Discrete and Continuous Realities According to Fundamental Laws of Nature by Rafael Emmanuel Castel

For John, Edwin, James, Xiang, Ray, and everyone:

John, you say:

*** Consider just what "motion" there is; Energy radiates out and mass collapses in. Given that even convention and observation agree these opposing processes are in equilibrium, the simplest explanation is a convection cycle, where radiation expands to the point of cooling down to the degree of coalescing out as a very elemental form of mass. Even the photon might be part of this stage, as it is a quantized amount of radiation essentially created by its absorption in existing mass. ***

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The idea of the formation or condensation of mass out of the gravity field, which I say is a motion field, is pretty much what we (Edwin and I) are saying.

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In his essay, Edwin says, "space can curve in upon itself to produce infinitely dense mass points" and he says "limits prevents this." He then says that "limiting phenomena are defined by mass, charge, and spin." Together these can be interpreted as saying that the curvature of space (the G-field) can collapse into a blackhole singularity--"the infinitely dense mass," although Edwin says "points", which needs clarification. But Edwin says that, because the process gets limited, "the C-field vortices condense to Marjorana neutrinos, electrons and quarks, and supply the mechanisms of weak and strong forces." Thus, curved space (the vortices), limited by some mechanism, condense into mass.

Edwin does not explain the cause or origin of the limiting mechanism that prevents the collapse into blackholes. He also does not explain how the mechanisms of the weak and strong forces work. I think this is because Edwin still has no clear appreciation of the idea of the transformations of motion and because he has not considered the origin of gravity. It is clear that Edwin still clings to the Einsteinian idea of the arbitrary transformations of space and time and he still embraces the idea of the big bang.

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Edwin's C-field idea brings to recollection the idea of dynamic space as particles that was noted, I think by Timothy Ferris in his historical "The Red Limit", as being something that theoreticians until the 70s already considered. The C-field idea also brings to mind the 90s ideas of Astekhar, Smolin and Rovelli regarding "loop space", "loop spacetime", "loop quantum gravity".

The idea of the G-field quantization into mass has actually also been treated by Hoyle, Burbidge, Naarlikar, Brans-Dicke, Barber and several others.

But, as far as I know, all these people failed to re-examine the fundamental relativistic transformation equations and the derivation of Einstein's famous formula E=mc2. This failure continued to mask Einstein's erroneous interpretation that the transformations involved in the phenomena of nature were that of space and time.

The crucial fact that Einstein overlooked is the fact that the variables for mass and energy were subtituted into the equations that led to the famous formula. This crucial fact suggests that the transformations were not that of space nor of time, but of something else indicated in the equations in so much that the substitution suggests that space and time are but backgrounds of the transformations in phenomena.

There is only one other thing represented in the equations -- the variables for the velocities (motions) involved in the transformations. This fact indicates that the fundamental thing that gets transformed into mass and energy is motion.

In my own essay, I emphasize the idea of only the motion of motions, the idea of motion transformations, which is according to the fundamental (foundational) principles of pure kinematics.

The idea of the motions of motions altogether drops the idea of the arbitrary transformations of space and time that Einstein put forth -- and hence it also drops the ideas of space curvature and time dilations or reversals.

Thus, instead of spacetime relativity, I present the idea of kinematic relativity in my essay. Therein I show the derivation of the relativistic transformation equations -- the Lorentzian half-tensor transformation equation and my new full-tensor transformation equation. And I interpret their application solely in terms of the transformations of motion, which has led to the derivation of the genesis formula.

In my essay, I describe the genesis formula as follows:

"This formulation indicates transformations resulting from the three-dimensional translations, instead of the transformations according to merely the two-dimensional translations described by the Lorentz-Einstein formulation."

"We have naturally occurring three-dimensional translations -- that of the gravitational systems. This evidently indicates naturally occurring transformations according to the three-dimensional translations of gravitational systems. Thus, there is the suggestion of continuous increases in the energy content of gravitational systems according to the formulation ΔE=mo[at]2, where the a signifies the gravitational acceleration and the t denotes the elapsed time according to the natural process of duration."

