| Effect of Charge Interaction on Baryon Rings Configurations and Stability Giulio C. Cima December 2009 (Copyright @ 2009 Giulio C. Cima All Rights Reserved) |
The Rings Model as presented by the Author in “The Rings Model of Elementary Particles” (outlined in "Rings
Model Overview") is based on the condition that the distance separating adjacent singlets in a ring is independent
of the velocity of rotation of the ring, and on the condition that rings are entities of zero charge with no influence
outside their perimeter. The definition of rings as entities of zero charge raises the question of what is keeping
rings together as there can be no stability without interaction between rings.
In this study, the effect of ring spin on the geometry and composition of the ring, and the effect of charge
interaction between rings are introduced and used to explore the degree of stability of the triangular and layered
three-ring configurations of Baryons. As the proton is the single strong attractor in the decay process of Baryons,
its rings configurations are used as models for the study.
The study is in three Parts: Part A examines the stability of the triangular configuration; Part B examines the
stability of the layered configuration; and Part C is a summary of Parts A and B.
Model Overview") is based on the condition that the distance separating adjacent singlets in a ring is independent
of the velocity of rotation of the ring, and on the condition that rings are entities of zero charge with no influence
outside their perimeter. The definition of rings as entities of zero charge raises the question of what is keeping
rings together as there can be no stability without interaction between rings.
In this study, the effect of ring spin on the geometry and composition of the ring, and the effect of charge
interaction between rings are introduced and used to explore the degree of stability of the triangular and layered
three-ring configurations of Baryons. As the proton is the single strong attractor in the decay process of Baryons,
its rings configurations are used as models for the study.
The study is in three Parts: Part A examines the stability of the triangular configuration; Part B examines the
stability of the layered configuration; and Part C is a summary of Parts A and B.
Contents
l
Effect of Spin on Ring Geometry and Composition
Part A: The Triangular Rings Configuration of Baryons
A1: The Proton Model
A2: Electrostatic Charge Interactions between Rings
A3: Effect of Resultant Force on Rings
A4: Rings Displacement Projection Methodology
A5: Rings Displacement Projection
A6: Effect of Spare Singlet on Rings
A7: Effect of Time Increments
A8: Effect of Rings Separation Distance
Part B: The Layered Rings Configuration of Baryons
B1: The Proton Model
B2: Doublets Identity in a Layered Configuration
B3: Electrostatic Charge Interactions between Rings
B4: The Strong Attractor in a Layered Configuration
B5: Effect of Rings Separation Distance
B6: Effect of Forces on a Layered Configuration
Part C: Summary: The Triangular and Layered Rings Configurations
Appendix:
Part A Tables
Part B Tables
l
Effect of Spin on Ring Geometry and Composition
Part A: The Triangular Rings Configuration of Baryons
A1: The Proton Model
A2: Electrostatic Charge Interactions between Rings
A3: Effect of Resultant Force on Rings
A4: Rings Displacement Projection Methodology
A5: Rings Displacement Projection
A6: Effect of Spare Singlet on Rings
A7: Effect of Time Increments
A8: Effect of Rings Separation Distance
Part B: The Layered Rings Configuration of Baryons
B1: The Proton Model
B2: Doublets Identity in a Layered Configuration
B3: Electrostatic Charge Interactions between Rings
B4: The Strong Attractor in a Layered Configuration
B5: Effect of Rings Separation Distance
B6: Effect of Forces on a Layered Configuration
Part C: Summary: The Triangular and Layered Rings Configurations
Appendix:
Part A Tables
Part B Tables
Effect of Spin on Ring Geometry and Composition
The separation between two adjacent singlets in a ring is given by:
sep = e ^ 2 / (m C ^ 2)
Where: e is the singlet charge of 4.8E-10 [esu]
m is the relativistic mass of the singlet
C is the speed of light
The separation is the chord of the arc subtended by the two singlets:
sep = 2 r sin (pi / s)
Where: r is the radius of the ring
s is the number of singlets in the ring
From the equations above, the radius of a ring is:
r = e ^ 2 / {2 sin (pi / s) m C ^ 2}
The radius of a ring is directly proportional to the numbers of singlets in the ring and inversely proportional to the
relativistic mass of the singlets.
The ring rotational velocity can be determined by using an iterative process that would find the relativistic mass of
a rotating ring that is equal to the rest mass of a target ring. More specifically: given a ring A of x doublets find a
ring B of y doublets, where y < x, so that the relativistic mass of B is equal to the rest mass of A. The velocity that
results in the relativistic mass of B is the spin velocity of the ring. However, since the radius of the ring that is
required by the iterative process (see equations below) is dependent on the relativistic mass of the singlets (see
equations above), the iterative process has to be repeated until there is no further change in the values of the
separation between singlets, relativistic mass of the singlets, radius of the ring, and spin velocity of the ring.
The following equations are required:
V ^ 2 = r F / m
m = mo / R
R = sqr {1 – (V / C) ^ 2}
Where: r is the radius of the ring
F is the force due to the spin of the ring on the singlet
m is the relativistic mass of the singlet
mo is the rest mass of the singlet
V is the linear velocity of the singlet
C is the speed of light
Using the proton as an example:
Rest mass 938.2723 [MeV]
Doublets relativistic mass 1.8451 [MeV]
Max number of doublets 508
Total relativistic mass 937.82 [MeV]
Number of rings 3
Doublets per ring 169, 170, 169
Rings rotational velocity 2.496E10 [cm/sec]
Ring radius:
169 doublets 8.40E-12 [cm]
170 doublets 8.45E-12 [cm]
In “The Rings Model of Elementary Particles”, where the distance separating adjacent singlets in a ring is held
constant and independent of the velocity of rotation of the ring, the proton has the following characteristics:
Rest mass 938.2723 [MeV]
Doublets relativistic mass 1.4361 [MeV]
Max number of doublets 653
Total relativistic mass 938.28 [MeV]
Number of rings 3
Doublets per ring 218, 217, 218
Rings rotational velocity 2.11E10 [cm/sec]
Ring radius:
217 doublets 1.95E-11 [cm]
218 doublets 1.96E-11 [cm]
The separation between two adjacent singlets in a ring is given by:
sep = e ^ 2 / (m C ^ 2)
Where: e is the singlet charge of 4.8E-10 [esu]
m is the relativistic mass of the singlet
C is the speed of light
The separation is the chord of the arc subtended by the two singlets:
sep = 2 r sin (pi / s)
Where: r is the radius of the ring
s is the number of singlets in the ring
From the equations above, the radius of a ring is:
r = e ^ 2 / {2 sin (pi / s) m C ^ 2}
The radius of a ring is directly proportional to the numbers of singlets in the ring and inversely proportional to the
relativistic mass of the singlets.
The ring rotational velocity can be determined by using an iterative process that would find the relativistic mass of
a rotating ring that is equal to the rest mass of a target ring. More specifically: given a ring A of x doublets find a
ring B of y doublets, where y < x, so that the relativistic mass of B is equal to the rest mass of A. The velocity that
results in the relativistic mass of B is the spin velocity of the ring. However, since the radius of the ring that is
required by the iterative process (see equations below) is dependent on the relativistic mass of the singlets (see
equations above), the iterative process has to be repeated until there is no further change in the values of the
separation between singlets, relativistic mass of the singlets, radius of the ring, and spin velocity of the ring.
The following equations are required:
V ^ 2 = r F / m
m = mo / R
R = sqr {1 – (V / C) ^ 2}
Where: r is the radius of the ring
F is the force due to the spin of the ring on the singlet
m is the relativistic mass of the singlet
mo is the rest mass of the singlet
V is the linear velocity of the singlet
C is the speed of light
Using the proton as an example:
Rest mass 938.2723 [MeV]
Doublets relativistic mass 1.8451 [MeV]
Max number of doublets 508
Total relativistic mass 937.82 [MeV]
Number of rings 3
Doublets per ring 169, 170, 169
Rings rotational velocity 2.496E10 [cm/sec]
Ring radius:
169 doublets 8.40E-12 [cm]
170 doublets 8.45E-12 [cm]
In “The Rings Model of Elementary Particles”, where the distance separating adjacent singlets in a ring is held
constant and independent of the velocity of rotation of the ring, the proton has the following characteristics:
Rest mass 938.2723 [MeV]
Doublets relativistic mass 1.4361 [MeV]
Max number of doublets 653
Total relativistic mass 938.28 [MeV]
Number of rings 3
Doublets per ring 218, 217, 218
Rings rotational velocity 2.11E10 [cm/sec]
Ring radius:
217 doublets 1.95E-11 [cm]
218 doublets 1.96E-11 [cm]
Part A: The Triangular Rings Configuration of Baryons
A1: The Proton Model
The triangular three-ring configuration of a Baryon particle has the centers of the rings at the vertices of an
equilateral triangle with sides equal to twice the radius of the rings plus the gap between rings.
A1: The Proton Model
The triangular three-ring configuration of a Baryon particle has the centers of the rings at the vertices of an
equilateral triangle with sides equal to twice the radius of the rings plus the gap between rings.
This triangular configuration is equilateral only if there is an
equal gap between rings of equal number of doublets. The
spare singlet of a charged Baryon is located at the center of
the triangle which is also the center of the particle. The
distance between the spare singlet and the centers of the
rings in the equilateral triangular configuration is given by:
d = (2 radius + gap) 2/3 sin (pi / 3) = (2 radius + gap) / sqr (3)
Since doublets in a ring are entities of zero charge, there is
no electrodynamic effect due to the spin of the ring.
Therefore this study only considers the electrostatic effect of
charge interaction within rings and among rings when all
rings lie in the same plane. To that purpose, it is
necessary to define the size of the gap between rings which is
of critical importance in determining the strength of the forces
acting between adjacent rings and the effect of those forces
on the motion of the rings. However, its initial value has no
meaningful importance to the outcome of the study as long as
it is equal to or greater than the separation distance between
singlets. Accordingly, it has been assumed to be twice the
equal gap between rings of equal number of doublets. The
spare singlet of a charged Baryon is located at the center of
the triangle which is also the center of the particle. The
distance between the spare singlet and the centers of the
rings in the equilateral triangular configuration is given by:
d = (2 radius + gap) 2/3 sin (pi / 3) = (2 radius + gap) / sqr (3)
Since doublets in a ring are entities of zero charge, there is
no electrodynamic effect due to the spin of the ring.
Therefore this study only considers the electrostatic effect of
charge interaction within rings and among rings when all
rings lie in the same plane. To that purpose, it is
necessary to define the size of the gap between rings which is
of critical importance in determining the strength of the forces
acting between adjacent rings and the effect of those forces
on the motion of the rings. However, its initial value has no
meaningful importance to the outcome of the study as long as
it is equal to or greater than the separation distance between
singlets. Accordingly, it has been assumed to be twice the
separation distance between singlets. The effect on rings when this assumption is not made and the gap is set to
be equal to the singlets separation distance is presented in Section A8.
It is also necessary to formulate the following conditions:
1) Alignment of Singlets
The alignment of the singlets of two adjacent rotating rings of equal number of doublets and same spin velocity is
given by the angular position A at a point in time of a singlet in one of the rings and the complementary angular
position B at the same point in time of a singlet in the other ring. The singlets of the two rings are said to be in
exact alignment if B = (180 – A) and the rotation of the two rings is then in phase. A deviation from exact alignment
where B is not equal to (180 – A) would result in a phase shift of the rotational motion of one ring with respect to
the adjacent ring.
