## General RST Questions

### 1) What is the Reciprocal System of Physical Theory (RST)?

- The RST is a system of physical theory that supports a new program of theoretical physics research differing substantially from the legacy system of physical theory (LST), supporting the traditional program of theoretical physics research. The LST program was initiated by Newton and is based on a definition of motion as the movement of physical objects within the container of space and time. The RST program was initiated by Larson and is based on a definition of motion as the progression of space and time itself. This new definition of motion is called scalar motion. By developing the necessary consequences of the RST, Larson developed the first theory of the reciprocal system, referred to as the Reciprocal System theory (RSt). The RSt is the world’s first general physical theory of the universe.

### 2) Who is Dewey Larson?

- Dewey Larson was an American Engineer born in 1900 who became the Chief Engineer of an Oregon utility company in Portland. He had a life-long love of science, especially physics, but was unable to pursue the traditional professional track due to economic conditions and family responsibilities during the depression era of the United States in the 1930s.

### 3) Is the RST-based RSt taught in universities?

- The RSt is not taught in universities, and probably won’t be until the definition of scalar motion upon which the RST is based is recognized by science. The idea that space is nothing more than the reciprocal of time in the equations of motion is a new and unfamiliar concept, which seems absurd to legacy physicists whose education consists of a rigorous and rigid preparation that ingrains into their minds the assumption of the scientific community that they know what the world is like. Since the universe of motion is a new view of the world, it is anathema to “normal” science and the educational process that prepares and licenses students for professional practice. Thomas Kuhn’s work,
*The Structure of Scientific Revolutions*, explains the dynamics of this process in great detail.

### 4) How can everything in the universe be motion?

- Since motion, by definition, is the inverse relation of changing space and changing time, ultimately the answer to this question is the long-sought answer to the questions of what is space and what is time? In the universe of motion the answer to these two questions are assumed: they are nothing but the reciprocal aspects of motion, which exists in three dimensions, and in discrete units. The consequences that necessarily follow these assumptions are then explored. The result is a universe of radiation and matter very similar to that which is observed in every respect.

### 5) Can the RST be proven?

- The RST consists of the Fundamental Postulates used to develop the details of the RSt, which are a set of logical consequences that necessarily must follow from these assumptions without any content from other sources, and the test of the system’s assumptions is conducted by comparing the resulting conclusions to observation. Therefore, as more comparisons of the results are made without finding a discrepancy, the possibility that a discrepancy will ever be found is reduced accordingly. Nevertheless, this certainty can never reach 100%. In physical matters, we can never obtain mathematical certainty, a condition in which the probability of error is zero. We must be satisfied with physical certainty, a condition in which the probability of error is negligible.

### 6) Does the RST include the classical laws of physics (mechanics)?

- Yes. The classical laws of physics have emerged from Newton’s program of research, which has been historically interpreted as a dictum to focus on forces. However, the measurement and understanding of these forces, as a function of the change in location of objects, defining the motion of objects, depends on the frame of reference in which they are viewed, the motion of which also must be taken into account. When various transformations from one reference system to another are applied, laws of conservation emerge that ensure us that physical principles are universally inviolate. This understanding of the “invariance” of physical law under reference system transformation worked very well until the high-speed and unusual properties of radiation were found that required a new definition of motion. Lacking the new definition, the results of invariance have been misinterpreted, leading to incorrect physical concepts. The RST clarifies these concepts.

### 7) Is the RST compatible with special and general relativity?

- Again, while the mathematics of wave mechanics works well as a solution to some of the problems encountered in the Newtonian program of research, which focuses on the forces of nature to explain physical phenomena, the LST definition of motion, and the requirement for employing a spatial reference system in that definition, is the root of the problem, which complex mathematics has been called upon to solve. And, once again, since the mathematical solutions have had so much success, it has only served to perpetuate the conceptual errors in the LST that are the real problems.

- These problems are most evident in the emergence of string theory in the last half of the twentieth century as the most promising approach to resolving the critical challenges facing the LST’s QM and the standard model. This approach seeks to resolve the difficulties introduced by the LST definition of motion, by postulating that the motion of tiny, unobservable, strings constitutes the various physical entities that are thought to be the fundamental particles of nature, as described in the standard model. In this way, the solution to the plague of infinities, or “singularities,” that are the bain of LST theories, but which, again, are problems, the root of which is found in the LST definition of motion, where the answers are being sought in the mathematical treatment of space and time.