"Because gravitation is evidently fundamental, there is a fundamental bias towards the increasing mass-energy content of the cosmos that could only be duly balanced by the expansion of the cosmos. This suggests a mechanism that establishes the lower and upper limits for the quantization of the nuclear particles and the cosmos as a whole. Tensors describe the kinematic transformations. This suggests that the revolutions of the cosmic systems may facilitate kinematic densifications and attenuations (i.e., the incident quantization) of the phenomena in nature--specifically so if the cosmos is infinitely hierarchical. Moreover, there is the suggestion regarding how the process of gravitation occurs."

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John, you also say:

*** I think we will, within a decade, come to realize the CMBR is not the residue of a universal singularity, but radiation which has traveled so far as to have fallen completely off the visible spectrum. . . I think we will understand black holes as gravitational vortices that release their energy out the poles. The laws of physics down break down at the boundary, because we just haven't formulated laws to define those jets. ***

In my www.kinematicrelativity.com website, I've actually discussed the source of the CMBR, the cause or origin of gravity, and also the cause of the oscillating mechanism that establishes (limits) the quantized cosmic mass and energy phenomena, and a lot of other things.

I so wish that the scientific community's realizations regarding the ideas that I have presented here in this FQXi Essay contest and in the Gravitational Research Foundation essay competition will not take more than decade.

In this FQXi contest, I've basically identified the fundamental component in nature that gets quantized - motion. I've presented how the motion transformation process involving the gravity field occurs according to the genesis formula and the basic transformation equations that suggest that the motions get rotated and folded into the essence of cosmic mass and energy. I've presented that the process needs a seed-mass. These answer the contest question regarding the analog or digital reality.

I was hoping that an FQXi win will help advance my ideas in the scientific community. But because I didn't even get into the 35 voted by the contest participants, I don't see any chance of winning any place in the contest. So, it looks like it will take many more years before my ideas will get the attention of the scientific community.

Rafael

As I've suspected all along, there are others who actually quite see the idea that motion is the fundamental reality underlying all "physical" things - mass, energy, gravity, the electric, the magnetic, the nuclear forces, etc.

Just today, 24-May-2011, I found something very interesting in the internet. This is from Dewey B. Larson's RS Theory.

In the interest of furthering the discoveries of the foundational principles here and to see whether the FQXi community is anywhere close to the new perspectives regarding motion and motion transformations (especially by the eyes of the contest judges as shall no doubt be evidenced by the result of the essay contest), I am posting the following full quote from http://rstheory.org/books/nbm/02.html.

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CHAPTER 2

A Universe of Motion

The thesis of this present work is that the universe in which we live is not a universe of matter, but a universe of motion, one in which the basic reality is motion, and all physical entities and phenomena, including matter, are merely manifestations of motion. The atom, on this basis, is simply a combination of motions. Radiation is motion, gravitation is motion, an electric charge is motion, and so on.

The concept of a universe of motion is by no means a new idea. As a theoretical proposition it has some very obvious merits that have commended it to thoughtful investigators from the very beginning of systematic science. Descartes' idea that matter might be merely a series of vortexes in the ether is probably the best-known speculation of this nature, but other scientists and philosophers, including such prominent figures as Eddington and Hobbes, have devoted much time to a study of similar possibilities, and this activity is still continuing in a limited way.

But none of the previous attempts to use the concept of a universe of motion as the basis for physical theory has advanced much, if any, beyond the speculative stage. The reason why they failed to produce any significant results has now been disclosed by the findings of the investigation upon which this present work is based. The inability of previous investigators to achieve a successful application of the "motion" concept, we find, was due to the fact that they did not use this concept in its pure form. Instead, they invariably employed a hybrid structure, which retained elements of the previously accepted "matter" concept. "All things have but one universal cause" which is motion"19 says Hobbes. But the assertion that all things are caused by motion is something quite different from saying that they are motions. The simple concept of a universe of motion" without additions or modifications--the concept utilized in this present work--is that of a universe which is composed entirely of motion.