The alignment of singlets is critical to the determination of the forces acting between two adjacent rings. This
study examines the condition where all singlets in a three-ring configuration are in exact alignment.
2) Charge of Facing Singlets
Given two adjacent rotating rings with singlets in exact alignment, the facing singlets of the rings are the two
singlets, one in each ring, that at the same point in time cross a line between the centers of the rings where the
distance between the rings is equal to the gap.
Two facing singlets can either have the same charge or opposite charges. For an equilateral triangular
configuration with singlets in exact alignment there can be four cases:
1) All facing singlets have the same charge
2) All facing singlets have opposite charges
3) One pair of facing singlets has the same charge
4) Two pairs of facing singlets have the same charge
This study examines the case where all facing singlets have the same charge (see condition 4 below).
3) Direction of Ring Spin
Ring spin can either be right-handed or left-handed. In a triangular configuration there can only be two cases:
1) All rings have the same spin
2) One of the rings has an opposite spin to the spin of the other rings
This study examines the case where all rings have the same spin.
4) Number of Doublets
The maximum number of doublets in a proton is 508 and the rings configuration is [169, 170, 169] doublets. To
determine the number of doublets in the rings model of the proton, however, it is necessary to consider the
conditions in the definition of the model, specifically the condition of rings with equal number of doublets with
singlets in exact alignment.
In a triangular equilateral configuration, the two singlets of a ring that are facing the singlets of the other two
adjacent rings are separated by an angular distance of 60 degrees, and the condition that all facing singlets are in
exact alignment and of the same charge can only be achieved in rings where the number of doublets is a multiple
of 6. For the proton particle, that number is 168. The condition that all facing singlets are in exact alignment and of
opposite charges can only be achieved in rings where the number of doublets is a multiple of 6 plus 3. For the
proton particle, that number is 171.
Noting that the relativistic mass of a doublet is 1.8451 MeV and that of a spare singlet is 0.511 MeV, the mass of the
proton using the condition of facing singlets of same charge is:
[168, 168+Z, 168] ---> 930.44 [MeV]
The mass of the proton using the condition of facing singlets of opposite charges is:
[171, 171+Z, 171] ---> 947.05 [MeV]
Since the later mass is greater than the rest mass of the proton of 938.2723 MeV, there is then only one possible
condition: all facing are singlets of same charge, and the rings configuration is [168, 168+Z, 168].
The complete definition of the rings model of the proton used in this study is:
The rings model of the proton is that of a three-ring configuration in an equilateral triangular
configuration with rings of 168 doublets lying in the same plane. The direction of the spin is the
same for all rings. The rings are separated by gaps equal to twice the separation distance between
singlets. All singlets are in exact alignment and the singlets facing each other across the gap are of
the same charge. The positive spare singlet is located at the center of the triangle which is also the
center of the particle.
According to the definition, the model of the proton has the following characteristics:
Number of doublets 504
Number of rings 3
Doublets per ring 168
Doublets relativistic mass 1.8451 [MeV]
Rings relativistic mass 309.97 [MeV]
Total relativistic mass 930.44 [MeV]
Proton rest mass 938.27 [MeV]
Rings rotational velocity 2.496E10 [cm/sec]
Singlets separation distance 1.56E-13 [cm]
Singlets angular separation 0.0187 [rad]
Rings radius 8.35E-12 [cm]
Particle radius 1.82E-11 [cm]
Singlets transit time 6.26E-24 [sec]
Singlets orbital time 2.10E-21 [sec]
The singlets transit time is equal to singlets angular separation times ring radius divided by ring velocity. The
singlets orbital time is the time that a singlet takes to complete one revolution.
The definition of a triangular configuration with rings lying in the same plane implies a two-dimensional
configuration that imposes a restriction on the motion of the rings: they can spin but cannot rotate about
diametrical axes. The configuration, however, is in a three-dimensional space where it can rotate as a whole in any
direction about any axis passing through its center.
From the above, a neutral Baryon particle can be thought as a two-dimensional triangular configuration of three
spinning rings held together by electrostatic forces. The two-dimensional configuration can rotate in a three-
dimensional space in any direction about any axis passing through its center. The rings have an equal number of
right-handed and left-handed single and double time helixes, each time helix being described by a quantum of
energy moving at the speed of light in a one-dimensional curled space. Depending on the charge of the particle,
charged Baryons have one (or at most two) right-handed or left-handed single and double time helixes located at
the center of the triangular configuration.
be equal to the singlets separation distance is presented in Section A8.
It is also necessary to formulate the following conditions:
1) Alignment of Singlets
The alignment of the singlets of two adjacent rotating rings of equal number of doublets and same spin velocity is
given by the angular position A at a point in time of a singlet in one of the rings and the complementary angular
position B at the same point in time of a singlet in the other ring. The singlets of the two rings are said to be in
exact alignment if B = (180 – A) and the rotation of the two rings is then in phase. A deviation from exact alignment
where B is not equal to (180 – A) would result in a phase shift of the rotational motion of one ring with respect to
the adjacent ring.
The alignment of singlets is critical to the determination of the forces acting between two adjacent rings. This
study examines the condition where all singlets in a three-ring configuration are in exact alignment.
2) Charge of Facing Singlets
Given two adjacent rotating rings with singlets in exact alignment, the facing singlets of the rings are the two
singlets, one in each ring, that at the same point in time cross a line between the centers of the rings where the
distance between the rings is equal to the gap.
Two facing singlets can either have the same charge or opposite charges. For an equilateral triangular
configuration with singlets in exact alignment there can be four cases:
1) All facing singlets have the same charge
2) All facing singlets have opposite charges
3) One pair of facing singlets has the same charge
4) Two pairs of facing singlets have the same charge
This study examines the case where all facing singlets have the same charge (see condition 4 below).
3) Direction of Ring Spin
Ring spin can either be right-handed or left-handed. In a triangular configuration there can only be two cases:
1) All rings have the same spin
2) One of the rings has an opposite spin to the spin of the other rings
This study examines the case where all rings have the same spin.
4) Number of Doublets
The maximum number of doublets in a proton is 508 and the rings configuration is [169, 170, 169] doublets. To
determine the number of doublets in the rings model of the proton, however, it is necessary to consider the
conditions in the definition of the model, specifically the condition of rings with equal number of doublets with
singlets in exact alignment.
In a triangular equilateral configuration, the two singlets of a ring that are facing the singlets of the other two
adjacent rings are separated by an angular distance of 60 degrees, and the condition that all facing singlets are in
exact alignment and of the same charge can only be achieved in rings where the number of doublets is a multiple
of 6. For the proton particle, that number is 168. The condition that all facing singlets are in exact alignment and of
opposite charges can only be achieved in rings where the number of doublets is a multiple of 6 plus 3. For the
proton particle, that number is 171.
Noting that the relativistic mass of a doublet is 1.8451 MeV and that of a spare singlet is 0.511 MeV, the mass of the
proton using the condition of facing singlets of same charge is:
[168, 168+Z, 168] ---> 930.44 [MeV]
The mass of the proton using the condition of facing singlets of opposite charges is:
[171, 171+Z, 171] ---> 947.05 [MeV]
Since the later mass is greater than the rest mass of the proton of 938.2723 MeV, there is then only one possible
condition: all facing are singlets of same charge, and the rings configuration is [168, 168+Z, 168].
The complete definition of the rings model of the proton used in this study is:
The rings model of the proton is that of a three-ring configuration in an equilateral triangular
configuration with rings of 168 doublets lying in the same plane. The direction of the spin is the
same for all rings. The rings are separated by gaps equal to twice the separation distance between
singlets. All singlets are in exact alignment and the singlets facing each other across the gap are of
the same charge. The positive spare singlet is located at the center of the triangle which is also the
center of the particle.
According to the definition, the model of the proton has the following characteristics:
Number of doublets 504
Number of rings 3
Doublets per ring 168
Doublets relativistic mass 1.8451 [MeV]
Rings relativistic mass 309.97 [MeV]
Total relativistic mass 930.44 [MeV]
Proton rest mass 938.27 [MeV]
Rings rotational velocity 2.496E10 [cm/sec]
Singlets separation distance 1.56E-13 [cm]
Singlets angular separation 0.0187 [rad]
Rings radius 8.35E-12 [cm]
Particle radius 1.82E-11 [cm]
Singlets transit time 6.26E-24 [sec]
Singlets orbital time 2.10E-21 [sec]
The singlets transit time is equal to singlets angular separation times ring radius divided by ring velocity. The
singlets orbital time is the time that a singlet takes to complete one revolution.
The definition of a triangular configuration with rings lying in the same plane implies a two-dimensional
configuration that imposes a restriction on the motion of the rings: they can spin but cannot rotate about
diametrical axes. The configuration, however, is in a three-dimensional space where it can rotate as a whole in any
direction about any axis passing through its center.
From the above, a neutral Baryon particle can be thought as a two-dimensional triangular configuration of three
spinning rings held together by electrostatic forces. The two-dimensional configuration can rotate in a three-
dimensional space in any direction about any axis passing through its center. The rings have an equal number of
right-handed and left-handed single and double time helixes, each time helix being described by a quantum of
energy moving at the speed of light in a one-dimensional curled space. Depending on the charge of the particle,
charged Baryons have one (or at most two) right-handed or left-handed single and double time helixes located at
the center of the triangular configuration.
A2: Electrostatic Charge Interactions between Rings
If rings are not considered entities of zero charge and have an electrostatic influence outside their perimeter then,
given two adjacent rings, each singlet in one of the rings is subjected to electrostatic forces from all of the singlets
in the other ring. The overall force F affecting the rings is computed by summation of the X and Y components of
each force and then taking the square root of the sum of the squares of the components. The direction alfa of the
overall force F is given by the arctangent of the Y component of the force divided by the X component.
F = sqr (Fxtot ^ 2 + Fytot ^ 2)
alfa = atn (Fytot / Fxtot)
If rings are not considered entities of zero charge and have an electrostatic influence outside their perimeter then,
given two adjacent rings, each singlet in one of the rings is subjected to electrostatic forces from all of the singlets
in the other ring. The overall force F affecting the rings is computed by summation of the X and Y components of
each force and then taking the square root of the sum of the squares of the components. The direction alfa of the
overall force F is given by the arctangent of the Y component of the force divided by the X component.
F = sqr (Fxtot ^ 2 + Fytot ^ 2)
alfa = atn (Fytot / Fxtot)
The overall force F and its direction vary depending on
the angular position of the singlets in one ring in
relation to the angular position of the singlets in the
other ring. For rings in an equilateral triangular
configuration there are two overall forces acting on
the center of each ring due to the presence of the
other two rings. If the three rings have equal number
of doublets and are rotating in the same direction then
these two forces are equal and their resultant is given
by:
Fr = 2 F cos (alfa + pi / 6)
Due to the geometry of the configuration, the three
resultant forces Fr are equal and their directions are
either towards the center of the triangle or away from it
(Figure 2).
