Appendix D. The At Theory
The Augustus Barto O'Barr and Lola May Peppers Family
HTML Version 2.0
copyright 1995 by Gerald L. O'Barr
The At Theory was first contemplated in late 1954. I was in
my teens, out of High school, and attending West Point. My
concern (totally private) was that of space reaching forces such
as gravity. How could the earth affect the moon with vacuum
(nothing) in between? I was sure that it had to be particles
that were "too small" to be seen. (I was not the first on this
score.) I had a firm understanding (High School Physics from Mr.
Lillywhite) that "bounces" made between colliding bodies were
very complicated. I could not allow myself to consider such
complicated interactions to be involved at our most fundalmental
levels. (Here is were I differed from all others.)
If you did not have "bounce," then what was it? Having been
a kid that lived through World War II, I knew a little about guns
and bullets and tanks. I knew about "spalls" and how they could
defeat armor. We specifically studied these things at West Point
in our Ordnance Course. I had all this understanding before I
had mathematical proof. I just knew that it was the way it was.
There just could not be any other way. And so the At Theory uses
spalls. This opened up a new approach which included a new
variable (changes in mass of the interacting particles) and a new
way to transfer momentum that could include attraction as well as
Before I went to BYU (1962-64) I had the mathematics well
developed. But I never wrote much down until a Bro. Alton Moody
(1970-71) encouraged it. So in 1971 I wrote my first "article"
where all the assumptions and math were fully examined and
presented. In this 1971 article
, I was more concerned with the
beauty of this theory. It had the ring of truth. In those
ancient days, we did not have computers in our homes (at least
not in my home.) The only way that I could prove my theory was
by mathematical approximations (taking the approximate values of
relationships) or by doing one set of velocity interactions and
observing the changes.
Today, with computers, thousands of interactions can easily
be "observed" and the actual paths that are followed by
interacting particles can be examined to prove specific
relationships. What a great blessing it has been to me to have
computers. I am going to include the 1971 At article
, and then a
later article written with the help of a computer. Over the
years, I have written at least ten articles on the At Theory.
They are basically all the same and if you have read one you have
read them all.
Let me state my thanks to a loving Father-in-Heaven. I have
been blessed to "know" many things. I have conceptualized an
infinitely variable, positive drive transmission system. (It was
notarized for me by a U.S Army Officer while I was stationed at
Davis-Monthan AFB, 1960-1962. It is now being used on the most
advanced GD battle tank, but with no credit to me, and maybe no
credit is due, I just do not know. The so called inventer of
this system would never return any of my communications.)
I know much about surface tension, and how a thin film is
mechanically stabilized (it takes more than attractive forces.)
I know about hollow ball bearings and manufacturing in space and
the exact shape that can be formed by liquids under "Zero"
Once NASA was using hollow ball bearings as a reason to have
Congress fund their space efforts. I showed one of our GD
"German Scientists" that was working with NASA that they could
not do this with what they had. Once their experts were
convinced that I was right, they felt a little embarrassed and
had to stop what they were doing. In just a little time, I came
up with a way for them to do what they wanted to do, but they
were then afraid to reconsider again a third position. This
would make them appear to not know what they were doing.
I know how to make a viewing screen reproduce the
electromagnetic fields that are produced by real objects. This
would give real 3-D viewing, with no eye strains or headaches or
needs for special glasses or any other problems. I am an expert
on Special Relativity, and I know that Special Relativity
requires an absolute reference frame to work.
Some of these ideas are important, some are not, but it has
been a joy to be with people and to see how they react to these
"new" ideas. Back in the days of Newton, Newton would be wrong
if he heard any of my ideas and did not act. But today, you can
be a good scientist, and still not be criticized for ignoring any
of my good ideas, because in our world today, there are just too
many good ideas being brought forth. No man can keep up with all
of it. And so, we must pick and choose. The fact that no one
will pick my ideas to verify or check is not my fault, but it
also is no one else's fault. It is just the way it is.
I do hope that some of you will read these two At articles.
It would be even greater if you would take the time to understand
them. And then it would be heaven to me if you would be able to
The At Theory was first contemplated in late 1954. I was in my teens, out of High school, and attending West Point. My concern (totally private) was that of space reaching forces such as gravity. How could the earth affect the moon with vacuum (nothing) in between? I was sure that it had to be particles that were "too small" to be seen. (I was not the first on this score.) I had a firm understanding (High School Physics from Mr. Lillywhite) that "bounces" made between colliding bodies were very complicated. I could not allow myself to consider such complicated interactions to be involved at our most fundalmental levels. (Here is were I differed from all others.)
If you did not have "bounce," then what was it? Having been a kid that lived through World War II, I knew a little about guns and bullets and tanks. I knew about "spalls" and how they could defeat armor. We specifically studied these things at West Point in our Ordnance Course. I had all this understanding before I had mathematical proof. I just knew that it was the way it was. There just could not be any other way. And so the At Theory uses spalls. This opened up a new approach which included a new variable (changes in mass of the interacting particles) and a new way to transfer momentum that could include attraction as well as repulsive "forces."
Before I went to BYU (1962-64) I had the mathematics well developed. But I never wrote much down until a Bro. Alton Moody (1970-71) encouraged it. So in 1971 I wrote my first "article" where all the assumptions and math were fully examined and presented. In this 1971 article , I was more concerned with the beauty of this theory. It had the ring of truth. In those ancient days, we did not have computers in our homes (at least not in my home.) The only way that I could prove my theory was by mathematical approximations (taking the approximate values of relationships) or by doing one set of velocity interactions and observing the changes.
Today, with computers, thousands of interactions can easily be "observed" and the actual paths that are followed by interacting particles can be examined to prove specific relationships. What a great blessing it has been to me to have computers. I am going to include the 1971 At article , and then a later article written with the help of a computer. Over the years, I have written at least ten articles on the At Theory. They are basically all the same and if you have read one you have read them all.
Let me state my thanks to a loving Father-in-Heaven. I have been blessed to "know" many things. I have conceptualized an infinitely variable, positive drive transmission system. (It was notarized for me by a U.S Army Officer while I was stationed at Davis-Monthan AFB, 1960-1962. It is now being used on the most advanced GD battle tank, but with no credit to me, and maybe no credit is due, I just do not know. The so called inventer of this system would never return any of my communications.)
