The Structure of the Physical Universe
Magnitudes <<<———->>>>> Formation
Material Sector Dimensions
Three Dimensions of Motion
Description:
Since the time aspect of the SUDR progresses uniformly, and the space aspect of the TUDR progresses uniformly, but the progression of the space aspect of the SUDR, and the time aspect of the TUDR, are continuously reversing, the SUDR is stationary in space, but progressing in time, while the TUDR is stationary in time, while progressing in space. Figure 1 illustrates this in a world line chart.
Figure 1. Stationary SUDR (S) and TUDR (T)
However, this also means that they can come into contact and combine, since a SUDR’s stationary space position may be in the path of a TUDR’s space progression, and a TUDR’s stationary time position may be in the path of a SUDR’s time progression. Figure 2 illustrates the SUDR|TUDR combination.
Figure 2. SUDR and TUDR Combine as SUDR|TUDR (S|T) Combo
In figure 2, the S|T combo is identified as a photon, but this has not yet been established.
First Reciprocal Number
The mathematical expression of the S|T combo is called the first reciprocal number (RN). The RN is the first number of the new scalar mathematics called the Reciprocal System of Mathematics (RSM). It has three terms, instead of two
(1|2 + 2|1) —-> (1|2 + 1|1 + 2|1),
where the pipe symbol indicates the fraction is operationally interpreted as a displacement, and the middle term accounts for the inward component of the total motion. Without the middle term, the sum of the motion in the S|T combo would be
(1|2 + 2|1) = 3|3,
which is incorrect, since it omits the inward component of the combined motion. The correct algebraic sum is
(1|2 + 2|1) —-> (1|2 + 1|1 + 2|1) = 4|4 num, [1]
where num is short for “natural units of motion.” In other words, because the “direction” reversals confine the progression of the reversing aspect to one unit, the inward/outward cycle actually constitutes two units of motion. Consequently, since the one-unit, increasing, portion of the ratio is only half of the two-unit cycle, the one-unit, decreasing, portion, constituting the second half of the two-unit cycle, is captured in the middle term.
The most general form of the RN is
((xn|2xn) + (xn|yn) + (2yn|yn)), [2]
where x is the number of SUDRs and the y is the number of TUDRs in the S|T combo. When n = x = y = 1, equation [1] is obtained.
The three, scalar, terms of equation [2] constitute three, scalar, “directions” of scalar motion. In the material sector, the physical dimension of the numerator in each term is space progression, and the physical dimension of the denominator in each term is time progression. When these dimensions are assigned units in the SI system, the natural unit of motion is c, or 2.997930 x 1010 cm/sec. In assigning units to the space and time dimensions, Larson first derived the natural unit of time, by assuming that the Rydberg frequency of hydrogen constitutes a manifestation of the basic unit of time. He explains in Chapter 13 of Nothing But Motion:
From the manner in which the Rydberg frequency appears in the mathematics of radiation, particularly in such simple relations as the Balmer series of spectral lines, it is evident that this frequency is another physical manifestation of a natural unit, similar in this respect to the speed of light. It is customarily expressed in cycles per second on the assumption that it is a function of time only. From the explanation previously given, it is apparent that the frequency of radiation is actually a velocity. The cycle is an oscillating motion over a spatial or temporal path, and it is possible to use the cycle as a unit only because that path is constant. The true unit is one unit of space per unit of time (or the inverse of this quantity). This is the equivalent of one half-cycle per unit of time rather than one full cycle, as a full cycle involves one unit of space in each direction. For present purposes the measured value of the Rydberg frequency should therefore be expressed as 6.576115 x 1015 half-cycles per second. The natural unit of time is the reciprocal of this figure, or 1.520655 x 10-16 seconds. Multiplying the unit of time by the natural unit of speed, we obtain the value of the natural unit of space, 4.558816 x 10-6 centimeters.
