Critics, which include much of the mainstream scientific community, generally consider the RST to be pseudoscience, charging that it is untestable by the scientific method and is thus unfalsifiable. Most physicists today who are aware of the Reciprocal System of Theory dismiss it outright because the RST lacks a mathematical basis which makes its predictive powers and thus utility minimal. In their view, its present form does not contain any mathematical properties and therefore does not make exact numerical predictions, making it impossible to compare and test the RST against the established scientific theories.
Larson’s arguments that this notion is misguided have fallen on deaf ears mostly, because scientists have become completely accustomed to equating mathematical complexity with complex theory. But members of ISUS point out that one prominent physicist and mathematician has gone to great lengths to prove, though it may seem counterintuitive, that simple models can actually produce greater complexity than complex models.
They cite Dr. Stephan Wolfram’s work, entitled A New Kind of Science, which among other things demonstrates that the simple rules of cellular automata (CA) can easily produce random and very complex behavior in discrete systems, which he contends is a capability of simple computational algorithms in general, both discrete and continuous. But, it’s Dr. Wolfram’s contention that complex mathematical models based on partial differential equations, for instance, are much more difficult to use for the study of complex behavior. Even so, he notes that they have been studied for 'about two hundred years' and that
But, he concludes, all this effort to construct complex mathematical models to explain nature may have been an unfortunate accident of history for if computers and knowledge of discrete systems had been discovered sooner, all this effort might have been avoided
Dr. Wolfram goes on to write that after all is said and done 'almost all the work [on continuous systems] has concentrated on just [three] specific equations' and their equivalents, which yield only simple behavior in the end. The three equations, he says, are the diffusion equation[?], the wave equation and the sineGordon soliton equation[?]. While Wolfram manages to show that it is possible to elicit complex behavior from continuous systems such as partial differential equations, he emphasizes the point that the phenomenon of complex behavior, which he discovered in his work, was 'immensely easier to discover in discrete systems.'
Other scientists have asserted the same argument. Donald Greenspan, in his book Discrete Models (AddisonWesley Publishing Company, 1973), states that the basic assumption of his book is that:
This, he observes, makes it possible for one interested in studying physics to have to 'be equipped only with the rudimentary mathematical knowledge of arithmetic and algebra in order to study highly complex physical phenomena.'
Edward Fredkin, Department of Physics, Boston University, coining a new term to describe his work with discrete systems, also argues for their superior suitability for the study of physics in a paper entitled Digital Mechanics An Informational Process Based on Reversible Universal Cellular Automata:
ISUS members insist that it must be recognized that simple programs, consisting of a few rules which stipulate how the state of a discrete system should change as its rules are repeatedly applied to the current state of its system, are a legitimate approach to the study of nature and are analogous to the central concepts of Larson’s RST. They claim that, like these simple computer algorithms in the work of Dr. Wolfram’s and others, the RST produces very complex results as a consequence of its application, and not by virtue of a complex mathematical model.
ISUS members argue that Dr. Wolfram’s discovery that simple discrete systems are able to produce great complexity is a very important fact that the critics who protest that the RST has 'no mathematical basis' need to grasp. Though very different than the complex continuous systems traditionally employed in the study of physics, the discrete system of the RST is nevertheless capable of generating complex theoretical structures whose properties are consistently and logically derived and can be tested just as much as the results of any other system can be tested, by comparing them with experimental data.
ISUS asserts that the discovery of Dr. Wolfram firmly establishes that there is no requirement for complex mathematical formulations in discrete systems such as the RST and that, as a result, the argument that the lack thereof is prima facia evidence of the inability of the system to make 'exact numerical predictions, making it impossible to compare and test the RST against established scientific theories,' is completely unfounded.
The basic ideas of the Reciprocal System of Theory
That the RST is indeed a simple discrete system can be seen clearly from its fundamental postulates:
According to its author, the RST is called a system of theory, as opposed to a theory, to indicate that it consists of a means for deriving a subset of theories corresponding to other physical theories such as the theory of relativity, the nuclear theory of the atom or the kinetic theory. The term reciprocal refers to the key concept of the RST that reflects the postulated relationship of space and time as reciprocals of each other in the definition of motion.
