Larson’s New System of Physical Theory
Note: This is Part one of a five-part article. References are listed at the end of part five.
- Larson’s new system of physical theory, the Reciprocal System of Physical Theory (RST), is explained. The new system is compared to Newton’s system, referred to as the legacy system of physical theory (LST). It is shown that the new system, based on the concept of a universal, scalar, motion, meets the requirements that modern theorists seek to find in the LST, but cannot due to the limitations of the definition of motion upon which the legacy system depends, and due to the requirement of a fixed frame of reference in that definition. It is shown that the new definition, by assuming that space and time are reciprocal aspects of a constant progression, opens the path to a “background-free” theory of energy, radiation and matter, based on the principles of symmetry, emerging from the perfect symmetry of reciprocity in scalar motion. Using this new system, Larson was able to construct the first and only general physical theory in the world, a Reciprocal System theory (RSt) of the universe.
It’s important to understand that Larson’s RST, is a new system of physical theory; that is, it is an alternative to Newton’s system of physical theory. To many, the idea of using a formal system of physical theory is undoubtedly unfamiliar, since the system we ordinarily use to construct physical theory is taken for granted, and seldom explicitly recognized.
However, when it is understood that Newton’s great accomplishment was the inauguration of a program of research that made the systematic investigation of physical phenomena possible in an unprecedented manner, it’s easy to see that underlying that program was a system of mechanics to investigate and classify the properties of all physical objects. Consequently, in the words of David Hestenes of Arizona State University, “Newtonian mechanics is, therefore, more than a particular scientific theory; it is a well defined program of research into the structure of the physical world.” 
Similarly, Dewey B. Larson, in publishing his three volume treatise, The Structure of the Physical Universe,  has done much more than introduce a particular scientific theory, he has inaugurated a well defined program of research into the structure of the physical world. While this claim may seem startling and therefore incredulous at first, it becomes a very compelling pronouncement upon further investigation. Here’s why: In the RST, Larson redefines the fundamental concepts of space and time.
Since the fundamental concepts of space and time are the foundation of Newtonian mechanics, as well as general relativity and quantum mechanics, their redefinition necessarily redefines the science, which is built upon them. According to Hestenes, under Newton’s program, our grand goal is to “describe and explain all properties of all physical objects.” He explains that the approach of this program is determined by two very important, general, assumptions: “first, that every physical object can be represented as a composite of particles, and, second, that the behavior of a particle is governed by interactions with other particles.” This means that we should be able to describe nature in terms of a few kinds of fundamental particles, which interact in a few fundamental ways.
The Power of Mathematics
The great power of this approach, according to Hestenes, is that the properties of the particles and the relationships between them via interactions can be precisely formulated mathematically. The expression of the existence of a particle over time in the function x(t), “when specified for all times in an interval…describes a motion of the particle.” From this it is clear that the central hypothesis of Newton’s program of research is that “variations in the motion of a particle are completely determined by its interactions with other particles,” leading to Newton’s second law of motion. Thus, this hypothesis defines the entire program from Newton’s day to this. As Hestenes puts it:
- Newton’s [second] law becomes a definite differential equation determining the motion of a particle only when the force f is expressed as a specific function of x(t) and its derivatives. With this much understood, the thrust of Newton’s program can be summarized by the dictum: focus on the forces. This should be interpreted as an admonition to study the motions of physical objects and find forces of interaction sufficient to determine those motions. The aim is to classify the kinds of forces and so develop a classification of particles according to the kinds of interactions in which they participate.
He adds, “The classification is not complete today, but it has been carried a long way.” Indeed, it has. The long road has been both an exciting and frustrating adventure for several centuries, and has brought unimaginable changes to world civilization, since its inception in the days of Newton. The really big news today, however, is that Newton’s program of research, focusing on the forces, is “stuck,” in the words of Steven Weinberg. While we have the standard model, that, though “ugly and ad hoc,” in the words of Hawking, is considered by many as the greatest intellectual achievement of the 20th Century, it is still missing a most fundamental interaction of physical objects, the very one that perplexed Newton himself: it is the force interaction of gravity. While this glaring failure has given rise to decades of effort leading to string theory, loop quantum gravity, and other lesser known approaches to find a solution, the inevitable conclusion, reached by more and more investigators, is that we can’t get there from here, that something else is needed.
