There's no doubt that Larson's RSt is problematic, but this is actually only an indication of his pioneering effort to apply the new scalar system. Pioneers are bound to take paths that later generations find problematic. The analogy of improving trails and creating roads out of trails, and highways out of roads, only goes so far, however. A better analogy is found in comparing the new Reciprocal System of Physical Theory to a new transportation system, which requires that the users of the system build new subsystems, similar to, but quite distinct from, those of the previous system of physical theory, the Newtonian system.
The essence of the scalar system is the reciprocal relation of space and time. Larson's discovery of this concept of scalar motion opens up a whole new frontier, not only in physics, but in math as well, as we discuss in The New Mathematics blog on this site. Thus, tackling the "problems" of Larson's RSt is really not the proper characterization for the work of the LRC, but the existence of these challenges does characterize why the new system needs a proper subsystem of mathematics. The major "problem" with Larson's RSt, which we seek to address at the LRC, can be seen by comparing the following descriptions of the initial scalar vibrations taken from the Preliminary Edition of SPU (PE), and the Revised and Enlarged Edition (REE). In Chapter 2 of the PE, Larson wrote:
"...it is apparent that where n units of one component replace a single unit in association with one unit of the other kind in a linear progression, the direction of the multiple component must reverse at each end of the single unit of the opposite variety. Since space-time is scalar the reversal of direction is meaningless from the space-time standpoint and the uniform progression, one unit of space per unit of time, continues just as if there were no reversals. From the standpoint of space and time individually the progression has involved n units of one kind but only one of the other, the latter being traversed repeatedly in opposite directions. It is not necessary to assume any special mechanism for the reversal of direction. In order to meet the requirements of the First Postulate the multiple units must exist, and they can only exist by means of the directional reversals. It follows that these reversals are required by the Postulate itself.
Because of the periodic reversal of direction the multiple unit of space or time replaces the normal unidirectional space-time progression with a progression which merely oscillates back and forth over the same path. But when the translatory motion in this dimension is eliminated there is nothing to prevent the oscillating unit from progressing in another dimension, and it therefore moves outward at the normal unit velocity in a direction perpendicular to the direction of vibration. When viewed from the standpoint of a reference system which remains stationary and does not participate in the space-time progression the resultant path of the oscillating progression takes the form of a sine curve.
It is now possible to make some identifications. The oscillating system which has been described will be identified as a photon. The process of emission and movement of these photons will be identified as radiation and the space-time ratio of the oscillation will be identified as the frequency of the radiation."
This pattern of scalar reversals is just a continuous "direction" reversal in the progression of one aspect, or the other, of the scalar motion. However, the result of such a pattern, the space-time ratio of oscillation that Larson identifies as the frequency of the emitted radiation, can only be a new ratio of s/t = 1/2, or 2/1, depending upon which aspect is the reversing aspect. Larson may have realized this later. It turns out that there is no way to modify this space-time ratio, by adding units of displacement, because adding units of 1/2 to other 1/2 units cannot change the space/time ratio of the displacement, but only the magnitude of the displacement. For instance, 1/2 + 1/2 = 2/4, which represents a displacement of two units, but the displacement ratio of 2/4 is still 1/2.
As far as I know, Larson never discussed this issue publically, but in the REE he changes the continuous reversal pattern, described in the quote above, to a new, periodic, reversal pattern, never mentioned anywhere in the PE. He describes the new, periodic, pattern as "another possibility" that is an option to the first pattern, which, he now concludes, results in a net zero scalar motion with respect to the fixed reference system. In Chapter 4 of the REE, Larson writes:
"Since the outward progression always exists, independent continuous negative motion is not possible by itself, but it can exist in combination with the ever-present outward progression. The result of such a combination of unit negative and unit positive motion is zero motion relative to a stationary coordinate system."
Obviously, this result was very problematic in Larson's development. How can a "zero motion relative to a stationary coordinate system," be the basis for the photon that propagates at light speed relative to a stationary coordinate system? Of course, it can't, so Larson had to change the concept of the PE, in which the photon is identified with this "oscillating system," to a new concept, in which the motion of the unit is not zero, but unity. So, he continues in Chapter 4:
"Another possibility is simple harmonic motion, in which the scalar direction of movement reverses at each end of a unit of space, or time. In such motion, each unit of space is associated with a unit of time, as in unidirectional translational motion, but in the context of a stationary three-dimensional spatial reference system the motion oscillates back and forth over a single unit of space (or time) for a certain period of time (or space)."
