# Thread: The Reciprocal System of Physical Theory

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## The Reciprocal System of Physical Theory

Ok, here goes. With this initial post, I'm introducing an alternative system of physical theory; that is, an alternative to Newton's system of physical theory. To many of you, the idea of using a system of physical theory is undoubtedly unfamiliar, since the system we ordinarily use to construct physical theory is taken for granted, and seldom explicity 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." [1]

Similarly, Dewey B. Larson, in publishing his three volume treatise, The Structure of the Physical Universe, [2] 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: 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. Under Newton's program, our grand goal is to "describe and explain all properties of all physical objects." [1] Hestenes 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 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 completly 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 Hestene's 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.
Hestenes 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 civilization, since its inception in the days of Newton. The really big news today, however, is that we are "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: 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 space-time, 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.

What Larson did was to redefine motion, thus 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 space-time, but in QFT, fields must propagate in a fixed background of space and time, 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.

If such a prospect interests you, stay tuned.

References:

1) David Hestenes, "New Foundations for Classical Mechanics, Second Edition," Kluwer Academic Publishers, 1986.

2) Dewey B. Larson, "The Structure of the Physical Universe, Revised and Enlarged Edition, in Three Volumes," 1979.

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HI Excal

Just a few thoughts.

In my opinion, referring to Newton’s “laws” of gravity as “laws” is misleading, despite the universal use of such a term. The relationship of F = g m1 m2 / D^2 is based upon observation rather than a theory or model. This is in contrast with E = mcc which was established from a theoretical model and then experimentally verified. E = mcc, is therefore, in my opinion, a law, F =gmm/dd is not.

General Relativity is a geometric model that does yield Newton’s “Laws”, hence it’s appeal.

I also somewhat agree with you when you stated the following..

“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.”

but it could be argued that General Relativity has not eliminated the “fixed background”, it is just superfluous.

I look forward to a listing of your premises and the relationships proposed.

Good luck.

Snowflake.

3. Hi Excal,

We ahad someone on the Universe Today forum start to tell us about Dewey Lasron's ideas, but we didn't get very far.

Can you start us off with something simple and show how Larson would describe something that to me would look like a billiard ball traveling at 3 meters per second striking head-on another billiard ball that had been at rest?

Larson's physics never really sunk in for me, and I think it was because the previous poster mostly pointed us to some of Larson's work and didn't help guide us.

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Originally Posted by snowflakeuniverse
In my opinion, referring to Newton’s “laws” of gravity as “laws” is misleading, despite the universal use of such a term. The relationship of F = g m1 m2 / D^2 is based upon observation rather than a theory or model. This is in contrast with E = mcc which was established from a theoretical model and then experimentally verified. E = mcc, is therefore, in my opinion, a law, F =gmm/dd is not.
In fact, Newton was troubled by the fact that he couldn't find the underlying motion of which the gravitational force is a property, and refused to propose a hypothesis without it. Today, however, modern investigators seem to have no such qualms. In fact, we have pretty much forgotten that force is a property of motion, and have permitted ourselves to accept autonomous forces that can exist by themselves without an underlying motion. The similarity of Newton's second law of motion to the gravitational law is intriguing, but it does not attract much attention in the mainstream community these days. Yet, Larson's opinion was that forces cannot exist as independent entities. In chapter 13 of the second volume of his work, The Basic Properties of Matter, he writes:

For application in physics, force is defined by Newton's second law of motion. It is the product of mass and acceleration, F = ma. Motion, the relation of space to time, is measured on an individual mass unit basis as speed, or velocity, v, (that is, each unit moves at this rate), or on a collective basis as momentum, the product of mass and velocity, mv, formerly called by the more descriptive name "quantity of motion." The time rate of change of the magnitude of the motion is dv/dt (acceleration, a) in the case of the individual unit, and m dv/dt (force, ma) when measured collectively. Thus force is, in effect, defined as the time rate of change of the magnitude of the total quantity of motion, the "quantity of acceleration" we might call it. From this definition it follows that a force is a property of a motion. It has the same standing as any other property, and is not something that can exist as an autonomous entity.
However, Newton's first and second laws are more often regarded as hypotheses that explain why massive objects move (or don't move), and thus are called laws because they are confirmed by all observations. Whereas, as you point out, the universal law of gravitation is observed, but it does not explain why objects are attracted to each other gravitationally. The gravitational force just exists, it cannot be applied, or manipulated, by an outside agency, as can other foces studied by Newton. Nevertheless, Newton realized that where there is a force, there must be an underlying motion, even if it hasn't been found. Larson's point is that we need to keep this in mind. Motion is prior to force.

Originally Posted by antoniseb
We had someone on the Universe Today forum start to tell us about Dewey Lasron's ideas, but we didn't get very far.

Can you start us off with something simple and show how Larson would describe something that to me would look like a billiard ball traveling at 3 meters per second striking head-on another billiard ball that had been at rest?
I think the reason it's been hard to introduce Larson's ideas is that those who have attempted it have tried to present it as a new theory, when, as I have tried to establish in the initial post, it's much more than that. Hopefully, I will be able to get further with this new approach.

I'm glad you asked the question above concerning the billiard ball, because it gives me the chance to clarify an important point: Larson's new definition of motion introduces a new type of motion he called scalar motion, which is the only entity that exists in the theoretical universe that he develops in his works. This means that the theorectical universe based on the Reciprocal System, is a universe of motion; that is, it is a universe of nothing but motion, as defined in the system. In other words, matter is emergent in the universe of motion.

However, once matter exists in the universe, a spatial coordinate system may be used to identify locations that these physical entities occupy, or may occupy, and the change of locations, as a function of time, x(t), then defines the motion of these entities as has been developed under Newton's program of research. These motions, referred to as "vectorial motions," are distinquished from scalar motion in the system, as we shall see.

Therefore, Larson's new system, does not replace Newton's system, but actually subsumes it. Hence, the principles of classical mechanics, and even special relativity still apply in the new system, albeit time and the speed of light are treated in a manner that is different than the way Einstein treats them. Therefore, the answer to your question as to how Larson would describe the moving billiard ball is that he would describe it just as mainstream physicists describe it.

Having said that, however, there are some important caveats as to the currently accepted limits of the relative velocity of matter, which I will eventually explain.

5. Congratulations - keep up the good work!

6. Excal, you've piqued my curiosity. I look forward to your explanations of this model.

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## RST Part II

In the initial post of this thread, I introduced Dewey B. Larson's Reciprocal System of Physical Theory (RST) as a new system of physical theory that goes beyond Newton's system and thus 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.

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: [1]

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 tantalyzing 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." Of course, eventually, the dues have to be paid, and it appears that the time has come for modern theoretical physics to pay up.

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 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, it clearly is better than an absolute background of space and time, it 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 function of x(t).

(see continuation in following post)

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## RST Part II (continued)

Larson takes a completely different approach to the problem. Instead of seeking a background independent theory directly, as Smolin et al do, that 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 motion.