Since the overall forces F and their directions vary
with the rotation of the rings, the resultant forces and
their directions (towards the center or away from it)
also vary.
the angular position of the singlets in one ring in
relation to the angular position of the singlets in the
other ring. For rings in an equilateral triangular
configuration there are two overall forces acting on
the center of each ring due to the presence of the
other two rings. If the three rings have equal number
of doublets and are rotating in the same direction then
these two forces are equal and their resultant is given
by:
Fr = 2 F cos (alfa + pi / 6)
Due to the geometry of the configuration, the three
resultant forces Fr are equal and their directions are
either towards the center of the triangle or away from it
(Figure 2).
Since the overall forces F and their directions vary
with the rotation of the rings, the resultant forces and
their directions (towards the center or away from it)
also vary.
Figure 3 shows one cycle of the overall force F between two adjacent rings of the proton model. The force has
two minimums at one quarter and three quarters cycle. A cycle can either be defined by the singlets transit time or
by the singlets separation distance.
Figure 4 shows the direction alfa of the same overall force F going counter-clockwise from 180 degrees (rings
are moving away from each other) through 360 degrees (rings are moving towards each other) and back to 180
degrees.
The direction of the overall force F is a linear function of the time increments of a cycle and is given by:
alfa = dt (2 pi / ndt) + pi
Where: dt = time increment (0 to ndt)
ndt = number of time increments
two minimums at one quarter and three quarters cycle. A cycle can either be defined by the singlets transit time or
by the singlets separation distance.
Figure 4 shows the direction alfa of the same overall force F going counter-clockwise from 180 degrees (rings
are moving away from each other) through 360 degrees (rings are moving towards each other) and back to 180
degrees.
The direction of the overall force F is a linear function of the time increments of a cycle and is given by:
alfa = dt (2 pi / ndt) + pi
Where: dt = time increment (0 to ndt)
ndt = number of time increments
Figure 5 shows the resultant force Fr between rings of the proton model for cycle 1 (in black) and cycle 3000 (in
red). If the orientation of the rings is that of Figure 2 then when Fr is positive its direction is 30, 150, or 270
degrees depending on the ring position; when negative the direction is opposite (210, 330, or 90 degrees).
red). If the orientation of the rings is that of Figure 2 then when Fr is positive its direction is 30, 150, or 270
degrees depending on the ring position; when negative the direction is opposite (210, 330, or 90 degrees).
A3: Effect of Resultant Force on Rings Structure
In the proton model the direction of the resultant force Fr is either towards the center of the equilateral triangle
described by the centers of the three rings or away from it. If the center of the triangle, which is also the locus of
the proton spare singlet, is taken as reference then the motion of the ring is towards the center if Fr is positive and
away from it if negative, resulting in an oscillating motion of contraction and expansion of the triangular structure
as the three rings go through rotation cycles.
The distance between the spare singlet and the centers of the rings in the equilateral triangular configuration is
given by (Section A1):
d = (2 radius + gap) 2/3 sin (pi / 3) = (2 radius + gap) / sqr (3)
For a stable structure the size of the gap between rings has to be equal to or greater than the separation distance
between singlets, with a maximum size set arbitrarily as four times the singlets separation. The minimum and
maximum distances between the spare singlet and the centers of the rings would then be:
dmin = (2 radius + singlets separation) / sqr (3)
dmax = (2 radius + 4 singlets separations) / sqr (3)
For a stable configuration, the amplitude of the oscillating motion has to be such that the distance
between the spare singlet and the center of the rings remains within the minimum and maximum
limits throughout the rotation cycles of the rings so that the gap separating two adjacent rings is
within one to four times the singlets separation.
In the proton model the direction of the resultant force Fr is either towards the center of the equilateral triangle
described by the centers of the three rings or away from it. If the center of the triangle, which is also the locus of
the proton spare singlet, is taken as reference then the motion of the ring is towards the center if Fr is positive and
away from it if negative, resulting in an oscillating motion of contraction and expansion of the triangular structure
as the three rings go through rotation cycles.
The distance between the spare singlet and the centers of the rings in the equilateral triangular configuration is
given by (Section A1):
d = (2 radius + gap) 2/3 sin (pi / 3) = (2 radius + gap) / sqr (3)
For a stable structure the size of the gap between rings has to be equal to or greater than the separation distance
between singlets, with a maximum size set arbitrarily as four times the singlets separation. The minimum and
maximum distances between the spare singlet and the centers of the rings would then be:
dmin = (2 radius + singlets separation) / sqr (3)
dmax = (2 radius + 4 singlets separations) / sqr (3)
For a stable configuration, the amplitude of the oscillating motion has to be such that the distance
between the spare singlet and the center of the rings remains within the minimum and maximum
limits throughout the rotation cycles of the rings so that the gap separating two adjacent rings is
within one to four times the singlets separation.
A4: Rings Displacement Projection Methodology
The effects of forces on the rings due to electrostatic charges are derived computationally from the geometrical
distribution in time of those charges in the structure of the model. Because of the nature of the model, time has to
be in discrete increments of the singlets transit time (equal to singlets angular separation times ring radius
divided by ring velocity): the smaller the increment the more accurate the results. For the proton model of three
rings of 168 doublets, the overall force between two static rings is the result of 336 ^ 2 = 112,896 interactions of
the charges between the singlets in the two rings. For two rotating rings with a singlets transit time divided into
256 increments the total number of interactions is 28,901,376. This is for one cycle: a distance equal to the
singlets angular separation times the ring radius traveled by a singlet in the singlets transit time. For the proton
there are 336 cycles in one revolution of a ring resulting in 710,862,336 interactions. With the technology
available for this study, it takes 70 minutes to perform the computations for 10 cycles with 256 time increments.
The time required to perform the computations for just one revolution of a singlet in a ring would be 39.2 hours.
As shown later in the study, the forces acting in the model and their effects on rings displacement have been
projected to 10,000 or more cycles which would have required 48 or more days of computing unless a projection
procedure had been used to reduce drastically that time without substantially affecting the overall outcome of
the study.
The procedure is in two parts: in Part 1, the base values required by the projection are determined using a data
set of computed gaps (gap values are directly dependent on the forces acting on the model); in Part 2, a gap
projection methodology is developed using the results of Part 1.
Part 1: Determination of base values
The data set used in Part 1 contains computed resultant force Fr and gap values between rings of the proton
model for 3000 cycles of 256 time increments.
Figure 6 displays gap values from cycle 1029 to cycle 1034. At the end of cycle 1031 (256th time increment), the
gap is equal to .9734 times the value of the gap at the same time increment of cycle 1.
The effects of forces on the rings due to electrostatic charges are derived computationally from the geometrical
distribution in time of those charges in the structure of the model. Because of the nature of the model, time has to
be in discrete increments of the singlets transit time (equal to singlets angular separation times ring radius
divided by ring velocity): the smaller the increment the more accurate the results. For the proton model of three
rings of 168 doublets, the overall force between two static rings is the result of 336 ^ 2 = 112,896 interactions of
the charges between the singlets in the two rings. For two rotating rings with a singlets transit time divided into
256 increments the total number of interactions is 28,901,376. This is for one cycle: a distance equal to the
singlets angular separation times the ring radius traveled by a singlet in the singlets transit time. For the proton
there are 336 cycles in one revolution of a ring resulting in 710,862,336 interactions. With the technology
available for this study, it takes 70 minutes to perform the computations for 10 cycles with 256 time increments.
The time required to perform the computations for just one revolution of a singlet in a ring would be 39.2 hours.
As shown later in the study, the forces acting in the model and their effects on rings displacement have been
projected to 10,000 or more cycles which would have required 48 or more days of computing unless a projection
procedure had been used to reduce drastically that time without substantially affecting the overall outcome of
the study.
The procedure is in two parts: in Part 1, the base values required by the projection are determined using a data
set of computed gaps (gap values are directly dependent on the forces acting on the model); in Part 2, a gap
projection methodology is developed using the results of Part 1.
Part 1: Determination of base values
The data set used in Part 1 contains computed resultant force Fr and gap values between rings of the proton
model for 3000 cycles of 256 time increments.
Figure 6 displays gap values from cycle 1029 to cycle 1034. At the end of cycle 1031 (256th time increment), the
gap is equal to .9734 times the value of the gap at the same time increment of cycle 1.
The increasing or decreasing trend of gap values can more easily be observed by using values of one specific
time increment of a cycle. The time increment chosen is the 256th .
1) A first rate of change of gap values for the 256th time increment of a cycle n with respect to the
corresponding values of a base cycle b (taken as cycle 1) is determined:
slope256(n) = [gap256(n) – gap256(b)] / (n – b)
n > b
2) A second rate of change of the rates of change above is determined:
slope2561(n) = [slope256(n) – slope256(b + 1)] / (n – (b + 1))
n > (b + 1)
3) A third rate of change of the rates of change above is determined:
slope25611(n) = [slope2561(n) – slope2561(b + 2)] / (n – (b + 2))
n > (b + 2)
Part 2: Gap projection methodology
The methodology is based on projecting the third rate of change (slope25611) for the 3000 cycle of the data set
and using that projection in a stepwise computation of the second rate of change (slope2561), first rate of change
(slope256), and gap (gap256). The accuracy of the projected values is checked by comparing them to the
computed values in the data set.
The change between the third rate of change of a cycle n1 and the third rate of change of base cycle b is
determined:
delta25611 = slope25611(n1) – slope25611(b)
n1 is defined below as equal to 2065 for b = 1
Using a cosine function equal to:
k1 = cos [(pi / 2) (n – (b + 3)) / (n1 – (b + 3))]
n > (b + 2)
then the projected values for cycle n are:
pslope25611(n) = slope25611(n1) – (k1 delta25611)
pslope2561(n) = slope2561(b + 2) + pslope25611 (n – (b + 2))
pslope256(n) = slope256(b + 1) + pslope2561 (n – (b +1))
pgap256(n) = gap256(b) + pslope256 (n – b)
Cycle (n1 – (b + 3)) in the definition of k1 above is the cycle where the gap between two adjacent rings is equal to
the gap of cycle 1; in other words, it is the cycle where the resultant force Fr is equal to the resultant force Fr of
cycle 1.
This is shown in Figure 7 where Fr is negative and decreasing until cycle 1031 after which is negative and
increasing until at cycle 2061 is again equal to the Fr of cycle 1. For b = 1 then n1 = 2065.
time increment of a cycle. The time increment chosen is the 256th .
1) A first rate of change of gap values for the 256th time increment of a cycle n with respect to the
corresponding values of a base cycle b (taken as cycle 1) is determined:
slope256(n) = [gap256(n) – gap256(b)] / (n – b)
n > b
2) A second rate of change of the rates of change above is determined:
slope2561(n) = [slope256(n) – slope256(b + 1)] / (n – (b + 1))
n > (b + 1)
3) A third rate of change of the rates of change above is determined:
slope25611(n) = [slope2561(n) – slope2561(b + 2)] / (n – (b + 2))
n > (b + 2)
Part 2: Gap projection methodology
The methodology is based on projecting the third rate of change (slope25611) for the 3000 cycle of the data set
and using that projection in a stepwise computation of the second rate of change (slope2561), first rate of change
(slope256), and gap (gap256). The accuracy of the projected values is checked by comparing them to the
computed values in the data set.
