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This page was created using WEB Wizard Version 1.2
Copyright © 1995 ARTA Software Group and David P. Geller
Copyright 1996,1997
Richard L. Marker
Mt. Vernon, WA 98273
All rights reserved
The author developed Discrete Donut Twisted Chain Theory (DDTC)
over an eighteen year period beginning in 1978. The fundamental
form of the theory developed during the first year, but it was
not until 1996 that useful calculations became possible. The
theory developed separately from mainstream theories, although
many parallels exist.
Any and all responses are appreciated. This is new and fertile
ground... dig in!
This article may be copied and distributed only in its entirety
to others for non-commercial purposes. Mass printed publication
of this document or portions of this document alone or as a part
of any other document, is prohibited without the express written
permission of the author.
Abstract
DDTC describes the fabric of space and matter as connected donut
chains. Each link of the chain develops from the path taken by a
"donut particle" (the only particle) traveling a helical path
around the donut surface. A chain segment with a pi/2 twist
defines charge.
This closely resembles super string theory with the string being
the donut particle path. Including time, the donut is 10 -
dimensional, three standard spatial dimensions, one time
dimension, and 6 donut dimensions. The discreteness of the donut
particle allows gravity to electromagnetic force ratio
calculations from basic principles.
The key to solving super string theory involves phasing the donut
particles so that they collide at minute collision angles. The
mathematics involved are strange. Phasing requirements make prime
numbers an important consideration. Phasing requirements also
cause the numerator and denominator that express the angle of
travel to be multiplied instead of divided.
Knowing the position of the donut particle along the donut path
is crucial for calculating gravity. Theories that are continuous
or lack the exact discrete form seem incapable of producing the
same results.
Do not confuse this donut theory with others that operate on a
much larger scale. The electron for example travels around a
closed group of donut chains. This entire connected chain
resembles the donut of some other theories.
Discrete Donut-Twisted-Chain Theory (DDTC)
Note that the physical descriptions in this theory are believed
by the author to be the real processes, not simply analogies to
the processes that occur. This theory differs from most theories
in its development. Rather than matching mathematical models or
functions to observed physical data, this theory developed from a
logical metaphysical approach (in a thought experiment sense, not
a religious sense). Thus, the foundations of this theory answer
as much "why it is so", as they do "what it is". Indeed, several
aspects of the discrete nature of space seem unreachable unless
approached from this "bottom up" method.
You will find that this theory departs from conventional wisdom
about general and special relativity and about stable paths of
motion. The author recognizes the seeming absurdity at first
glance of some of the conclusions or logic. Nevertheless, the
ultimate test of logic is reality.
Do not make your understanding of this material more complicated
than it is. The concepts, regardless of how foreign, are simple
and few.
One assumption principally leads to the results of this theory.
No force can be communicated through empty space regardless of
the smallness of the distance . Only opposing contact motions
between donut particles can transmit a force.
The universe consists of a single particle type called a donut
particle residing in empty space (absence of everything , i.e. a
void). The donut particle is a single element of something with
no special characteristics. Assume that it is a round uniform
ball of fluid for simplicity. Also, note that the author uses the
term "space" alone to refer to a vacuum as opposed to "empty
space".
The discrete donut particle travels along the path of a spiral
wrapped around on itself to form the overall shape of a donut.
Adjacent donuts form the links of a donut chain. All donuts of a
connected space must be either right or left-handed, but not
both, in order to smoothly mesh with adjacent donuts. For space
the donut chain contains donuts with a 90 degree axis rotation
from the adjacent donut (i.e. it takes a chain of four donuts to
return to the starting orientation).
The shape of the donut is fundamental to the donut theory. A few
important mind games are helpful to understand why the donut
particle achieves its dynamic path shape and why there exists a
space fabric forming a preferred coordinate system.
Before a space fabric existed there existed only donut particles
residing in empty space. Empty space has no preferred coordinate
system. Each particle was of course stationary relative to
itself. Relative to another donut particle the motion could take
on any path of motion and that motion could be represented by a
series of circular motions superimposed on each other (similar to
a Fourier series). Note that this description of the donut
particle occurs before the donut path of motion is achieved. Note
also that this is why motion exists.