- To make this mathematical approach work, however, LST scientists are willing to go way beyond Einstein in attributing properties to space and time that, in the RST, they don’t have. Indeed, they now find it necessary to construct a concept of space with nine or ten dimensions, and time with one dimension, but with the proviso that time is not actually real, but is something that emerges from quantum phenomena into the classical world. Thus, even if the increasingly complex mathematical content can eventually resolve the existing problems, as they were able to do previously, the conceptual content of these theories becomes more and more bizarre and removed further and further from the simple concepts of the Reciprocal System.

- On the other hand, since the standard model is based on observation, it’s not correct to say that the RST “does not include the standard model.” Larson’s RSt deals with some of the elements of the standard model, but it should be understood that this LST model is actually an LST theory, explaining the observations of high energy physics, provided that two dozen, or so, so-called “free parameters,” are input into the theory. RST-based theory cannot have any free parameters. Nothing is put into these theories, but everything, including the observed properties of mass, charge, spin, etc. that the elements of the standard model exhibit, must follow as necessary consequences of the RST. Consequently, the scope of this work is tremendous, and has only begun, but is not anywhere complete, at this point in time.

- However, since these mathematical corrections work well, as a solution to the difficulties encountered by the Newton program, the conceptual errors are perpetuated in the LST. Meantime, using the Reciprocal System, the concept of motion itself supplies the solution, since the new definition of motion permits its magnitude to be measured relative to an absolute frame of reference, something that is not possible in the LST. Therefore, magnitudes of motion (thus, the magnitudes of space and time, as well) are absolute in the RST, whereas in the LST they must be relative. This difference in turn requires the LST to regard space and time as dimensions of something real and tangible apart from the matter that it contains or interacts with.

- In contrast, space and time do not have dimensions in the RST; that is, they don’t exist as entities that can be considered apart from the definition they have as reciprocal aspects of motion. Hence, they cannot have properties such as magnitude, dimension and direction; only motion can possess these properties. This means that space cannot be warped by the presence of matter in order to explain gravity, and that lengths cannot be shrunk, nor time dilated, in order to correct the equations of high-speed motion between relatively moving frames of reference. In the RST, gravity is the force property of the inherent space motion constituting mass, and the errors of the LST high-speed speed measurements are introduced by an unrecognized component of time motion.

### 8) Does the RST include quantum mechanics and the standard model?

- Yes and No. Again, while the mathematics of wave mechanics works well as a solution to some of the problems encountered in the Newtonian program of research, which focuses on the forces of nature to explain physical phenomena, the LST definition of motion, and the requirement for employing a spatial reference system in that definition, is the root of the problem, which complex mathematics has been called upon to solve. And, once again, since the mathematical solutions have had so much success, it has only served to perpetuate the conceptual errors in the LST that are the real problems.

- These problems are most evident in the emergence of string theory, in the last half of the twentieth century, as the most promising approach to resolving the critical challenges facing the LST’s QM and the standard model. This approach seeks to resolve the difficulties introduced by the LST definition of motion, by postulating that the motion of tiny, unobservable, strings constitutes the various physical entities that are thought to be the fundamental particles of nature, as described in the standard model. In this way, the solution to the plague of infinities, or “singularities,” which, again, are problems, the root of which is found in the LST definition of motion that the LST community is seeking to solve through the mathematical treatment of space and time.

- To make this mathematical approach work, however, LST scientists are willing to go way beyond Einstein in attributing properties to space and time that, in the RST, they don’t have. Indeed, they now find it necessary to construct a concept of space with ten dimensions, and time with one dimension, but with the proviso that time is not actually real, but is something that emerges from quantum phenomena into the classical world. Thus, even if the increasingly complex mathematical content can eventually resolve the existing problems, as they were able to do previously, the conceptual content of these theories becomes more and more bizzare and removed further and further from the simple concepts of the Reciprocal System.

In the development of RST-based theory, on the other hand, the phenomena of quantum behavior such as uncertainty in position and momentum, wave-particle duality, the propagation of radiation quanta, and the mass and charge of gravitating quanta, are the result of the central role of the underlying reference system, the universal, scalar, motion. Since this motion does not involve the changing location of an object, the very concepts of mass, momentum, and energy, so crucial to the LST, are redefined in a way that explains the foundations of quantum mechanics; that is, it gives us a broader context, in which to view these phenomena, which removes much of the mystery that is so confounding without it. Hence, the phenomenological part of quantum mechanics and the standard model are included in RST-based theory.