I know much about surface tension, and how a thin film is mechanically stabilized (it takes more than attractive forces.) I know about hollow ball bearings and manufacturing in space and the exact shape that can be formed by liquids under "Zero" gravity.
Once NASA was using hollow ball bearings as a reason to have Congress fund their space efforts. I showed one of our GD "German Scientists" that was working with NASA that they could not do this with what they had. Once their experts were convinced that I was right, they felt a little embarrassed and had to stop what they were doing. In just a little time, I came up with a way for them to do what they wanted to do, but they were then afraid to reconsider again a third position. This would make them appear to not know what they were doing.
I know how to make a viewing screen reproduce the electromagnetic fields that are produced by real objects. This would give real 3-D viewing, with no eye strains or headaches or needs for special glasses or any other problems. I am an expert on Special Relativity, and I know that Special Relativity requires an absolute reference frame to work.
Some of these ideas are important, some are not, but it has been a joy to be with people and to see how they react to these "new" ideas. Back in the days of Newton, Newton would be wrong if he heard any of my ideas and did not act. But today, you can be a good scientist, and still not be criticized for ignoring any of my good ideas, because in our world today, there are just too many good ideas being brought forth. No man can keep up with all of it. And so, we must pick and choose. The fact that no one will pick my ideas to verify or check is not my fault, but it also is no one else's fault. It is just the way it is.
I do hope that some of you will read these two At articles. It would be even greater if you would take the time to understand them. And then it would be heaven to me if you would be able to appreciate them.
|Sincerely: Gerald L. O'Barr (1995)|
THE AT THEORY (PART 1) 1971 +This is a retyping of the first At article I wrote in 1971. I will try to be exact and type it exactly as the original. If I make any additional comments not in the original, I will start them on a separate line, and I'll use a "+" sign to begin and end each set. The comments now being made are following this format. A portion of the title page is given below, and the next page was the dedication page for this article, which included a reference to an ancient prophet of God.+ THE AT THEORY (PART 1) 1971 Gerald L. O'Barr Page D-3 All that is good comes from MAN Even the Lord, being the son of MAN Therefore, this is dedicated to MAN Father of the SON of MAN Who is Father to us all, for He Is And He is our Father, the Perfect MAN Upon American shores, some 2550 years ago, a man named Lehi (who had been raised in Jerusalem) expressed our law of existence - the law of reality - Unless reality is as simple as indicated herein, what hope can one have who has a mind as the author's? +(See note 1.)+ ii Page D-4 THE AT THEORY (Part 1, 1971) "For it must needs be, that there is an opposition in all things.... Wherefore, all things must be a compound in one...." 1 INTRODUCTION (Preliminary Postulates) U There is an existence. V It is, at least partially, an observable existence. W No thing can be simpler than its parts. X Therefore, ultimate reality must be as simple or simpler than all observable things. +(See note 2.)+ The author is aware of the reasons and fears expressed by many that ultimate reality may be extremely complicated and so unnatural that it may be beyond the comprehension of man. However, the above thoughts do not indicate such a direction. Indeed, a direction of utmost simplicity is strongly indicated. Until there is reason to do otherwise, let it be postulated that: X' Ultimate simplicity is indistinguishable from ultimate reality. The power of simplicity has been noted and utilized before. Little did we realize that its power may be basic. Under these conditions there is the strongest hope that: Y Ultimate reality is comprehensible to the human mind. It should be clear that the position taken is not one that assumes something magical in "simplicity." It is merely a simple recognition that ultimate simplicity is itself determined by ultimate reality. Ultimate reality determines what ultimate simplicity was, is or ever will be. Once ultimate simplicity is defined or discovered, the bounds of ultimate reality will be very strongly defined if not entirely naked before us. What is ultimate simplicity? Isn't ultimate simplicity absolutely nothing? If so, there would be no existence, which contradicts the very first statement made, the most basic of all other concepts. Does this mean that we now have reason to reject "X'"? Before this is done, let's ask the above question in a slightly different way. What is the ultimate simplicity in which an existence could occur? Z No object can exist except it be differentiable from its background. Page D-5 Therefore, ultimate simplicity (ultimate reality), within and consistent with this principle of existence, must at least consist of a minimum of two different things (e.g. an object and its background.) It can be noted that the law of existence, "Z", is identical to the first law of observability: Z' No object can be observed except it be differentiable from its background. Therefore, to this extent, reality and observability are one and the same. It is at this point that we may now restate the preliminary postulates to the At Theory in slightly more emphatic terms: A There is an existence. B It is an observable existence. C No thing can be simpler than its parts. D Therefore, ultimate reality must be the simplest of all observable things. E No object can exist or be observed except it be differentiable from its background. F Therefore, ultimate reality must consist of at least two different things. "C" and "D" have placed a limit on the maximum complexity of ultimate reality. "B," "E" and "F" have placed a limit on the minimum simplicity of ultimate reality. There is reason sufficient to conclude that these limits may have one and only one common result. However, for ease and for future use, let our guide be used and restated: G The simplest possibility will always be assumed unless reason exists to do otherwise. Therefore, H' Ultimate reality is a single, simple compound of two different things. I Ultimate reality is comprehensible to the human mind. Before concluding this introduction, let's again review and add to these basic thoughts. How simple can ultimate reality be? If there be but one continuous body, forming as it were a uniform and continuous medium, without any observable boundaries, all points identical with no differentiations from place to place, there could be no observable existence. This is true regardless of what that medium might be. In the words of Lehi, "...if it should be one body it must needs remain as dead, Page D-6 having no life neither death,...neither sense nor insensibility." Nothing can exist or be detectable except it be distinguishable from its background. Therefore, if an observable reality exists, it must have objects which have boundaries. And what is a boundary? It is where one thing ends and a different thing begins. Therefore, if one thing exists, two things exist. We can go one further step. These two different things which must exist in order to give existence (observability) to the other, must be opposites to each other. We should not really worry too much about this because it is a very automatic result. Everything common between them would reflect no boundaries, and with all being of one body with respect to this "commonality," the "commonality" would be insensible. The only boundaries established would center about the differences between them. In the ultimate sense, this difference, what ever it might be, can only be sensed as complete