Thus, in this new version, the "direction" reversals occur only for "a certain period of time (or space)." He doesn't attempt to explain how this happens or why he felt it was necessary to change the concept, but further on in the same chapter he explains:
"The magnitude of a simple harmonic motion, like that of any other motion, is a speed, the relation between the number of units of space and the number of units of time participating in the motion. The basic relation, one unit of space per unit of time, always remains the same, but by reason of the directional reversals, which result in traversing the same unit of one component repeatedly, the speed of a simple harmonic motion, as it appears in a fixed reference system, is 1/x (or x/1). This means that each advance of one unit in space (or time) is followed by a series of reversals of scalar direction that increase the number of units of time (or space) to x, before another advance in space (or time) takes place. At this point the scalar direction remains constant for one unit, after which another series of reversals takes place."
Thus, the period of oscillation, or the total units of time (space), x, per cycle of space (time) oscillation changes for different frequencies. The boundaries marking the number of time (space) units, x, are single units where the "direction" reversals cease for one unit, before "another series of reversals takes place." Fortunately, with the recent advent of the progression algorithms (PAs), we are now able to clearly see these periods and we can clearly understand how that, when they are expanded, by adding units of 1/2 displacement to them, the space-time ratio of the displacement,as well as its magnitude, is changed accordingly.
However, careful analysis of these PAs showed that the periodic pattern is actually a combination of a 1/2 time-displacement, and a 2/1 space-displacement, resulting in an initial 2/3, or 3/2 space-time ratio. Adding a 1/2 displacement unit to a 2/3 unit increases the space-time ratio by 1 unit: 1/2 + 2/3 = 3/5, which is a two-unit displacement at a different space-time ratio. However, not only does Larson fail to explain why he changed the patterns or how the new, periodic, pattern was supposed to emerge from the original, continuous pattern, but he also did something else that should have been challenged, but was not: he defines the resulting scalar motion as a one-dimensional displacement, seemingly leaving two dimensions in a three-dimensional system undisplaced.
Consequently, the question then arises as to how the other dimensions are to be displaced. Although, he never explicitly attributes these additional displacements to "direction" reversals in the remaining dimensions, the fact is, to be consistent, they would have to be displaced in a similar fashion, which not only implies that three dimensions of unit progression must exist, something not supported by the fundamental postulates, but also that, if they don't exist, then some other way has to be found to develop two and three dimensional scalar displacements out of one "direction" reversal.
At the LRC, we take the position that, to be logically consistent, if only one, universal, unit, progression exists (ds/dt = 1/1), as posited by the system, that can be displaced by "direction" reversals, then the dimensions of this scalar value must be zero; that is, the dimensions of the oscillation cannot be differentiated one at a time. They must be displaced all together, as one 3D oscillation, to remain scalar.
Nevertheless, it's, again, desirable to look upon the failure to recognize this, as the inevitable error of Larson's pioneering effort. Our intention at the LRC is to extend the work of Larson, following the path he blazed, using the system he authored. Thus, we will use the information and knowledge we have gained from discovering Larson's error to attempt to build a subsystem that will meet the challenge and send us hurtling along in the direction Larson blazed. The following document initiates the exposition of how this subsystem will be approached:
The important point to recognize, however, is that Larson took another route in addressing this issue. He concluded that the "direction" reversals of the initial, scalar, oscillating system, as described in Chapter 4 of REE, is only effective in one dimension of the 3D stationary coordinate system, leaving the two remaining dimensions "vacant" so that the oscillating unit (photon) is carried outward, in one of these two dimensions, relative to matter in a stationary coordinate system, since all three of the dimensions of matter are displaced by what Larson calls "scalar rotation."
Consequently, the difference between the direction of the LRC reciprocal system development, and that of the RSt of Larson, is significant in several important respects. Notwithstanding this difference, however, the new development claims to be the apodictically valid results of the new, scalar, system; that is, it consists of the necessary consequences of Larson's RST.
Of course, the way to test any set of qualitative theoretical results, regardless of logical arguments involved, is to compare quantitative calculations based on them to the observations of physical phenomena. To the degree that these agree, the theoretical results are established. It is the immediate goal of the LRC to develop the theoretical results, based on the new conclusions, to the point of enabling us to calculate the properties of radiation and matter, and the relations between them, sufficiently to account for the observed properties of the electron, positron, electron neutrino, proton, neutron,the elements of the periodic table, and the atomic spectra of the elements.
