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The '''Reciprocal System of Theory''' (RST) is a set of ideas that is claimed to be a theoretical framework that is capable of comprehensively explaining all physical phenomena from [[subatomic particle]]s to [[galactic cluster]]s. 
The framework, based on the work of [[Dewey B. Larson]], an [[United States of America|American]] [[engineer]] and author, was originally described in his book ''The Structure of the Physical Universe'' in [[1959]] and has more recently been published in three revised and enlarged volumes. The ideas are promoted by the members of '[[The International Society of Unified Science]], Inc.' (ISUS) whose only stated objective is to "advance in all ways deemed feasible the Reciprocal System of physical theory as proposed by Dewey B. Larson".

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 [[physicist]]s 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 counter-intuitive, 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
:''Almost all the traditional mathematical models that have been used in physics and other areas of science are ultimately based on partial differential equations.  Thus, for example, Maxwell’s equations for electromagnetism, Einstein’s equations for gravity, Schrödinger’s equations for quantum mechanics…are all examples of partial differential equations.''

But, he admits, 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
:''It is in a sense surprising that systems which involve such a high level of mathematical abstraction should have become so widely used in practice.  For…it is certainly not that nature fundamentally follows these abstractions.  And I suspect that in fact the current predominance of partial differential equations is in many respects a historical accident – and that had computer technology been developed earlier in the history of mathematics, the situation would probably now be very different.''

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 sine-Gordon 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.'

ISUS members insist that such 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 analogous to the central concepts of Larson’s RST.  They claim that, like these simple computer algorithms in Dr. Wolfram’s work, 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: 
*The physical universe is composed entirely of one component, motion, existing in three dimensions, in discrete units, and with two reciprocal aspects, space and time. 

*The physical universe conforms to the relations of ordinary commutative mathematics, its primary magnitudes are absolute, and its geometry is [[Euclidean geometry|Euclidean]]. 

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.

==== Reciprocity in 3D ====
Larson’s idea that time and space are reciprocals is difficult to understand when considered in the context of the conventional space-time framework as if to say that the march of time is the reciprocal of extension space, which we ordinarily think of as a container of matter. It is much easier to grasp when one considers a theoretical universe of motion in which the only significant physical quantity is the magnitude of that motion, measured as speed or [[velocity]]. As Larson explains it,
:''Motion is defined as the relation of space to time. Its mathematical expression is the quotient of the two quantities. An increase in space therefore has exactly the same effect on the speed, the mathematical measure of the motion, as a decrease in time, and vice versa.''
Thus, as Larson explains, in the equation of motion, time is the reciprocal of space and space is the reciprocal of time.  This leads to a new concept of motion, which Larson calls scalar motion.

====Scalar Motion====
Larson’s concept of scalar motion is new and unfamiliar although examples of it are all around us.  Consider one dimension of motion.  Mathematically, one dimension of motion is represented by the ratio of space to time or v = s/t.  Though this notation is sufficient for indicating the velocity of an object through space in our everyday experience, a vector, it is not sufficient to represent Larson's concept of scalar motion completely.  In our usual idea of motion, the equation of motion above represents a change in the position of an object over time, or, as we say, its rate of change.  But fundamentally, since motion is defined as simply a ratio of space and time, it follows that no object is required for its existence.  The only requirement to satisfy this definition is the provision of both space and time.  So how can one symbolically represent this more completely?  One way is with the output of a simple program such as a CA that produces units of space and time in the proper ratio.

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.  

[[image:ProgAlgo1.png|Figure 1 - Unit Progression]]


'''Figure 1'''

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 one-for-one, 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.

====3D Scalar Motion Requires 3D Time====
Another difficulty frequently experienced by those encountering the RST for the first time, is the postulated existence of three-dimensional scalar motion. But, again, it is helpful to realize that the RST is a complete departure from the ordinary assumption that space is a three-dimensional container of matter, and that time is simply a one-dimensional, unidirectional 'flow' of events within that container. Ordinarily, in applying the velocity equation v = s/t, s has a direction in space and t has no direction in space. However, asserts Larson, ‘it doesn't follow that t has no direction in time.’ The RST, then, simply assumes that its postulated three-dimensional motion has three aspects of time corresponding to the three aspects of space.

Notice once again that three-dimensional 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 Progression - Scalar Expansion of 3D Space and 3D Time==== 
Larson claims that by logically developing the consequences of the Fundamental Postulates of the RST, he is able to hypothesize theoretical concepts of radiation, subatoms?, matter, gravity, etc. that compare to their actual physical counterparts. The key to understanding how he does this is to first understand what he calls the ‘Progression.’ This is the hypothetical concept of an eternal progression of space and time: One unit of space associated with one unit of time constitutes unit motion (c), or the natural Progression, which Larson designates a ‘natural frame of reference.’  This is the same concept as that discussed above and illustrated in figure 1, but expanded to include three dimensions.

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).

====Let There Be Light . . .====
Having developed the concept of a featureless, expanding universe of space and time, the next concepts Larson develops are the concepts of radiation and matter, which, he explains, follows when the space or time aspects of a unit of uniform motion are displaced from unity in one or more dimensions. That is, when the ratio of space and time in a given unit of motion is less than unity in at least one dimension, we can say that something tangible exists. 