The trouble is, of course, that most suggestions all have one thing in common: they are constructed under the same system of physical theory; that is, they are constructed under Newton’s program of research that focuses on the forces of interaction between particles contained in space and time. It might be argued that modern theoretical physics has long since abandoned the concept of particles for the field concept, and the concept of force interaction for the concept of particle exchange, but just as replacing Newton’s concept of absolute space and time, with Einstein’s spacetime continuum, doesn’t alter the definition of motion, even so modifying the concepts of particles and interactions doesn’t alter the definition of motion, and it’s the definition of motion, the function x(t), upon which Newton’s program of research is founded.
A New Definition of Motion
What Larson did was to redefine motion, hence making it possible to initiate a new program of research founded on the new definition. To understand Larson’s new definition, it’s important to recognize that motion in Newton’s program is always the one-dimensional motion of objects, or fields, defined in terms of a stationary reference, or background, of space and time. This leads immediately to a conflict between general relativity (GR), which must be used to describe gravity, and quantum field theory (QFT), which is used to describe the rest of physical phenomena in the standard model. Since, in GR, gravity is a consequence of Einstein’s spacetime continuum interacting with matter, while, in QFT, fields must propagate in a fixed background of space and time, according to a wave function, the perplexing question is, how can a wave function of gravity evolve over itself?
This predicament has lead to the dire need of a non-pertubative string theory, or a background-free string theory, in which a quantum theory of gravity can be formulated, which is currently, and has been for many years, the holy grail of modern theoretical physics. Whether or not this can be done remains to be seen and depends on such esoteric subjects as the evidence for SUSY, etc. However, the point here is that this predicament is fundamentally based in the definition of motion, which in QFT requires a fixed background of space and time, but which GR has eliminated. Thus, we have a choice; we can give up GR as a description of gravity, and by so doing free up the background of space and time, or we can keep our pet theory of gravity and give up our ability to describe fundamental particles in terms of fundamental interactions.
Of course, no one has the clout to do either, so we are “stuck.” Unless, that is, we can find a way to define motion without having to incorporate a non-dynamic background of space and time to describe the time evolution of fields in the Schroedinger equations, and without having to incorporate a dynamic background of spacetime to describe gravity in the Einstein equations. Dewey B. Larson’s Reciprocal System of Physical Theory (RST), as a new system of physical theory, goes beyond Newton’s system and provides the basis for a new program of research that, while it has the same grand goal of Newton’s program, is based on a new definition of motion.
The Nature of Space and Time
Larson’s new definition of motion is based, in turn, on his novel definition of space and time. The nature of space and time has been at the center of the physics philosophical debate for centuries. Discussing this in a recent paper, Lee Smolin, of the Perimeter Institute for Theoretical Physics, summarizes the, as yet, unanswered, fundamental, challenges facing the mainstream physics community for the last three decades: 
- During the last three decades research in theoretical physics has focused on four key problems, which, however, remain unsolved. These are
- 1. The problem of quantum gravity.
- 2. The problem of further unifying the different forces and particles, beyond the partial unification of the standard model.
- 3. The problem of explaining how the parameters of the standard models of particles physics and cosmology, including the cosmological constant, were chosen by nature.
- 4. The problem of what constitutes the dark matter and energy, or whether the evidence for them are to be explained by modifications in the laws of physics at very large scales.
- One can also mention a fifth unsolved problem, that of resolving the controversies concerning the foundations of quantum mechanics.
In his paper, Smolin shows how, in spite of some tantalizing clues, the vigorous pursuit of a solution to these challenges, by a cast of thousands of the most bright and talented people in the world, using the string theory approach, has only led to some perplexing and recalcitrant difficulties. This situation drives him to hypothesize that “some wrong assumption was made somewhere in the course of the development of [string] theory,” and he further surmises that the false assumption has to do with the nature of space and time. Specifically, he refers to the age old debate between relational and absolute theories of space and time, “which,” he notes, “has been central to the thinking about the nature of space and time going back to the beginning of physics.”