The change between the third rate of change of a cycle n1 and the third rate of change of base cycle b is
determined:
delta25611 = slope25611(n1) – slope25611(b)
n1 is defined below as equal to 2065 for b = 1
Using a cosine function equal to:
k1 = cos [(pi / 2) (n – (b + 3)) / (n1 – (b + 3))]
n > (b + 2)
then the projected values for cycle n are:
pslope25611(n) = slope25611(n1) – (k1 delta25611)
pslope2561(n) = slope2561(b + 2) + pslope25611 (n – (b + 2))
pslope256(n) = slope256(b + 1) + pslope2561 (n – (b +1))
pgap256(n) = gap256(b) + pslope256 (n – b)
Cycle (n1 – (b + 3)) in the definition of k1 above is the cycle where the gap between two adjacent rings is equal to
the gap of cycle 1; in other words, it is the cycle where the resultant force Fr is equal to the resultant force Fr of
cycle 1.
This is shown in Figure 7 where Fr is negative and decreasing until cycle 1031 after which is negative and
increasing until at cycle 2061 is again equal to the Fr of cycle 1. For b = 1 then n1 = 2065.
Figure 8 displays the three rates of change of the computed gaps in the data set as well as the three rates of
change of the projected gaps: slope256 and pslope256 are in black, slope2561 and pslope2561 are in red, and
slope25611 and pslope25611 are in blue. Computed and projected values for each of the three rates of change
are shown as one curve since the values are almost identical.
change of the projected gaps: slope256 and pslope256 are in black, slope2561 and pslope2561 are in red, and
slope25611 and pslope25611 are in blue. Computed and projected values for each of the three rates of change
are shown as one curve since the values are almost identical.
Figure 9 displays the computed values of the gap at the 256th time increment of the cycles in the data set (in
black) and the projected values of the same gaps (in red) using the projection methodology. Both curves appear
as one in red since all values are almost identical (see Appendix Table 1).
black) and the projected values of the same gaps (in red) using the projection methodology. Both curves appear
as one in red since all values are almost identical (see Appendix Table 1).
The gap (for the 256th time increment) decreases from cycle 1 to cycle 1031 where it reaches its minimum value
of 0.9734 gap0. Gap0 is the initial value of the gap equal to twice the singlets separation distance. Beyond that
cycle the gap increases until at cycle 2061 is again equal to gap0. The gap then keeps on increasing until its
values of cycle 3000 are:
computed gap: 3.305808E-13 [cm]
projected gap: 3.306562E-13 [cm]
projected / computed ratio: 1.00023
of 0.9734 gap0. Gap0 is the initial value of the gap equal to twice the singlets separation distance. Beyond that
cycle the gap increases until at cycle 2061 is again equal to gap0. The gap then keeps on increasing until its
values of cycle 3000 are:
computed gap: 3.305808E-13 [cm]
projected gap: 3.306562E-13 [cm]
projected / computed ratio: 1.00023
A5: Rings Displacement Projections
In a triangular ring configuration the distance between adjacent rings, or gap, is critical for the stability of the
structure. In Section A3 the limits of that distance have been set to be within one to four times the singlets
separation. In order for the structure to be stable, the amplitude of the oscillating motion of the rings has to be
such that all three gaps remain within those limits throughout the rotation cycles of the rings.
Assuming that the trend of the projection method is valid beyond the 3000 cycles of the data set, the projected
gap will exceed its upper limit of four times the singlets separation distance at cycle 6198 as shown in Figure 10.
It takes 336 cycles to complete one revolution of a ring in 2.10E-21 seconds (Section A1); 6198 cycles would
then complete 18.4 revolutions in 3.87E-20 seconds.
In a triangular ring configuration the distance between adjacent rings, or gap, is critical for the stability of the
structure. In Section A3 the limits of that distance have been set to be within one to four times the singlets
separation. In order for the structure to be stable, the amplitude of the oscillating motion of the rings has to be
such that all three gaps remain within those limits throughout the rotation cycles of the rings.
Assuming that the trend of the projection method is valid beyond the 3000 cycles of the data set, the projected
gap will exceed its upper limit of four times the singlets separation distance at cycle 6198 as shown in Figure 10.
It takes 336 cycles to complete one revolution of a ring in 2.10E-21 seconds (Section A1); 6198 cycles would
then complete 18.4 revolutions in 3.87E-20 seconds.
A6: Effect of the Spare Singlet on Rings Structure
The proton spare singlet is subjected to electrostatic forces from all of the singlets in the three rings of the
proton model. Due to the geometry of the model, the resultant force on the spare singlet is null. However, the
opposite is not true: the spare singlet is affecting the surrounding rings although in such a small way that the
effect can be ignored.
Given the condition in the proton model of 168 doublets that the singlets facing each other across the gap are of
the same charge, then the singlet facing the spare singlet is also of the same charge as the spare singlet, and
the magnitudes of the forces are:
For cycle 1 of the data set:
Minimum resultant force Fr: -1,686,444 [g cm/sec2]
Minimum spare singlet force: 1.471E-05 [g cm/sec2]
Maximum resultant force Fr: 1,685,791 [g cm/sec2]
Maximum spare singlet force: 2.758E-05 [g cm/sec2]
For cycle 3000:
Minimum resultant force Fr: -1,137,704 [g cm/sec2]
Minimum spare singlet force: 1.153E-05 [g cm/sec2]
Maximum resultant force Fr: 1,137,811 [g cm/sec2]
Maximum spare singlet force: 2.326E-05 [g cm/sec2]
The proton spare singlet is subjected to electrostatic forces from all of the singlets in the three rings of the
proton model. Due to the geometry of the model, the resultant force on the spare singlet is null. However, the
opposite is not true: the spare singlet is affecting the surrounding rings although in such a small way that the
effect can be ignored.
Given the condition in the proton model of 168 doublets that the singlets facing each other across the gap are of
the same charge, then the singlet facing the spare singlet is also of the same charge as the spare singlet, and
the magnitudes of the forces are:
For cycle 1 of the data set:
Minimum resultant force Fr: -1,686,444 [g cm/sec2]
Minimum spare singlet force: 1.471E-05 [g cm/sec2]
Maximum resultant force Fr: 1,685,791 [g cm/sec2]
Maximum spare singlet force: 2.758E-05 [g cm/sec2]
For cycle 3000:
Minimum resultant force Fr: -1,137,704 [g cm/sec2]
Minimum spare singlet force: 1.153E-05 [g cm/sec2]
Maximum resultant force Fr: 1,137,811 [g cm/sec2]
Maximum spare singlet force: 2.326E-05 [g cm/sec2]
A7: Effect of Time Increments
Due to the nature of the model, time has to be used in discreet increments of the singlets transit time: the
smaller the increment the more accurate the results. The data set on which the projections are made contains
computed gaps between rings of the proton model for 3000 cycles of 256 time increments per cycle. A second
data set containing computed gaps for 40 cycles with 1024 time increments per cycle has been created and
used to derive a relation between the two sets.
Figure 11 shows computed gaps for cycles 1 to 40 using 1024 time increments (in red) plotted at a scale of
5E19 to 1, and for the same cycles using 256 time increments (in black) plotted at the same scale. The difference
(256gap – 1024gap) between the two gaps is plotted in blue at a scale of 3E21 to 1.
Due to the nature of the model, time has to be used in discreet increments of the singlets transit time: the
smaller the increment the more accurate the results. The data set on which the projections are made contains
computed gaps between rings of the proton model for 3000 cycles of 256 time increments per cycle. A second
data set containing computed gaps for 40 cycles with 1024 time increments per cycle has been created and
used to derive a relation between the two sets.
Figure 11 shows computed gaps for cycles 1 to 40 using 1024 time increments (in red) plotted at a scale of
5E19 to 1, and for the same cycles using 256 time increments (in black) plotted at the same scale. The difference
(256gap – 1024gap) between the two gaps is plotted in blue at a scale of 3E21 to 1.
The values of the 256 and 1024 gaps at the end of each cycle and the rates of change of the differences are
shown in Appendix Table2 for the first forty cycles. For instance:
cycle 1:
256gap: 3.121679E-13 [cm]
1024gap: 3.121677E-13 [cm]
delta gap: 2.675152E-19 [cm]
cycle 40:
256gap: 3.115838E-13 [cm]
1024gap: 3.115731E-13 [cm]
delta gap: 1.069864E-17 [cm]
The rates of change of the differences are:
cycle 1: 2.675152E-19 [cm] per cycle
cycle 40: 2.674660E-19 [cm] per cycle
For the first forty cycles the rate of change of the differences is not exactly linear and, for the purposes of this
study, can be considered equal to the rate of change at cycle 40 plus an increment for each cycle beyond the
40th equal to the difference between the rate at cycle 40 and the rate at cycle 39.
Using the above, at cycle 6198 (which is the cycle at which the projected 256gap exceeds the upper
displacement limit of four times the singlets separation distance) the values of the projected 256gap and
1024gap are:
cycle 6198:
256gap: 6.24367E-13 [cm]
1024gap: 6.22790E-13 [cm]
delta gap: 1.57630E-15 [cm]
The above shows that it would require more cycles for the 1024gap to reach the upper displacement limit since
the value of delta gap is greater than zero. This, however, does not substantially affect the outcome of the study.
shown in Appendix Table2 for the first forty cycles. For instance:
cycle 1:
256gap: 3.121679E-13 [cm]
1024gap: 3.121677E-13 [cm]
delta gap: 2.675152E-19 [cm]
cycle 40:
256gap: 3.115838E-13 [cm]
1024gap: 3.115731E-13 [cm]
delta gap: 1.069864E-17 [cm]
The rates of change of the differences are:
cycle 1: 2.675152E-19 [cm] per cycle
cycle 40: 2.674660E-19 [cm] per cycle
For the first forty cycles the rate of change of the differences is not exactly linear and, for the purposes of this
study, can be considered equal to the rate of change at cycle 40 plus an increment for each cycle beyond the
40th equal to the difference between the rate at cycle 40 and the rate at cycle 39.
Using the above, at cycle 6198 (which is the cycle at which the projected 256gap exceeds the upper
displacement limit of four times the singlets separation distance) the values of the projected 256gap and
1024gap are:
cycle 6198:
256gap: 6.24367E-13 [cm]
1024gap: 6.22790E-13 [cm]
delta gap: 1.57630E-15 [cm]
The above shows that it would require more cycles for the 1024gap to reach the upper displacement limit since
the value of delta gap is greater than zero. This, however, does not substantially affect the outcome of the study.
A8: Effect of Rings Separation Distance
The initial value of the separation distance or gap between rings has been arbitrarily chosen to be twice the
separation distance between singlets because it has been assumed that it has no meaningful importance to the
results of the study as long as it is equal to or greater than the separation distance between singlets. This is
based on the fact that the distance between two singlets of opposite charge is equal to the classical electron
radius which is dependent only on the relativistic mass of the electron (or positron). The gap between rings
cannot be smaller than the separation distance between singlets because otherwise it would violate the
principle on which that distance is based.
Referring to Figure 9, for an initial value of the gap equal to twice the singlets separation distance, the gap (at
the 256th time increment) decreases from cycle 1 to cycle 1031 where it reaches its minimum value of 0.9734
times its initial value (1.9468 times the separation distance). Beyond that cycle the gap increases until at cycle
2061 is again equal to the initial value. After that point the gap increases indefinitely.
If the initial value of the gap is decreased, the minimum value of the gap also decreases as well as the number
of cycles that are required to reach it. There would then be a point where the minimum gap is equal to the
singlets separation distance. Beyond that point there is no further reduction to the value of the gap.