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.

[[image:ProgAlgo2.png|Displacement from unity]]

'''Figure 2'''

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, and its datum, or point of reference, is zero, not unity as it is with the postulated scalar motion.

[[image:ProgAlgo3.png|Time Displacement]]  [[image:ProgAlgo4.png|No Displacement]]   [[image:ProgAlgo4.png|No Displacement]]   

'''Figure 3. Three-Dimensional 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 three-dimensional 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 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.

====And Radiating Subatoms====
Subsequently, Larson found that other fundamental motions could be added to the basic linear vibration of the photon type of motion such as linear and vibrating rotations, thus producing displacement in more than one dimension.  However, a unit of scalar motion with displacement in two of the three possible dimensions, as represented in figure 4, such that unit speed exists in at least one remaining dimension, will also move at unit speed (1/1) in that dimension. Consequently, physical entities other than those of pure radiation (photons) will also radiate, as do photons, though they may possess extra-photonic properties. These theoretical entities vary somewhat according to the type and degree of displacement in the two effected dimensions, but Larson identifies this type of theoretical entity with physical subatoms having no mass.

[[image:ProgAlgo3.png|Time Displacement]]    [[image:ProgAlgo3.png|Time Displacement]]   [[image:ProgAlgo4.png|No Displacement]]   


'''Figure 4. Three-Dimensional Scalar Motion with Displacement in Two Dimensions.'''

====Solving the Enigma of Mass and Inertia====
Finally, a scalar motion with displacement in three dimensions, as represented in figure 5, cannot radiate at all, but must instead gravitate. Larson identifies this type of theoretical entity with physical subatoms and atoms, which possesses the property known as mass. Because there exists displacement in all three dimensions of the given motion, the properties of this theoretical entity are quite distinct from those with displacement in only one or two dimensions and, depending upon the quantity and configuration of the actual displacements within its three dimensions of scalar motion, the properties of this type of entity varies greatly in different environments. 

[[image:ProgAlgo3.png|Time Displacement]]    [[image:ProgAlgo3.png|Time Displacement]]    [[image:ProgAlgo3.png|Time Displacement]]    



'''Figure 5.  Three-Dimensional 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. If such an inward scalar motion is effective in three dimensions and of sufficient degree, it can be seen that the effected entity will possess a property called mass, which is an inward three-dimensional scalar motion opposing the outward three-dimensional 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 one-dimensional displacement of radiation to the three-dimensional displacement of matter is highly involved and that only the notion of the theory is depicted in the figures presented above.

====The Motion of Gravity====
Ever since the days of Newton, physicists have had to accept the fact that the force of gravity just is. No one can explain how it originates or how it does what it does. Einstein's General Theory of Relativity? asserts that matter causes a curvature in the 'fabric' of space-time, which in turn causes matter to move along the curved space. However, no one knows how matter causes the medium of space-time to curve or how the mechanism involved, whatever it is, operates. Actually, the problem extends even further than is generally recognized because whatever principle of gravity is formulated must account for the fact that gravity does not act uniformly throughout the universe. If it did the structure of the universe would be tending to one large aggregate. All evidence indicates that this is not the case, however.

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 screened-off, 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 three-dimensional inward scalar motion of matter opposes the three-dimensional outward scalar progression of space and causes each mass aggregate to independently move inward towards all space locations and thus all other mass aggregates in sufficient proximity.  But the three-dimensional displacement is also distributed three-dimensionally in extension space and thus attenuated by the inverse square law so that at a certain distance, Larson calls the gravitational limit, the three-dimensional 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.

====Summary==== 
By deducing the kinds of motions that are logically possible given the Fundamental Postulates of the Reciprocal System of Theory, Larson claims that he can develop a hypothetical universe of expanding space and of expanding time, an expansion he designates as the Progression. Taking the development further, he contends, produces theoretical entities with theoretical properties that can be identified with experimental photons and other particles radiating in all directions at the speed of light. Extending the theory still further enables him to formulate other hypothetical entities with the properties of mass, which gravitate and concentrate into large aggregates of matter. The balance between the opposite “directions” of the motions of mass (gravity) on the one hand, and the Progression of space and time on the other hand, give the theoretical universe of the RST its large structure, and the theoretical matter of the RST its atomic structure.

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 derive many aspects of nature from the theory, predict physical discoveries and even calculate actual values such as electric charge, inter-atomic distances and the periodic table of elements. Such mighty claims remain yet to be proven however. Only time will tell. 

== Criticism of RST == 

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 self-evident; 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 choosen definition. The [[geocentric theory]] was formulated in the same mannor: 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
non-peer-reviewed 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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'''External links'''

* [http://www.rsystem.org The official 'Reciprocal System of Theory' homepage']
* [http://www.reciprocalsystem.com/nbm/index.htm Volume I <em>The Stucture of the Physical Universe</em>]
* [http://www.reciprocalsystem.com/bpm/index.htm Volume II <em>The Stucture of the Physical Universe</em>]
* [http://www.reciprocalsystem.com/um/index.htm Volume III <em>The Stucture of the Physical Universe</em>]
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[[talk:Reciprocal_System_of_Theory|/Talk]]
[[Reciprocal_System_of_Theory/Old Talk|Old Talk]]