The significant difference between these two viewpoints lies in the role that they assign to space and time. In a universe of matter it is necessary to have a background or setting in which the matter exists and undergoes physical processes, and it is assumed that space and time provide the necessary setting for physical action. Many differences of opinion have arisen with respect to the details, particularly with respect to space--whether or not space is absolute and immovable, whether such a thing as empty space is possible, whether or not space and time are interconnected, and so on--but throughout all of the development of thought on the subject the basic concept of space as a setting for the action of the universe has remained intact. As summarized by J. D. North:

Most people would accept the following: Space is that in which material objects are situated and through which they move. It is a background for objects of which it is independent. Any measure of the distances between objects within it may be regarded as a measure of the distances between its corresponding parts.20

Einstein is generally credited with having accomplished a profound alteration of the scientific viewpoint with respect to space, but what he actually did was merely to introduce some new ideas as to the kind of a setting that exists. His "space" is still a setting, not only for matter but also for the various "fields" , that he envisions. A field, he says, is "something physically real in the space around it."21 Physical events still take place in Einstein's space just as they did in Newton's space or in Democritus' space.

Time has always been more elusive than space, and it has been extremely difficult to formulate any clear-cut concept of its essential nature. It has been taken for granted, however, that time, too, is part of the setting in which physical events take place; that is, physical phenomena exist in space and in time. On this basis it has been hard to specify just wherein time differs from space. In fact the distinction between the two has become increasingly blurred and uncertain in recent years, and as matters now stand, time is generally regarded as a sort of quasi-space, the boundary between space and time being indefinite and dependent upon the circumstances under which it is observed. The modern physicist has thus added another dimension to the spatial setting, and instead of visualizing physical phenomena as being located in three-dimensional space, he places them in a four-dimensional space-time setting.

In all of this ebb and flow of scientific thought the one unchanging element has been the concept of the setting. Space and time, as currently conceived, are the stage on which the drama of the universe unfolds--"a vast world-room, a perfection of emptiness, within which all the world show plays itself away forever."22

This view of the nature of space and time, to which all have subscribed scientist and layman alike, is pure assumption. No one, so far as the history of science reveals, has ever made any systematic examination of the available evidence to determine whether or not the assumption is justified. Newton made no attempt to analyze the basic concepts. He tells us specifically, "I do not define time, space, place and motion, as being well known to all. " Later generations of scientists have challenged some of Newton's conclusions, but they have brushed this question aside in an equally casual and carefree manner. Richard Tolman, for example, begins his discussion of relativity with this statement: "We shall assume without examination...the unidirectional, one-valued, one-dimensional character of the time continuum."23

Such an uncritical acceptance of an unsubstantiated assumption "without examination" , is, of course, thoroughly unscientific, but it is quite understandable as a consequence of the basic concept of a universe of matter to which science has been committed. Matter, in such a universe, must have a setting in which to exist. Space and time are obviously the most logical candidates for this assignment. They cannot be examined directly. We cannot put time under a microscope, or subject space to a mathematical analysis by a computer. Nor does the definition of matter itself give us any clue as to the nature of space and time. The net effect of accepting the concept of a universe of matter has therefore been to force science into the position of having to take the appearances which space and time present to the casual observer as indications of the true nature of these entities.

In a universe of motion, one in which everything physical is a manifestation of motion, this uncertainty does not exist, as a specific definition of space and time is implicit in the definition of motion. It should be understood in this connection that the term "motion," as used herein, refers to motion as customarily defined for scientific and engineering purposes; that is, motion is a relation between space and time, and is measured as speed or velocity. In its simplest form, the "equation of motion," which expresses this definition in mathematical symbols, is v = s/t.

The definition as stated, the standard scientific definition, we may call it, is not the only way in which motion can be defined. But it is the only definition that has any relevance to the development in this work. The basic postulate of the work is that the physical universe is composed entirely of motion as thus defined. What we are undertaking to do is to describe the consequences that necessarily follow in a universe composed of this kind of motion. Whether or not one might prefer to define motion in some other way, and what the consequences of such a definition might be, has no bearing on the present undertaking.

Obviously, the equation of motion, which defines motion in terms of space and time, likewise defines space and time in terms of motion. It tells us that in motion space and time are the two reciprocal aspects of that motion, and nothing else. In a universe of matter, the fact that space and time have this significance in motion would not preclude them from having some other significance in a different connection, but when it is specified that motion is the sole constituent of the physical universe, space and time cannot have any significance anywhere in that universe other than that which they have as aspects of motion. Under these circumstances, the equation of motion is a complete definition of the role of space and time in the physical universe. We thus arrive at the conclusion that space and time are simply the two reciprocal aspects of motion and have no other significance.