This is a point of discontinuity where the motion of the rings suddenly comes to a stop.
Figure 12 shows 45 cycles of gap data for two adjacent rings of the proton model separated by a gap equal to
1.05 times the singlets separation distance. The gap decreases from cycle 1 to cycle 35 (specifically the 237th
time increment of the 35th cycle) where it reaches its minimum value of 1.0034 times the singlets separation
distance. Beyond that cycle the gap increases indefinitely.
The initial value of the separation distance or gap between rings has been arbitrarily chosen to be twice the
separation distance between singlets because it has been assumed that it has no meaningful importance to the
results of the study as long as it is equal to or greater than the separation distance between singlets. This is
based on the fact that the distance between two singlets of opposite charge is equal to the classical electron
radius which is dependent only on the relativistic mass of the electron (or positron). The gap between rings
cannot be smaller than the separation distance between singlets because otherwise it would violate the
principle on which that distance is based.
Referring to Figure 9, for an initial value of the gap equal to twice the singlets separation distance, the gap (at
the 256th time increment) decreases from cycle 1 to cycle 1031 where it reaches its minimum value of 0.9734
times its initial value (1.9468 times the separation distance). Beyond that cycle the gap increases until at cycle
2061 is again equal to the initial value. After that point the gap increases indefinitely.
If the initial value of the gap is decreased, the minimum value of the gap also decreases as well as the number
of cycles that are required to reach it. There would then be a point where the minimum gap is equal to the
singlets separation distance. Beyond that point there is no further reduction to the value of the gap.
This is a point of discontinuity where the motion of the rings suddenly comes to a stop.
Figure 12 shows 45 cycles of gap data for two adjacent rings of the proton model separated by a gap equal to
1.05 times the singlets separation distance. The gap decreases from cycle 1 to cycle 35 (specifically the 237th
time increment of the 35th cycle) where it reaches its minimum value of 1.0034 times the singlets separation
distance. Beyond that cycle the gap increases indefinitely.
There is a region where the initial gap is between 1.05 times the singlets separation distance and the singlets
separation distance when the rings of the proton model collapse unto the center of the rings configuration until
the singlets separation distance is reached. The Table below shows the cycle and time increment at which two
rings with a given initial gap reach the singlets separation distance:
Initial Gap Cycle Time Increment
1.02 * sep 9 164
1.01 * sep 4 199
1.005 * sep 2 207
1.00001 * sep 1 144
(1 + 1E-15) * sep 1 143
1 * sep 1 0 and 143
Figure 13 shows gap data (in black) and resultant force data (in red) for the first cycle of 256 time increments for
two adjacent rings of the proton model with an initial gap equal to the singlets separation distance. After an initial
period of separation, the rings start to collapse towards each other until at the 143rd time increment they reach
again the singlets separation distance. They remain at that distance as long as the resultant force between the
two rings is positive (attractive). When the resultant force becomes negative at the 173rd time increment they start
breaking away from each other and continue with that motion indefinitely. The break away starts 4.22E-24
seconds after the time of formation.
separation distance when the rings of the proton model collapse unto the center of the rings configuration until
the singlets separation distance is reached. The Table below shows the cycle and time increment at which two
rings with a given initial gap reach the singlets separation distance:
Initial Gap Cycle Time Increment
1.02 * sep 9 164
1.01 * sep 4 199
1.005 * sep 2 207
1.00001 * sep 1 144
(1 + 1E-15) * sep 1 143
1 * sep 1 0 and 143
Figure 13 shows gap data (in black) and resultant force data (in red) for the first cycle of 256 time increments for
two adjacent rings of the proton model with an initial gap equal to the singlets separation distance. After an initial
period of separation, the rings start to collapse towards each other until at the 143rd time increment they reach
again the singlets separation distance. They remain at that distance as long as the resultant force between the
two rings is positive (attractive). When the resultant force becomes negative at the 173rd time increment they start
breaking away from each other and continue with that motion indefinitely. The break away starts 4.22E-24
seconds after the time of formation.
Part B: The Layered Rings Configuration of Baryons
B1: The Proton Model
The three-ring layered configuration of a Baryon particle has the centers of the rings lying on a line of length
equal to twice the gap between the rings. The spare singlet of a charged Baryon is located at the center of the
middle ring which is also the center of the particle (Figure B1).
B1: The Proton Model
The three-ring layered configuration of a Baryon particle has the centers of the rings lying on a line of length
equal to twice the gap between the rings. The spare singlet of a charged Baryon is located at the center of the
middle ring which is also the center of the particle (Figure B1).
Since doublets in a ring are entities of zero
charge, there is no electrodynamic effect
due to the spin of the ring. Therefore this study
only considers the electrostatic effect of charge
interaction within rings and among rings.
To that purpose, it is necessary to define the size
of the gap between rings which is of critical
importance in determining the strength of the
forces acting between rings and the effect of
those forces on the motion of the rings. The
minimum gap between rings cannot be smaller
than the separation distance between singlets
because otherwise it would violate the principle
on which that distance is based.
It is also necessary to formulate the following
conditions:
charge, there is no electrodynamic effect
due to the spin of the ring. Therefore this study
only considers the electrostatic effect of charge
interaction within rings and among rings.
To that purpose, it is necessary to define the size
of the gap between rings which is of critical
importance in determining the strength of the
forces acting between rings and the effect of
those forces on the motion of the rings. The
minimum gap between rings cannot be smaller
than the separation distance between singlets
because otherwise it would violate the principle
on which that distance is based.
It is also necessary to formulate the following
conditions:
1) Equal Number of Doublets
The layered configuration is based on rings with equal number of doublets. Rings with equal number of doublets
have the same spin velocity.
2) Alignment of Singlets
In a layered configuration, the alignment of the singlets of two rotating rings of equal number of doublets is given
by the angular position A at a point in time of a singlet in one of the rings and the angular position B at the same
point in time of a singlet in the other ring. The singlets of the two rings are said to be in exact alignment if A = B.
The rotation of the two rings is uniform if the direction of rotation is the same for the two rings, and it is in phase if
the direction of rotation is not the same. A deviation from exact alignment where A is not equal B would result in a
shift of position of the singlets of one ring with respect to the singlets of the other ring. The alignment of singlets
is critical to the determination of the forces acting between two facing rings.
3) Charge of Facing Singlets
Given two rotating rings in a layered configuration with singlets in exact alignment, the facing singlets of the rings
can either have the same charge or opposite charges.
4) Direction of Ring Spin
Ring spin can either be right-handed or left-handed. In a three-ring layered configuration there can only be two
cases:
1) All rings have the same spin
2) One of the rings has an opposite spin to the spin of the other rings
For rings with equal number of doublets and same spin velocity, if the direction of the spin is the same for all
rings then their motion has no effect on the forces acting between them.
5) Number of Doublets
The maximum number of doublets in a proton is 508 and the rings configuration is [169, 170, 169] doublets.
Noting that the relativistic mass of a doublet is 1.8451 MeV and that of a spare singlet is 0.511 MeV, the mass of
the proton model using the condition of equal number of doublets is:
[169, 169+Z, 169] ---> 935.98 [MeV]
The definition of the layered rings model of the proton used in this study is:
The rings model of the proton is that of a layered three-ring configuration with rings of 169
doublets. The centers of the rings are lying on a line of length equal to twice the gap between
rings which is equal to the separation distance between singlets. The direction of the spin is the
same for all rings. The positive spare singlet is located at the center of the middle ring.
According to the definition, the model of the proton has the following characteristics:
Number of doublets 507
Number of rings 3
Doublets per ring 169
Doublets relativistic mass 1.8451 [MeV]
Rings relativistic mass 311.82 [MeV]
Total relativistic mass 935.98 [MeV]
Proton rest mass 938.27 [MeV]
Rings rotational velocity 2.496E10 [cm/sec]
Singlets separation distance 1.56E-13 [cm]
Singlets angular separation 0.01859 [rad]
Rings radius 8.40E-12 [cm]
Particle radius 8.40E-12 [cm]
Singlets transit time 6.26E-24 [sec]
Singlets orbital time 2.11E-21 [sec]
The singlets transit time is equal to singlets angular separation times ring radius divided by ring velocity. The
singlets orbital time is the time that a singlet takes to complete one revolution.
The definition of a layered configuration imposes a restriction on the motion of the rings: they can spin but
cannot rotate about diametrical axes. The configuration, however, can rotate as a whole in any direction about
any axis passing through its center.
A neutral Baryon particle can be thought as a three-dimensional layered configuration of three two-dimensional
spinning rings held together by electrostatic forces. The rings have an equal number of right-handed and
left-handed single and double time helixes, each time helix being described by a quantum of energy moving at the
speed of light in a one-dimensional curled space. Charged Baryons also have a right-handed or left-handed
single and double time helixes located at the center of the middle ring.
The layered configuration is based on rings with equal number of doublets. Rings with equal number of doublets
have the same spin velocity.
2) Alignment of Singlets
In a layered configuration, the alignment of the singlets of two rotating rings of equal number of doublets is given
by the angular position A at a point in time of a singlet in one of the rings and the angular position B at the same
point in time of a singlet in the other ring. The singlets of the two rings are said to be in exact alignment if A = B.
The rotation of the two rings is uniform if the direction of rotation is the same for the two rings, and it is in phase if
the direction of rotation is not the same. A deviation from exact alignment where A is not equal B would result in a
shift of position of the singlets of one ring with respect to the singlets of the other ring. The alignment of singlets
is critical to the determination of the forces acting between two facing rings.
3) Charge of Facing Singlets
Given two rotating rings in a layered configuration with singlets in exact alignment, the facing singlets of the rings
can either have the same charge or opposite charges.
4) Direction of Ring Spin
Ring spin can either be right-handed or left-handed. In a three-ring layered configuration there can only be two
cases:
1) All rings have the same spin
2) One of the rings has an opposite spin to the spin of the other rings
For rings with equal number of doublets and same spin velocity, if the direction of the spin is the same for all
rings then their motion has no effect on the forces acting between them.
5) Number of Doublets
The maximum number of doublets in a proton is 508 and the rings configuration is [169, 170, 169] doublets.
Noting that the relativistic mass of a doublet is 1.8451 MeV and that of a spare singlet is 0.511 MeV, the mass of
the proton model using the condition of equal number of doublets is:
[169, 169+Z, 169] ---> 935.98 [MeV]
The definition of the layered rings model of the proton used in this study is:
The rings model of the proton is that of a layered three-ring configuration with rings of 169
doublets. The centers of the rings are lying on a line of length equal to twice the gap between
rings which is equal to the separation distance between singlets. The direction of the spin is the
same for all rings. The positive spare singlet is located at the center of the middle ring.
According to the definition, the model of the proton has the following characteristics:
Number of doublets 507
Number of rings 3
Doublets per ring 169
Doublets relativistic mass 1.8451 [MeV]
Rings relativistic mass 311.82 [MeV]
Total relativistic mass 935.98 [MeV]
Proton rest mass 938.27 [MeV]
Rings rotational velocity 2.496E10 [cm/sec]
Singlets separation distance 1.56E-13 [cm]
Singlets angular separation 0.01859 [rad]
Rings radius 8.40E-12 [cm]
Particle radius 8.40E-12 [cm]
Singlets transit time 6.26E-24 [sec]
Singlets orbital time 2.11E-21 [sec]
The singlets transit time is equal to singlets angular separation times ring radius divided by ring velocity. The
singlets orbital time is the time that a singlet takes to complete one revolution.