Thus, Smolin asserts that, if string theory is to succeed in meeting the key issues facing modern physics, as many hope it will, it must be reformulated in a way that does not depend on the current assumption, regarding the nature of space and time as a background for physical phenomena. He writes:
- The reason that we do not have a fundamental formulation of string theory, from which it might be possible to resolve the challenge posed by the landscape, is that it has been so far developed as a background dependent theory. This is despite there being compelling arguments that a fundamental theory must be background independent. Whether string theory turns out to describe nature or not, there are now few alternatives but to approach the problems of unification and quantum gravity from a background independent perspective.
The idea of background independence is the modern articulation of the famous debate between Newton and Leibniz over whether space and time are properly regarded as something that exists substantively and absolutely, or whether they have no meaning other than that given to them by the relative positions of objects in different spatial locations at different moments in time. Newton argued that space and time are to be regarded as absolute, and he eventually won the argument after presenting his famous water bucket thought experiment.
However, Smolin points out that Leibniz’s argument for the “principle of sufficient reason,” eliminates the philosophical problem that Newton’s position raises: namely that “a theory that begins with the choice of a background geometry, among many equally consistent choices,” must provide the justification for that choice. But, since no theory can justify the position or orientation of the universe as a whole, relative to a given background, the theoretical requirement for a fixed background of space and time becomes a philosophical liability. Smolin writes:
- This is sometimes called the problem of under determination: nothing in the laws of physics answers the question of why the whole universe is where it is, rather than translated or rotated.
This is not the only philosophical argument Leibniz raised against a background dependent theory, there are others having to do with global symmetries and conserved charges that modern physics eventually has come to recognize in the context of general relativity. Nevertheless, Smolin notes, “a physics where space and time are absolute can be developed one particle at a time, while a relational view requires that the properties of any one particle are determined self-consistently by the whole universe.” Since it is so much easier to take the former route, science ran with it for several centuries without looking back and with good effect. Of course, eventually, the philosophical dues have to be paid, and it appears that the time has come for modern theoretical physics to pay up.
The Physicists’ Relational Conception of Space and Time
Change comes slowly, however, and the recognition of the need for a background independent theory is not as universally acknowledged as Smolin would like. He and his colleagues, however, have tried to come to grips with the problem, and in so doing have arrived at a “rough consensus” as to what a relational view of space and time actually is. They refer to it as “the physicists’ relational conception of space and time.” There are three elements to this concept that Smolin discusses:
- 1) There is no background.
- 2) The fundamental properties of the elementary entities consist entirely in relationships between those elementary entities.
- 3) The relationships are not fixed, but evolve according to law. Time is nothing but changes in the relationships, and consists of nothing but their ordering.
Smolin characterizes the dynamics of such a concept as consisting of the changes of the relationship of its entities over time, which he summarizes in statement 3 above. “Thus,” he continues, “we often take background independent and relational as synonymous. The debate between philosophers that used to be phrased in terms of absolute vrs relational theories of space and time is continued in a debate between physicists who argue about background dependent vrs background independent theories.”
In this debate, Smolin articulates a strategy for those seeking background-independent theories:
- Relational strategy: Seek to make progress by identifying the background structure in our theories and removing it, replacing it with relations which evolve subject to dynamical law.
Smolin cites Mach’s ideas, and Einstein’s successful exploitation of them, as an encouraging indication that the correct paradigm for the relational strategy is found in Mach’s principle:
- Mach’s principle is the paradigm for this strategic view of relationalism. …Mach’s suggestion was that replacing absolute space as the basis for distinguishing acceleration from uniform motion with the actual distribution of matter would result in a theory that is more explanatory, and more falsifiable. Einstein took up Mach’s challenge, and the resulting success of general relativity can be taken to vindicate both Mach’s principle and the general strategy of making theories more relational.
However, this is obviously a compromise, since Mach’s principle provides a relational background, which, while, in the final analysis, is clearly better than an absolute background of space and time, is a background nevertheless, and, though it addresses the global symmetry problem, it does not affect the description of motion, which still must be defined as a change in an object’s position, as a function x(t).