On this basis, space is not the Euclidean container for physical phenomena that is most commonly visualized by the layman; neither is it the modified version of this concept which makes it subject to distortion by various forces and highly dependent on the location and movement of the observer, as seen by the modern physicist. In fact, it is not even a physical entity in its own right at all; it is simply and solely an aspect of motion. Time is not an order of succession, or a dimension of quasi-space, neither is it a physical entity in its own right. It, too, is simply and solely an aspect of motion, similar in all respects to space, except that it is the reciprocal aspect.

The simplest way of defining the status of space and time in a universe of motion is to say that space is the numerator in the expression s/t, which is the speed or velocity, the measure of motion, and time is the denominator. If there is no fraction, there is no numerator or denominator; if there is no motion, there is no space or time. Space does not exist alone, nor does time exist alone; neither exists at all except in association with the other as motion. We can, of course, focus our attention on the space aspect and deal with it as if the time aspect, the denominator of the fraction, remains constant (or we can deal with time as if space remains constant). This is the familiar process known as abstraction, one of the useful tools of scientific inquiry. But any results obtained in this manner are valid only where the time (or space) aspect does, in fact, remain constant, or where the proper adjustment is made for whatever changes in this factor do take place.

The reason for the failure of previous efforts to construct a workable theory on the basis of the "motion," concept is now evident. Previous investigators have not realized that the "setting" concept is a creature of the "matter" concept; that it exists only because that basic concept envisions material "things" existing in a space-time setting. In attempting to construct a theoretical system on the basis of the concept of a universe of motion while still retaining the "setting" concept of space and time, these theorists have tried to combine two incompatible elements, and failure was inevitable. When the true situation is recognized it becomes clear that what is needed is to discard the "setting" concept of space and time along with the general concept of a universe of matter, to which it is intimately related, and to use the concept of space and time that is in harmony with the idea of a universe of motion.

In the discussion that follows we will postulate that the physical universe is composed entirely of discrete units of motion, and we will make certain assumptions as to the characteristics of that motion. We will then proceed to show that the mere existence of motions with properties as postulated, without the aid of any supplementary or auxiliary assumptions, and without bringing in anything from experience, necessarily leads to a vast number and variety of consequences which, in total, constitute a complete theoretical universe.

Construction of a fully integrated theory of this nature, one, which derives the existence, and the properties of the various physical entities from a single set of premises, has long been recognized as the ultimate goal of theoretical science. The question now being raised is whether that goal is actually attainable. Some scientists are still optimistic. "Of course, we all try to discover the universal law," says Eugene P. Wigner, "and some of us believe that it will be discovered one day."24 But there is also an influential school of thought which contends that a valid, generally applicable, physical theory is impossible, and that the best we can hope for is a "model" or series of models that will represent physical reality approximately and incompletely. Sir James Jeans expresses this point of view in the following words:

The most we can aspire to is a model or picture which shall explain and account for some of the observed properties of matter; where this fails, we must supplement it with some other model or picture, which will in its turn fail with other properties of matter, and so on.25

When we inquire into the reasons for this surprisingly pessimistic view of the potentialities of the theoretical approach to nature, in which so many present-day theorists concur, we find that it has not resulted from any new discoveries concerning the limitations of human knowledge, or any greater philosophical insight into the nature of physical reality; it is purely a reaction to long years of frustration. The theorists have been unable to find the kind of an accurate theory of general applicability for which they have been searching, and so they have finally convinced themselves that their search was meaningless; that there is no such theory. But they simply gave up too soon. Our findings now show that when the basic errors of prevailing thought are corrected the road to a complete and comprehensive theory is wide open.

It is essential to understand that this new theoretical development deals entirely with the theoretical entities and phenomena, the consequences of the basic postulates, not with the aspects of the physical universe revealed by observation. When we make certain deductions with respect to the constituents of the universe on the basis of theoretical assumptions as to the fundamental nature of that universe, the entities and phenomena thus deduced are wholly theoretical; they are the constituents of a purely theoretical universe. Later in the presentation we will show that the theoretical universe thus derived from the postulates corresponds item by item with the observed physical universe, justifying the assertion that each theoretical feature is a true and accurate representation of the corresponding feature of the actual universe in which we live. In view of this one-to-one correspondence, the names that we will attach to the theoretical features will be those that apply to the corresponding physical features, but the development of theory will be concerned exclusively with the theoretical entities and phenomena.