Figure 1 shows the output of such a program. The CA rule number 254 as shown by Wolfram produces black cells that are mirror images of one another extending horizontally from the center column outward in opposite directions. Notice how that with each iteration of the program (each new row) a black cell is added to each side of the center column. In this case, the ratio of the number of black cells produced on the left, to the number of black cells produced on the right, is 1:1.
Figure 1. Output of Cellular Automaton 254 and RST Adaptation
In Dr. Wolfram’s work, the output of a CA such as that in figure 1 is usually treated as if 'space' were represented horizontally and 'time' vertically. However, if instead we designate the left side as 'space' and the right side as 'time,' we have a complete representation of scalar motion in one dimension. Here, in one symbol, space and time are represented as the inverse of one another and as expanding outward at a oneforone, or unit (1/1), rate. Notice that no vector, that is, no direction in space, is indicated here. This is because scalar quantities have no vector in space, they can only increase or decrease relative to some reference or datum. Thus a 'direction' of up or down, in or out, away or towards, relative to such a datum may be ascribed to the scalar value, but it has no direction in coordinate space as a vector does.
But it’s interesting to note that figure 1 is more than a symbolic representation too for if we assign values to these 'space' and 'time' cells we can then calculate the quotient or speed of the 'motion' being computed by the program. In fact, if we assign the proper values to the units of space and time, the speed calculated is the speed of light (c) and the output can be considered as an analog or simulation of the expansion of space and time in one dimension and thus might be used in a quantitative manner as well as in the qualitative sense that it is used here. In fact, it is the determination of these unit values of space and time that enables Larson to derive quantitative values for subsequent entities in the RST.
Notice once again that threedimensional scalar motion cannot be expressed as a vector however. Scalar motion can have no direction in space other than outward or inward. Most people are unfamiliar with this type of motion, because scientists have not studied the nature of it much, but it’s the type of motion that is similar to the motion of the surface of an expanding balloon. In scalar motion such as this, direction is relative to the chosen reference point. Since every point on the balloon is moving away from every other point on the balloon, the direction of any given point with reference to any other given point is simply outward when the balloon is inflating or inward when it is deflating.
The origin, or datum, of this frame of reference is unity (s/t = 1). Larson sees this natural frame of reference as the true reference of motion, while what he calls a ‘coordinate frame of reference’ is the ordinary frame of reference of our everyday experience, which we are accustomed to using to measure the motion of objects. Larson theorizes that the effect of the natural Progression is to disperse the locations of space and the ‘locations’ of time in three dimensions. The expansion of space over time produces a featureless universe of expanding space with no physical entities, as does the expansion of time over space (the RST concept of ‘locations’ of time expanding over space will be discussed more fully below).
Now let us turn once again to figure 1 to help us in understanding this new concept of time or space displacement. As previously explained, figure 1 results from a simple algorithm called CA rule 254 by Dr. Wolfram, which produces 1 additional black cell on either side of the center column with each iteration of the program, which maintains the ratio of left to right cells at 1:1. But suppose one found another CA rule that produced more black cells on one side than it produced on the other side of the center column. Such a program would generate a graphic similar to figure 2 where the edge of the left side of the triangle is displaced inward from the position it would have otherwise obtained with rule 254, which expands outward at a 1:1 ratio or what Larson would call unit speed, 1/1.
Figure 2. Time and space displacement.
If the displacement ratio were say ½ and we used the same convention for space and time as in figure 1, we would find twice as many 'time' units (on the right side) as 'space' units (on the left side.) This condition is called a time displacement, because the larger term (2 in this case) is in the denominator of the ratio ½ even though the less effective 'space' progression actually causes the displacement. Clearly, the opposite condition could also exist where a greater number of 'space' than 'time' units is produced and we would term that condition a space displacement.
But notice what has happened in terms of the scalar motion itself. As the time aspect of the motion increases, relative to its space aspect, its value, or speed, is decreased. That is, it decreases from its maximum value at unit speed to something less than unit speed. Clearly, increasing the displacement, or space to time ratio, is limited as the speed would continue to decrease to the point of approaching zero (that is, the slope of the displacement line would approach the vertical.) This is an important point the consequences of which are beyond the scope of this article, but for now suffice it to say again that the natural datum of measurement in this system is not zero, as is usually the case in most physical systems, but rather it is unity and displacement of time or space is always away from unity towards zero.