### 9) Does the RST include the big bang and inflationary cosmology?

- No. The hot big bang theory is strictly an LST theory of matter interacting with the spacetime of general relativity. In contrast, the cosmology of the RST is the universe of motion, wherein the limits of discrete units of motion, existing in three dimensions, produces four distinct regions of motion: two regions of space motion, where the limits of the space aspect of scalar motion create macro and micro physical phenomena of classical and quantum behavior in the observable sector of the universe, and where the limits of the time aspect of scalar motion create similar physical phenomena, but in an inverse manner in an unobservable sector of the universe. The interaction of these two sectors creates an infinite cycle of matter and radiation that accounts for the dynamics of the respective sectors, in an inter-dependent fashion, totally unrelated to concepts of LST cosmology.

### 10) Does the RST predict anything?

- The RST predicts everything, since it posits that all existing physical entities, and all physical phenomena are the necessary consequences of the assumptions found in its fundamental postulates; that is, it predicts that all things are either a motion, a combination of motions, or a relation between motions. Therefore, a conclusion regarding the motion, combination of motions, or relations between motions that should enter into a physical situation, enable the prediction of the phenomena from first principles.

- A wonderful example of this is Larson’s prediction of exploding galaxies, and the associated radio galaxies and quasars ejected from them, which he made several years before quasars were discovered. Another dramatic example, this time of the postdicting power of the RST, is found in its “prediction” of the periodic table of the elements, with the atomic numbers and atomic weights calculated from first principles. In contrast, quantum mechanics is unable to do this.

### 11) Is there a new set of RST equations?

- The RST introduces a new concept of motion, which changes existing concepts of space and time, clarifies the nature of force and acceleration, showing them to be properties of motion, which cannot exist autonomously, and provides an absolute reference of motion that enables the measure of absolute magnitudes of motion, and thus the absolute measure of its reciprocal aspects, space and time. However, the expressions of the LST equations of motion,

- v = s/t, f = ma, p = mv, E = mc
^{2}, E = hν, etc,

- remain the same. The new concepts, explaining why these observed relations hold, is what the RST brings to the table.

- This said, however, the mathematical implications of these new concepts are important too. For instance, the definition of motion, in the equation of speed as v = ds/dt, without requiring the changing location of an object over time, as an essential part of the definition, implies that v = dt/ds is also a legitimate expression of the reciprocal relation of space and time, and, in fact, these are the dimensions of energy, the reciprocal of speed. This in turn leads to the realization that the units of force, or the units of energy per unit of space, having dimensions, t/s * 1/s = t/s
^{2}, are, in a sense, the reciprocal of those of the units of acceleration, speed per unit of time, with dimensions s/t * 1/t = s/t^{2}, as can be seen when units of energy are viewed as units of inverse speed, t/s, and inverse acceleration, as inverse speed per unit of inverse time, 1/t, which has dimensions t^{2}/s, which dimensions are the mathematical inverse of the dimensions of units of acceleration, s/t^{2}.

- However, since the role of space and time are inverted in the inverse sector, t
^{2}/s in that sector is actually equivalent to t/s^{2}in our sector, or the dimensions of force. Thus, the dimensions of the equations of motion are consistent in the context of each sector, but are inverted in the context of the reciprocal sector, so that force is equivalent to inverse acceleration and vice-versa.

- In this sense then, the RST does introduce a new set of physical equations, a set that doubles the current set, and is its inverse. Furthermore, the RST affects mathematics in another, more direct way. Recall that the idea of an imaginary number, i, was invented to integrate the concept of direction with the concept of magnitude, since magnitudes naturally are regarded as only having the positive values associated with the set of real numbers. However, the necessity to use the concept of directions with real numbers eventually forced the acceptance of negative numbers and the ad hoc expedient that the square of some unknown, or imaginary, number would equal the negative value of one, or -1.

- While it was recognized that no such thing as negative substance exists, and that the use of negative numbers in connection with units of quantity is conceptually problematic, the expedient was very successful in calculations, though negative roots of equations were considered false solutions, “pretended” by the only true ones, the positive roots. Interestingly, however, the conceptual challenge in this case, as in every case since then, relates to the definition of motion, and the implications of this definition on concepts of space and time.