The definition of a layered configuration imposes a restriction on the motion of the rings: they can spin but
cannot rotate about diametrical axes. The configuration, however, can rotate as a whole in any direction about
any axis passing through its center.
A neutral Baryon particle can be thought as a three-dimensional layered configuration of three two-dimensional
spinning rings held together by electrostatic forces. The rings have an equal number of right-handed and
left-handed single and double time helixes, each time helix being described by a quantum of energy moving at the
speed of light in a one-dimensional curled space. Charged Baryons also have a right-handed or left-handed
single and double time helixes located at the center of the middle ring.
B2: Doublets Identity in a Layered Configuration
The Rings Model defines doublets as pairs of opposite singlets separated by a distance equal to the classical
electron radius, and rings as doublets strung together, positive end to negative end. If a ring is represented as:
… 1 2 3 4 5 6 …
where the odd numbers indicate negatively charged singlets and even numbers indicate positively charged
singlets, then doublets can be identified either as:
[1, 2] [3, 4] [5, 6]
or
[2, 3] [4, 5] [6, 1]
Both identifications are valid and exist at the same time. This is the doublets identification uncertainty in the
triangular configuration discussed in Part A where rings are independent from each other, the nearest contact
being at the gap. The identification uncertainty is increased in a layered configuration with rings of equal number
of doublets and same spin direction, with facing singlets of opposite charges, and with gaps between rings equal
to the singlets separation distance. This is shown in Figures B2a and B2b where all possible identifications are
displayed using connecting lines between singlets shown as red or blue dots.
All of the identifications are present at any point in time if the singlets in the layered configuration are in exact
alignment. If singlets are not in exact alignment due to a phase shift between the singlets of a ring and the
singlets of a facing ring then the identification uncertainty is suddenly reduced to that shown in Figure B3. This
is because the distance between facing singlets is increased by the shift and is no longer equal to the classical
electron radius. A shift, no matter how small, reduces the uncertainty from a property of the whole configuration
to that of the individual ring.
The identification uncertainty is also reduced to that of an individual ring if the facing singlets are of the same
charge.
The Rings Model defines doublets as pairs of opposite singlets separated by a distance equal to the classical
electron radius, and rings as doublets strung together, positive end to negative end. If a ring is represented as:
… 1 2 3 4 5 6 …
where the odd numbers indicate negatively charged singlets and even numbers indicate positively charged
singlets, then doublets can be identified either as:
[1, 2] [3, 4] [5, 6]
or
[2, 3] [4, 5] [6, 1]
Both identifications are valid and exist at the same time. This is the doublets identification uncertainty in the
triangular configuration discussed in Part A where rings are independent from each other, the nearest contact
being at the gap. The identification uncertainty is increased in a layered configuration with rings of equal number
of doublets and same spin direction, with facing singlets of opposite charges, and with gaps between rings equal
to the singlets separation distance. This is shown in Figures B2a and B2b where all possible identifications are
displayed using connecting lines between singlets shown as red or blue dots.
All of the identifications are present at any point in time if the singlets in the layered configuration are in exact
alignment. If singlets are not in exact alignment due to a phase shift between the singlets of a ring and the
singlets of a facing ring then the identification uncertainty is suddenly reduced to that shown in Figure B3. This
is because the distance between facing singlets is increased by the shift and is no longer equal to the classical
electron radius. A shift, no matter how small, reduces the uncertainty from a property of the whole configuration
to that of the individual ring.
The identification uncertainty is also reduced to that of an individual ring if the facing singlets are of the same
charge.
B3: Electrostatic Charge Interactions between Rings
If rings are not considered entities of zero charge and have an electrostatic influence outside their perimeter then,
given two rings A and B in a layered configuration, each singlet in one of the rings is subjected to electrostatic
forces from all of the singlets in the other ring. Using the coordinate system of Figure B1, the overall force F
affecting a target singlet in ring A is computed by summation of the X, Y, and Z components of the force from each
singlet in ring B and then taking the square root of the sum of the squares of the components.
The direction of the overall force F on the target singlet in ring A is given by two angles: alfa, which is the angle
subtended by the projection of F on the XY plane and the X or Y axis; and beta, which is the angle subtended by
the projection of F on the XY plane and the overall force F.
F = sqr (Fxtot ^ 2 + Fytot ^ 2 + Fztot ^2)
alfa = atn (Fytot / Fxtot)
pF = Fytot / sin (alfa) = Fxtot / cos (alfa)
beta = atn (Fztot / pF)
There are two cases to be considered depending on the alignment of singlets of rings with equal number of
doublets and same spin direction.
Case 1) Rings with facing singlets in exact alignment
If the two rings A and B have an equal number of doublets, have the same spin direction, and the facing singlets
are in exact alignment, then the overall forces acting on positive target singlets of ring A are equal in magnitude
and direction to the overall forces acting on negative target singlets.
If ring B has a spare singlet located at its center, then the magnitudes and directions of the overall forces acting
on positive and negative target singlets of ring A are not equal.
Appendix Table 3 displays the forces acting on a positive target singlet in ring A from the first ten and the last
ten singlets in ring B with spare singlet of a proton model with facing singlets of opposite charges in exact
alignment. The coordinate system is that of Figure B1 where the view is from the front of the layered
configuration: X is the width, Y the depth, and Z the height of the configuration. X, Y, and Z are positive in the right,
away, and upwards directions.
The resultant force acting on ring A due to the presence of ring B is:
Resultant force: 1,368,184,378 [g cm/sec2]
X component: Null
Y component: 9,200,979 [g cm/sec2]
Z component: -1,368,153,439 [g cm/sec2]
alfa direction: 90 [degrees]
beta direction: 270.39 [degrees]
The very strong Z component of the resultant force tends to move ring A towards ring B. There is a slight shift
away from B due to the Y component, and no lateral shift due to the null X component. The same result is
obtained when the spare singlet is not present. The two rings are strongly attracted to each other and are held
together at a distance equal to the singlets separation which cannot be reduced.
Case 2) Rings with facing singlets not in exact alignment
A deviation from exact alignment of facing singlets in rings with the same number of doublets and same spin
direction would result in a shift of position of the singlets in one ring with respect to the position of the singlets in
the facing ring. The direction of the shift is assumed to be towards the right or counterclockwise with respect to
the facing ring and is expressed as a ratio of the singlets angular separation. If at exact alignment (shift = 0)
the facing singlets are of opposite charges, then at shift equal to the singlets angular separation
(shift = 1) the facing singlets are of the same charge. At half way, a singlet in one of the rings is at an
equal distance from the two nearest singlets in the other ring. At that point the singlet is of opposite charge to one
of the nearest singlets in the other ring and of same charge as the other nearest singlet in the other ring.
Figure B4 shows the components of the overall force (at a scale of 1 to 1,000) acting on a positive target singlet
of ring A due to the presence of ring B of equal number of doublets and facing singlets of opposite charges when
its singlets are shifted from exact alignment (shift = 0) to the singlets angular separation (shift = 1). The same data
is also shown in Appendix Table 4 for every 20 increments of the singlets angular separation.
If rings are not considered entities of zero charge and have an electrostatic influence outside their perimeter then,
given two rings A and B in a layered configuration, each singlet in one of the rings is subjected to electrostatic
forces from all of the singlets in the other ring. Using the coordinate system of Figure B1, the overall force F
affecting a target singlet in ring A is computed by summation of the X, Y, and Z components of the force from each
singlet in ring B and then taking the square root of the sum of the squares of the components.
The direction of the overall force F on the target singlet in ring A is given by two angles: alfa, which is the angle
subtended by the projection of F on the XY plane and the X or Y axis; and beta, which is the angle subtended by
the projection of F on the XY plane and the overall force F.
F = sqr (Fxtot ^ 2 + Fytot ^ 2 + Fztot ^2)
alfa = atn (Fytot / Fxtot)
pF = Fytot / sin (alfa) = Fxtot / cos (alfa)
beta = atn (Fztot / pF)
There are two cases to be considered depending on the alignment of singlets of rings with equal number of
doublets and same spin direction.
Case 1) Rings with facing singlets in exact alignment
If the two rings A and B have an equal number of doublets, have the same spin direction, and the facing singlets
are in exact alignment, then the overall forces acting on positive target singlets of ring A are equal in magnitude
and direction to the overall forces acting on negative target singlets.
If ring B has a spare singlet located at its center, then the magnitudes and directions of the overall forces acting
on positive and negative target singlets of ring A are not equal.
Appendix Table 3 displays the forces acting on a positive target singlet in ring A from the first ten and the last
ten singlets in ring B with spare singlet of a proton model with facing singlets of opposite charges in exact
alignment. The coordinate system is that of Figure B1 where the view is from the front of the layered
configuration: X is the width, Y the depth, and Z the height of the configuration. X, Y, and Z are positive in the right,
away, and upwards directions.
The resultant force acting on ring A due to the presence of ring B is:
Resultant force: 1,368,184,378 [g cm/sec2]
X component: Null
Y component: 9,200,979 [g cm/sec2]
Z component: -1,368,153,439 [g cm/sec2]
alfa direction: 90 [degrees]
beta direction: 270.39 [degrees]
The very strong Z component of the resultant force tends to move ring A towards ring B. There is a slight shift
away from B due to the Y component, and no lateral shift due to the null X component. The same result is
obtained when the spare singlet is not present. The two rings are strongly attracted to each other and are held
together at a distance equal to the singlets separation which cannot be reduced.
Case 2) Rings with facing singlets not in exact alignment
A deviation from exact alignment of facing singlets in rings with the same number of doublets and same spin
direction would result in a shift of position of the singlets in one ring with respect to the position of the singlets in
the facing ring. The direction of the shift is assumed to be towards the right or counterclockwise with respect to
the facing ring and is expressed as a ratio of the singlets angular separation. If at exact alignment (shift = 0)
the facing singlets are of opposite charges, then at shift equal to the singlets angular separation
(shift = 1) the facing singlets are of the same charge. At half way, a singlet in one of the rings is at an
equal distance from the two nearest singlets in the other ring. At that point the singlet is of opposite charge to one
of the nearest singlets in the other ring and of same charge as the other nearest singlet in the other ring.
Figure B4 shows the components of the overall force (at a scale of 1 to 1,000) acting on a positive target singlet
of ring A due to the presence of ring B of equal number of doublets and facing singlets of opposite charges when
its singlets are shifted from exact alignment (shift = 0) to the singlets angular separation (shift = 1). The same data
is also shown in Appendix Table 4 for every 20 increments of the singlets angular separation.
At shift equal to zero the Z component is at its negative maximum and the X component is null. At shift equal to
half the angular separation the Z component is null and the X component is at its negative maximum. At shift
equal to the angular separation the Z component is at its positive maximum and the X component is null.
Because of its small magnitude, the Y component can be ignored.
The direction of the resultant of the X and Z components is 270 degrees (down) at shift equal zero; 180 degrees
(left) at shift equal half the angular separation; and 90 degrees (up) at shift equal to the angular separation
(Figure B5 and Appendix Table 5). If the Y component is not ignored then the alfa and beta directions of the
resultant of the X, Y and Z components are shown in Appendix Table 4.
half the angular separation the Z component is null and the X component is at its negative maximum. At shift
equal to the angular separation the Z component is at its positive maximum and the X component is null.