Notice that the concept of space and time being reciprocals makes it theoretically possible to express motion in time (t/s, s >1) as the inverse of motion in space. However, Larson stresses that this is not the concept of 'time travel' wherein one might imagine traveling up or down the 'stream' of time, but only a simple relation of time to space, which is the inverse of motion in space (s/t, t >1). Larson designates the time displacement side of the system as the 'Material' sector (motion in space) and the space displacement side of the system as the 'Cosmic' sector (motion in time.) This concept too has immense consequences but discussion of them is beyond our present scope.
Now recalling Larson’s assumption that in the RST motion exists in three dimensions, one can see that either a time or space displacement is possible in one or more given dimensions. But while a simple, discrete algorithm produced the analogous displacements we have examined in figures 1 and 2, Larson, restricted by the rules, or the fundamental postulates of the RST, had to find a motion consistent with those postulates that could produce such a displacement in nature.
He found that if he assumed that a linear oscillation, a motion of harmonic vibration, occurred in the 'direction' of the natural progression of space such that the 'direction' of the space progression oscillated from the outward 'direction' to the inward 'direction,' then the outward progression of space in the affected dimension would be less than the corresponding outward progression of time (s/t = 1/n, n > 1). That is, just as in the CA of figure 2, the units of space that progress in the space progression as compared to the corresponding units of time that progress in the time progression, is less due to a periodic reversal in the 'direction' of the space progression, which occurs on the space side of the equation, reducing the space that effectively progresses outward as compared to the time, which continues to progress outward in the normal manner. Thus, the ratio of space to time is altered in this case from unity to some value less than unity depending on the frequency of the linear vibration in the affected dimension.
Figure 3 shows three graphics representing each of the three dimensions of a unit of scalar motion. One should be careful here, however. To avoid confusion in the RST, it is important to distinguish the dimensions of scalar motion from the dimensions of coordinate space, or the extension space of our ordinary experience as Larson calls it. The three coordinates of extension space, x, y and z, are only capable of representing one dimension of scalar motion as a vector. This is because all three coordinates are required to define a vector in extension space for any one dimension of scalar motion, and all vectors with a common origin must be summed into a resultant vector. This and the fact that the datum of coordinate space, or its point of reference, is zero, not unity as it is with the postulated scalar motion, makes it impossible to represent more than one dimension of scalar motion in coordinate space. Larson asserts that one consequence of this fact is that two dimensional and threedimensional motions are not currently recognized as motions, but are erroneously attributed to "force fields" such as socalled electrostatic, magnetetic and even gravitational "fields." Larson contends that force is a property of motion and cannot exist independently of it, at least in the RST.
Figure 3. ThreeDimensional Scalar Motion with Displacement in One Dimension.
With this dual use of the word dimension in mind, let the first graphic on the left hand side in figure 3 indicate a time displacement in one scalar dimension, while the two graphics to its right show no displacement at all in the other two scalar dimensions. Since the scalar motion in the two undisplaced dimensions of this threedimensional unit of motion remains at unit speed, this theoretical entity would then be oscillating at some frequency in one scalar dimension, but moving at unit speed (c) in one of the other two scalar dimensions. Larson identifies this type of theoretical entity with the physical radiating photon. The direction of the photon, its vector, described by the three coordinates, x, y, and z in extension space, is dependent upon the laws of probability, the orientation of its source in extension space, and any intervening objects in its path. But the motion of the photon itself, is completely determined, or driven we might say, by displacements, or the lack thereof, in its three scalar dimensions.
Figure 4. ThreeDimensional Scalar Motion with Displacement in Two Dimensions.
Figure 5. ThreeDimensional Scalar Motion with Displacement in Three Dimensions.
Larson argues that motions causing displacements from unity necessarily oppose the outward direction of the Progression in the system. This motion is therefore inward with respect to the outward motion of the Progression, as can be seen in figure 6.
Figure 6. Motion Opposing Progression is Necessarily Inward.
If such an inward scalar motion is effective in three dimensions or of sufficient degree in two dimensions, it can be seen that the effected entity will possess a property called mass, which is an inward threedimensional scalar motion opposing the outward threedimensional Progression, and such a motion will always resist any outward movement imposed upon it whether scalar or vectorial, a property called inertia. It should be understood, however, that the actual theoretical development from the relatively simple onedimensional displacement of radiation to the threedimensional displacement of matter is much more involved, actually combining the motions of double units and including the concept of twodimensional rotation. Only the notion of the theory is depicted in the figures presented above.