This unwieldy view of space seemed to lack any useful
characteristics for helping to understanding it. Indeed, it is
not until one donut particle contacts another donut particle that
something interesting happens. The two donut particles average
their opposing motions relative to one another. Eventually, more
donut particles collide and average opposing motions to create a
preferred coordinate system of the space fabric.
Each donut particle has two stable particle motions relative to
the space fabric. The two motions are the major angular revolving
speed around the center of the donut and the secondary rotating
speed around the donut edge. Achieving stable non-canceling
geometries usually results in donuts with the line of contact at
45 degrees to the major axis of each donut (i.e. adjacent donuts
have major axes at 90 degree angles).
A circular stable path of motion is foreign to our senses. That
is because in ordinary life we view the physics of the space
fabric and not the physics of empty space. With no contact what-
so-ever outside of itself, a particle has no way to "know" if it
is traveling in a circle. Thus, the first argument for the donut
is the non-existence of centrifugal force in empty space.
The second argument for the donut is one of need. Due to our
principal assumption of the existence of only pushing contact
forces we need a way for a particle to exert its force on another
particle and not continually push other particles away with no
return. The circle (donut) provides a mechanism by which pushing
forces can exist and be stable. Descartes also used interlocking
circles in work he did centuries ago. The author did not have
access to this work (still in French) to know how similar his
circles may have been.
The third argument for the donut is the consistency of the
averaging mechanism with views of the big bang. Originally, all
donut particle were traveling randomly. This was before a big
bang. Particles collided and then formed small separated regions
of space of different sizes, different handedness and different
"gauge". The 138 donut chain segment length of normal space was
only achieved after much transition. Initially each donut chain
could have formed or combined in any length. After more activity
(time passage) early on some of the stable space gauges could
still have been different.
Probably the closest view resembling the big bang would not have
been at initial formation, but rather, a while after that, when
the different separated space regions ("mini-universes") collided
with each other to form larger regions (same handedness) or
destroy portions of each other (different handedness).
The number of universes have decreased, but not to a single
universe. Indeed, a single universe may be impossible. If the
handedness of universes sum to zero, then the final collision
between the single remaining right-handed universe and the single
remaining left-handed universe could destroy both universes and
return conditions back to the near beginning of a big bang.
Many readers will likely question how the space fabric can be
consistent with special relativity. On first (and second) glance
it appears to be non-sensical that the two could co-exist.
Details of this co-existence are omitted from this write-up.
However, Special Relativity transformations can be developed
directly from the assumption of an Euclidian space with no
special characteristics except that a body in motion will seek
the same electromagnetic equilibrium between its component
particles as the equilibrium that existed at rest.
This view of relativity gives some insight into the paradoxes of
Special Relativity. The resulting transformations consist of a
"real" part and "apparent" part. If the observer is at rest
relative to the space fabric then the entire transformation is
real. Otherwise, it is not. If an observed body instantly changes
speed, its apparent distance from an observer also changes. It is
this discontinuity of apparent measurement that needs to be
considered in order for a paradox not to exist. Back to space
fabric.
Space fabric consists of donut chain segments that are 138 donuts
long outside the range of the strong force.
Time is fundamental with ddtc. Each major revolution of the donut
particle about the major axis is a unit of local time. Adjacent
donuts are very closely synchronized with each other, forming a
giant interconnecting "gearing system" that can be considered to
be a space clock made up of each donut particle in space
connected to adjacent space clocks. Differences between adjacent
clock speeds form time dilation and gravity. Before the existence
of the donut chain fabric the term "time" would seem to have a
vague meaning.
Charge (charge source, not charge field) results from twisting a
donut chain segment. A donut removed from an untwisted chain
segment requires a twist in order to reconnect with the adjacent
donut chain segments.
Assuming you twist the donut chain segment the shortest distance
needed to reconnect for every addition or removal you do, then
the removal of a donut link will create a negative charge or the
addition a positive charge. Thus, if the non-charged donut chain
length is 138 and you remove one donut, the resulting length of
137 will carry the negative charge. If the non-charged length is
136 and you add one donut, the resulting length of 137 will carry
the positive charge.