- With the advent of the RST, and its definition of scalar motion, the ideas of positive magnitudes and direction are reconciled in a natural and intuitive fashion, without the need for imaginary numbers and the accompanying violence to the concepts of magnitude, dimension, and direction that are involved.

- To understand how this is possible, it is necessary to consider the meaning of zero and its use in connection with negative numbers that was the source of consternation for centuries. The difficulty has always been in the relations between physical reality and its mathematical modeling. If one considers that a negative number represents something subtracted from nothing, the concept will always seem absurd, in spite of the utility of the operation in the context of algebra.

- However, if one employs an operational interpretation of magnitude, and considers the unit ratio of two positive numbers, and the two possible directions of this ratio, as positive and negative directions of magnitude from the unit reference, the whole conceptual difficulty with the quantitative interpretation of magnitude, and its problematic concept of zero, which mankind struggled with for centuries, and still struggles with, in the teaching of mathematics to upcoming generations, and in the formulation of consistent physical theory, disappears entirely. That this change in the mathematical definition of magnitude, which has such a salutatory effect on conceptual difficulties encountered with negative numbers, happens to correspond precisely to the RST change in the definition of the magnitudes of motion, is no coincidence.

- Indeed, we can say that the new, simple but startling, equation of the RST is: n|m = 0, where n is any positive integer equal to m, and where the relation operator symbol, “|”, signifies a reciprocal relation. Of course, this equation only makes sense, when one understands that it redefines the meaning of zero, from nothing to something; that is, the definition of zero is changed, from meaning nothing, to meaning the perfect symmetry, or balance, of unity, which is really something. Thus, x = n|m, for any positive integers n and m, operationally defines a number that denotes the balance of two, equal, quantities, inversely related. The solution to the equation is x = n - m, and is either zero, positive or negative, but x always has the explicit form n|m. Therefore, x is positive when n > m, negative when n < m, and zero when n = m, defining the system of signed integers.

### 12) What’s the best way to learn more about the RST?

- Study Larson’s works (available on Amazon and online at http://www.reciprocalsystem.com) and participate in LRC events and online discussions.

## Specific LRC Questions

### 1) What is the purpose of the Larson Research Center (LRC)?

- The purpose of the LRC is to develop physical theory using the RST. In other words, its purpose is to apply the new system and to conduct the new program of theoretical physics research that it makes possible.

### 2) How does the LRC differ from the International Society of Unified Science (ISUS)?

- The purpose of ISUS is to diffuse and to advance the knowledge of RST physics in much the same way that the purpose of the American Physical Society (APS) is to advance the knowledge of LST physics. However, while the APS publishes a journal of scholarly articles on physics, and sponsors many activities in connection with its purpose, it doesn’t pay researchers to conduct research. Theoretical physics research is the province of the institutions of government, industry, and academia, which employ the members of the APS.

- Similarly, ISUS doesn’t, and shouldn’t, employ researchers to conduct the RST physics research of the new system. It is the job of outside institutions, such as the LRC, to do this.

### 3) Is the work of the LRC based on Larson’s works?

- Yes. We believe that it is crucial to make the important distinction between Larson’s new
*system*of physical theory, called the Reciprocal System of Physical Theory, and the subsequent*theory*he developed, using his new system, called the Reciprocal System theory (RSt). The RST consists of the fundamental postulates of the scalar system and the definition of scalar motion that follows from them, as a necessary consequence. The RSt consists of the set of logical conclusions that necessarily follow from the RST, as identified by Larson in his three volume work,*The Structure of the Physical Universe*(SPU). The work of the LRC is to carry on the work of Larson in developing his RST-based physical theory, or RSt; that is, we seek to extend, expand, and refine his initial theory of the universe of motion, the world’s first general physical theory.

### 4) Is the LRC’s Reciprocal System of Mathematics (RSM) part of the RST?

- No. When Larson published the SPU, he was constantly asked if a mathematical formalism existed for the RSt, but he was emphatic that the contribution of the RST was primarily conceptual, not mathematical. In his book
*Beyond Newton,*he explains:

- Present-day basic physical theory does not need more mathematics—it is overflowing with mathematics already. What it needs is a conceptual clarification that will enable making full use of the physical knowledge and the mathematical tools already available. This is the objective of this present work: not to add to the profusion of abstruse mathematical speculations now in existence, but to identify the conceptual errors in the previous development of theory and to point the way to the changes in thinking that are necessary in order to make full use of the mathematical and theoretical equipment already on hand.