However, this was not the avenue by which he arrived at the conclusion. Rather, he arrived at it because he noticed 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 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 work 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 fixating on gauge symmetries, and applying group theory to quantum mechanics. Nevertheless, a comparison of the RST with Smolin et al's concept of relational space and time, 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 RST, 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 soley as a result of, and as the necessary consequences of, the two fundamental assumptions of the system that Larson called the Fundamental Postulates. 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 entites 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. I hope to be able to present, and sucessfully defend, the bonafides of that claim in the ensuing discussion that I anticipate will take place here. Let me close this post by providing you with the formal expression of the basis of the Reciprocal System, composed by Larson, the two Fundamental Postulates from which the entire universe of motion is deduced:

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.

References:

1) Lee Smolin, The Case for Background Independence, hep-th/0507235, 25 July 2005

9. Excal - I agree with both of the Postulates.

I wish it had been you rather than me trying to explain and justify my theories.

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Hi Excal

You state that,
"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. "

And earlier you state,
"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, "

In these statements the term “space” is actually referring to a distance measure, (v = ds/dt ). The volume of spacetime is realized by incorporating three degrees of freedom. Also the first postulate includes so many ideas, that the meaning of the first postulate is diffused. Might I suggest the following?

Rewriting the first postulate.

First fundamental postulate : the physical universe is compose of one component, motion. Motion describes a reciprocal relationship between distance and time, V = ds/dt.

Second postulate. Motion is expressed in space by allowing motion to exist with three degrees of freedom.

Third postulate : Motion is expressed in discrete (or Quanta sized ?) units.

Snowflake.

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Originally Posted by Snowflake
In these statements the term “space” is actually referring to a distance measure, (v = ds/dt ). The volume of spacetime is realized by incorporating three degrees of freedom. Also the first postulate includes so many ideas, that the meaning of the first postulate is diffused.
Larson initially composed the postulates from seven assumptions, I believe, and later decided, for the sake of conciseness, not to explicitly include those that were clearly implicit. He observed that at least one of these implicit assumptions, could later be expressed explicitly, if omitting it caused confusion.

However, the fact that you infer from the postulates that "the term 'space' is actually referring to a distance measure," indicates the difficulty inherent in clearly, yet succinctly, expressing the assumptions. The term "distance" indicates a span of space measured by a velocity over time. Thus, ds = v*dt. However, we can also indicate the same measure of space in terms of an interval of time. Thus, dt = ds/v. This fact reveals that velocity may be interpreted as a meter of space and time wherein it, in a sense, creates space (distance), given time, or time (interval), given space.

However, there is another interpretation that, although subtle, reveals an important distinction. This interpretation is that the equation v = ds/dt states that motion is equivalent to a ratio of a change in space to a change of time; that is, they are the same thing. Given this interpretation, motion cannot exist except in terms of this ratio of changing space and time. The first fundamental postulate posits the existence of motion, as the sole constituent of the universe. Therefore, it posits the existence of its equivalent, a ratio of changing space and time, as the sole constituent of the physical universe.

Thus, your second postulate, that posits "motion expressed in space" presents a conundrum, similar to the one we see arising from the conflict of GR and QFT: how do we describe motion in space, when space is defined as an aspect of motion? It's like trying to write a wave equation for gravity that must evolve over time, when time is an aspect of gravity! There's a built in contradiction stemming from the definition of things.

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Dear Excal

I hope my suggestions do not come off too much as criticisms; the intent is to clarify. It is from my perspective which is biased from a personal theoretical model that I am being particular at to how you use the term “space”.

You said
“The term "distance" indicates a span of space measured by a velocity over time. Thus, ds = v*dt. However, we can also indicate the same measure of space in terms of an interval of time. Thus, dt = ds/v. This fact reveals that velocity may be interpreted as a meter of space and time wherein it, in a sense, creates space (distance), given time, or time (interval), given space.”

This confuses, for me, the difference between the meaning of distance and space. ( more specifically, note “creates space (distance)”

Defining “space” is not that easy, but blurring the distinction or meaning between the words “distance” and “space” only makes things worse. Looking ahead, once time is integrated into the relationships of spatial configurations, the description of what is Spacetime, will become particularly confusing.

This apparently minor issue is more important to me than most, which is a result of my own theoretical perspective. Since my theoretical perspective is unique and not conventional, my suggestions may or not have any validity. It is rude to interject one’s own personal “agenda” on another’s thread, so I will refrain from interjecting too much of my ideas on your work.

Snowflake

13. I have a couple basic questions I'm hoping you can clarify before this goes further, Excal:

1) What is meant by the term "background" in this context?

2) It is stated that the relationships between these entities are relative "according to law." What law is being referred to here? How is it a law when, apparently, everything is relative?

3) 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.

I'm not certain that the conclusion ("makes perfect sense") follows. Perhaps you can clarify what is meant by "space being the reciprocal of time." Mathematically, I see it in the equation, but I'm not sure what this means in a practical sense.

4) The model basically reduces all measurements to a form of motion, correct? As snowflakeuniverse points out, this seems to complicate things such as distance. In this model, how would one express a measurement such as "three feet from point A to point B" and why would it rely on a function of time? Or, is the time considered negligible somehow?

Thanks for dealing with this. It's a very fascinating idea, though I'm reserving judgement until I see more and understand it a little better.

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For some reason, my browser often freezes on this site. I've just spent time answering Snowflake and Kesh, but apparently have lost it in another browser freeze. I will have to defer rewriting it until I have more time, sorry.

Excal

Update:
This is ridiculous. My browser is freezing 9 times out 10 when I try to post to this site. Other sites are fine. Anybody know what's going on?

Never mind, I think I found the problem.
Last edited by Excal; 2005-Sep-09 at 10:18 PM. Reason: To expand

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## RST Part III

As explained in the previous posts, Larson realized that the definition of motion does not require a change in the location of a physical entity, measured in terms of a background of space and time. He realized that motion is the equivalent of a space/time ratio, marking the continuous march, or a progression, of space and time. Consequently, he posited the existence of such motion, or ratio of progressing space and time, as the sole constituent of a theoretical universe.

Since the entire Newtonian system of physical theory is based on the definition of motion as the change of a physical entity's location, x, in some interval of time, t, or the function x(t), the change in this definition requires a new system of physical theory. One that is based on the new definition of motion. However, as mentioned previously, the new definition of motion does not replace the former definition. Rather, it expands the range and meaning of motion into a new realm, while preserving the results obtained on the basis of the former definition in the Newtonian system, even though some of these may now need to be reinterpreted in light of the new definition.

Needless to say, when one considers the significance of such a prospect, given the almost mind-boggling body of work accomplished in the Newtonian system, it's rather difficult to assimilate it adequately. Especially, when one regards the level of technical sophistication, which modern theoretical physics has reached in the last 100 years. The disconnect between the practicing professionals in the Newtonian system, and the neophytes endeavoring to embrace the possibilities of the new system, is immense to say the least.

Yet, there is a crisis in the Newtonian system today, as Smolin points out so eloquently in the paper we've been discussing. Such a crisis is exactly the sort of development that, according to Thomas Kuhn, presages a scientific revolution. [1] In fact, the shift in paradigm that Kuhn describes as necessary to precipitate the revolution has been widely anticipated for many years, but no one in the community has had a clue as to what it might be, except that there seems to be a consensus that, whatever it is, it is likely to have something to do with our understanding of the nature of space and time.