For example, the "matter" that enters into the theoretical development is not physical matter; it is theoretical matter. Of course, the exact correspondence between the theoretical and observed universes that will be demonstrated in the course of this development means that the theoretical matter is a correct representation of the actual physical matter, but it is important to realize that what we are dealing with in the development of theory is the theoretical entity, not the physical entity. The significance of this point is that physical "matter," "radiation" and other physical items cannot be defined with precision and certainty, as there can be no assurance that our observations give us the complete picture. The "matter" that enters into Newton's law of gravitation, for example, is not a theoretically defined entity; it is the matter that is actually encountered in the physical world: an entity whose real nature is still a subject of considerable controversy. But we do know exactly what we are dealing with when we talk about theoretical matter. Here there is no uncertainty whatever. Theoretical matter is just what the postulates require it to be--no more, no less. The same is true of all of the other items that enter into the theoretical development.

Although physical observations have not yet given us a definitive answer to the question as to the structure of the basic unit of physical matter, the physical atom--indeed, there is an almost continuous revision of the prevailing ideas on the subject, as new facts are revealed by experiment--we know exactly what the structure of the theoretical atom is, because both the existence and the properties of that atom are consequences that we derive by logical processes from our basic postulates.

Inasmuch as the theoretical premises are explicitly defined, and their consequences are developed by sound logical and mathematical processes, the conclusions that are reached with respect to matter, its structure and properties, and all other features of the theoretical universe are unequivocal. Of course, there is always a possibility that some error may have been made in the chain of deductions, particularly if the chain in question is a very long one, but aside from this possibility, which is at a minimum in the early stages of the development, there is no doubt as to the true nature and characteristics of any entity or phenomenon that emerges from that development.

Such certainty is impossible in the case of any theory, which contains empirical elements. Theories of this kind, a category that includes all existing physical theories, are never permanent; they are always subject to change by experimental discovery. The currently popular theory of the structure of the atom, for example, has undergone a long series of changes since Rutherford and Bohr first formulated it, and there is no assurance that the modifications are at an end. On the contrary, a general recognition of the weakness of the theory as it now stands has stimulated an intensive search for ways and means of bringing it into a closer correspondence with reality, and the current literature is full of proposals for revision.

When a theory includes an empirical component, as all current physical theories do, any increase in observational or experimental knowledge about this component alters the sense of the theory, even if the wording remains the same. For instance, as pointed out earlier, some of the recently discovered phenomena in the sub-atomic region, in which matter is converted to energy, and vice versa, have drastically altered the status of conventional atomic theory. The basic concept of a universe of material "things," to which physical science has subscribed for thousands of years, requires the atom to be made up of elementary units of matter. The present theory of an atom constructed of protons, neutrons, and electrons is based on the assumption that these are the "elementary particles" ; that is, the indivisible and unchangeable basic units of matter. The experimental finding that these particles are not only interconvertible, but also subject to creation from non-matter and transformation into non-matter, has changed what was formerly a plausible (even if somewhat fanciful) theory into a theory that is internally inconsistent. In the light of present knowledge, an atom simply cannot be constructed of "elementary particles" of matter.

Some of the leading theorists have already recognized this fact, and are casting about for something that can replace the elementary particle as the basic unit. Heisenberg suggests energy:

Energy... is the fundamental substance of which the world is made. Matter originates when the substance energy is converted into the form of an elementary particle.26

But he admits that he has no idea as to how energy can be thus converted into matter. This "must in some way be determined by a fundamental law," he says. Heisenberg's hypothesis is a step in the right direction, in that he abandons the fruitless search for the "indivisible particle," and recognizes that there must be something more basic than matter. He is quite critical of the continuing attempt to invest the purely hypothetical "quark" with a semblance of reality:

I am afraid that the quark hypothesis is not really taken seriously today by its proponents. Questions dealing with the statistics of quarks, the forces that keep them together, the reason why the quarks are never seen as free particles, the creation of pairs of quarks inside an elementary particle, are all left more or less undefined.27

But the hypothesis that makes energy the fundamental entity cannot stand up under critical scrutiny. Its fatal defect is that energy is a scalar quantity, and simply does not have the flexibility that is required in order to explain the enormous variety of physical phenomena. By going one step farther and identifying motion as the basic entity this inadequacy is overcome, as motion can be vectorial, and the addition of directional characteristics to the positive and negative magnitudes that are the sole properties of the scalar quantities opens the door to the great proliferation of phenomena that characterizes the physical universe.