Because of its small magnitude, the Y component can be ignored.
The direction of the resultant of the X and Z components is 270 degrees (down) at shift equal zero; 180 degrees
(left) at shift equal half the angular separation; and 90 degrees (up) at shift equal to the angular separation
(Figure B5 and Appendix Table 5). If the Y component is not ignored then the alfa and beta directions of the
resultant of the X, Y and Z components are shown in Appendix Table 4.
If singlets in one of the rings are shifted by an amount which is less than or equal to half the singlets angular
separation then the negative X component generated by the shift will force the ring to realign towards exact
alignment. The negative Z component provides an increasingly stronger force that keeps the rings together
during realignment but has no effect on the separation distance between the rings since that distance cannot be
violated. If the singlets are shifted by an amount which is greater then half the singlets angular separation then
the direction of the resultant of the X and Z components is less than 180 degrees and greater than or equal to 90
degrees. Although the X component is still negative and forces the ring to realign towards exact alignment, the Z
component is now positive and forces the rings to move away from each other in the direction of the resultant
force.
The above is true whether the shift is positive or negative, that is, to the right of exact alignment with respect to
the facing ring (as above) or to the left of it (Appendix Table 6).
Figure B6 is a plot of the X and Z components of the overall force from a shift equal to minus the singlets
angular separation (shift = -1) to a shift equal to the singlets angular separation (shift = 1) showing the sinusoidal
trend of the X component (in black) and the complementary trend of the Z component (in red).
separation then the negative X component generated by the shift will force the ring to realign towards exact
alignment. The negative Z component provides an increasingly stronger force that keeps the rings together
during realignment but has no effect on the separation distance between the rings since that distance cannot be
violated. If the singlets are shifted by an amount which is greater then half the singlets angular separation then
the direction of the resultant of the X and Z components is less than 180 degrees and greater than or equal to 90
degrees. Although the X component is still negative and forces the ring to realign towards exact alignment, the Z
component is now positive and forces the rings to move away from each other in the direction of the resultant
force.
The above is true whether the shift is positive or negative, that is, to the right of exact alignment with respect to
the facing ring (as above) or to the left of it (Appendix Table 6).
Figure B6 is a plot of the X and Z components of the overall force from a shift equal to minus the singlets
angular separation (shift = -1) to a shift equal to the singlets angular separation (shift = 1) showing the sinusoidal
trend of the X component (in black) and the complementary trend of the Z component (in red).
B4: The Strong Attractor in a Layered Configuration
To determine the forces acting between two rings the motion of the rings due to those forces and the time
during which that motion occurs must be taken into account. Due to the nature of the model, the time has to be
in discreet increments, the smaller the increment the more precise the result. The increment used is 1/20000 of
the proton model singlet transit time of 6.26E-24 seconds (Section B1).
The results are shown in Figure B7 which displays the ratio gap/sep versus shift from exact alignment of
facing singlets of two rings separated by an initial gap equal to the singlets separation distance (sep). The
curves are for initial shifts from 0 to 2 in steps of 0.2. At shifts equal to 0 and 2 the alignment is exact and the
facing singlets are of opposite charges. At shift equal to 1 the alignment is again exact but the facing singlets are
of the same charge.
To determine the forces acting between two rings the motion of the rings due to those forces and the time
during which that motion occurs must be taken into account. Due to the nature of the model, the time has to be
in discreet increments, the smaller the increment the more precise the result. The increment used is 1/20000 of
the proton model singlet transit time of 6.26E-24 seconds (Section B1).
The results are shown in Figure B7 which displays the ratio gap/sep versus shift from exact alignment of
facing singlets of two rings separated by an initial gap equal to the singlets separation distance (sep). The
curves are for initial shifts from 0 to 2 in steps of 0.2. At shifts equal to 0 and 2 the alignment is exact and the
facing singlets are of opposite charges. At shift equal to 1 the alignment is again exact but the facing singlets are
of the same charge.
The motion of a ring A with respect to a ring B is either clockwise or counterclockwise (to the left or to the right
of ring B), and either away from B or towards B as follows:
Initial shift Motion
0 to 0.5 Ring A moves to the left towards exact alignment of opposite charges at shift 0.
0.5 to 1 Ring A moves away from B but then moves towards B and to the left towards exact alignment of
opposite charges at shift 0.
1 to 1.5 Ring A moves away from B but then moves towards B and to the right towards exact alignment
of opposite charges at shift 2.
1.5 to 2 Ring A moves to the right towards exact alignment of opposite charges at shift 2.
The maximum gap between the two rings during the motion is equal to about ten times the singlets separation
distance.
There are two regions of motion:
1) From shift 0 to shift 1 the motion is clockwise (to the left) towards the exact alignment of opposite charges
at shift 0.
2) From shift 1 to shift 2 the motion is counterclockwise (to the right) towards the exact alignment of
opposite charges at shift 2.
At shift equal to 1 there is an equal probability for ring A to move either clockwise (to the left) towards shift 0 or
counterclockwise (to the right) towards shift 2.
In any case, regardless of the value of the initial shift, the rings would move so that the final result is the strong
attraction between the two rings when the facing singlets are in exact alignment of opposite charges across a
gap between the rings that is equal to the singlets separation distance.
The exact alignment of singlets of opposite charges in two rings with equal number of doublets
and same spin direction in a layered configuration with rings separated by a gap equal to the
singlets separation distance is the strong attractor that is required for the stability of the
configuration.
of ring B), and either away from B or towards B as follows:
Initial shift Motion
0 to 0.5 Ring A moves to the left towards exact alignment of opposite charges at shift 0.
0.5 to 1 Ring A moves away from B but then moves towards B and to the left towards exact alignment of
opposite charges at shift 0.
1 to 1.5 Ring A moves away from B but then moves towards B and to the right towards exact alignment
of opposite charges at shift 2.
1.5 to 2 Ring A moves to the right towards exact alignment of opposite charges at shift 2.
The maximum gap between the two rings during the motion is equal to about ten times the singlets separation
distance.
There are two regions of motion:
1) From shift 0 to shift 1 the motion is clockwise (to the left) towards the exact alignment of opposite charges
at shift 0.
2) From shift 1 to shift 2 the motion is counterclockwise (to the right) towards the exact alignment of
opposite charges at shift 2.
At shift equal to 1 there is an equal probability for ring A to move either clockwise (to the left) towards shift 0 or
counterclockwise (to the right) towards shift 2.
In any case, regardless of the value of the initial shift, the rings would move so that the final result is the strong
attraction between the two rings when the facing singlets are in exact alignment of opposite charges across a
gap between the rings that is equal to the singlets separation distance.
The exact alignment of singlets of opposite charges in two rings with equal number of doublets
and same spin direction in a layered configuration with rings separated by a gap equal to the
singlets separation distance is the strong attractor that is required for the stability of the
configuration.
B5: Effect of Rings Separation Distance
This section examines the effect of rings separation distance on the stability of the layered configuration. In
Section B4 it was shown that two rings of the proton model separated by a gap at the time of formation (initial
gap) equal to the singlets separation distance and with facing singlets not in exact alignment may reach a
maximum separation of ten times the initial gap during the shifting motion towards stability. It is important to
know the effect of the size of the initial gap on the stability of the layered configuration.
The results for the indicated initial shifts from exact alignment of opposite charges and initial gaps (expressed
in terms of singlets separation distances) are shown in the following tables for two rings when their motion is
computed using a time increment of 1/10000 of the singlet transit time:
Initial gap = 1
Initial shift Maximum gap
0 to 0.5 1.00
0.6 6.08
0.7 9.42
0.8 9.65
0.9 9.79
1.0 9.89
1.1 9.79
1.2 9.65
1.3 9.42
1.4 6.08
1.5 to 2 1.00
Initial shift = 0.2
Initial gap Maximum gap Time increments Ring revolutions
1 1 539 0.000160
4 4 2,397 0.000711
6 6 12,112 0.00359
8 8 60,258 0.0179
9 9 128,734 0.0382
10 10 218,429 0.0648
12 12 339,109 0.101
Initial shift = 0.4
Initial gap Maximum gap Time increments Ring revolutions
1 1 621 0.000184
4 4 3,001 0.000890
6 6 15,350 0.00455
8 8 76,397 0.0227
9 9 159,471 0.0473
10 10 252,558 0.0749
12 12 367,545 0.109
Initial shift = 0.6
Initial gap Maximum gap Time increments Ring revolutions
1 6.08 1,507 0.000447
4 9.26 154,544 0.0458
6 9.29 1,469,270 0.436
8 9.29 1,852,044 0.549
10 10 1,875,604 0.556
12 12 1,885,903 0.560
Initial shift = 0.8
Initial gap Maximum gap Time increments Ring revolutions
1 9.65 5,193 0.00154
4 9.72 706,609 0.210
6 9.73 3,177,014 0.943
8 9.73 3,448,995 1.023
10 10 3,461,617 1.027
12 12 3,466,390 1.028
Initial shift = 1.0
Initial gap Maximum gap Time increments Ring revolution
1 9.89 8,861 0.00263
4 9.92 1,261,007 0.374
6 9.92 4,222,505 1.253
8 9.92 4,461,091 1.324
10 10 4,471,039 1.326
12 12 4,474,514 1.328
The number of time increments and the rings revolutions shown are those which are required by the shifting
motion to reach exact alignment of opposite charges at shift 0. For the proton model of 169 doublets per ring, it
takes 2.11E-21 seconds to complete one revolution.
Figure B8 displays the ratio gap/sep versus shift from exact alignment for the following conditions:
Initial shift Initial gap Color
1.0 1 black
0.6 0.8 1.0 4 blue
0.6 0.8 1.0 12 red
This section examines the effect of rings separation distance on the stability of the layered configuration. In
Section B4 it was shown that two rings of the proton model separated by a gap at the time of formation (initial
gap) equal to the singlets separation distance and with facing singlets not in exact alignment may reach a
maximum separation of ten times the initial gap during the shifting motion towards stability. It is important to
know the effect of the size of the initial gap on the stability of the layered configuration.
The results for the indicated initial shifts from exact alignment of opposite charges and initial gaps (expressed
in terms of singlets separation distances) are shown in the following tables for two rings when their motion is
computed using a time increment of 1/10000 of the singlet transit time:
Initial gap = 1
Initial shift Maximum gap
0 to 0.5 1.00
0.6 6.08
0.7 9.42
0.8 9.65
0.9 9.79
1.0 9.89
1.1 9.79
1.2 9.65
1.3 9.42
1.4 6.08
1.5 to 2 1.00
Initial shift = 0.2
Initial gap Maximum gap Time increments Ring revolutions
1 1 539 0.000160
4 4 2,397 0.000711
6 6 12,112 0.00359
8 8 60,258 0.0179
9 9 128,734 0.0382
10 10 218,429 0.0648
12 12 339,109 0.101
Initial shift = 0.4
Initial gap Maximum gap Time increments Ring revolutions
1 1 621 0.000184
4 4 3,001 0.000890
6 6 15,350 0.00455
8 8 76,397 0.0227
9 9 159,471 0.0473
10 10 252,558 0.0749
12 12 367,545 0.109
Initial shift = 0.6
Initial gap Maximum gap Time increments Ring revolutions
1 6.08 1,507 0.000447
4 9.26 154,544 0.0458
6 9.29 1,469,270 0.436
8 9.29 1,852,044 0.549
10 10 1,875,604 0.556
12 12 1,885,903 0.560
Initial shift = 0.8
Initial gap Maximum gap Time increments Ring revolutions
1 9.65 5,193 0.00154
4 9.72 706,609 0.210
6 9.73 3,177,014 0.943
8 9.73 3,448,995 1.023
10 10 3,461,617 1.027
12 12 3,466,390 1.028
Initial shift = 1.0
Initial gap Maximum gap Time increments Ring revolution
1 9.89 8,861 0.00263
4 9.92 1,261,007 0.374
6 9.92 4,222,505 1.253
8 9.92 4,461,091 1.324
10 10 4,471,039 1.326
12 12 4,474,514 1.328
The number of time increments and the rings revolutions shown are those which are required by the shifting
motion to reach exact alignment of opposite charges at shift 0. For the proton model of 169 doublets per ring, it
takes 2.11E-21 seconds to complete one revolution.