David Gross, a recent recipient of the Nobel Prize in physics, and a leading light in string theory, discussed this subject with a PBS NOVA correspondent in an interview for the show "The Elegant Universe," based on Briane Green's book with the same title. [2] Gross clearly expects that the coming revolution will change our view of the nature of space and time:

This revolution will likely change the way we think about space and time, maybe even eliminate them completely as a basis for our description of reality.
Gross, like many physicists today, places his bets on string theory, but he understands that string theory may only be a harbinger of what's to come:

In string theory I think we're in sort of a pre-revolutionary stage. We have hit upon, somewhat accidentally, an incredible theoretical structure, many of whose consequences we've worked out, many of which we're working out, which we can use to explore new questions. But we still haven't made a very radical break with conventional physics. We've replaced particles with strings—that in a sense is the most revolutionary aspect of the theory. But all of the other concepts of physics have been left untouched—a safe thing to do if you're making changes.
Indeed. By the same token, however, it's clear that the change needed must be a "sea change," a revolution cannot be precipitated by a minor change. As Gross puts it:

On the other hand, many of us believe that that [replacing particles with strings] will be insufficient to realize the final goals of string theory, or even to truly understand what the theory is, what its basic principles are. That at some point, a much more drastic revolution or discontinuity in our system of beliefs will be required. And that this revolution will likely change the way we think about space and time, maybe even eliminate them completely as a basis for our description of reality—that is, leave us regarding them rather as emergent approximate concepts that are useful under certain circumstances. That is an extraordinarily difficult change to imagine, especially if we somehow change what we mean by time, and is probably one of the reasons why we're still so far from a true understanding of what string theory is.
Clearly, the pursuit of string theory has raised some startling issues about our most fundamental assumptions regarding the nature of space and time. This implies in turn that a change in these assumptions, when it comes, will have an astonishing impact on the science of physics. Gross characterizes it as a new idea that breaks with the concepts of the past that have been the basis of physical theory historically:

In order to achieve a true understanding of string theory, some new idea will be required, and most likely, some break with the concepts on which we've traditionally based physical theory. This has happened before. In the last century, there were two such revolutions having to do with relativity and with the quantum theory, which was an incredible break with the classical notions of physics. Those revolutions were achieved in the end by discontinuous jumps that broke completely with the past in certain respects. It's not too hard to predict that such a discontinuity is needed in string theory.
But Gross stresses the point that the nature of the coming change is impossible to predict:

What's harder to predict is what kind of discontinuity is needed. Discontinuity jumps like that—revolutions—are impossible to predict. They require some totally new idea. A lot of us are waiting for such a new idea that will give us an alternate to our traditional notion of space and time perhaps—or perhaps some other new idea. Something is missing that is most likely not just another technical development, another improvement here or there, but something that truly breaks with the past. And all the indications are that it has to do with the nature of space and time.
So, a revolution is expected, one that entails a "totally new idea" that "has to do with the nature of space and time." Moreover, it is expected that the impact of this new idea of space and time will cause "a break with the concepts" of the past "on which we've traditionally based physical theory." Obviously, the new idea of the nature of space and time that forms the basis of Larson's Reciprocal System is a perfect candidate to fulfill Gross's prediction.

(See continuation in following post)

16. Originally Posted by Excal
For some reason, my browser often freezes on this site. I've just spent time answering Snowflake and Kesh, but apparently have lost it in another browser freeze. I will have to defer rewriting it until I have more time, sorry.

Excal
A very good practice is to write long responses in WordPad or whatever text editor you have on hand, then copy & paste it into the forum for posting. If it fails, you can just copy & paste again.

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## RST Part III (continued)

However, to recognize the promise of Larson's innovation across the huge disconnect that exists between the modern day practicioner, working within the Newtonian system, and the neophyte amatuer, embracing Larson's system, is exceedingly difficult. To succeed, it seems that we must find some common ground that will entice those whose professional career is one large investment in the Newtonian system to risk their careers to investigate the promise of the new system. The most likely prospect for finding that common ground, I believe, lies in the principles of symmetry.

One of the most important developments in the field of physics in the last hundred and twenty years is the understanding of invariance principles. These principles underlie the processes of theory development in the Newtonian system of physical theory, in a deep and intriguing manner. They began to be applied as it became clear that the validity of physical laws, explaining the regular behavior of physical phenomena, had to persist across transformations of space and time separately, as in different locations in space, and at different moments in time, as well as together, as in moving frames of reference. However, it soon became apparent that these tests of invariance of physical laws could be expressed as laws in and of themselves. Invariance leads to laws of conservation of energy, momentum and charge, for instance, as first proven by Emmy Noether.

Eventually, the idea of invariance grew to include the concept of scale as well, which as it turned out, led to a great increase in the ability to classify force laws, and to identify those that are fundamental by means of symmetries that could be seen to exist in group theory, and they enabled the prediction of events based on laws whose invariance arises from the principles of symmetry in these groups. Since the grand goal of the Newtonian program of research is the classification of these force laws, in terms of a few fundamental particles and a few fundamental interactions, the effacacy of this approach has had a major impact on the philosophy of physics.

In fact, Gross, following Wigner and others, asserts that "the primary lesson of physics in this century is that the secret of nature is symmetry;" that is, that "symmetry dictates interactions." [3] Gross attributes this deep understanding and appreciation of symmetry to Einstein, whose "great advance in 1905 was to put symmetry first, to regard the symmetry principle as the primary feature of nature that constrains the allowable dynamical laws." Gross stresses that such a change in point of view "is a profound change of attitude," that enabled Einstein to "score a spectacular success" ten years later, with general relativity. GR is based on a local symmetry, the principle of equivalence between inertial and gravitational mass, which dictates the dynamics of gravity. Then, as quantum mechanics emerged in the 20th Century, principles of symmetry assumed an even more fundament role, until today, "it serves as a guiding principle in the search for further unification and progress." [4]

However, there are two kinds of symmetry that have been the focus of modern physics, global symmetry that embodies the invariance of space and time separately as locations, and the invariance of space and time together, as motion, and local symmetry, which has to do with the scale of space and time. Thus, global symmetries express the invariance of physical laws in different physical situations, such as the locations of events that are translated or rotated, or the timing of events that occur at different times, or events in a moving frame of reference, a so-called inertial frame of reference.