In the development of the consequences of the RST, here at the LRC, we accept this assumption, as a starting point, but also recognize the possibility that the Rydberg frequency of hydrogen may not be a manifestation of the natural unit of time. Only time will tell, if some other unit is necessary, but in the meantime, we follow Larson’s lead in adopting the Rydberg frequency, as the basis for determining the natural unit of time.
The latest value of this frequency is 3.2899 x 1015 Hz. Doubling this frequency, because the full cycle of the reversals totals two units of motion, we get 6.5798 x 1015 Hz, the time component of which is the reciprocal of this number, or 1.519803 x 10-16 seconds, as the natural unit of time.
The natural unit of space is then obtained by multiplying the natural unit of motion, c, by the natural unit of time. The latest value of c is 2.99792458 x 1010 cm/sec, so multiplying this number by 1.519803 x 10-16 would give us 4.556255 x 10-6 cm, as the natural unit of space.
However, the centimeter unit is a one-dimensional unit of length, while the scalar unit of space, like the scalar unit of time, cannot be one-dimensional, because scalar magnitudes do not have direction, and, in a three-dimensional system such as that assumed in the first fundamental postulate of the RST, the natural unit of space, as the basic unit of scalar increase in the material sector, must be a unit increase in all directions of a 3D volume, in order to be a magnitude of scalar motion existing in three dimensions. Naively, therefore, the 4.556255 x 10-6 cm unit would have to be the radius of the natural unit of space, which is actually a volume unit, or 4/3 * pi * (4.556255 x 10-6)3 = 3.961983 x 10-16 cubic cm.
However, a 3D scalar expansion of space expands from a point outward in all three dimensions simultaneously and therefore has the four dimensions of a 1x2x2x2 stack of unit cubes: Namely, the 0 dimension of the point, the 1 dimension of the line, the 2 dimensions of the area and the 3 dimensions of the volume. Each of these four dimensions has two “directions,” the 20 = 1 “direction” of the point, the 21=2 “directions” of the line, the 22=4 “directions” of the area and the 23=8 “directions” of the volume.
In addition to the physical dimensions of space and time in the material sector, the three geometric dimensions of all directions in space and the zero dimensions of time, scalar motion has the three scalar dimensions of motion represented by the three terms of equation [2]:
- The time-like “direction” of the (xn/2xn) term (less than unity).
- The space-like “direction” of the (2yn/yn) term (greater than unity).
- The light-like, “direction” of the (xn/yn) term (equal to unity).
These three “directions” must be understood in terms of the reciprocity, or the duality, of the RST concept of space|time; that is, in the material sector, speed-displacement is to be understood either as a time-displacement, which is less than unity (red color), or a space-displacement, which is greater than unity (blue color). However, when these two types of speed-displacement are combined, in an S|T unit, the inward component of the less than unity displacement, and the inward component of the greater than unity displacement, constitute a third magnitude, which can be displaced or not, and, if displaced, takes the form of a time-like, or space-like, displacement.
Of course, the middle term of inward motion is not an independent term, but is determined by the relative values of x and y. Thus, the inward term, (S|T)Inward, is equal to the ratio of x to y, or
(S|T)I = x/y,
the number of SUDRs relative to the number of TUDRs in a given S|T combo. If x = y, then the value of the inward term is unity, but if x > y, then the inward term is inward space-wise, and, if x < y, the inward term is inward time-wise.
Now, when we consider the geometric dimensions of the physical dimensions, we find that the number of space dimensions of the SUDR is three, while the number of time dimensions is zero. The “geometric” dimensions of the TUDR are the inverse of those of the SUDR; that is, the number of time dimensions of the TUDR is three, while the number of space dimensions is zero. This follows mathematically from the binomial expansion, where 20 = 1 is the number of “directions” in the SUDR’s time dimension, 21 = 2 is the number of “directions” in its first space dimension, 22 = 4 is the number of “directions” in its second space dimension, and 23 = 8 is the number of “directions” in its third space dimension. Again, the “geometric” dimensions of the TUDR are just the inverse of these.