It should also be recognized that a theory of the composite type, one that has both theoretical and empirical components, is always subject to revision or modification; it may be altered essentially at will. The theory of atomic structure, for instance, is simply a theory of the atom--nothing else--and when it is changed, as it was when the hypothetical constituents of the hypothetical nucleus were changed from protons and electrons to protons and neutrons, no other area of physical theory is significantly affected. Even when it is found expedient to postulate that the atom or one of its hypothetical constituents does not conform to the established laws of physical science, it is not usually postulated that these laws are wrong; merely that they are not applicable in the particular case. This fact that the revision affects only a very limited area gives the theory constructors practically a free hand in making alterations, and they make full use of the latitude thus allowed.

Susceptibility to both voluntary and involuntary changes is unavoidable as long as the development of theory is still in the stage where complex concepts such as "matter" must be considered unanalyzable, and hence it has come to be regarded as a characteristic of all theories. The first point to be emphasized, therefore, in beginning a description of the new system of theory based on the concept of a universe of motion, the Reciprocal System, as it is called, is that this is not a composite theory of the usual type; it is a purely theoretical structure which includes nothing of an empirical nature.

Because all of the conclusions reached in the theoretical development are derived entirely from the basic postulates by logical and mathematical processes the theoretical system is completely inflexible, a point that should be clearly understood before any attempt is made to follow the development of the details of the theory in the following pages. It is not subject to any change or adjustment (other than correction of any errors that may have been made, and extension of the theory into areas not previously covered). Once the postulates have been set forth, the entire character of the resulting theoretical universe has been implicitly defined, down to the minutest detail. Just because the motion of which the universe is constructed, according to the postulates, has the particular properties that have been postulated, matter, radiation, gravitation, electrical and magnetic phenomena, and so on, must exist, and their physical behavior must follow certain specific patterns.

In addition to being an inflexible, purely theoretical product that arrives at definite and certain conclusions which are in full agreement with observation, or at least are not inconsistent with any definitely established facts, the Reciprocal System of theory is one of general applicability. It is the first thing of its kind ever formulated: the first that derives the phenomena and relations of all subdivisions of physical activity from the same basic premises. For the first time in scientific history there is available a theoretical system that satisfies the criterion laid down by Richard Schlegel in this statement:

In a significant sense, the ideal of science is a single set of principles, or perhaps a set of mathematical equations, from which all the vast process and structure of nature could be deduced.28

No previous theory has covered more than a small fraction of the total field, and the present-day structure of physical thought is made up of a host of separate theories, loosely related, and at many points actually conflicting. Each of these separate theories has its own set of basic assumptions, from which it seeks to derive relations specifically applicable to certain kinds of phenomena. Relativity theory has one set of assumptions, and is applicable to one kind of phenomena. The kinetic theory has an altogether different set of assumptions, which it applies to a different set of phenomena. The nuclear theory of the atom has still another set of assumptions, and has a field of applicability all its own, and so on. Again quoting Richard Feynman:

Instead of having the ability to tell you what the law of physics is, I have to talk about the things that are common to the various laws; we do not understand the connection between them.15

Furthermore, each of these many theories not only requires the formulation of a special set of basic assumptions tailored to fit the particular situation, but also finds it necessary to introduce a number of observed entities and phenomena into the theoretical structure, taking their existence for granted, and accepting them as "given" , so far as the theory is concerned.