The fact that 139 and 137 constitute are prime adds to the
electron stability since intervening in-phase modes are less
likely. (About primed pairs, see "The Mirror Has Two Faces --
Barbara Streisand", coincidentally my favorite movie person. How
did Ms. Streisand realize the importance of primed pairs! Tell
the good old boys to get off their butts and give her the Oscar
she so richly deserves for several of her productions).
All mass results from charge or the movement of charge. At least
for the electron, the twist in the donut chain is compensated for
by the donut adopting a different ratio of main angular revolving
speed(around the donut center) to secondary rotation speed
(around the donut edge) in an attempt to realign the angle of
contact with adjacent donuts to zero. The stable pattern adopted
does not quite close the angle of contact to zero. The resulting
small angle of contact yields slight opposing motions that simply
average each other and slow the donut particle speed ever so
slightly due to this contact drag.
The sum of all the contact drags for the connections that
constitute a particular real particle produce that particle's
aggregate particle time drag (i.e. time dilation summed over a
surface integral that encloses the various contact drags for the
particle). Note that the particle motion (spin and translational)
as well as simple angular donut chain twist adds to the contact
drag. A donut time unit is treated as time it takes a donut
particle to make one revolution around the donut.
The change over donut distance (i.e. donut unit distance) in the
time dilation caused by a distant particle's contract drag
produces the acceleration "warp" of space-time resulting from
that particle.
The calculation of contact drag requires matching the elapsed
number of donut revolutions until contact between adjacent
donuts, together with the primary revolution speed and secondary
rotation speed. All three of these numbers must be in phase
before contact is achieved .
The elapsed number of donut revolutions for in phase contact
seems to be the key that must be known before superstring theory
will work for calculating gravity. The donut path traveled is not
a continuous string but simply the path of a donut particle. The
calculation of this number for the main electron donut chain
segment is included in a later section, notice that prime numbers
play an important role.
The current state of the electron mass calculation indicates that
gravity travels about 4.65E+34 times the speed of light! However,
it does not travel as a wave. Gravity is extremely inefficient
and results from simply averaging the "clock" time of adjacent
donut particles at contact. This inefficiency doesn't affect our
standard measurement of energy in physics because energy as we
know it is determined by the donut configurations and not by
cumulative drag over time on the clock of space.
The averaging assumption for donut collisions produces
gravitational time dilation that equals that produced by General
Relativity at large distances. However, there are important
distinctions. Donut collisions are a discrete process. At
distances much larger than the diameter of the electron,
continuous approximations are reasonable.
Gravity does not cause time dilation. Matter is a cross-
connection that slows the local "space-clock". It is this time
dilation that causes gravity .
Pure black holes with a "Schwarzschild radius" below which
nothing can escape do not accord with donut theory. The donut
space is discrete long before reaching this small dimension
making the calculation of such a radius moot.
Planck's constant results from the energy in the pi/2 twist in an
imaginary donut chain one link long multiplied by the time to
travel around the donut link at the speed of light.
Ratio of Gravitational Force to Electromagnetic Force
The theory develops the ratio of gf to ef as being equal to the
sum of the contact drag ratios per unit of donut time. For the
main electron chain segment this is equal to:
137 connections
x contact angle squared / 2 x pi^2 / 8
x 1/number of units of donut time before contact
or
137 x (8.087280E-11)^2 / 2 x pi^2 / 8
/ (2 x 137 x 139 x 74445^2 (74445^2 + 274^2 x
278^2)) = 2.308 E-43 (versus 2.40004 E-43
actual)
note:
This is the gravitational drag due to the main electron donut
chain segment only. There is some additional drag from movement
of the electron segment (by adding one donut to it and
subtracting one from the next segment). Hopefully, this can be
calculated accurately when the path the spinning electron travels
is determined.
The 8.0872.... collision angle results from looking for stable
collision angle modes that match the twist in the donut chain.