But as Hestenes, in his book,

*New Foundations for Classical Mechanics*, points out:

There is a tendency among physicists to take mathematics for granted, to regard the development of mathematics as the business of mathematicians. However, history shows that most mathematics of use in physics has origins in successful attacks on physical problems. The advance of physics has gone hand in hand with the development of a mathematical language to express and exploit the theory…The task of improving the language of physics…is one of the fundamental tasks of theoretical physics.

- Hence, it follows from this that, if the RST indeed clarifies the physical picture, as much as Larson was convinced it does, then we should expect to see an improvement in the mathematical language used to express the new concepts. In other words, the improved mathematical concepts follow the
*successful*clarification of the physical concepts, not the other way around. The RSM illustrates this perfectly. The mathematical advance that it represents is a direct result of the insight gained from Larson’s clarification of fundamental physical concepts.

### 5) Can the RSM be proven?

- This is an interesting question. The RSM is a new system of mathematics, not a new mathematical theorem in the legacy system of mathematics (LSM), just as the RST is a new system of physical theory, not a new theory in the legacy system of physical theory (LST). Therefore, the question really should be “can RSM theorems be proven?” The answer to this question is presumably yes, because the properties of the system are the properties of scalars. Thus, set theory, group theory, etc, should apply as well to the operationally defined reciprocal numbers (RNs) of the RSM, as they do to the quantitatively defined number systems of the LSM, but this remains to be demonstrated, at this time.

### 6) Is the RSM taught in universities?

- No. The RSM is so new that, currently, it is only studied and taught at the LRC.

### 7) Does the RSM include abstract algebras, such as the four normed division

algebras?

- Definitely. However, unlike the normed division algebras of the LSM, which lose their algebraic properties as a function of the complex root, the algebras of the LSM are fully ordered, commutative, and associative. This is because the reciprocal numbers of the RSM are scalars, with a duality property, not vectors, with a direction property.

- This is possible because the operational interpretation of a reciprocal number is employed in the RSM, as opposed to the quantitative interpretation of a reciprocal number used in the LSM. Thus, the square root of -1 is reinterpreted, not as the value of an “imaginary” quantity, but as the value of an operational relation, the reciprocal relation. This means that there is only one root to the number one, (1|1)
^{1|2 }= 1|1, since no negative quantity numbers are used in the reciprocal operation of unity.

- In the RSM, 1|1 = 0, 1|2 = -1 and 2|1 = +1 and the square root, in each case of magnitude one, (1|2)
^{1|2}, and (2|1)^{1/2}, are definitely not equal, but are also not defined, since these numbers, like the LSM integers, are a group under addition. The difference means that either side of zero can be distinguished, giving the reciprocal numbers of the RSM a duality property, or two “directions,” along the number line: one on the “positive” side of zero, and the other on the “negative” side of zero, without invoking the*ad hoc*invention of the imaginary number.

However, there are two operational interpretations of reciprocal numbers, in the RSM. The second interpretation, n/n = 1, is a group under multiplication. The operation that yields the value, in this case, is division, not subtraction. The product of two negative elements of this group is also negative, and the product of a negative and positive element is either positive or negative, depending on the relative value of the binary elements. Hence, 1/2 = .5, not -1, and 2/1 = 2, not 1, and the square root of 1/2 is the square root of .5, aproximately .7071, the reciprocal of the square root of 2, approximately 1.4142.

### 8) Does the RSM include geometry?

- The quantity, duality, and dimension properties of the RSM’s RNs lead to a numerical equivalent of fractal geometry, while the components of the RNs are analogous to the points, lines, areas, and volumes of Euclidean geometry. Nevertheless, the notion that the relation of various locations, satisfying the postulates of Euclidean geometry, is something that implies that “space” exists between these locations, which can possess properties such as quantity, duality, and dimension, is simply erroneous. The only properties that space has are the properties it has in the definition of motion, as the reciprocal aspect of time. What we measure as distance between locations is a measure of a past, or contemplated, motion, not something we can call space.