The essence of the scalar system is the reciprocal relation of space and time. Larson's discovery of this concept of scalar motion opens up a whole new frontier, not only in physics, but in math as well, as we discuss in The New Mathematics blog on this site. Thus, tackling the "problems" of Larson's RSt is really not the proper characterization for the work of the LRC, but the existence of these challenges does characterize why the new system needs a proper subsystem of mathematics. The major "problem" with Larson's RSt, which we seek to address at the LRC, can be seen by comparing the following descriptions of the initial scalar vibrations taken from the Preliminary Edition of SPU (PE), and the Revised and Enlarged Edition (REE). In Chapter 2 of the PE, Larson wrote:
"...it is apparent that where n units of one component replace a single unit in association with one unit of the other kind in a linear progression, the direction of the multiple component must reverse at each end of the single unit of the opposite variety. Since space-time is scalar the reversal of direction is meaningless from the space-time standpoint and the uniform progression, one unit of space per unit of time, continues just as if there were no reversals. From the standpoint of space and time individually the progression has involved n units of one kind but only one of the other, the latter being traversed repeatedly in opposite directions. It is not necessary to assume any special mechanism for the reversal of direction. In order to meet the requirements of the First Postulate the multiple units must exist, and they can only exist by means of the directional reversals. It follows that these reversals are required by the Postulate itself.
Because of the periodic reversal of direction the multiple unit of space or time replaces the normal unidirectional space-time progression with a progression which merely oscillates back and forth over the same path. But when the translatory motion in this dimension is eliminated there is nothing to prevent the oscillating unit from progressing in another dimension, and it therefore moves outward at the normal unit velocity in a direction perpendicular to the direction of vibration. When viewed from the standpoint of a reference system which remains stationary and does not participate in the space-time progression the resultant path of the oscillating progression takes the form of a sine curve.
It is now possible to make some identifications. The oscillating system which has been described will be identified as a photon. The process of emission and movement of these photons will be identified as radiation and the space-time ratio of the oscillation will be identified as the frequency of the radiation."
This pattern of scalar reversals is just a continuous "direction" reversal in the progression of one aspect, or the other, of the scalar motion. However, the result of such a pattern, the space-time ratio of oscillation that Larson identifies as the frequency of the emitted radiation, can only be a new ratio of s/t = 1/2, or 2/1, depending upon which aspect is the reversing aspect. Larson may have realized this later. It turns out that there is no way to modify this space-time ratio, by adding units of displacement, because adding units of 1/2 to other 1/2 units cannot change the space/time ratio of the displacement, but only the magnitude of the displacement. For instance, 1/2 + 1/2 = 2/4, which represents a displacement of two units, but the displacement ratio of 2/4 is still 1/2.
As far as I know, Larson never discussed this issue publically, but in the REE he changes the continuous reversal pattern, described in the quote above, to a new, periodic, reversal pattern, never mentioned anywhere in the PE. He describes the new, periodic, pattern as "another possibility" that is an option to the first pattern, which, he now concludes, results in a net zero scalar motion with respect to the fixed reference system. In Chapter 4 of the REE, Larson writes:
"Since the outward progression always exists, independent continuous negative motion is not possible by itself, but it can exist in combination with the ever-present outward progression. The result of such a combination of unit negative and unit positive motion is zero motion relative to a stationary coordinate system."
Obviously, this result was very problematic in Larson's development. How can a "zero motion relative to a stationary coordinate system," be the basis for the photon that propagates at light speed relative to a stationary coordinate system? Of course, it can't, so Larson had to change the concept of the PE, in which the photon is identified with this "oscillating system," to a new concept, in which the motion of the unit is not zero, but unity. So, he continues in Chapter 4:
"Another possibility is simple harmonic motion, in which the scalar direction of movement reverses at each end of a unit of space, or time. In such motion, each unit of space is associated with a unit of time, as in unidirectional translational motion, but in the context of a stationary three-dimensional spatial reference system the motion oscillates back and forth over a single unit of space (or time) for a certain period of time (or space)."