Local symmetry transformations, however, do not change the location or time or move the frame of events. Local symmetry transformations change the description of the event in terms of the scale (gauge), or phase of the event. For instance, an EM field can be changed by merely introducing a vector potential, but the values of the E and B fields are not affected by the potential. At first, these local symmetries were not regarded as real, eventually, however, they came to dominate the thinking of physicists, and in fact, are now believed to be more real than global symmetries. Gross states:

Indeed today we believe that global symmetries are unnatural. They smell of action at a distance. We now suspect that all fundamental symmetries are local gauge symmetries. Global symmetries are either all broken (such as parity, time reversal invariance, and charge symmetry) or approximate (such as isotopic spin invariance) or they are the remnants of spontaneously broken local symmetries.
The dramatic success with symmetry has led to the inquiry as to why nature should be so symmetrical as this, and to the search for the "fundamental symmetries." As Gross puts it:

When searching for new and more fundamental laws of nature we should search for new symmetries. Current theoretical exploration in the search for further unification of the forces of nature, including gravity, is largely based on the search for new symmetries of nature. Theorists speculate on larger and larger local symmetries and more intricate patterns of symmetry breaking in order to further unify the separate interactions.
Of course, the most famous of these, and the one string theorists have searched for decades to find, is supersymmetry. But they haven't found it. Many think that this is because it doesn't exist, but others are convinced that it will be found at higher energies, which is why the LHC at Cern is so important.

Meanwhile, however, a new, fundamental, symmetry has been found. It is the symmetry of space and time as the reciprocal aspects of scalar motion. This symmetry is both local and global; that is, changing the scale of the discrete units that form the space/time ratio does not alter the symmetry, but altering the symmetry of the space/time ratio has the global effect that creates the physical constituents of radiation, matter, and energy, together with their properties such as propagation, gravitation, and entropy.

In the next post, we will explore the mathematical aspects of this symmetry and show how it is broken, the consequences that follow, and how it answers Gross's question, "Why is nature symmetric?" In regards to this question, Gross explains:

There are at least two views. The first is based on the paradigm of condensed matter systems where unexpected and new symmetries often occur, although they are not present in the fundamental laws. The prime example is the appearance of symmetry in the behavior of long-range fluctuations of a system undergoing a second-order phase transition. Here one has the phenomenon that at the fundamental, short distance or high energy, level there is no symmetry. Rather the symmetry emerges dynamically at large distances.

Could this be the reason for the "fundamental symmetries" that we observe in nature? Could they be dynamical consequences of an asymmetric physics? I believe not. The lesson of the history of physics in this century points to the opposite conclusion. As we explore physics at higher and higher energy, revealing its structure at shorter and shorter distances, we discover more and more symmetry. This symmetry is usually broken or hidden at low energy. I like to think of the first paradigm as Garbage in--Beauty out, and the second as Beauty in--Garbage out.
In the light of space and time, however, we see that neither of these paradigms are descriptive of the true situaltion. Indeed, we find that the hidden beauty found in the the perfect symmetry of scalar motion is manifest over and over again as the source of the beauty of nature's plethora of physical forms.

References:

1) Thomas Kuhn, Structure of Scientific Revolutions, www.des.emory.edu/mfp/Kuhn.html

2) David Gross, "Viewpoints on String Theory," NOVA, http://www.pbs.org/wgbh/nova/elegant/view-gross.html

3) David Gross, "Gauge Theory- Past, Present, Future?" psroc.phys.ntu.edu.tw/cjp/v30/955.pdf

4) David Gross, "The Role of Symmetry in Fundamental Physics," http://www.pnas.org/cgi/content/full/93/25/14256

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Snowflake wrote:

You said
“The term "distance" indicates a span of space measured by a velocity over time. Thus, ds = v*dt. However, we can also indicate the same measure of space in terms of an interval of time. Thus, dt = ds/v. This fact reveals that velocity may be interpreted as a meter of space and time wherein it, in a sense, creates space (distance), given time, or time (interval), given space.”

This confuses, for me, the difference between the meaning of distance and space. ( more specifically, note “creates space (distance)”

Defining “space” is not that easy, but blurring the distinction or meaning between the words “distance” and “space” only makes things worse. Looking ahead, once time is integrated into the relationships of spatial configurations, the description of what is Spacetime, will become particularly confusing.

In the Reciprocal System there are two kinds of motion, scalar motion and vectorial motion. Vectorial motion is the motion of physical entities that we are all familiar with. It has magnitude and direction. Scalar motion is new to most of us. It has magnitude, but no specific direction, because, by definition, a scalar value is a magnitude that can only increase or decrease, like the prices of stock on the stock exchange.

In the case of vectorial motion between an object at point A, moving toward point B, we can quantify the distance between A and B, the magnitude of the motion, and the direction of the motion. The distance between the point A and the object increases, and the distance between point B and the object decreases, as a function of time.

On the other hand, scalar motion between point A and B does not require an object to define it. It has only magnitude, and the distance between the points A and B either increases or decreases as a function of time. An observer at point A would see point B moving directly away from or directly towards point A. However, an observer at point B would disagree and maintain that point A is moving directly away from or directly towards point B. The best example of this kind of motion is the motion of the receeding galaxies. An observer on any one galaxy will always report the same thing: all other galaxies are moving directly away from the observer, regardless of which galaxy is selected.

So, what we regard as distance between points is nothing more or less than the space aspect of a past or future motion; that is, the motion, when it occurs, creates the distance between objects. We can understand this, when we think about measuring the distance. We can't measure the space aspect of motion without repeating it somehow. In other words, to measure the distance between any set of points, we must supply a motion of some kind and measure the space aspect of the motion we are measuring. We can run a rule from one point to the other, but we have to move the rule into place. We don't care about the time aspect of the motion, so it doesn't matter how fast we move the rule. We just need to count the space aspect of the motion.

We can try all sorts of different methods to measure the distance, but all of them require motion: the light of a laser, the sound of sonar, the ambient light that our eyes use to triangulate, etc. In short, there is no way to measure distance directly. We must provide a motion of some sort to do so. Therefore, it follows that space doesn't exist apart from motion, only the motion exists, and what we measure when we measure distance is simply the space aspect of the past motion, which we recreate in the measuring process, or some future motion between the points that we contemplate.

Kesh wrote:

I have a couple basic questions I'm hoping you can clarify before this goes further, Excal:

1) What is meant by the term "background" in this context?

Smolin uses the term background to refer to the 3D non-dynamic structure of space and time required by QFT, and the 4D dynamic structure of spacetime required by GR.

2) It is stated that the relationships between these entities are relative "according to law." What law is being referred to here? How is it a law when, apparently, everything is relative?

It means that the relationships between entities are determined by events that are governed by the properties of the entities and the regular patterns of behavior, identified as physical laws, that apply to them; that is, they are causal. In contrast, the structure of space that we imagine exists, consisting of the set of points satisfying the postulates of geometry, do not meet this requirement.

3) 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.

I'm not certain that the conclusion ("makes perfect sense") follows. Perhaps you can clarify what is meant by "space being the reciprocal of time." Mathematically, I see it in the equation, but I'm not sure what this means in a practical sense.

When we think of extension space, we imagine that it consists of a set of points that satisfies specified geometric postulates. To think of this expanse as the reciprocal of time is absurd. However, when we realize that space is nothing more than a progressing aspect of motion, the reciprocal of progressing time, in the equation of motion, and that it doesn't exist as such apart from motion, as some kind of static lattice structure, for instance, then it's much easier to understand. The abstract set of points that we are accustomed to calling space, are only an abstraction of locations, to which motion can move, is moving, or has moved, things. These locations and the distances separating them do not exist in reality.

4) The model basically reduces all measurements to a form of motion, correct?