opposites since the existing of one is in terms of its compared or relative absence in the other. In other words, if only two things exist, there can be but one comparison; a degree of comparison less than complete oppositeness would require a third (or more) intermediate body for such a comparison. With this background, we can now understand the words used by Lehi. We can also understand that this is a self existing principle. The complete form for postulate "H" is: H Ultimate reality is a single, simple compound of opposites. At this point, all previous postulates could be ignored or directly derived from this self existing principle. (Let it be noted that these preliminary postulates are not intended to be "scientifically" acceptable. They were given to explain the beliefs, attitudes and feelings of the author and are to be used by the reader accordingly. It was with these postulates, however, that the At Theory was derived. Certainly there is nothing unique about what has been said or in the words that have been used. Many have and will find more appropriate ways to state or present these same results.) You can not have something ugly Unless there is something lovely You cannot have a downward Unless there is an upward You can not even have nothing Unless there is something Page D-7 THE AT THEORY (Basic postulates) 1. Ultimate reality is a single, simple compound of opposites. The opposites are the ultimate extremes of opposites: "Something" and "nothing." The names given to these opposites are: "Mass" and "Space." The property associated with mass, which makes it "something," is inertia. (Since "nothing" is one part of the compound of ultimate reality, we now see the true nature of the apparent problem that existed when we first investigated what ultimate simplicity might be. Thus, when we thought of "nothing" as being absolutely the ultimate of simplicity, we were not wrong. We were only incomplete. "X'" is acceptable in a most amazing way.) 2. The mass is found, on the average, randomly distributed within space in particles called "ats." Ats do not have any fixed size or predetermined shape, although groupings do appear in frequency distribution curves. The ats move, again on the average, in random directions with random velocities. All at particles have the same basic property and any part of one must be identical to any of the other parts of itself or any other at. The same is true of any part of space compared to any other part of space. 3. There are no space reaching forces between ats: no magnetic, electrical, nuclear or gravitational forces. Inertia is the one and only basic property. (There is a natural "cleaving" of like to like: mass to mass or space to space, which exists as a pure contact force only, energyless and of no immediate concern.) 4. All interactions between ats occur during and only during direct physical contact (collisions.) (A partial description of the collisional interaction will be given.) 5. Newtonian mechanics, the simplest of all mechanics, operate in all applicable aspects, to include the implied geometrics of space, time and conservation of mass, energy and momentum. (As a very interesting side note, for those interested in the higher criticism of Newton's second law, with the absence of all space reaching forces, the concept of force and acceleration could be, but is not in this presentation, ignored in the At Theory. The true appreciation of this fact, and other possible relationships, are not discussed in this article.) These are the basic postulates of the At Theory. However, a multitude of possibilities and choices immediately appear, with subsequent and important decisions. The two main areas relate to variances in sizes of ats and the type and nature of the interactions during collisions. All of the possibilities will not be discussed in this article. One type of interaction, however, will be presented, and an example of the results of such interactions will be mathematically described. In many ways, the Page D-8 mental jump required to conceptualize this particular type of interaction has been one key to the successful development of this theory. When two billiard balls collide and rebound, as simple as it seems, it is really a very complicated energy exchange requiring particular types of force fields, changes of relative positions of certain atoms within these force fields, and then a forceful return of these atoms to approximately their original positions. However, the At Theory involves collisions in which such complications can not exist and in which mass actually contacts mass. The interaction is much different than what one might directly expect. The interaction is called a perfect or non-perfect, duplicative mass exchange. The nature of this "new" interaction does have some complications just as the billiard ball collision, but the results of the interaction are also just as simple. Some years have been spent in considering the mechanics of this new interaction, but the details of the mechanics are not really critical to the At Theory. Therefore, only a simple description will be given. As two ats approach each other, no matter how close or fast they come, no influence of one upon the other exists until actual contact is made. At the instant of contact, where pure, solid matter contacts solid matter (something never done in what we see as collisions), an infinite stress instantly appears through each at. Along the lines projected through the points of instantaneous contact, which may progressively change during the interaction, ejection of mass with a projected thickness equal to the projected thickness of the smaller mass will occur upon the side of the larger mass opposite the impact side. The projected thickness of the smaller mass will remain upon the impact side of the larger mass. The mass lost in the ejection will continue to move in the same initial direction as the smaller mass. In this amazing way, not only has the interaction duplicated the mass of the smaller, but also, to some extent, even the shape of the smaller (superimposed upon the compound shape of the larger) has been duplicated. Although most of these details are to some extent modified in the actual mechanics, the essential features are appropriately described. Although the mechanics are certainly not the same, the results are similar to a ballistic interaction where a bullet becomes stuck in a target but a spall from the target continues on in the original direction of the bullet. In a perfect, duplicative mass interaction, the ejected mass is exactly equal to the original smaller at. When this occurs, no change in velocity or energy occurs to either of the re-identified particles. It is where slight changes in mass occurs, the non-perfect, duplicative mass interactions, that will result in important momentum and energy exchanges. (It should be noted that the finite stress required to shear and or eject these masses are entirely energyless functions and that no energy can be associated with shape or changes in shape during these interactions) Page D-9 The mathematics of this interaction is much more direct. As was stated before, the details of the mechanics are not really critical to the theory. The important point (and mathematically, the only important point) is that the interaction on the at level is different than the interaction we normally work with; and mathematically, there is only one other choice other than the normal one used. If we have a normal, one-dimensional, two body interaction, with conservation of energy and momentum, we can write the following equations: m1*V1 + M1*U1 = m2*V2 + M2*U2 1) 1 2 1 2 1 2 1 2 -m1*V1 + -M1*U1 = -m2*V2 + -M2*U2 2) 2 2 2 2 (m and M being the masses of two different bodies, V and U their respective velocities; subscript 1 used before the interaction, subscript 2 used after the interaction.) Solving these equations for V2 and U2, we have: --------- m1V1 + M1U1 +/- (V1 - U1) \/ M1M2m1/m2 V2 = ----------------------------------------- 3) m1 + M1 and - --------- m1V1 + M1U1 + (V1 - U1) \/ m1m2M1/M2 U2 = ----------------------------------------- 4) m1 + M1 These equations have been solved many times. However, they are seldom written in this form since normally m1=m2 and M1=M2. Under these conditions, the radical immediately disappears and only a choice in sign remains to be determined. In a normal interaction, the choice in signs is determined in a very obvious and direct way, so obvious and direct that it is very seldom mentioned. The final results normally given are: m1V1 + M1U1 - (V1 - U1) M1 V2 = ------------------------------- 5) m1 + M1 and m1V1 + M1U1 + (V1 - U1) m1 U2 = ------------------------------- 6) m1 + M1 Page D-10 These equations (or slight rearrangements) are found in almost all first year physics courses. ((As a side note, far too many good physics books (no need to mention names, anyone can pull out their own texts and check) follow the simple method below of dividing the gain or loss in momentum of each mass into twice the gain or loss in energy for the respective masses (simple rearrangements of equations 1) and 2) where m1 = m2 and M1 = M2, etc.): 2 2 2 2 m1(V1 - V2 ) = M1(U2 - U1 ) 7) m1(V1 - V2 ) = M1(U2 - U1 ) 8) Equation 7) divided by 8) results in: V1 + V2 = U2 + U1 9) a relationship which can then be most easily used with equations 1) or 8) to solve for V2 or U2 as found in equations 5) and 6). +( The "1" for "equation 1)" above should be a "7." This was certainly a typing error where the 7 must have been seen as a 1.)+ In this approach, the choice in sign is "forced". The "error" of this approached is obvious. Everyone knows how algebra can be "used" to prove that 2=1: Let x = y therefore, x^2 = xy (multiply each side by equals) x^2 - y^2 = xy - y^2 (subtract equals from each side) (x+y)(x-y) = y(x-y) (factor each side) (x+y) = y (cancel out common factors) (y+y) = y (substitute equals for equals, x=y) therefore, 2 = 1 The same error made in proving that 2 = 1 is the same "error" made in deriving equation 9). Has it been this simple "error", that is repeated over and over in so many physics books, which has caused the at theory relationship to be overlooked?)) The basic equations used in the at theory consists of equations 3) and 4), but choosing the opposite sign than that used in deriving equations 5) and 6). Retaining the possibility that m1 does not equal m2 and M1 does not equal M2, we have: Page D-11 ---------------- m1V1 + M1U1 + (V1 - U1) \/ m1M1(M1+d)/(m1-d) V2 = -------------------------------------------- 10) m1 + M1 and ---------------- m1V1 + M1U1 - (V1 - U1) \/ m1M1(m1-d)/(M1+d) U2 = -------------------------------------------- 11) m1 + M1 where M2 = M1 + d and m2 = m1 - d (which maintains conservation of total mass) (It must be emphasized that these equations are mathematically as correct as 5) and 6) as far as conservation of momentum and energy are concerned, i.e. the sign before the radical is unimportant mathematically) Equations 10) and 11) are normally difficult to work with (unless m1 = m2, i.e. d = 0; or m1 = M2, i.e. d = m1 - M1 etc.) However, if it is assumed that d/m1 and d/M1 << 1, equations 10) and 11) can be approximated, to the second order, as: 1 d d(3M1-m1) V2 = V1 + -(V1-U1)- [1 + --------- + .... ] 12) 2 m1 4M1m1 and 1 d d(M1-3m1) U2 = U1 + -(V1-U1)- [1 + --------- + .... ] 13) 2 M1 4M1m1 Equations 12) and 13) indicates two important relationships. First, no changes in velocity occurs for either object if d = 0. This result is much different than normal (billiard ball type) interactions, and allows much greater flexibility in the physical relationships that can be established. Second, the change in velocities are directly proportional to their relative or initial difference in velocity, but is non-linear with respect to "d." This non-linearity, with differences between "+" and "-" d's, can effectively result in apparent forces between various interacting bodies over multiple interactions, even when no net changes in mass occurs. Page D-12 Using equations 10) and 11), a very simple example will now be given to show a type of relationship that can be established by these interactions. The interactions in this example will all be one dimensional interactions. Two identical masses, MA and MB, will be placed on a line, each with zero initial velocity. The smaller masses, m1 and m2, will each be sent, one at a time, from the same direction along this line, to interact first with MA, then MB. The two smaller masses will each have, initially, identical masses and velocities. The first interaction, m1 with MA and MB, will give "+d" mass to MA and then obtain back "+d" mass from MB. The second series of interactions, m2 with MA and MB, will take "+d" from MA and give it back to MB. At the end of these four interactions, all particles will have been returned back to their original mass size. Their resulting velocities, however, will have been changed. The accompanying table shows initially assumed mass values and velocities for each particle and the results of each interaction. Observing the final states of MA and MB, they can be seen moving towards each other. Each time the four interaction cycle is repeated, even if m1 and m2 came from the other direction, MA and MB would in every case move faster towards each other. These two objects, MA and MB, could be said to be attracting each other. In a three dimensional field, with m1 and m2 moving randomly in all directions, the attraction would appear to be a 1/r2 function, similar in some ways to the force fields of gravity or electrostatic charges. It has thus been shown, that such interactions as have been described, can result in apparent "force fields" or force relationships between objects placed in an otherwise symmetrical background. This can be done even without any progressive loss or gain in masses of the interacting particles, with complete conservation of energies and momentum in each individual interaction. The establishment of force fields by the use of masses (such as billiard balls on a billiard table) have been attempted before. But these have usually failed due to certain features which were initially overlooked - such as multiple hits or reflections between the subject masses or conservation of energy relationship, etc.. In the At Theory, multiple hits or reflections are not possible since ats pass "through" each other. There are possibilities that in the one simple example given, something may have been overlooked. However, all considerations that have so far been applied have not changed the basic relationships as described. Even though we started with what was to be ultimate simplicity, the following potential complications of our world (as we know it) may already begin to appear. First, an effective "force field" has been found without loss of energy or momentum. Second, the interactional exchanges of masses, +/- d, may be considered to be in some ways matter, +d, and anti-matter,-d, particles! Third, the large intermediate, random motions of the particles, "M", superimposed upon their general drift or average directed motion, can give a rise to certain aspects of Page D-13 TABLE I. INTERACTIONS OF FOUR AT PARTICLES RESULTING IN ATTRACTIVE FORCES INTERACTING PARTICLES AND THEIR RESPECTIVE PARAMETERS ----------------------------------------------------------------- NO. 1 NO. 2 NO. 3 NO. 4 ---------------------------------------------------------- INITIAL m1 V1 m2 V2 MA UA MB UB STARTING VALUES ---------------------------------------------------------- 100 1000 100 1000 500 0 500 0 INTERACTIONS ----------------------------------------------------------------- NO. 1 BEFORE 100 1000 " " 500 0 " " AFTER 99 1005.04 " " 501 1.001 " " NO. 2 BEFORE 99 1005.04 " " " " 500 0 AFTER 100 999.99 " " " " 499 -1.004 NO. 3 BEFORE " " 100 1000 501 1.001 " " AFTER " " 101 995.04 500 .005 " " NO.4 