This number was the only one that looked stable, and it looked
exceptionally stable with a bonus of exact and important matching
properties between even and odd donuts in the chain.
The Pi^2/8 results from assuming a sine wave distribution of
collision angles. This is speculative. It is equally likely that
this factor will be omitted when the factor discussed in the next
paragraph is finally determined.
The (2 x 137 x 139 x 74445^2) depends on matching the time
elapsed between adjacent donut particles before they collide.
This number depends in part on how much the donuts in the
electron chain segment "stretch" to fill the same distance as a
138 donut connecting chain segment. This factor likely will
change some.
The (74445^2 + 274^2 x 278^2) depends on matching the rotational
and revolutional phases between adjacent donuts. This factor
looks solid and develops from the same configuration that
determines the collision angle.
The build-up and tear-down of the twisted chain segment as the
electron spins adds something to its mass. That is not included
in this calculation.
Corrections in the model not shown or discussed above have
brought this number to well within experimental error. There are
still some speculative elements, but the number and theory seem
to be holding up well.
The three corrections not shown are: 1) the sum of the collision
angles has been spread over 136 donuts rather than 137 (the end
donuts of the chain appear almost fixed due to frequent
interaction with donuts located outside the e-leg); 2) the amount
has been corrected to reflect slightly different masses for the
electron and positron (this results from different chain lengths
and conflicts with the standard view of matter/ antimatter); and
3) the mass of the electron is reduced by the anomalous magnetic
moment in calculating the actual gravity/em force ratio (this
correction is used by some to adjust the mass of the electron, I
suspect it may relate to the pieces not included that were
mentioned).
Fine Structure Constant
The fine structure constant is reproduced by the expression:
(138^2 - 3^2) / (138^2 - 2^2) / 137
or
(135 * 141) / (136 * 140) / 137
= 0.00729735325
versus 0.00729735308 (33) 1986 CoData
The adjustment comes from the transition between two
complementary donut configuration modes that carry the
electromagnetic wave. Complementary modes have an equal number of
nodes added and subtracted from adjacent donuts, where the
standard number of nodes is 138. The number of nodes is the
number of revolutions made around the donut tube for each major
revolution around the donut central axis.
It is conceivable that different adjustments may be needed to the
1/137 value for different purposes, but that the same value has
been used for all purposes in general calculations.
Proton to Electron mass ratio
A triangle with a chain segment for each side seems to be a
likely candidate for a stable particle such as a proton. The
smallest such candidate that seems reasonable has a perimeter
totaling seventeen donuts. The particle spin requires that the
dimensions of the sides change as the external connection to a
triangle corner moves.
If mass is viewed as the sum of the inverse squares of the chain
length times the charge squared, then the three seemingly most
natural stages for the triangle produce:
internal charge
external add to each: triangle sides mass units
(-1,+1,-1)
stage 1 : (5+,5-,7+) 1/25 + 1/25 + 1/49 (0,0,+2)
stage 2 : (5+,6 ,6) 1/25 (+1,0,+1)
and
stage 3 : (6++,5-,6) 4/36 + 1/25 (+1,-1,+2)
average : 0.062451 (-1,+2,+2)/3 divided by 1/137/137 1823.84
(mp/me = 1836.15)
Additional mass comes from charges on the attachments of the legs
to the main space fabric. An exact picture of the connections
must be determined before completing this calculation.
There is a problem with this mass calculation. It seems to come
from a different calculation than that of the electron g-force to
e-force ratio. This could mean it is wrong or simply not fully
understood yet.
Initial calculations suggest that the proton, neutron, Sigma, Xi
and Omega- particles may all have this basic triangle size (some
with different charges). It is too early to tell, but mass ratios
of 2^1/3 and 2^1/2 appear to play a role if the basic core is the
same. The Lambda particle is an odd-ball with a (5+,5-,6; 5+,6,5-
; 6++,5-,6) core triangle shape.
These calculations are all quite speculative, but intriguing. The
fractional powers of two seem quite possible with ddtc, but do
not provide an immediately obvious answer. An understanding of
what the mesons and muons are may provide the clue needed to
complete this area.