All measurements of space and time, yes.

As snowflakeuniverse points out, this seems to complicate things such as distance. In this model, how would one express a measurement such as "three feet from point A to point B" and why would it rely on a function of time? Or, is the time considered negligible somehow?

See answer to Snowflake above. The only thing that exists is motion, so to measure distance, we have to measure the space aspect of a motion. After we have measured it, we can then refer to the distance as "three feet from point A to point B." If we don't care about the time aspect of the motion separating the points, then we can disregard it as we do when using a yardstick, or tape measure. How fast we move the measure is not relevant. However, if we are measuring the distance with a laser or sound wave, then we have to know the speed of the motion we are measuring and the time involved, in order to calculate the distance.

I hope this helps. If not, don't give up. Just let me know.

Regards,

Excal

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## RST Part IV

As we have seen, according to Hestenes, the grand goal of Newton's program of research is to "describe and explain all properties of all physical objects." Hestenes identifies two fundamental assumptions that are necessary to accomplish this ambitious goal. First, it is assumed that all physical objects are composites of particles, and, second, it is assumed that the behavior of a particle is governed by its interactions with other particles. Thus, the program seeks "to explain the diverse properties of objects in terms of a few kinds of interactions among a few kinds of particles." [1]

Hestenes explains that the power of this approach lies in the fact that particles, and their interactions, can be precisely defined in terms of the motion of the particle; that is, the description of its existence at a given location, at a given moment of time, consists of a mathematical function, x(t). Using this function and the principles of calculus, physicists can define the velocity and momentum of any particle at a given location, x, and at a given instant of time, t, and quantify interactions between them in terms of the acceleration and force aspects of these motions, because the derivatives and integrals of the calculus enable them to precisely model both the existence of the particles and the interactions between them, and consequently predict their behavior.

However, there is an additional assumption in this program that Hestenes fails to clearly elucidate. It is that the description and explanation of the behavior of the particles, in terms of their interactions, assumes a knowledge of the inertial, magnetic, and electrical properties of the particles. In other words, the Newtonian program that seeks to describe nature in terms of the existence of particles and their interactions from moment to moment, must assume first that particles exist with a given value of mass, magnetic moment, and charge; that is, these values must be put into the system, before the power of the system, to investigate the properties of particles of matter and to classify them and their interactions accordingly, can be applied!

Thus, given two particles, particle A and B, the properties of one of which, particle A, are unknown, we can calculate its properties, if we know its interaction with B, the properties of which are known. Or, alternately, if we know the properties of particle A, we can predict its interaction with B. However, because the foundation of the system is based on the function x(t), a function of space and time, and the dimensions of inertia, magnetic, and electrical properties are not known in terms of space and time, the function x(t), used to describe the behavior of particles and their interactions is an observed relationship; that is, f, the force, or quantity of acceleration, is simply a unit of acceleration, expressed in terms of space and time, multiplied by mass, a measured quantity with an unknown relationship to space and time.

In other words, we don't know why the total quantity of acceleration is determined by the number of mass units of a particle. We just know that it is, and we use this knowledge in our system. Without the knowledge of the mass (or magnetic moment, or charge, if applicable) of a particle, we must know the total acceleration, the force acting on it. Without a knowledge of the force, we must know the mass. For instance, given the mass, we can find the momentum of a particle, located at point x, at time t, because it is a function of x(t). Conversely, given the momentum, we can find the mass of a particle located at point x, at time t, for the same reason.

What this means is that Hestenes' characterization of the grand goal of Newton's program, as an effort to "describe and explain all properties of all physical objects ... in terms of a few kinds of interactions among a few kinds of particles," is entirely limited to the description and explanation of how the given properties of particles are related to one another.

Moreover, because the function x(t), which is the fundamental relationship in the system, upon which everything is based, is a relation of space and time, the definition of space and time is crucial to its operation. Therefore, the definition of space and time that the system employs, Newton's definition initially, is crucial to the operation of the system. Consequently, whenever the system has failed to produce the correct results, it is the definition, or interpretation of the definition, of the nature of space and time, that has been the target that physicists naturally zero in on.

Fundamentally, this problem is seen as a challenge of coping with the frame of reference that the definition of space, as a set of points that satisfies the postulates of geometry, creates. Early on, they had to contend with relatively moving frames of reference of space and time, wherein corrections were needed to ensure that comparisons were made in proper inertial frames to preserve the integrity of the function x(t). Thus, we see the Galilean transformations, the Lorentzian transformations, and, then, the gauge transformations devised to cope with increasingly sophisticated issues of space and time.

However, we don't need to know the details of these issues and their resolutions to know that they are issues stemming from the definition of space and time, used in the Newtonian system of physical theory. This is clear to all, as we've seen in the discussion of David Gross's interview on PBS, in the previous post. Hence, the question, how can we define space and time in such a way as to avoid these problems, is clearly coming more and more into focus. As we saw in the beginning of this series, the major recalcitrant problems that face modern physicists are once again being attributed to the background reference of space and time, required by the function x(t). Indeed, it introduces into the latest and most modern of research projects in Newton's program, namely GR, QFT, and string theory, irreconcilable contradictions. So, this time they don't just seek to change it, as was done in the past, but they seek to eliminate it altogether.

Nevertheless, it's vital to point out, that, if the problems and challenges that persist in the Newtonian program, are so obviously connected with the nature of space and time, then maybe that's a clue that our efforts to describe and explain how the properties of the constituents of radiation, matter and energy, namely their inertial, magnetic, and electrical properties, are related to one another, are in trouble, because we don't know the true nature of the properties themselves. Maybe, the most important lesson we have learned in the course of pursuing the Newtonian research program, is that the nature of these properties is intimately related to space and time. The fact that needed corrections to the frame of reference used are constantly arising, indicates that the properties themselves, not just the relations between them, have something to do with space and time intrinsically.

Therefore, perhaps the time has come to change the program. To change it from a program that seeks to describe and explain how, given the properties of particles, they relate to one another in a reference frame of space and time that describes their motion, to a program that seeks to describe and explain their intrinsic properties, in terms of the only known relation of space and time, motion.
Last edited by Excal; 2005-Sep-10 at 04:55 PM. Reason: Edit Title

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## RST Part V

Clearly, given the trouble that the traditional concept of space and time has brought to mankind's efforts to understand the physical universe, there ought to be a better way. Indeed, it would really be helpful, if we had an absolute reference, against which we could measure magnitudes of motion, thus avoiding the need for corrections altogether. However, as we know, there can be no special rest frame of reference relative to which all motion can be defined. The closest to such a thing, and the solution Einstein turned to, was Mach's idea of the array of fixed stars forming an absolute reference, but this concept too, is, in the final analysis, not satisfactory. Consequently, we need to go back to the drawing board and see what the options are.

The only known relationship of space and time is motion. In this relationship, time is the reciprocal of space. Larson's positing of this relationship as the sole constituent of the physical universe, existing in discrete units, and in three dimensions, leads to a concept of a progression of space, which corresponds to the familiar progression of time. That we can observe evidence of such a space progression in the motion of the distant galaxies, receeding away from us and each other at extreme velocities, lends credence to the assumption. Larson adds one other assumption to this motion: that it exists in discrete units. This means that we can quantify it as the ratio of two magnitudes that either are constantly increasing, or constantly decreasing.