BEFORE " " 101 995.04 " " 499 -1.004 AFTER " " 100 1000.01 " " 500 -0.005 ----------------------------------------------------------------- -- FINAL 100 999.99 100 1000.01 500 +.005 500 -0.005 RESULTS ----- ----- Page D-14 the uncertainty principle. Fourth, the relationship between change in mass and the apparent "force fields" can result in a relationship between mass and energy. Any at that began to continuously lose or gain mass during every interaction (rather than oscillating back and forth around some average size would drastically affect its surroundings. This completes the presentation for this article. Depending upon the readers responses to this article, and the goodness of the publishers, additional articles will be presented after the first responses have been heard and assessed. Depending upon the above, the next article (at least four months from now) will explore certain kinds (size distributions) of ats, their potential relative force relationships, and the first "at" compound with indication that a maximum velocity is associated with certain relationships. This will be the first hint for the entry of relativistic effects. There is only one warning to be given. Although the start of many relationships will readily appear to be seen (as related to the world that we know), there will eventually be found another world of intermediate particles that will have to be built first before we actually enter our presently known atomic world. The author does not contend that this has been done, and anyone (everyone) has an opportunity to be first with any point that they may wish to present. No one should miss the fun, it has just begun. You can not have something lovely Unless there is something ugly You cannot have an influence upward Unless there is an influence downward You can not even have something Unless there is nothing Thus, no matter what we might be We each play a part in eternity Page D-15 References: 1) Words of Lehi, given some 2550 years ago, English translation by Joseph Smith, Jun., first published in English in 1830 and now found in 2 Nephi 2, verse 11, of the Book of Mormon. 2) Ibid. +Note 1. I could have been more complete with these thoughts. The law of reality is given at the top of the next page, but I should have stated it here also, that all things are a simple compound of opposites. Also, just to be more than clear, I should have said "... a mind as weak as the author's ...."+ +Note 2. Ultimate reality can be defined as the most basic thing or things from which all other things are made. At one time, certain elements were thought to be our "ultimate reality." Then atoms were thought to be the basic building blocks, then protons and electrons, and now quarks. Eventually, we must come to the limit where there is an end to finding things within things. This limit is what I am calling "ultimate reality." The statement "W" could be improved. To be a little more clear, it could be stated that: No thing, as a whole, can be simpler than any of its individual parts. Thus follows "X": the simplest object we can find must be composed of portions of ultimate reality. Thus, ultimate reality must be as simple or simpler than the simplest object that can be found.+ +There is no note for this comment, but it is good to repeat these basic concepts: ultimate reality cannot be more complicated than the simplest object that can be observed. Ultimate reality cannot be simpler than consisting of at least two different things. It seems reasonable that these two limits are the same since one either is or at least determines the other. If they are the same or not, assuming that they are the same is at least a good starting point, and any efforts we put forth to make them the same should quickly let us know how correct we might be in this assumption.+ Page D-16
(This page and those that follow is an example of the At Theory
as can be presented in the 1990's, with the use of computers.
This page includes a portion of the title and abstract page, and
the rest of this appendix includes the body of this article as it
was written in 1994.)
A simple means of exchanging mass on a Newtonian level between
spatially separated bodies results in the appearance of force
fields. Symmetry, and the three conservational laws of mass,
momentum and energy, are completely maintained. These force
fields include both attractive and repulsive components. The
nature of these fields automatically produce several quantum
mechanical characteristics to include the uncertainty principle
for all appropriate characteristics of these particles. This
approach is believed to contain the key that will establish
unification between Newtonian physics and quantum mechanics.
(C) 1994 by Gerald L. O'Barr
A simple means of exchanging mass on a Newtonian level between spatially separated bodies results in the appearance of force fields. Symmetry, and the three conservational laws of mass, momentum and energy, are completely maintained. These force fields include both attractive and repulsive components. The nature of these fields automatically produce several quantum mechanical characteristics to include the uncertainty principle for all appropriate characteristics of these particles. This approach is believed to contain the key that will establish unification between Newtonian physics and quantum mechanics.
(C) 1994 by Gerald L. O'Barr
INTRODUCTIONToday, we use a "kinetic interaction" force theory. It is called the "ideal gas law." By making the assumption that gases are composed of atoms, and making assumptions about the collisions of these atoms, we can obtain the "P v = n R T" function. This tells us how "P," the pressure, which results in a force upon any exposed surface, is established due to simple, conservative, Newtonian collisions.
This theory was (and still is) extremely successful. The atomic theory of matter, and that atomic collisions obeyed the conservational laws, have acted as a guide that can not be equaled. It was especially valuable when the complete understanding of atoms did not exist. But today we have gone much beyond atoms. We are now down to the parts that make up the atoms, and to space reaching forces that are not yet explainable by Newtonian physics. Newtonian physics, as understood today, cannot explain such forces as gravity, or electrical forces, or any of the long or short range nuclear forces.
The At theory is a new "kinetic interaction" force theory which will help us explain these additional forces. It is Newtonian. It deals with a particle concept for our reality clear down to the lowest level of our reality. In future research efforts, it will play a similar role now played by the atomic theory of matter and the ideal gas law. It will establish the overall characteristics of all forces that can exist. This article is only a partial introduction to the theory, but it will introduce the basic concepts of forces. Therefore, for this article, the At theory is a proposed explanation of space reaching forces.
Again, the ideal gas law cannot explain all forces: it can only explain "pressure" forces. No Newtonian explanation presently exists for space reaching forces, especially the attractive type of forces such as gravity. The At theory will give to Newtonian physics the power to explain these types of forces.
BASIC ASSUMPTIONSWhat is the lowest level of our reality? We of course do not know what the lowest level is. It might be near the lowest level that we now know, or, most likely, it might be many levels deeper. The At theory does take the position that there is a lowest level, and it makes certain assumptions about this lowest level. The lowest level must be as simple or simpler than all systems existing above it, and it must therefore be as simple or simpler than any thing that we can see or observe. Details of this approach will not be given in this article, but the significant results, as relating to forces, are presented.