Quarks
In discrete donut twisted chain theory (ddtc) the quark is simply
the connection between three donut chain segments, the minimum
number of segments needed in order to have separate segments. As
such it is difficult to discuss quarks as a separate entity.
The 1/3 fractional charge on the quark results from the proton,
for example, having three donut chain sides with spin. This
results in the charge appearing to be the average charge from
three (or more) different states. Additionally, the attachment
chain segments may have changes that add to the total apparent
charge for each quark.
Ten dimensional space
The casual usage of three dimensional space creates the
appearance of naiveté on the part of the author. What magic does
three dimensions possess?
The author believes that our three dimensional world does not
dictate that a three dimensional space could be the only answer.
Rather, that the dimensions which our world displays are merely
reflective of the primary dimensions of space.
Each donut possesses a major axis that can have three
orientations and magnitudes. Additionally, each donut possesses a
rotating axis for the donut particle to create the spiral aspect
of the path. These rotating axes also can have three orientations
and magnitudes. Including time this makes ten dimensions.
Several of the donut's dimensions are related to other
dimensions. The primary donut orientations are limited by the
chain relationships to one another. The secondary donut
orientations of the rotating axes almost always would be parallel
to the motion of the donut particle around its major axis. For
most calculations it seems that this would be a likely
occurrence.
Space handedness
Try to connect donuts of opposite handedness. You will soon
discover that the same handedness is needed in order for adjacent
donuts to have their donut particle motions be parallel at the
point of collision (usually at 45 degrees to their major axis).
This handedness of space violates one's sense of natural
symmetry. The beta decay of the neutron produces a neutrino
always with the same spin lending support to this aspect of
discrete donut twisted chain theory.
Gibbs' description of sine-Gordon equation
Philip Gibbs in his Cyclotron notebooks, (notebook 6., The
Superstring Mystery ), describes an analogy to the sine-Gordon
equation for creating and propagating particles and antiparticles
in one dimensional space. The analogy in one dimension consisted
of clothes pins on a wire clothes line. Pulling up one of the
pins about the line pulled up neighboring pins. Releasing the pin
could cause a wave to travel down the line in one dimension.
Donut chains might accommodate this same motion in three
dimensions. Take a branch donut in a chain (i.e. donut connecting
three segments) and twist it 180 degrees about two of the donut
segments before connecting it to the third. A release of this
twist might travel down the donut chain and choose one of two
paths each time it came to a fork.
Donut size
Determining the scale of the donut has been one of the most
perplexing problems. The Planck Length seemed to indicate a size
many orders of magnitude smaller than the size eventually
developed. While it is possible that the structure may be that
small, all calculations indicate that the donut size equals the
traditional radius of the electron divided by 137.
The size of the donut particle traveling around the donut path is
probably between about 10^-19 cm. and 10^-24 cm. Calculations
that include "misses" between adjacent donuts to form a "symmetry
break" likely will narrow this range considerably.
Comments and speculation
The author apologizes for taking his share of liberties in the
remaining sections. Readers may stop here without missing much of
the meat. Otherwise, take off your scientist hat and enjoy.
Antigravity, hot! . . . Time travel, not
How many of us have shared a seat with Walter Mitty* in wondrous
travels through time? Maybe we visited a race track of past . . .
or lingered another moment with that special person. These
passions beget a sad chapter in the story unfolding. Time travel,
not...
Disappointment may consume us, but fear not! Mr. Mitty never dies
if you truly hold rank as a daydreamer.
Antigravity and free energy entice the uninitiated. Donut theory
offers us a glimmer of hope that these animals exist. But, can we
harness them? Most well bred scientists and all well behaved
scientists consider free energy (I define as the creation of
significant energy without the destruction of matter) to be a
joke. Ironically, this leaves the uninitiated and usually less
educated to discover the answer.
The dogma of science builds on all of itself, including its
mistakes. Those who most vigorously defend or deny something
usually act from strong prejudice. Prejudice that keeps eyes
closed. The messengers of free energy may sound like crackpots.