In the case in which both space and time are increasing at the same rate, we can express the progression ratio as the unit ratio, s/t = 1/1; that is, for every increase in the number of space units, there exists a corresponding increase in the number of time units. This then is the initial condition of the motion. Notice the perfect symmetry inherent in this relationship of space and time. Also notice that the symmetry can be broken exactly two ways: the progression of one aspect or the other can be larger than unit ratio. For instance, the progression of time can be larger than unity, in which case s/t = 1/n, or the progession of space can be larger than unity, in which case s/t = n/1, where n > 1.

Of course, the magnitude of this universal motion depends upon the size of the space and time units we select. Since the constant speed of light plays such a central role in physical phenomena, it is reasonable to assume that the magnitude of the unit ratio, s/t = 1/1, is equal to c. This means that, if we can find the size of either the space unit, or the time unit, we can calculate the size of the unit of the reciprocal aspect. Larson selected the Rydberg constant for this purpose, since it also seems to play a central role in the phenomena of radiation of the hydrogen atom. The Rydberg frequency is 3.2899 x 10^15 Hertz, so the reciprocal of this frequency is a time unit equal to 3.03961 x 10^-16 seconds. The accepted value of the Rydberg constant has changed slightly since Larson's day, so this figure differs slightly from his.

For reasons which will be explained below, the actual unit of time, which Larson called the natural unit of time, that enters into the unit progression ratio, is half this value, which he calculated as 1.520655 x 10^-16 seconds, as seen in his publications. Hence, the natural unit of space is then calculated as c divided by the quantity of time, or 4.558816 x 10^-6 cm. So, the physical situation, at this point, is a constant increase of space/time, the magnitude of which is 2.997930 x 10^10 cm/sec, the speed of light (again, using the figures in Larson's publications, which have been slightly modified since.)

However, it's important to note, that this is nothing but a ratio of the discrete units of a scalar progression. There is no information in the equation, s/t = 1/1, indicating dimensions, and there is only one progression ratio. Nevertheless, the assumptions in the first postulate are that the motion of the universe exists in discrete units and in three dimensions. So, given that this universal progression is the initial state of our theoretical universe, the question is, how do we proceed and end up with discrete units of motion existing in three dimensions?

Notice that, in this initial state of unit motion, there is no reference frame, no structure against which the magnitude of the unit motion can be referenced. The state of the unit progression is all that exists at this point. It is the equivalent of nothing. In order for something to exist, in order for discrete (separate) units of motion to exist, there must be a deviation from this initial state of uniform motion. Earlier, it was pointed out that there are two possibilities, or "directions," in which the perfect symmetry of unit motion could be "broken." One possibility exists when the space/time progression ratio is greater than unity, (1+n)/1 and the other when it is less than unity, 1/(1+n).

(See continuation in following post)
Last edited by Excal; 2005-Sep-10 at 10:29 PM. Reason: Correct a typo

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## RST Part V (continued)

Of course, this is a result of our interpreting the definition of magnitude in an "operational" sense, as opposed to a "quantitative" sense. The difference is enlightening. Hestenes traces the history of mathematical development with respect to the Clifford algebras and the geometric product, which Clifford developed by combining the algebraic ideas of Grassmann and Hamilton, and he explains the meaning of the two interpretations that was uncovered by Clifford:

Clifford may have been the first person to find significance in the fact that two different interpretations of number can be distinguished, the quantitative and the operational. On the first interpretation, number is a measure of 'how much' or 'how many' of something. On the second, number describes a relation between different quantities.
It is the operational relation between the units of the space/time progression that constitutes the magnitude of scalar motion, and it is only because of this that the possibility exists that it can have two "directions." The two "directions" may be designated positive and negative, up and down, left and right, or whatever. The important thing to understand, however, is that the special meaning of "direction," with respect to this magnitude, has a scalar meaning of "direction" that is not geometrical. For this reason, the distinction will be made between the two by placing quotation marks around the word to indicate its scalar meaning, as opposed to its geometric meaning.

There is a point of deep significance here. The story is told of a young school girl in a poor Welsh village who, when she was introduced to negative numbers, "got into a crying jag:" [5]

Hanmer school left its mark on my mental life, though. For instance, one day in a grammar school maths lesson I got into a crying jag over the notion of minus numbers. Minus one threw out my universe, it couldn’t exist, I couldn’t understand it. This, I realised tearfully, under coaxing from an amused (and mildly amazed) teacher, was because I thought numbers were things. In fact, cabbages. We’d been taught in Miss Myra’s class to do addition and subtraction by imagining more cabbages and fewer cabbages. Every time I did mental arithmetic I was juggling ghostly vegetables in my head. And when I tried to think of minus one I was trying to imagine an anti-cabbage, an anti-matter cabbage, which was as hard as conceiving of an alternative universe.
I think this anecdote ought to included in every textbook for elementary math teachers. I had a similar experience when I was introduced to imaginary numbers by an inept teacher who couldn’t, or didn’t bother, to adequately explain the idea behind the “number” ‘i’. What I have learned since is that, just because we can grasp an idea abstractly, by divorcing it from physical concepts, it doesn’t necessarily mean that we understand the meaning underlying the concept, only that we can understand how to use it as a method.

For instance, the idea of negative space is absurd, but, nevertheless, we can use it to great advantage. However, it took mankind centuries to take this giant leap for the first time, and it was not done without a lot of hand wringing and pain. Fortunately, I’ve finally found that we can understand the meaning of the idea as well as how to use it abstractly, but only if we are willing to ferret it out by thinking on our own, definitely not by reading textbooks. The key is to understand that space doesn’t exist as stuff that has properties, like cabbages, or fabric, and that the early Greeks were wise in keeping the ideas of magnitude and numbers separate.

It turns out that the ideas of operationally defined magnitudes as opposed to quantitatively defined magnitudes, and the proper use of real numbers in these respective definitions, can help us avoid a lot of grief, not only for naïve school children, trying to learn mathematics, but also for the sophisticated adults they later turn into, who then try to formulate physical theories.

Under the current definition of space, as a set of points satisfying the postulates of geometry, negative space doesn't exist. But under the new definition of space, as the reciprocal aspect of time, in the equation of motion, a negative magnitude of motion does exist, and just as positive space can be generated by positive motion, so inverse space, or time, can be generated by negative motion. But this is getting ahead of ourselves. The important thing to understand now is that two "directions" of scalar motion exist in the universe of motion, under the new definition.

Not only is it important to understand the two possible "directions" of scalar motion, but it's also very important to understand that the datum for these possible magnitudes, the "zero" reference from which they are measured, is 1/1, not zero. The easiest way to keep this in mind is to think of the motion as an old fashioned pan balance, where equal weights on either side balance out, so that 1:1 is actually zero, and 1:2 or 2:1 is a magnitude of one, in two different "directions."

