*PI, or about 3.8 hours. The tangential velocity would be reported in terms such as miles per hour, and would range from about 1000 mph at the equator to 0 mph at the north and south poles.
From this comparison, the possible improvement in both simplicity of measurements and associated (imaginary) mathematics made possible through the use of "relative" units of measurement (in lieu of the our current system of fixed, irrelevant units) is obvious.
Kepler’s studies also resulted in the conclusion that a mathematical relationship exists between the radius of rotation and period of rotation for the family of planets. He advised that the square of the period of rotation divided by the cube of the radius was a mathematical constant that applied to the entire family of planets: P^2/R^3 =K.
Using modern (absolute) units of measurement, the period of rotation is equal to the circumference of the orbit divided by the tangential velocity of the planet: P=2PI*R/V. Substituting, Kepler’s equation becomes (2PI/V)^2/R=K, or RV^2=[(2PI)^2]/K =K’.
From this it is clear that the mathematical value of the radius of any planet must be proportional to the inverse value of the square of the tangential velocity of that same planet.
Once again, it becomes obvious that there is a direct mathematical relationship between the factors man perceives as distance and has defined as velocity. However, this is not the same mathematical relationship which exists when the observation of interest was limited to a single planet.
Now once again, let us apply the concept of "relative" units of values. We are aware that the unit of length is R, and that the relative distance of R=V =1 when the angle of rotation of the planet around the Sun is one radian. Kepler’s equation is based not on one radian of rotation but rather a complete orbit which encompasses 2PI radians. In terms of relative units of measurement, his equation becomes 1 (unit of distance) times 1^2 (units of motion)=2PI (units of time) divided by K. or simply 1=2PI/K. And from that result it becomes clear that the value of K is simply 2PI or simply the number of relative units of time involved during one complete rotation of the planet around the Sun.