The Reciprocal System now replaces this multitude of separate theories and subsidiary assumptions with a fully integrated structure of theory derived in its entirety from a single set of basic premises. The status of this system as a general physical theory is not a matter of opinion; it is an objective fact that can easily be verified by an examination of the theoretical development. Such an examination will disclose that the development leads to detailed conclusions in all major physical fields, and that these conclusions are derived deductively from the postulates of the system, without the aid of any supplementary or subsidiary assumptions, and without introducing anything from experience. The new theoretical structure not only covers the field to which the conventional physical theories are applicable; it also gives us answers to the basic physical questions with which the theories based on the "matter" concept have been unable to cope, and it extends the scope of physical theory to the point where it is capable of dealing with those recent experimental and observational discoveries in the far-out regions of science that have been so baffling to those who are trying to understand them in the context of previously existing ideas.

Of course, the theoretical development has not yet been carried to the point where it accounts for every detail of the physical universe. That point will not be reached for a long time, if ever. But it has been carried far enough to make it clear that the probability of being unable to deal with the remaining items is negligible, and that the Reciprocal System is, in fact, a general physical theory.

The crucial importance of this status as a general physical theory lies in the further fact that it is impossible to construct a wrong general physical theory. At first glance this statement may seem absurd. It may seem almost self-evident that if validity is not required there should be no serious obstacle to constructing some kind of a theory of any subject. But even without any detailed consideration of the factors that are involved in the case of a general physical theory, a review of experience will show that this offhand opinion is incorrect. Construction of a general physical theory has been a prime goal of science for three thousand years, and an immense amount of time and effort has been devoted to the task, with no success whatever. The failure has not been a matter of arriving at the wrong answers; the theorists have not been able to formulate any single theory that would give them any answers, right or wrong, to more than a mere handful of the millions of questions that a general physical theory must answer. A long period of failure to find the correct theory is understandable, since the field that must be covered by a general theory is so immense and so extremely complicated, but thousands of years of inability to construct any general theory are explainable only on the basis that there is a reason why a wrong theory cannot be constructed.

This reason is easily understood if the essential nature of the task is carefully examined. Construction of a general physical theory is analogous to the task of deciphering a very long message in code. If a coded message is short--a few words or a sentence--alternative interpretations are possible, any or all of which may be wrong, but if the message is a very long one--a whole book in code would be an appropriate analogy to the subject matter of a general physical theory--there is only one way to make any kind of sense out of every paragraph, and that is to find the key to the cipher. If, and when, the message is finally decoded, and every paragraph is intelligible, it is evident that the key to the cipher has been discovered. The possibility that there might be an alternative key, a different set of meanings for the various symbols utilized, that would give every one of the thousands of sentences in the message a different significance, intelligible but wrong, is preposterous. It can therefore be definitely stated that a wrong key to the cipher is impossible. The correct general theory of the universe is the key to the code of nature. As in the case of the cipher, a wrong theory can provide plausible answers in a very limited field, but only the correct theory can be a general theory; one that is capable of producing explanations for the existence and characteristics of all of the immense number of physical phenomena. Thus a wrong general theory, like a wrong key to a cipher, is impossible.

The verification of the validity of the theoretical structure as a whole that is provided by the demonstration that it is a general physical theory does not eliminate the need for checking each of the conclusions of the theory individually. It is not unlikely that those persons who carry out the process of development of the details of the theory will make some mistakes. But the fact that the individual conclusions have been derived by extension of a correct general structure of theory creates a strong presumption of their validity, a presumption that cannot be overcome by anything other than definite and conclusive contrary evidence. Hence, as conclusions are reached in the course of the development, it is not necessary to supply positive proof that they are correct, or to argue that the case in favor of their validity is superior to that of any competitor. All that is required is to show that these conclusions are not inconsistent with any definitely established facts.

Recognition of this point is essential for a full understanding of the presentation in the pages that follow. Many persons will no doubt take the stand that they find the arguments in favor of certain of the currently accepted ideas more persuasive than those in favor of the conclusions derived from the Reciprocal System. Indeed, some such reactions are inevitable, since there will be a strong tendency to view these conclusions in the context of present-day thought, based on the no longer tenable concept of a universe of matter. But these opinions are irrelevant. Where it can be shown that the conclusions are legitimately derived from the postulates of the system, they participate in the proof of the validity of the structure of theory as a whole, a proof that has been established by two independent means: (1) by showing that this is a general physical theory, and that a wrong general physical theory is impossible, and (2) by showing that none of the authentic deductions from the postulates of the theory is inconsistent with any positively established information from observation or experiment.