The At theory takes the view that all of reality is composed of particles. Down on the lowest level of this reality, there are no space reaching forces such as gravity, or electrical forces, or short or long range nuclear forces. These forces, along with all other space reaching forces, must therefore be ultimately explained as the results of certain interactions of particles. The At theory makes certain assumptions about these particles and the interactions that they can experience.
The only interactions allowed in the At theory are collisions. In all collisions, conservation of mass, momentum and energy are strictly observed. Thus, again, the At theory could be called a "kinetic force" theory. In essence, the At theory claims that there is one grand mechanical system that explains all of our reality.
It is a fact that the basic assumptions of the At theory, up to the collisions of the particles, contain all of the concepts of the "ideal gas law." The ideal gas law actually forms part of the At theory. The At theory can "split" into two or more different theories at the point where collisions occur. The ideal gas law comes from the collisions where the first solution set is used (where particles, in one-dimensional interactions, return or bounce back in the same directions from which they came.) The part of the theory that holds our attention in this article will relate to the second solution set that can be obtained from the collision equations. This will be called the At theory, even though the "ideal gas law" type of interaction, and others, are part of the total theory.
There are many limitations to the At theory. These limitations are similar to the limitations in the atomic theory of matter or the ideal gas law. These present theories tell us something about all atoms and gases, they tell us little about any specific atom or gas. In this same way, the At theory will tell us little about any specific fundamental particle. It will not tell us details about gravitons or gluons. But it will outline some of the general principles and limitations of the actions of all fundamental particles.
The ideal gas law is not always perfect. There are some gases and conditions where deviations from the law occur. These deviations do not invalidate the theory. The deviations can be attributed to limitations in the assumptions, not the mechanics. In the same way, there will be imperfections in the At theory. But again, these limitations will not be in the mechanics.
Even though there are these many limitations, the At theory will eventually explain to us the generality of the uncertainty principle, Planck's constant, particle- anti-particle duality, relativity, the limit to the speed of light, the ether, all on a Newtonian basis. It will one day be the unification theory.
SIMPLIFICATIONSThis article will present the At theory in a very condensed form. We will show the principles of the At theory in a simple, one-dimensional setting. Although there are no theoretical limits as to the number of sizes of particles in our reality, we will use a system of only nine sizes (or mass) of particles. For this presentation, we will assign these sizes to be 99, 100, 101, 399, 400, 401, 799, 800, and 801 mass units. The unit for their mass remains unspecified. The 99, 100 and 101 mass of particles are classed as a type A, the 399, 400 and 401 are classed as type B, and the 799, 800 and 801 are type C particles. Thus we see that we have three basic sizes of particles. A, B, and C. Each of these three ranges or classes of particles consist of a below average, average and above average size.
The A particles relative to B and C particles are very small. In mechanical systems where collisions are the basic interactions, such as in the ideal gas law, an "equal partitioning of energy" is observed. This exists in the At theory. This results in the lighter A particles having higher kinetic velocities than the higher mass particles. The lighter A particles are used as the "field" particles, and the heavier particles are the ones that are "acted upon" by the field particles. It will be the motions of the heavier particles that will be of interest to us in terms of forces.
If two B particles, or two C particles, exposed to a field of A particles, find themselves being driven together, it will be said that an attractive force exists between them. If any two particles are driven apart, it will be said that they repel each other. This article is this simple. Interactions that can occur between A and B particles, and A and C particles, will be determined and/or specified. Pairs of B and C particles will then be exposed (by computer simulations) to a uniform, symmetrical exposure of type A field particles. The results of their overall motions will then be used to determine if a "force" exists.
If overall accelerated motions between these particles can be established, we will have at least one, and the first, mechanical explanation or understanding of space reaching forces. We will have done this through a mechanical system that follows Newtonian physics. Knowledge of the ideal gas law will be useful, but hardly sufficient. The ideal gas law works through the first set of solutions which result on a "first order" transfer of momentum. This is done by a "bounce" where up to twice the momentum of the incoming particle can theoretically be transferred to the body that is hit. In the system that we will analyze, the momentum transfer is a second order transfer, and the net results must be obtained after a series of interactions have occurred. This makes it more difficult to follow or understand or conceptualize, but it is based upon the same type of mathematics upon which the ideal gas law is established.
Such efforts to create "forces" by mechanical or kinetic interactions have been tried before. Ever since Newton discovered that the earth was applying a force on the moon, almost all great men have tried to explain how this force could be. They have all failed. Not only did they fail to create the right kind of force: They failed to create any force at all. All previous theories, under conditions of symmetry, where conservation of mass, momentum and energy were followed, resulted in no net forces. No net forces were possible. 1,2
One of the best examples of this effort was done by a man who lived in the days of Newton named LeSage. 1,2 He came close, but it was his belief in God that resulted in his failure. He believed that the particles that he was considering were as eternal as the God who made them, and therefore, these particles were not susceptible to change in their collisions. Everyone else has followed his assumptions, to include us, until today.
THE MATHEMATICS FOR COLLISIONSSince this is an introduction of a new concept, we will present this new concept in the simplest possible way. We will do a one-dimensional development. With this simplicity, the mathematics can be developed in seven simple equations.
We will assume a simple one-dimensional collision (a direct, central hit with no rotations) and require complete conservation of mass, momentum and energy. A body of mass m1, moving to the right (assumed to be the positive direction), with a velocity of V1, hits a body of mass M1 that has a velocity of U1. Following this collision, new bodies of mass m2 and M2 appear, with velocities of V2 and U2 respectively.