Thus, in this new version, the "direction" reversals occur only for "a certain period of time (or space)." He doesn't attempt to explain how this happens or why he felt it was necessary to change the concept, but further on in the same chapter he explains:
"The magnitude of a simple harmonic motion, like that of any other motion, is a speed, the relation between the number of units of space and the number of units of time participating in the motion. The basic relation, one unit of space per unit of time, always remains the same, but by reason of the directional reversals, which result in traversing the same unit of one component repeatedly, the speed of a simple harmonic motion, as it appears in a fixed reference system, is 1/x (or x/1). This means that each advance of one unit in space (or time) is followed by a series of reversals of scalar direction that increase the number of units of time (or space) to x, before another advance in space (or time) takes place. At this point the scalar direction remains constant for one unit, after which another series of reversals takes place."
Thus, the period of oscillation, or the total units of time (space), x, per cycle of space (time) oscillation changes for different frequencies. The boundaries marking the number of time (space) units, x, are single units where the "direction" reversals cease for one unit, before "another series of reversals takes place." Fortunately, with the recent advent of the progression algorithms (PAs), we are now able to clearly see these periods and we can clearly understand how that, when they are expanded, by adding units of 1/2 displacement to them, the space-time ratio of the displacement,as well as its magnitude, is changed accordingly.
However, careful analysis of these PAs showed that the periodic pattern is actually a combination of a 1/2 time-displacement, and a 2/1 space-displacement, resulting in an initial 2/3, or 3/2 space-time ratio. Adding a 1/2 displacement unit to a 2/3 unit increases the space-time ratio by 1 unit: 1/2 + 2/3 = 3/5, which is a two-unit displacement at a different space-time ratio. However, not only does Larson fail to explain why he changed the patterns or how the new, periodic, pattern was supposed to emerge from the original, continuous pattern, but he also did something else that should have been challenged, but was not: he defines the resulting scalar motion as a one-dimensional displacement, seemingly leaving two dimensions in a three-dimensional system undisplaced.
Consequently, the question then arises as to how the other dimensions are to be displaced. Although, he never explicitly attributes these additional displacements to "direction" reversals in the remaining dimensions, the fact is, to be consistent, they would have to be displaced in a similar fashion, which not only implies that three dimensions of unit progression must exist, something not supported by the fundamental postulates, but also that, if they don't exist, then some other way has to be found to develop two and three dimensional scalar displacements out of one "direction" reversal.
At the LRC, we take the position that, to be logically consistent, if only one, universal, unit, progression exists (ds/dt = 1/1), as posited by the system, that can be displaced by "direction" reversals, then the dimensions of this scalar value must be zero; that is, the dimensions of the oscillation cannot be differentiated one at a time. They must be displaced all together, as one 3D oscillation, to remain scalar.
Nevertheless, it's, again, desirable to look upon the failure to recognize this, as the inevitable error of Larson's pioneering effort. Our intention at the LRC is to extend the work of Larson, following the path he blazed, using the system he authored. Thus, we will use the information and knowledge we have gained from discovering Larson's error to attempt to build a subsystem that will meet the challenge and send us hurtling along in the direction Larson blazed. The following document initiates the exposition of how this subsystem will be approached:
http://lrcphysics.com/reciprocal-system-mathematics/
The important point to recognize, however, is that Larson took another route in addressing this issue. He concluded that the "direction" reversals of the initial, scalar, oscillating system, as described in Chapter 4 of REE, is only effective in one dimension of the 3D stationary coordinate system, leaving the two remaining dimensions "vacant" so that the oscillating unit (photon) is carried outward, in one of these two dimensions, relative to matter in a stationary coordinate system, since all three of the dimensions of matter are displaced by what Larson calls "scalar rotation."
Consequently, the difference between the direction of the LRC reciprocal system development, and that of the RSt of Larson, is significant in several important respects. Notwithstanding this difference, however, the new development claims to be the apodictically valid results of the new, scalar, system; that is, it consists of the necessary consequences of Larson's RST.
Of course, the way to test any set of qualitative theoretical results, regardless of logical arguments involved, is to compare quantitative calculations based on them to the observations of physical phenomena. To the degree that these agree, the theoretical results are established. It is the immediate goal of the LRC to develop the theoretical results, based on the new conclusions, to the point of enabling us to calculate the properties of radiation and matter, and the relations between them, sufficiently to account for the observed properties of the electron, positron, electron neutrino, proton, neutron,the elements of the periodic table, and the atomic spectra of the elements.