Scalar Mechanics

Scalar Mechanics: Lifted from Wiki, before this excellent explanation disappeared from the Net. It may have returned by now, but I am taking no chances and will continue to reference it from this page.

This is the great theoretical work of the late dissenting Cosmologist DB Larson as explained by Wiki. They did an excellent job of doing so, therefore I have referenced it here.

The Reciprocal System of Theory (RST) is a simple discrete system as 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.

According to its author, Dewey B. Larson, 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 time 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 algorithm, such as those found in a cellular automata (CA), which produces units of space and time in the proper ratio.

Figure 1a 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 (left) and RST Adaptation (right)

In Dr. Wolfram’s work, the output of a CA such as that in figure 1a 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 (fig1b). 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 requires 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 is 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 surface of an expanding 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 shows 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 concept of an eternal progression of space and time: One unit of space associated with one unit of time constitutes a speed of 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 1b.

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. 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, follow 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 is equivalent to 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 unlimited 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,) but never reach it (Zeno’s paradox). 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 motion. This is because all three coordinates are required to define a motion in extension space for any one dimension of scalar motion, since 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. One consequence of this fact is that two-dimensional and three-dimensional motions are not recognized as motions, and are erroneously attributed to “force fields” such as so-called electrostatic, magnetetic and even gravitational “fields.” Larson points out that force is a property of motion and cannot exist independently of it. This means that any force must be produced by motion by definition, a fact that modern physics has disregarded because of the difficulty in identifying the underlying motion of observable forces.

Figure 3. Three-Dimensional Scalar Motion with Displacement in One Dimension.

With this dual meaning 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 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.

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 affected dimensions, but Larson identifies this type of theoretical entity with physical subatoms having little or no mass.

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 possess the property known as mass. Because there exists displacement in all three dimensions of the given unit of 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.

Figure 5. Three-Dimensional Scalar Motion with Displacement in Three Dimensions.

Motions causing displacements away 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 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 much more involved than outlined here, actually combining the motions of double units and including the concept of two-dimensional rotation. Only the notion of the theory is depicted in the figures presented above.

The Motion of Gravity in the Macrocosm

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 assumes 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. The existence of this extremely simple, but powerful mechanism, is the necessary consequence of the nature of the proportions of space and time in the equation of motion.

The reasons, therefore, 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 towards 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, which Larson calls the gravitational limit, the three-dimensional outward Progression of space is greater than the inward motion of mass, and thus commences to disperse the locations of space, maintaining the separation of heavenly bodies.

The Motion of Gravity in the Microcosm

In the RST, while the inherent motion of mass, the inward scalar motion we call gravity, and the omnipresent motion of the Progression, the outward scalar motion we call the expansion of space and time, combine to define the large scale structure of the universe, they also combine to define the small scale structure of matter. In the RST, there is no provision for ‘bonds’ such as currently described in modern physics and chemistry that employ ad hoc concepts such as ‘ionic bonds,’ ‘covalent bonds’ or other types of ‘bonds’ to explain the cohesion of solids and liquids. 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 atoms 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.

Motion in Time

As noted earlier, in the RST’s postulated three-dimensional motion, three-dimensional time-motion is the inverse of three-dimensional space-motion. But it is important to remember that space-motion has no direction in time, just as time-motion has no direction in space. So, while in the equation of space-motion, v = s/t, s has direction in space, usually specified in a three-dimensional coordinate system in terms of x, y and z units, t has no direction in space and is a scalar value. Likewise, in the equation of time-motion, ‘v’ = t/s, t has direction in time, but s has no direction in time and is a scalar value. Indeed, this is why both space and time are scalar in space-time motion. Larson summarizes this concept as follows:

  • In the equations of motion in space, time is scalar.
  • In the equations of motion in time, space is scalar.
  • In the equations of motion in space-time, both space and time are scalar.

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 vice-versa. 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 constitutes 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 direction. On crossing into the one unit boundary separating space and time, the ‘directions’ of these motions change from inward to outward or vice-versa. 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, while the Progression, opposing the action of mass, now 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 by this negative feedback that provides the required stability.

However, 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.


By deducing the kinds of motions that are logically possible given the Fundamental Postulates of the Reciprocal System of Theory, Larson shows 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 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 contention between the opposing 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-scale structure, and the theoretical matter of the RST its small-scale atomic and molecular structure. Although, in this brief introductory tutorial, it is only possible to outline a few of the basic features of the theory, the detailed development published by Mr. Larson deduces many aspects of nature from the theory, predicts physical discoveries and even calculates actual values such as electric charge, inter-atomic distances in elements and compounds, and produces the periodic table of elements.

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 to find a completely new basis for physical theory. Perhaps a universe of motion is just what they need to consider, for many problems confronting the theorists today, such as the origin and nature of the problems causing physicists to postulate the existence of new forms of exotic matter and energy such as ‘dark matter’ amd ‘dark energy,’ which are now considered to be the greatest challenge facing modern physicists, are easily and straightforwardly explained in the RST without the need for ad hoc 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 developments.

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 ad hoc 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 is the repulsive force that causes the expansion of the universe or what is the attractive force 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 re-examination of the fundamentals of physics, namely the nature of motion.