For conservation of mass, we can write:
m1 + M1 = m2 + M2 . 1)
For conservation of momentum:
m1*V1 + M1*U1 = m2*V2 + M2*U2 . 2)
For conservation of energy:
1 2 1 2 1 2 1 2 -m1*V1 + -M1*U1 = -m2*V2 + -M2*U2 . 3) 2 2 2 2
Simultaneously solving these three equations for V2 and U2, we obtain:
--------- m1V1 + M1U1 +/- (V1 - U1) \/ M1M2m1/m2 V2 = ----------------------------------------- 4) m1 + M1 and - --------- m1V1 + M1U1 + (V1 - U1) \/ m1m2M1/M2 U2 = ----------------------------------------- 5) m1 + M1
We must now choose a solution. Also, we will introduce the variable "d," that represents the exchange of mass. The chosen solutions are:
--------- m1V1 + M1U1 + (V1 - U1) \/ M1M2m1/m2 V2 = ----------------------------------------- 6) m1 + M1 --------- m1V1 + M1U1 - (V1 - U1) \/ m1m2M1/M2 U2 = ----------------------------------------- 7) m1 + M1
Here, m2 has been replaced with "m1 - d", and M2 by "M1 + d."
This maintains conservation of mass, but shows that there is really only one new variable being introduced. Also, if "d" is assumed to be small (which we do assume in this presentation), then it is easy to expand these equations in "d/m" and/or "d/M," to obtain approximate solutions if one cared to obtain such solutions.
DISCUSSIONS OF NEW EQUATIONSEquations 6) and 7) are the equations for which we seek. They are a solution set to equations 1), 2) and 3). Very few texts show the complete solution sets, equations 4) and 5), and fewer yet work with the set of solutions which we have chosen.
It does need to be observed that m2 has a more positive velocity than M2. This means that m2, the body that is associated with m1 because of size (d being small), is now to the right of M2. This seems to indicate that m1 went through M1. What really occurs is a "spall." When m1 hits M1, it becomes a part of M1, and a piece of M1, opposite of the point of hit, breaks off and continues on in the same direction as the original m1. Figure 1 shows a collision between two bodies where a spall is produced. On this basic level, there are no losses of energy associated with these spalls.
A spall does not have to be the same amount of mass as the particle that caused the spall. Therefore, the spall concept provides a reasonable means for an exchange of mass between interacting bodies. It allows a solution that provides for a more free movement of bodies through space. It also provides for certain momentum exchanges that will allow Newtonian particles to produce other results found in Quantum Mechanics.
The conservation of mass requires only that the total sum of mass remains equal. By allowing the mass of the individual bodies to change in mass, we have found an additional degree of freedom in our equations. This additional degree of freedom will allow us to do things that could not be done before. It also presents us with a complete set of solutions, which includes a solution set that has not been used before.
In the old way of collisions, where only a specific, not the general conservation of mass relationship is allowed, where no exchange of mass occurs (d=0), the square root function disappears, and a linear equation appears. With linear equations, no net forces are possible in kinetic interactions. When "d" is finite, there exists nonlinear equations, and net forces can now exist. If one wants to get into off-handed comments, you could say that for 400 years we have dealt with only one-half of physics. The other half of the set of solutions will just now begin to be considered.
APPLICATIONS OF EQUATIONS
Having these new equations are meaningless without knowing how to use them. Some general principles will now be established. We will assume that there is a background of particles that are moving throughout space with reasonably random distributions in their directions, speeds, mass, energies, momentums, etc. They are too small to be individually discerned. Existing within this background of particles are larger particles that can be more readily observed. These larger particles are interacting with the background particles. Up to here, we are closely following the thoughts of LeSage.
Some general principles follow from assuming that all interactions are spall type interactions as expressed in equations 6) and 7). These kinds of interactions, where mass can be exchanged ("d" has a finite value), mean that one body must increase in mass, and the other body must decrease in mass. If these are stable bodies, then by necessity, in some following interaction, the exchange of mass must be such that the opposite occurs, where these particles are returned to their original mass values. Now this return does not have to occur at once, or even in every collision, but only within some range of magnitude and numbers of collisions so that there is established some norm to their mass.
If we assume that stability also exists in the background, and the background is the results of spalls, then certain balances must exist between the spalls and the background. Therefore, spalls can only be the type of particles that exist in the background, or saying the same thing, the background can only consist of the particles that are produced by spalls. The mix or ratio of particle types must also be identical.
Using this kind of logic, the following can be said:
EXAMPLE OF A FORCE FIELDA simple example would now be helpful to give us a better understanding of some of these concepts. We will describe a simple, one-dimensional field.
We establish a line with a left boundary at 0 and a right boundary at 4000 unit distance. At the left boundary we will have field particles enter with the following masses, velocities and times:
mass velocity time of entry ------------------------------------------------- 1) 100 100,000 0.125 2) 100 100,000 0.250 3) 101 100,000(100/101)^1/2 0.625 4) 99 100,000(100/99 )^1/2 0.750
The positive velocities mean that they are moving to the right. This cycle of four particles is repeated continuously with a fixed time of one time unit between each repeating particle.
On the right boundary, we have the exact same particles enter except that their velocities are negative (they are moving to the left) and their times of entry are offset by 0.25 time units from each matched particle on the left. Thus, over large time intervals, a very complete symmetry is maintained in the field particles that enter the two boundaries of this line.
It can be noted that the velocities of the 101 and 99 mass particles are slightly different than the 100 mass particles. This is done to give each particle an "equal partitioning of energy." It is known that when free particles are interacting with each other, this is a natural occurrence, and by doing this by assignment, it helps to maintain consistency in the rest of the interactions. If a computer program were written so that the field particles could reach equilibrium velocities, they would approach the ratio of velocities that are being assigned.
One basic assumption for this article is that there are no mass exchanges between any of the field particles among themselves (d=0). The only mass exchanges are between field particles with the larger, stable particles that exist.
We will now place upon this line two large particles of one or two types. We can then observe their interactions. If they accelerate towards each other, we will say that they attract each other; if they accelerate away from each other, we will say that they repel each other.
The following table shows the masses for one of these large stable particles, and the mass ("d") that is exchanged when a collision occurs with one of the field particles:
399 400 401 (Mass of stable particle) ----------------- Field 101 1 1 1 Mass 100 0 0 0 99 -1 -1 -1
The other large stable particle has the following exchanges:
799 800 801 (Mass of stable particle) -------------------- Field 101 0 0 0 Mass 100 1 -1 -1 99 0 0 0
Some time can be spent in considering what all these tables might mean or include. These tables do control the spalls that these particles produce. The medium-mass-range particles (400 mass range) only allow spalls that are exactly a mass of 100. The largest-mass-range particles (800 mass range) allow only 101 or 99 mass spalls. It could be said that one particle decreases the dispersions seen in the background, the other particle increases the dispersions. These tables do allow for at least a form of stability for each of these particles. These tables also collectively reproduce the same mix of field particles that were assumed in the original field, exactly so if we assume that there are an equal number of these two types of particles.