Larson calls this unit motion, where the space/time progression ratio is balanced, the natural reference system. It is an absolute reference system from which magnitudes of scalar motion may be reckoned, providing, at long last, the widely sought basis for a background free definition of motion.

References:

5) Sean Carroll, "Minus Numbers," preposterousuniverse blog, http://cosmicvariance.com/2005/08/03...bers/#comments

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## Commentary

Ok, I'm going to stop there (Part V) with the introduction. I've tried to show how the Reciprocal System, by defining motion with a new interpretation of the nature of space and time, provides an absolute reference for reckoning motion that is impossible to attain with the Newtonian interpretation of the nature of space and time. In providing this new, dynamical, reference system of motion, the Reciprocal System happens to fit the description of what is wanted in the world of modern theoretical physics, both from the point of view of eliminating the background structure of space and time, and from the point of view of discovering nature's "fundamental" symmetry.

In short, we may say that , now, the game has changed. In the Newtonian system of physical theory, which I'm going to presumptiously refer to as the legacy system of physical theory (LST), for brevity's sake, everything is based on the function x(t), given Newton's laws of vectorial motion. In the Reciprocal System of physical theory (RST), everything is based on the function x(t), and a new function, t(x), given the new interpretation of the nature of space/time, as the two reciprocal aspects of scalar motion.

More on this later.

23. Wow. Okay, you'll have to excuse me for not writing anything until now. This is a lot to absorb, especially for someone who's been out of school for years. I'll try to come back and tackle it a bit at a time.

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Do you have an example of a calculation in the Larsonian framework? For example, say I drop a ball from a height of 5 metres. How long does it take to fall (for simplicity assume that g=10 m/s^2)?

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Originally Posted by Fortis
Do you have an example of a calculation in the Larsonian framework? For example, say I drop a ball from a height of 5 metres. How long does it take to fall (for simplicity assume that g=10 m/s^2)?
Larson's Reciprocal System of Physical Theory consists of a definition of a new type of motion, called scalar motion, which is based in turn on a new interpretation of space and time, as the reciprocal aspects of a universal progression. Larson posits that the physical universe is composed entirely of this motion, and the theory he developed, in which he assumes this, begins with nothing but this motion, as its initial condition, and then Larson develops its logical consequences; that is, the necessary consequences that must follow from the basic assumptions.

As a result, theoretical entites emerge in the course of the theory's development that correspond to observed physical entities with the properties of radiation, matter, and energy. Since these properties include mass and gravity, the behavior that Newton first observed and formulated as his laws of motion, and the universal law of gravity, hold. It's in the explanation of the origin of mass, magnetic moment, and charge, that the RST goes beyond the LST. It does not change the observed relationship of physical entities as formulated by Newton. Therefore, there is no Larsonian framework in which the description of the ball's gravitational interaction differs from that which was first described by Newton. Newton's laws are observed relationships, and in the low limit, as they say, are very accurate.

What the RST brings to the table goes beyond the LST, in that it describes and explains the origin of the mass and the gravitational force. Roughly speaking, the origin of the mass of a physical object is is due to a combination of discrete, inward, scalar motions. The gravitational force is a manifestation of the same motion that constitutes the matter. It is the mutual, independent, inward, motion of matter that appears to exert a force at a distance, which we observe in the expression F = Gmm'/r^2. However, the reason that we cannot detect a gravitational force (except by its effects), neither modify it, neither screen it off, is that it is simply an inward scalar motion, causing gravitating bodies to follow an independent path, inward toward all other bodies.

This inward scalar motion is the inverse of the outward scalar motion observed in the distant galaxies, which are receding outward from one another in every direction. The origin, limits, and interactions of these scalar motions is what the RST deals with. It does not redo what the LST has already done. A simple example of a calculation in the Larson framework would be the periodic table, where the atomic number of the elements, and the approximate mass of the isotopes is calculated. The RST theoretical result matches the observed atomic numbers exactly, and it derives the observed isotopic masses as well as can be expected, given the complex environmental factors involved.

Interestingly, however, the RST atomic model differs radically from the quantum mechanical, nuclear, model. Yet, the QM model does not correctly predict the atomic numbers of the elements, nor the isotopic masses. A brief article on this is available on the RST Wiki here:

http://www.rstheory.com/wiki/index.php/Wheel_of_Motion

The Wheel of Motion is simply a different format for the periodic table of elements that shows more clearly why the gaps appear in the table and why the table rows of equal length appear in pairs. I would include it here, but I don't know how except as an attachment. Do image attachments display in these posts? I'll try it and see what happens.

26. I think I agree with Fortis that a few real examples would be in place now, some physics instead of philosophy. It may all be clear to you Excal, but for me it would work better with some gedanken experiments.
I have e.g. the idea that your scalar velocity is just the total velocity, i.e. v(scalar) = sqrt(vx^2 + vy^2 + vz^2).

edited coz I forgot the 2nd part

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## Gedanken Experiments

Originally Posted by tusenfem
I think I agree with Fortis that a few real examples would be in place now, some physics instead of philosophy. It may all be clear to you Excal, but for me it would work better with some gedanken experiments.
I have e.g. the idea that your scalar velocity is just the total velocity, i.e. v(scalar) = sqrt(vx^2 + vy^2 + vz^2).
Without a background structure of space and time, there are no x, y, and z coordinates to work with initially. In the relationalist view that Smolin calls the "physicists' relational conception of space and time, the fundamental properties of the elementary entities consist entirely in relationships between those elementary entities." Normally, these, "elementary entities" are regarded as particles of matter, but this presents a problem right from the start, because if we start with matter, we have immediately separated it from space and time, and therefore have implicitly defined a container, which is a background structure of space and time.

So, the really big problem is primarially a philosophical, or a conceptual, problem of how to describe matter in terms of space and time. Aristotle put it this way:

The entire preoccupation of the physicist is with things that contain within themselves a principle of movement and rest.
Einstein wrote:

The development during the present century is characterized by two theoretical systems essentially independent of each other: the theory of relativity and the quantum theory. The two systems do not directly contradict each other; but they seem little adapted to fusion into one unified theory. For the time being we have to admit that we do not possess any general theoretical basis for physics which can be regarded as its logical foundation. The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built by pure deduction.
and, finally, Smolin writes:

A successful unification of quantum theory and relativity would necessarily be a theory of the universe as a whole. It would tell us, as Aristotle and Newton did before, what space and time are, what the cosmos is, what things are made of, and what kind of laws those things obey. Such a theory will bring about a radical shift - a revolution - in our understanding of what nature is. It must also have wide repercussions, and will likely bring about, or contribute to, a shift in our understanding of ourselves and our relationship to the rest of the universe.
So, first the RST should tell us "what space and time are." It does. Space and time are the two reciprocal aspects of motion. Next, it should tell us, "what the cosmos is." It does. It tells us that the cosmos is something that is composed of one component, motion, existing in three dimensions, in discrete units, and with two reciprocal aspects, space and time. Finally, it should tell us "what things are made of, and what kind of laws those things obey." It does. It tells us that all things are motion, combinations of motion, or relations between motion. By so doing, the RST "brings about a radical shift - a revolution - in our understanding of what nature is," and it has "wide repercussions."