This second method of verification is analogous to the manner in which we would go about verifying the accuracy of an aerial map. The traditional method of map making involves first a series of explorations, then a critical evaluation of the reports submitted by the explorers, and finally the construction of the map on the basis of those reports that the geographers consider most reliable. Similarly, in the scientific field, explorations are carried out by experiment and observation, reports of the findings and conclusions based on these findings are submitted, these reports are evaluated by the scientific community, and those that are judged to be authentic are added to the scientific map, the accepted body of factual and theoretical knowledge.

But this traditional method of map making is not the only way in which a geographic map can be prepared. We may, for instance, devise some photographic system whereby we can secure a representation of an entire area in one operation by a single process. In either case, whether we are offered a map of the traditional kind or a photographic map we will want to make some tests to satisfy ourselves that the map is accurate before we use it for any important purposes, but because of the difference in the manner in which the maps were produced, the nature of these tests will be altogether different in the two cases. In checking a map of the traditional type we have no option but to verify each significant feature of the map individually, because aside from a relatively small amount of interrelation, each feature is independent. Verification of the position shown for a mountain in one part of the map does not in any way guarantee the accuracy of the position shown for a river in another part of the map. The only way in which the position shown for the river can be verified is to compare what we see on the map with such other information as may be available. Since these collateral data are often scanty, or even entirely lacking, particularly along the frontiers of knowledge, the verification of a map of this kind in either the geographic or the scientific field is primarily a matter of judgment, and the final conclusion cannot be more than tentative at best.

In the case of a photographic map, on the other hand, each test that is made is a test of the validity of the process, and any verification of an individual feature is merely incidental. If there is even one place where an item that can definitely be seen on the map is in conflict with something that is positively known to be a fact, this is enough to show that the process is not accurate, and it provides sufficient justification for discarding the map in its entirety. But if no such conflict is found, the fact that every test is a test of the process means that each additional test that is made without finding a discrepancy reduces the mathematical probability that any conflict exists anywhere on the map. By making a suitably large number and variety of such tests the remaining uncertainty can be reduced to the point where it is negligible, thereby definitely establishing the accuracy of the map as a whole. The entire operation of verifying a map of this kind is a purely objective process in which features that can definitely be seen on the map are compared with facts that have been definitely established by other means.

One important precaution must be observed in the verification process: a great deal of care must be exercised to make certain of the authenticity of the supposed facts that are utilized for the comparisons. There is no justification for basing conclusions on anything that falls short of positive knowledge. In testing the accuracy of an aerial map we realize that we cannot justify rejecting the map because the location of a lake indicated on the map conflicts with the location that we think the lake occupies. In this case it is clear that unless we actually know just where the lake is, we have no legitimate basis on which to dispute the location shown on the map. We also realize that there is no need to pay any attention to items of this kind: those about which we are uncertain. There are hundreds, perhaps thousands, of map features about which we do have positive knowledge, far more than enough for purposes of comparison, so that we need not give any consideration to features about which there is any degree of uncertainty.

Because the Reciprocal System of theory is a fully integrated structure derived entirely by one process--deduction from a single set of premises--it is capable of verification in the same manner as an aerial map. It has already passed such a test; that is, the theoretical deductions have been compared with the observed facts in thousands of individual cases distributed over all major fields of physical science without encountering a single definite inconsistency. These deductions disagree with many currently accepted ideas, to be sure, but in all of these cases it can be shown that the current views are not positive knowledge. They are either conclusions based on inadequate data, or they are assumptions, extrapolations, or interpretations. As in the analogous case of the aerial map, conflicts with such items, with what scientists think, are meaningless. The only conflicts that are relevant to the test of the validity of the theoretical system are conflicts with what scientists know.

Thus, while recognition of human fallibility prevents asserting that every conclusion purported to be reached by application of this theory is authentic and therefore correct, it can be asserted that the Reciprocal System of theory is capable of producing the right answers if it is properly applied, and to the extent that the development of the consequences of the postulates of the theory has been correctly carried out, the theoretical structure thus derived is a true and accurate representation of the actual physical universe.

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So, what say ya all?