According to Larson, in the RST, the origin of the inward gravitational motion and the motion of the outward expansion of space and time are one and the same. Together they interact forming both the large structure of the universe, and the microcosmic structure of matter. The origin of gravity, the expansion of the universe and the cohesion of solids are all produced by the same theoretical motion that constitutes radiation and matter itself.
Larson reveals that the reasons why gravity cannot be detected except in its effects, and why it cannot be screenedoff, or modified in any way, is simple and straightforward: it is because the same motion that constitutes mass and inertia is also producing the action of gravity; the threedimensional inward scalar motion of matter opposes the threedimensional outward scalar progression of space and causes each mass aggregate to independently move inward towards all space locations and thus towards all other mass aggregates in sufficient proximity. But the threedimensional displacement is also distributed threedimensionally in extension space and thus attenuated by the inverse square law so that at a certain distance, which Larson calls the gravitational limit, the threedimensional outward Progression of space is greater than the inward motion of mass and commences to disperse the locations of space, thus maintaining the separation of heavenly bodies.
Everything in a universe of nothing but motion, must either be a motion, a combination of motions or a relationship between motions or combinations of motions. This means that the cohesion of solids and liquids must arise from motion as well. Ordinarily, the two opposing forces of the outward progression and inward gravity reinforce themselves in a positive feedback fashion. That is, the inward motion of gravity concentrates mass, thus increasing the effect of the inward motion of gravity. On the other hand, the outward motion of the Progression disperses locations in space, thus decreasing the effect of the inward motion of gravity, and increasing its own outward effect. Therefore, there can never be an equilibrium between these two motions.
However, when two or more masses come together until the space between them is reduced to one unit of space, an important change takes place at that point that enables them to move closer than one unit of space and 'interlock' somewhat like two rail cars joined together by a mechanical coupling. To understand how the inward motion of gravity and the outward motion of the Progression combine to accomplish this, it is necessary to discuss the concept of motion in time.
As we have seen with the help of CA rules, the 'direction' of time in scalar motion is the inverse of the 'direction' of space in scalar motion. So, 'outward' in scalar space is 'inward' in scalar time and viceversa. Figure 7 shows why this is so. At the boundary between space and time shown in figure 7, represented by the center column of single cells that is the zero point of the system, the 'directions' of the outward motion of progression and the inward motion of displacement relative to the outer line or datum of unity, reverse. On crossing into the one unit boundary separating space and time, the 'directions' of these motions change from inward to outward or viceversa. In other words, the inward 'direction' of displacement away from unity towards zero (towards the center of the triangle) is transformed into an outward 'direction' at the boundary between space and time. Likewise, the outward 'direction' of progression away from zero towards unity (towards the edges of the triangle) is transformed into an inward 'direction' at the boundary.
Figure 7. The 'Direction' Reversal of Scalar Motion at Unit Distance
With this reversal in the 'directions' of the motions of gravity and the Progression, the former positive feedback interaction that induced instability outside of unit space, is now transformed into a negative feedback interaction that reaches equilibrium inside unit space. That is, once inside unit space, the action of mass (gravity) works to disperse locations in space and oppose the action of the Progression, which opposes the action of mass and acts to concentrate locations in space. Thus, if the atoms move closer, the transformed 'outward' motion of gravity increases, pushing them apart, while if they move farther apart the transformed 'inward' motion of the Progression increases to pull them together again. Thus, a point of equilibrium is established that provides the required stability.
But, given the discrete nature of the system, less than one unit of space is not possible. How then can atoms move closer together and cross into the one unit boundary area between them? The answer is they can't, the Fundamental Postulates prevent it. But they can move farther apart in time, which is equivalent, because of the inverse relationship of space and time, to moving closer together in space, and when they do the transformation of the 'inward' and 'outward' motions of gravity and Progression takes place, producing the cohesion of the atoms. The details of how the motion in time takes place are beyond the scope of this article. But, in general, the space component of the motion is scalar, while it's time component is vectorial and the motion that occurs is consistent with the postulates of the system.