As you can imagine, something that meets these requirements is difficult even to introduce, at least in a way that people can readily understand. It's not something you can just print on a t-shirt. So, that's why I have taken such pains to describe the philosophical context here. Now, there is a call for some gedanken experiment, some example of scalar motion that we can sink our teeth into, and I can understand that. However, to do this, we have to be prepared to step back and take ourselves out of the context of the concept that space and time are a container of matter, that there exists a priori a framework of spatial coordinates in which an object of matter can exist at point x, at time t.

This is not easy to do, because every equation that we are accustomed to using assumes that matter exists in a container of space and time, or spacetime. Even the idea of scalar expansion, which tusenfem refers to, assumes first that a point of view, a point of origin, exists, at the center of an expanding sphere that gives meaning to x, y, and z. Thus, if we have such a point, we can define the motion in the expression,

x^2 + y^2 + z^2 - c^2t^2 = 0,

because, as t increases, any point, x, y, z on the surface of the expanding sphere defines a 1D line to the origin that is a solution to the equation, at time t. The thing is, though, how do we do this without defining an initial location at time 0? In other words, as soon as we identify a location at t0, we have necessarily introduced a structure of space and time, x, y, z and t, as the setting for our theoretical universe that eventually will dog us.

The solution to solving this age-old problem lies in the RST's definition of scalar motion as the progression ratio of space/time. Starting with this ratio at unit value, that is, assuming that there is an increase of one unit of space for every unit of increase in time, ds/dt = 1/1, if we then assume that one, or the other, of these aspects reverses the "direction" of its progression continuously, so that it alternately increases, then decreases, instead of uniformly increasing, the unit progression ratio is changed from 1/1 to 1/2 or 2/1, depending upon which aspect's progression is altered.

This is the next step in the development, and I will explain it in more detail in the next part of this series, but I can say here that what this does is profound, because when such a reversal in "direction" occurs, it effectively stops the progression of the reversing aspect of the motion at that point in the progression, creating a reference point, or a zero point, in the space/time progression, depending upon which aspect of the progression is reversing "direction;" that is, it creates a point of reference relative to the ds/dt = 1/1 progression, a difference in the magnitude of the space aspect's, or the time aspect's, progression at that "location" in the progression, relative to the normal 1 to 1 progression.

It is clear that the magnitude of this difference is one unit of motion, which, since we have selected c as the basis of our units, means a relative velocity of magnitude c now exists between the "location" in the progression at which the reversals commenced, and the normal unit progression, which we call the "natural reference system." Since the universal space/time progression is scalar, that means that the magnitude of this difference, c, is effective in three dimensions, because we assume three dimensions are possible in the fundamental postulates. Therefore, the equation,

x^2 + y^2 + z^2 - c^2t^2 = 0,

is a solution to any point on an abstract, expanding, sphere of possible "locations" from the "location" in the progression where the reversals commenced. Therefore, we have effectively "created" a spatial (temporal) coordinate system, by establishing a "point" in the scalar progression, relative to which a set of points can be identified that satisfies the postulates of Euclidean geometry. If we plot these "locations" on a worldline chart, we find something very interesting: "things that contain within themselves a principle of movement and rest," as Aristotle put it. However, now I'm getting too far ahead of myself.

I hope this answer is satisfactory for now. As soon as we understand how we can deduce the existence of physical entities in this system, we can then use that information to develop some interesting gedanken experiments that lead to units of radiation and their properties, units of subatomic matter and their properties, and units of atomic matter and their properties, as in the periodic table of elements. BTW, what do you think of the Wheel of Motion?

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## New Cosmology

In the next post, I'll be getting into more of the details of the fundamentals, but it occurs to me that I might just mention the fact here that an entirely new theory of cosmology comes out of the Reciprocal System. It's fascinating, because it explains, from first principles, the dynamics of the cosmos, from the life cycle of the stars, to the universal expansion of the galaxies, to the operation of gravity and its interaction with the universal expansion on the scale of galactic clusters as well as that of molecules.

It explains, in fact it predicted, galactic explosions before they were observed, and it explains the quasar intrinsic redshift that has surrounded Arp and company in controversy. Indeed, Larson carried on quite a bit of correspondence with Arp, but I haven't had a chance to read it yet. I plan too as soon as I can though.

Again, however, what's so fascinating is that all of the theory stems from the discovery of scalar motion, and the associated reinterpretation of the nature of space and time as the reciprocal aspect of motion and nothing else. Because of this, we have an absolute reference for the magnitude of motion, which leads to physical entities and their properties, which relate to one another as observed by Newton, Oersted, and Maxwell.

But the Newtonian functions x(t) associated with these properties, being observed relationships, cannot be used to explain their origin. In the Newtonian system, these properties necessarily must be a given. In the Reciprocal System, however, the functions associated with x(t) (and t(x)), give rise to the properties of radiation, matter and energy themselves. This leads to the discrete frequencies of radiation, the acceleration of mass, and a completely different model of the atom. The model of the atom leads to a thermal limit, and even an age limit of matter, which in turn explains the energetic explosions of stellar aggregates that cannot be matched by the nuclear model.

The speeds imparted to matter in these gigantic explosions are so great that the properties of mass, magnetic moment, and electrical charge are related by t(x) functions, rather than x(t) functions, which produces phenomena that appears bizzare from our point of view, but that are perfectly understandable given the t(x) functions. Amazingly, the speeds attained can reach a point so great that the roles of space and time are reversed in one, then two, and finally, in all three dimensions of motion, and at this point the matter can no longer be considered matter, but becomes inverse matter and enters the inverse side of the universe of motion as high-speed material rays, the analog of our cosmic rays that are coming to us from the inverse, or cosmic, side of the universe.

Hence, the universe of motion is as symmetric as motion itself, and we find that we live on one side of the symmetry, while an anlogous universe exist on the other side. Matter cycles between the two sectors, as Larson called them, in an eternal cycle, explaining many mysteries that today are perplexing and confounding, given no knowledge of the fundamental symmetry of the universe and the functions t(x), which, like the x(t) functions, proceed from the spontaneous broken symmetry of the equation of motion.

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Originally Posted by Excal
But the Newtonian functions x(t) associated with these properties, being observed relationships, cannot be used to explain their origin. In the Newtonian system, these properties necessarily must be a given. In the Reciprocal System, however, the functions associated with x(t) (and t(x)), give rise to the properties of radiation, matter and energy themselves.
Will you eventually explain how to carry out a calculation using this formalism? No matter how abstract a physical theory is (GR which is coordinate independent, or QM which has a probabilistic aspect), if it can't make a prediction in terms of physically measurable quantities, then it isn't very useful.

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By the way, if I seem to want to jump to straight to the mathematical meat of the formalism, it's because I first came across the Larsonian approach in the postings of Robert E M'cElwaine (should have a smilie for a crucifix, and garlic ), who failed to leave a postive impression.

See, for example, http://www.ratbags.com/ranters/mcelwaine000323.htm

That's why I appreciate the fact that you're actually appear to be trying to answer the questions that people are asking.

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