Adding these dimensions to the numbers of equation [2], we get:
((x3n|2x0n) + (x3n|y3n) + (2y0n|y3n)), [3]
which, numerically, because both x and y are equal to 2, works out to
8|2 + 8|8 + 2|8 = 18|18 num,
But, if we change our view from the algebriac equation of displacement units to the mathematical function of space and time, by recalling that the middle term was introduced to account for the spatial and temporal oscillations of the SUDR and TUDR, and we treat the terms in the equation, representing spatial and temporal expansions, as inverse rotations, then we get
16|2 + 2|16 —> (2π/1)|(2π/1) = 2π + 2π = 4π radians of rotation, [4]
in the sense of total rotations, if one cycle of expansion/contraction is equivalent to 2π radians of rotation. In other words, it takes two, 2π rotations, to complete one cycle.
Consequently, just as the heart of conventional physics is found in the dynamics of momentum and position, as captured in terms of the Hamiltonian, the power of equation [4] is in its dynamics and the symmetry of the dynamics, implying a law of conservation through change; that is, as the SUDR|TUDR combination oscillates, time volume is exchanged for space volume and vice versa, or velocity is exchanged for inverse velocity, as time and space increase, but the total motion, in natural units, represented by the number 4π, is conserved, just as the total energy in the dynamics of a swinging pendulum is preserved, as it is transformed from kinetic energy to potential energy and back again in the form of changing conjugate variables, momentum and position.
Of course, it’s easy to see that neither a change of momentum nor a change of position can be defined in these scalar space|time terms. Change of momentum can’t be defined, because there is no moving mass involved, and change of position can’t be defined, because the process is one in which nothing actually moves. It is more of growth process than a moving process. A 20 unit grows, or is transformed, into a 23 unit, and then it shrinks back to a 20 unit, continuously.
Obviously, this means that a whole new system of physics is portended by these concepts.
(to be continued)
Discuss the Three Dimensions of Motion Description
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The RSt Concept
Larson didn’t use the LRC terminology, UPR, SUDR, TUDR, etc, and although he concluded not to investigate the consequences of the continuous “direction” reversals, opting for “another possibility” instead, his concept of the time unit speed-displacement (SUDR) and the space unit speed-displacement (TUDR) is identical. As it turns out, the other possibility that he followed in his development (see Chapter IV of NBM) is an alternate pattern of “direction” reversals that, instead of being continuous, is periodic, and this pattern is the pattern of the SUDR|TUDR combo, even though Larson didn’t realize it.
Discuss the RSt Concept
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The LRC Concept
The Net Zero Project, which was the forerunner of the LRC, gets its name from the fact that the space aspect of the SUDR progression is a net zero motion, and the time aspect of the TUDR progression is net zero motion. When the SUDR and TUDR progressions are combined, however, the time progression of the SUDR and the space progression of the TUDR combine to produce a space/time progression they don’t have apart. Hence, the SUDR|TUDR combo propagates outward in both space/time, while the isolated SUDRS are stationary in space, and the isolated TUDRs are stationary in time, as shown in figure 2 above.
As a result of this propagation motion, the possibility of the S|T combo interacting with both SUDRs, stationary in space, and TUDRs, stationary in time, arises. The purpose of the SPUD is to document the results of these interactions, using hyperlinks to explore the possibilities of various interaction sequences.
Discuss the LRC Concept
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The LST Concept
The LST community doesn’t recognize scalar motion, but only the vectorial motion of objects or fields. Thus, since motion is limited to less than c-speed, in the vectorial system, nothing can exist below the green diagonal lines of the world line charts in the two figures above, since the speeds below the green line are greater than c-speed. However, in the scalar system, greater than c-speed is actually inverse speed, and since objects, or fields, are not part of the motion, these speeds are quite possible.
Discuss the LST Concept
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