Indeed, they may even be crackpots. Let them not shut our eyes
anymore than one immersed in the dogma of science.
Antigravity and free energy, hot!
* James Thurber created Walter Mitty, daydreamer extraordinaire,
as the lead character in one of his stories.
Einstein and his Seductress
The beauty of Einstein's space-time continuum equations seduced
their creator for understandable reasons. Few creators could
compromise such a beautiful creation. Ironically, Einstein's
greatest handicap may have been his greatest achievement.
A space-time continuum does not exist under DDTC. It appears to
exist at large distances, but fails miserably at short distances.
It patently offends most relativists to hear that a preferred
coordinate system exists and a space-time continuum does not.
Yet, that is exactly what donut theory does and it is logically
consistent with Special and General Relativity, both
mathematically and intuitively. Contact the author if you want
more information on this.
Time, the Mystical Ruler
DDTC reduces time to the clock position of a gear (donut) in
space, but elevates time to the master controlling all
interactions. The gears of space synchronize so closely with one
another that transmission of an enormous force through them
creates hardly a whisper. When a donut frisks about sufficiently
out of step with other donuts, we elevate it to the position of
matter. Egocentricity is a joke with DDTC.
Before donut particles learned to travel in the donut path, time
did not exist. The first part of a second after the big bang has
limited meaning with DDTC, since the big bang gradually created
the beginning of the sequence of current time.
Donuts are the engine driving the universe. Matter slows them
down and gradually slows down the more distant donuts in space.
These distant donuts revolve at higher rates than those close to
matter to create the time warps that produce gravity. The donut
is its own clock. You can slow it down all you want and it still
behaves as though it were going the original speed since the
measure of time slows in unison with it.
Time travel slowed down
The donut dances many exciting paths. Contrariwise, the boredom
of time is limitless. All adjacent donuts do when their donut
particles collide is average opposing motions. Donuts are about
as average as you can get.
The averaging process is extremely inefficient. But it doesn't
matter since the passage of time changes correspondingly.
Time is not a dimension that can be traveled in two directions.
Or, even in one direction at other than its natural speed. The
averaging process has no corresponding "unaveraging" process.
Free energy, does it belong to the Kooks?
In recent years there has been more and more talk about
extracting energy from the fabric of space. Main streamers mainly
discounted that this could be possible due to conservation
requirements of space and matter.
The donut fabric "wastes" limitless energy in its averaging
process. We don't notice this waste since we observe the
resulting positions of the donuts themselves. The fact that all
clocks have slowed relative to an earlier clock is not
detectable.
Can we extract the energy? Is it "free"? This question has no
clear answer, yet. The limitless energy available in the donut
combined with so many reports of free energy arrangements of
moving magnets stir one's imagination to hope that it could be
true.
Reports of free energy machines becoming colder at times helps
support their credibility. If the donuts could collide in a
pattern that inputs energy to the system, it seems likely that
they could also do the opposite.
Free energy input/extraction could easily escape detection.
Consider a surfer on the ocean. The surfer might go up and down
all day long without gaining speed. With skill the surfer learns
how to ride the wave to extract the energy. Can mankind learn how
to "ride the wave"? The implications abound.
Antigravity, are your hopes up?
Antimatter might at first glance seem to provide a path to
antigravity. Alas! Both antimatter and matter produce positive
gravity and attract one another. They each slow the clock of
space. This is consistent with donut theory.
If free energy can be extracted from the fabric of space, it
likely would slow down the space from which it was extracted.
Slowing down the space above an object would change the time warp
and accelerate the object upward.
An antigravity engine could be used for propulsion in outer space
to speeds near the speed of light assuming other difficulties of
such high speed travel could be overcome. Does this mean we could
visit other solar systems? And they visit us?
Feedback
The author appreciates input or questions from others. Don't
hesitate to contact him.
Thanks for your interest, Rich Marker
Subject: Re: Rich Marker or author's address
Richard L. Marker
RLMarker@aol.com [Rich does not respond diligently to email]
Mt. Vernon, WA 98273
voice phone (before 10 pm Pacific Standard Time):
(360)428-5997
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