Appendix A....The At Theory.... (21May97)
The At Theory is a very important theory. It will one day
be accepted as the foundations of our physics. A more correct
statement would be that the principles that are elucidated in the
At Theory will one day be the base for all of our physics. The
actual name that they will use might be another name.
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 certainly 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. (A bounce required the action of forces,
the very thing that was trying to be explained. It just did not
seem right to explain forces by using a system that required
forces.) I could not allow myself to consider such complicated
interactions to be involved at our most fundamental 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 any specific 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
changes in velocity relationships) or by doing one set of
calculations 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.
I hope some of you will read these two articles.
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
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.)+
i
-------------------------------------------------------
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.
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,
having no life neither death,...neither sense nor
insensibility."2 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
-------------------------------------------------------------
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
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)
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 1 1 1
-m1*V1^2 + -M1*U1^2 = -m2*V2^2 + -M2*U2^2 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
-------------------------------------------------------
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.):
m1(V1^2 - V2^2) = M1(U2^2 - U1^2) 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, x2 = xy (multiply each side by equals)
x2 - y2 = xy - y2 (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:
----------------
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.
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.
----------------------------------------------------------
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 ---- ------
---------------------------------------------------------------
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/r^2 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
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
--------------------------------------------------------
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.+
---------------------------------------------
***End of 1971 At article***
---------------------------------------------
(Here follows an example of the At Theory as can be presented in
the 1990's, with the use of computers. This includes a portion
of the title and abstract page, and includes the body of this
article as it was written in 1994.)
--------------------------------------------------------------
The At Theory
Gerald L. O'Barr
6 April 1994
ABSTRACT
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 i
-----------------------------------------------------
INTRODUCTION
Today, 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 ASSUMPTIONS
What 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.
LIMITATIONS
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.
SIMPLIFICATIONS
This 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.
HISTORICAL NOTES
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. (See 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 COLLISIONS
Since 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 (times 2):
m1*V1^2 + M1*U1^2 = m2*V2^2 + M2*U2^2 3)
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) \/ M1(M1+d)m1/(m1-d)
V2 = ---------------------------------------------- 6)
m1 + M1
and
----------------
m1V1 + M1U1 - (V1 - U1) \/ m1(m1-d)M1/(M1+d)
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 EQUATIONS
Equations 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:
1) Every particle that exists must have the same kind of mass
as every other particle that exists. This is due to the fact
that all particles are constantly exchanging mass directly with
each other or with some common set of particles.
2) A "stability of mass" function must exist for all stable
particles, which allows the mass of a particle to vary, but
within some limited range.
3) In order to have even a minimum kind of an existence, there
must be at least two different types of large, stable particles
(Our class B and C particles.)
4) If there were two different types of large, stable
particles, it would be reasonable to assume (it would be
expected) that there would be some kind of difference in the
spalls that they produce.
5) If we assume that 4) is true, then "normal" space would
consist of a mix of spalls that was being produced from the two
different types of large, stable particles.
6) If their mix of spalls makes up normal space, then the
space near one type of stable particle would be the opposite of
the space around the other type of particle, being opposite in
terms of what ever was the difference in their spalls that had
previously been assumed.
EXAMPLE OF A FORCE FIELD
A 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)^.5 0.625
4) 99 100,000(100/99 )^.5 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.
RESULTS
Figure 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 RELATIONSHIPS
The 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 CONCEPTS
No 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.
CONCLUSIONS
As a quick review, the following has been done:
1) We have discovered a force field mechanism (a first.)
2) This mechanism included both an attractive and a repulsive
force field. Examples of each were shown.
3) It will eventually be established, under equilibrium
conditions, that these forces are automatically opposite and
equal to each other. It did occur in the given examples.
4) There are mass exchanges involved in the mechanism which
provides an uncertainty in particle masses.
5) Uncertainties in positions, velocities, momentums and
energies automatically result from these mass exchanges.
6) A matter/anti-matter concept exists with this mechanism.
7) This matter/anti-matter concept includes zero mass
particles.
8) An energy/momentum ratio the same as for quantum mechanical
particles exists.
9) A translational mechanism is introduced. (This might
eventually provide explanations for certain inherent motions of
particles, such as photons, intrinsic particle spins, etc.)
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.
----------------------------------------------------
REFERENCES
1) 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.
----------------------------
Figure 1. Collision With Spall.
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 mass body.
-----------------------------------------------------------
****End to the At Theory Presentation********