Although we are not going to discuss each of these points in this article, each of these points are important in obtaining the type of response that is desirable. To achieve some of these points, we had to pick some very particular values in these tables. However, just as with the velocities assigned, some of these relationships will be found to be automatic if we had a way of letting certain relationships go to equilibrium. Again, these points, even if important, do not have to be fully discussed in this article in order to observe the results.
RESULTSFigure 2 shows the results of the computer plot of two 800 mass particles. At time 0, the 800 mass particle on the left was placed on the line at point 1990 with a velocity of 3.6 units. The 800 mass particle on the right was placed at 2010 with a velocity of -3.6. A plot was made of the positions of these two bodies for 25 time units, and shown on a plot that extended from position 1940 to 2060.
It is clearly demonstrated that an attraction appears to exist between these two bodies. Calculations of their average accelerations gave values of approximately 0.3136 +/- 0.001 units. Average accelerations were estimated by noting the successive changes in positions in two adjoining time periods, calculating the average velocity for each period, and then dividing the change in velocity by the time period average. Time periods equal to units of field cycle times were used. Forces were estimated by taking the acceleration and multiplying it by the initial particle mass.
Since this is only a one-dimensional interaction, the force between these two bodies is fairly constant and does not vary with distance. In a three-dimensional set-up, the force should approach a force inverse to distance squared if the distance between them were large compared to their diameters.
Figure 3 shows the actions of two 400 mass particles. They are plotted over the same plot boundaries and times as was used in Figure 2. The 400 mass particle on the left was started at position 1946 with a velocity of -8. The 400 mass particle on the right began at point 2052 with a velocity of 8.
These two bodies are repelling each other. Their accelerations were calculated to be close to the values of 0.6230 +/- 0.0001 units. Considering that these two repelling bodies are one-half the mass of the two attracting bodies, it can be noted that the forces of attraction and repulsion are fairly equal to each other.
The difficulty of making an exact measurement between these forces is obvious. Since the masses of these particles are constantly changing, some kind of time integration value would have to be sought. Also, since these particles are each moving back and forth on this line from 5 to 10 units, it is difficult to say, with high accuracy, what their acceleration might be. Again, some kind of averaging must be considered. None of these kinds of calculations were used in determining the above figures.
QUANTUM MECHANICS RELATIONSHIPSThe difficulties noted above are interestingly similar to certain quantum mechanical relationships. The 400 mass particles "jump around" more than the 800 mass particles, as would be expected in quantum mechanics. This indicates that they each had the same "h" value. The "h" value can be controlled by the number of impacts experienced per unit time, the velocity of the field particles, and the amount of mass exchanged in these interactions. Simple inspection shows that there are constant changes in the positions and velocities (and therefore momentums and energies) of these particles.
The field particles could be identified as 100+d, 100+0, and 100-d. If one used the mass unit "d" as a particle, the "+d" state and the "-d" state could be seen as a particle, anti- particle relationship. By definition, the +d must be exactly opposite to -d. If one ignored the normal 100 mass units of the field particles, and only considered the "d's," you would have an exchange of "d" particles occurring between your interacting particles. You would then have, as desired, a "+d" mass, a "0" mass, and a "-d" mass particle system.
Therefore, we see an uncertainty in the mass, in the position, in the velocities, momentum and energies for these particles. We can also see how a particle, anti-particle relationship could be conceptualized.
There are many other relationships that can be considered. For example, in Newtonian physics, the linear kinetic energy of a particle, divided by its momentum, is one-half of its velocity. For a photon (a quantum mechanics particle,) its energy divided by its momentum is its velocity, c. This energy/momentum ratio is twice as large as is found in Newtonian physics. In Figure 1, we can take the change in velocity of M2, multiply this by its mass, and get the effective momentum that was transferred when the mass "d" was absorbed. If we associate this effective momentum with "d," we will get an energy, momentum ratio for the "d" particles to be the same as for photons.
Also, in the reactions of a 400 mass particle to a 800 mass particle, a mechanism for explaining the spins of subatomic particles or the motions of photons might be shown ( Figure 4.)
UNEXPLORED CONCEPTSNo one should think that this is a very complete article. For example, the field particles used in this particular article used only one order of entry. For the four particles that we used in each of two directions, there are 10,080 different ordered combinations that could be used. They do not all produce the same results for both types of large bodies. There is also a choice of a random order, which has almost an unlimited range of combinations. We have only allowed fixed magnitudes of mass changes. What if we allowed the "d" value to vary? There are many ways to achieve stability in masses, and in controlling the spalls, and in establishing differences in the spalls produced by different "size" particles. And of course, we were only working in one-dimension space, without spins or other three-dimensional effects. The full acceptance of such a new theory would want to wait until some of these other aspects are considered.
CONCLUSIONSAs a quick review, the following has been done:
Each of the above, considered singularly by themselves, could be entirely incidental and of no real importance or meaning. But taken as a whole, they cannot be ignored. When a multitude of events are coincidental, occurring as natural and automatic as they are here, with out any force or effort, these are strong indications that there is something fundamental to the approach.
It is obvious that this article is short and many concepts were not explored. It is important, however, to state one particular point. However close or far apart the forces described in this article approaches any known forces, an attractive force and a repulsive force have been demonstrated. If this has really been done, it is a first. This is the first successful description of an attractive force field based upon Newtonian physics with full compliance of symmetry and all the conservational laws. This is an important accomplishment, not only historically, but for our present advancement in certain theories of physics. All are encouraged to begin to consider this new and important concept.
REFERENCES1) Taylor, W. B., "Kinetic Theories of Gravitation," Smithsonian Institution Annual Report, 1876 (U.S. Government Printing Office, Washington D.C. 1877), pp 205-282.
2) Stallo, J. B., "The Concepts and Theories of Modern Physics," reprint of the third American edition published in 1888, edited by P. W. Bridgman (Belknap Press of Harvard University Press, 1960) pp 92-94.
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Figure 2. Attractive forces between two 800 mass bodies.
Figure 3. Repulsive forces between two 400 mass bodies.
Figure 4. Translational motion, 400 mass body chasing 800 body.