Larson takes a completely different approach to the problem. Instead of seeking a background independent theory directly, as Smolin et al do, which is motivated by modern theoretical perplexities, he concludes that the definition of motion not only does not require a background of space and time, but he also realizes that it does not even require a separate entity in its definition; that is, in the equation of motion, v = ds/dt, the only requirement is a change of two reciprocal magnitudes, space and time. In retrospect, we might imagine him thinking that since the universal “march of time” is observed locally, and the universal “march of space,” is observed globally, in the recession of the distant galaxies, that one approach might be to assume that these observed phenomena are the reciprocal aspects of a universal space|time motion.
However, this was not the avenue by which he arrived at the conclusion. Rather, he arrived at it noticing that the data from his studies of inter-atomic distances in solids made more sense, if he assumed a reciprocal relation between space and time. Of course, if we think of space and time as a background, then the idea of space being the reciprocal of time seems absurd, but in considering the equation of motion, the reciprocal relationship of these two enigmatic concepts makes perfect sense.
Recognizing that this approach to the nature of space and time, as reciprocals, would work if space and time were quantized, he soon arrived at the basis for a new system of physical theory: If somehow the progression of space|time formed discrete units of motion, they could provide the basis for physical entities, consisting of nothing but space|time.
Of course, Larson knew nothing of Smolin’s arguments in the decades before he published a preliminary edition of his work in 1959. In fact, Smolin wasn’t even alive at that time. More importantly, the perplexities that dog background dependent physical theories had not yet emerged, and physicists were fascinated with QFT, and they were fixating on gauge symmetries and applying group theory to quantum mechanics. Nevertheless, a comparison of Larson’s RST-based theory with the relational space and time concept of Smolin et al, is very revealing:
1) There is no background.
Larson’s concept of space and time, as nothing more than the reciprocal aspects of a universal motion, eliminates entirely the concept of a space and time background, as the initial condition of the theory. It thus complies perfectly with Leibniz’s principle of sufficient reason in this regard. In fact, it will be shown later that the degrees of freedom associated with space and time in modern theories are actually more properly attributed to motion, and that exactly three degrees of freedom are sufficient for all geometries, including non-Euclidean geometries such as elliptical and hyperbolic geometries.
2) The fundamental properties of the elementary entities consist entirely in relationships between those elementary entities.
Again, in Larson’s theory, the RSt, as we refer to it, the elementary entities of the theoretical universe are not pre-existing particles of matter. They are discrete units of the universal motion, which Larson called scalar motion, because it consists of a scalar increase of space and time, reciprocally related. The initial state of this scalar motion is altered when a continuous reversal in the scalar “direction” of the progression of one or the other of the reciprocal aspects occurs at a given point in the progression. A more detailed explanation of this change in state will be provided later, but the result is that emerging degrees of freedom produce various properties in these entities due to the relationships between them.
3) The relationships are not fixed, but evolve according to law. Time is nothing but changes in the relationships, and consists of nothing but their ordering.
Larson’s universe of motion consists entirely of units of motion, combinations of units of motion, and relations between units of motion. These entities emerge and evolve solely as a result of, and as the necessary consequences of, the two fundamental assumptions of the system, which Larson called the “Fundamental Postulates” of the system. Time, in this system, is on an equal footing with space. However, all the dynamics of the system stem from the initial dynamic relationship of space and time. Therefore, while time is the change in the relationships, it does not exist apart from space in the equation of motion. Neither space nor time can exist as separate entities apart from motion. In the RST, space is ordered by time, and time is ordered by space. Hence, the spatial position of physical entities cannot change without time, neither can the temporal position of physical entities change without space.
Clearly, Larson’s Reciprocal System anticipated the requirements of a background independent theory. Meeting the need for a modern theory that can explain how the physical entities that populate the universe, as constituents of radiation, matter, and energy, can acquire the observed properties they have without invoking a background of space and time, is exactly what it claims it can do. The formal expression of the basis of the RST, composed by Larson and called the two Fundamental Postulates of the system, from which the entire universe of motion is deduced, follows:
First Fundamental Postulate: 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.
Second Fundamental Postulate: The physical universe conforms to the relations of ordinary commutative mathematics, its magnitudes are absolute and its geometry is Euclidean.
(See also: Larson’s New System of Physical Theory - Part II - Larson’s New System of Physical Theory - Part III - Larson’s New System of Physical Theory - Part IV - Larson’s New System of Physical Theory - Part V)