Since there are three dimensions in which this interaction is possible, four states of matter are encountered: the gaseous state wherein there are no dimensions coupled in this manner; the vapor state wherein one dimension is coupled; the liquid state wherein two dimensions are coupled, and, finally, the solid state wherein all three dimensions are coupled to other atoms in this way.
Although, in this brief overview, it is only possible to outline a few of the basic features of the theory, the detailed development published by Mr. Larson claims it is possible to deduce many aspects of nature from the theory, predict physical discoveries and even calculate actual values such as electric charge, interatomic distances and the periodic table of elements. Such mighty claims remain yet to be proven however. Only time will tell.
However, it is interesting to note that while the state of physical theory today seems to be in turmoil and some physicists are openly speaking of their 'great embarassment' as experimental data continues to make the universe of matter appear 'preposterous' in the light of current theory, the RST offers a radical alternative. In fact, many are of the opinion that things are so bad that the only way out is a completely new basis for physical theory. Perhaps a universe of motion is just what they need to consider, for as we have seen in this brief overview, many problems confronting the theorists today, such as the origin and nature of 'Dark Energy,' considered to be the greatest challenge facing modern physicists, are easily and straightforwardly explained in the RST without the need for adhoc inventions such as Einstein's revived 'Cosmological Constant,' (the correct value of which is proving to be impossible to calculate with existing theory) or other, more recent attempts, to deal with the 'new' development.
In the universe of motion, there also is no conflict between the Euclidian geometry of the universe (as seen in the Cosmic Microwave Background (CMB) measurements, and other recent experiments) and the density of matter in the universe, since the density of matter does not affect the geometry of the universe in the RST. Space only has properties that are affected by matter in Einstein's equations, but in the RST space can have no properties or even any meaning apart from the equations of motion. In the RST, there also is no need for other adhoc theories such as the 'Big Bang,' 'Inflation,' 'Quintessence,' etc. to explain the values of cosmological parameters and the large scale structure of the universe. In a universe of motion the universe, though dynamic, is cyclic and the 'Great Coincidence' of the relative balance between its matter and energy content presents no problem at all since the expansion of the universe happens without a 'Big Bang' and the proportions of matter and energy may be continual and unending or not, but there is no need for an adhoc invention such as the 'anthropic principle' to explain it.
Whether it's the challenge of explaining what the repulsive force is that causes the expansion of the universe or what the attractive force is that causes gravity, Larson's proposed universe of motion theory, the RST, presents a compelling case. In fact, in light of Mr. Larson's discoveries, maybe all that is needed today to meet these many serious challenges in physics, is a reexamination of the fundamentals of physics, namely the nature of motion.
Members of the mainstream scientific community that know of RST point out that there is no basis to believe the two fundamental assumptions of this "system of theory" and therefore any predictions that arise from it are not scientifically valid. They further argue that the "postulates" proposed by Larson are not postulates at all and can therefore not be the basis for anything scientific. The definition of a postulate being: "a position or supposition assumed without proof, or one which is considered as selfevident; a truth to which assent may be demanded or challenged, without argument or evidence." Therefore "postulates" are reserved for mathematical theorems such as "the sum of the angles of a triangle are 180 degrees."  which is just a starting definition for what a triangle is so that it can be used for practical purposes and does not purport to say anything fundamental about how the universe works.
The assertion that that universe is composed of only one thing "motion", they say, does not follow from being a "supposition assumed without proof", is not at all "self evident" and since it is labeled as a "postulate" it is not testable in the classic sense and can only serve as an arbitrarily chosen definition. The geocentric theory was formulated in the same manner: it supposed that the universe revolved around the earth and through some very complicated mathematics this theory was able to make some valid predictions about heavenly movements. This theory was also fundamentally flawed in that it's first assumption was incorrect. The mainstream scientific community also say that this "theory" is similarly flawed.
RST claims to be a revolution in physical theory, however it denies the existence of matter and energy as we know them which is a preposterous supposition in light of hundreds of years of confirmatory evidence. Instead of a revolution, RST is a complete breakdown of every current physical theory because of the denial of matter and energy. All of science would have to be replaced. electric and magnetic fields inducing each other having never been explained, when they have claim to be scientific but deny the very basis of current physics: matter and energy. no mathematical content nonpeerreviewed research work in philosophy metaphysics Very similar to the disproven idea of Heraclitus that the only thing in the universe is motion.
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