Figure B8 displays the ratio gap/sep versus shift from exact alignment for the following conditions:
Initial shift Initial gap Color
1.0 1 black
0.6 0.8 1.0 4 blue
0.6 0.8 1.0 12 red
The threshold (black curve) set by the maximum gaps established by an initial shift equal to 1 and initial gap equal
to the singlets separation distance is never trespassed regardless of the values of initial shifts or initial gaps (blue
and red curves).
The threshold separates the space between facing rings into two regions:
1) If the values of the initial gap are below the threshold (blue curves) ring A moves away from ring B until the
threshold is reached and then changes its direction to the left and follows the threshold towards exact alignment
of opposite charges at shift 0.
2) If the values of the initial gap are above the threshold (red curves) ring A moves towards ring B until the
threshold is reached and then changes its direction to the left and follows the threshold towards exact alignment
of opposite charges at shift 0.
For the second region, however, as the rings separation increases the forces between the two rings decrease in
the inverse square relation and may become so weak that the time required to reach exact alignment of opposite
charges is so large that it may make it impossible for the two rings to reach stability.
Accordingly, the definition of the strong attractor required for the stability of a layered configuration given in
Section B4 is amended as follows:
The exact alignment of singlets of opposite charges in two rings with equal number of doublets
and same spin direction in a layered configuration with rings separated by a gap that is less than or
equal to a threshold value is the strong attractor that is required for the stability of the configuration.
There are two regions of stability for facing rings separated by gaps that are less than or equal to the threshold
value:
1) The alignment of facing singlets of opposite charges is within 0 and 0.5 times the singlets angular
separation. A clockwise (to the left) shifting motion is initiated and continues until exact alignment of opposite
charges is reached. The threshold distance is equal to the singlets separation and the gap between rings remains
at that distance throughout the motion.
2) The alignment of facing singlets of opposite charges is greater than 0.5 but less then or equal to 1 times the
singlets angular separation. An expanding motion is initiated and continues until the gap between rings reaches
the threshold value. After that point of maximum separation, the rings start to collapse towards each other with a
clockwise (to the left) motion until the singlets separation distance is reached and remain at that distance until
exact alignment.
The same two regions are present when the alignment of facing singlets of opposite charges is equal to 1 but less
than 2. However, the shifting motion is counterclockwise (to the right) towards exact alignment instead of
clockwise.
At exact alignment of opposite charges the attractive electrostatic force is at its maximum and the shifting force is
null, keeping the rings strongly bound together.
As indicated in Section B4, at the critical point when the alignment is equal to 1 (that is, when singlets of facing
rings are in exact alignment of same charge) the layered configuration has the same probability to move either
clockwise or counterclockwise towards the stability offered by the strong forces of the exact alignment of
opposite charges.
The probability to reach stability for rings in region 2 is less than those in region 1 due to: 1) the initial expanding
motion of the rings and consequent reduction of active forces which, at maximum threshold, are considerably less
than those at the singlets separation distance; and 2) given the same initial distance, rings in region 2 take longer
to reach stability than rings in region 1.
The above can be more simply stated by saying that rings with alignment shift (from exact alignment of opposite
charges) less than half the singlets angular separation have 100% probability to reach stability while rings with
alignment shift greater than half the singlets angular separation have less than 100% probability to reach stability.
This is true only for facing rings separated at the time of formation by gaps that are less than or equal to the
threshold distance. Rings that are separated at the time of formation by gaps that are greater than the threshold
distance may not reach stability.
It is important to notice that the stability of the layered configuration depends only on the rings
having an equal number of doublets and the same spin direction, and on the condition that at the
time of formation the rings are at a distance that is less than about ten times the singlets
separation distance. The number of doublets in the rings has no effect on the stability of the
layered configuration.
to the singlets separation distance is never trespassed regardless of the values of initial shifts or initial gaps (blue
and red curves).
The threshold separates the space between facing rings into two regions:
1) If the values of the initial gap are below the threshold (blue curves) ring A moves away from ring B until the
threshold is reached and then changes its direction to the left and follows the threshold towards exact alignment
of opposite charges at shift 0.
2) If the values of the initial gap are above the threshold (red curves) ring A moves towards ring B until the
threshold is reached and then changes its direction to the left and follows the threshold towards exact alignment
of opposite charges at shift 0.
For the second region, however, as the rings separation increases the forces between the two rings decrease in
the inverse square relation and may become so weak that the time required to reach exact alignment of opposite
charges is so large that it may make it impossible for the two rings to reach stability.
Accordingly, the definition of the strong attractor required for the stability of a layered configuration given in
Section B4 is amended as follows:
The exact alignment of singlets of opposite charges in two rings with equal number of doublets
and same spin direction in a layered configuration with rings separated by a gap that is less than or
equal to a threshold value is the strong attractor that is required for the stability of the configuration.
There are two regions of stability for facing rings separated by gaps that are less than or equal to the threshold
value:
1) The alignment of facing singlets of opposite charges is within 0 and 0.5 times the singlets angular
separation. A clockwise (to the left) shifting motion is initiated and continues until exact alignment of opposite
charges is reached. The threshold distance is equal to the singlets separation and the gap between rings remains
at that distance throughout the motion.
2) The alignment of facing singlets of opposite charges is greater than 0.5 but less then or equal to 1 times the
singlets angular separation. An expanding motion is initiated and continues until the gap between rings reaches
the threshold value. After that point of maximum separation, the rings start to collapse towards each other with a
clockwise (to the left) motion until the singlets separation distance is reached and remain at that distance until
exact alignment.
The same two regions are present when the alignment of facing singlets of opposite charges is equal to 1 but less
than 2. However, the shifting motion is counterclockwise (to the right) towards exact alignment instead of
clockwise.
At exact alignment of opposite charges the attractive electrostatic force is at its maximum and the shifting force is
null, keeping the rings strongly bound together.
As indicated in Section B4, at the critical point when the alignment is equal to 1 (that is, when singlets of facing
rings are in exact alignment of same charge) the layered configuration has the same probability to move either
clockwise or counterclockwise towards the stability offered by the strong forces of the exact alignment of
opposite charges.
The probability to reach stability for rings in region 2 is less than those in region 1 due to: 1) the initial expanding
motion of the rings and consequent reduction of active forces which, at maximum threshold, are considerably less
than those at the singlets separation distance; and 2) given the same initial distance, rings in region 2 take longer
to reach stability than rings in region 1.
The above can be more simply stated by saying that rings with alignment shift (from exact alignment of opposite
charges) less than half the singlets angular separation have 100% probability to reach stability while rings with
alignment shift greater than half the singlets angular separation have less than 100% probability to reach stability.
This is true only for facing rings separated at the time of formation by gaps that are less than or equal to the
threshold distance. Rings that are separated at the time of formation by gaps that are greater than the threshold
distance may not reach stability.
It is important to notice that the stability of the layered configuration depends only on the rings
having an equal number of doublets and the same spin direction, and on the condition that at the
time of formation the rings are at a distance that is less than about ten times the singlets
separation distance. The number of doublets in the rings has no effect on the stability of the
layered configuration.
Part C: Summary: The Triangular and Layered Rings Configurations
In this study, the effect of ring spin on the geometry and composition of the ring, and the effect of charge
interaction between rings are introduced and used to explore the degree of stability of triangular and layered
three-ring configurations of Baryons. As the proton is the single strong attractor in the decay process of Baryons,
its rings configurations are used as models for the study.
Part A of the study examined the stability of the triangular configuration and Part B examined the stability of the
layered configuration.
Part A: Triangular Configuration
The subject is a model of the proton consisting of three rings of 168 doublets in an equilateral triangular
configuration with rings lying in the same plane and separated by gaps equal to twice the separation distance
between singlets. The model has the following characteristics: the direction of the spin is the same for all rings; all
singlets are in exact alignment; and the singlets facing each other across the gap are of the same charge. The
positive spare singlet is located at the center of the triangle.
Using that model, the study shows that the triangular configuration is unstable. After an initial collapsing period,
the rings break away from the center of the configuration and continue with that motion indefinitely. The gaps
between rings will reach twice their initial value in about 4E-20 seconds after the time of formation of the rings.
If the model is modified so that the rings are separated by gaps with values near or equal to the singlets
separation distance, the triangular configuration, after a collapsing period, still breaks away from its center and
continues with that motion indefinitely.
Part B: Layered Configuration
The subject is a model of the proton consisting of a layered three-ring configuration with rings of 169 doublets.
The centers of the rings are on a line of length equal to twice the gap between rings which is equal to the
separation distance between singlets. The direction of the spin is the same for all rings. The positive spare singlet
is located at the center of the middle ring.
Using that model, the study shows that the layered configuration is stable, or will reach stability, if at the time of
formation the facing rings of the configuration are separated by a gap that is less than or equal to a threshold
value which is dependent on the alignment of the singlets in one ring with respect to the singlets in the facing
ring. The stability is reached by a shift in the position of the rings towards exact alignment of opposite charges as
the gap between the rings is reduced from the threshold value to the singlets separation distance. If the gap
between two facing rings is greater than the threshold value then the rings may break away from each other and
continue with that motion indefinitely.
It is important to notice that the stability of the layered configuration depends only on the rings having an equal
number of doublets and the same spin direction, and on the condition that at the time of formation the rings are at
a distance that is less than a threshold value of about ten times the singlets separation distance. The number of
doublets in the rings has no effect on the stability of the layered configuration.
In addition, the doublets identification uncertainty for a three-ring layered configuration with rings of equal
number of doublets spinning in the same direction presented in Section B2 is at its maximum when the rings
have singlets of opposite charges in exact alignment. Under that condition, doublets in the configuration lose
their identity and the whole configuration becomes a homogeneous spinning entity bound together by
extraordinarily strong forces. Should this entity be breached by stronger forces then the result would
be a burst of high energy gamma rays, neutrinos, and undetectable Z helixes.
In this study, the effect of ring spin on the geometry and composition of the ring, and the effect of charge
interaction between rings are introduced and used to explore the degree of stability of triangular and layered
three-ring configurations of Baryons. As the proton is the single strong attractor in the decay process of Baryons,
its rings configurations are used as models for the study.
Part A of the study examined the stability of the triangular configuration and Part B examined the stability of the
layered configuration.
Part A: Triangular Configuration
The subject is a model of the proton consisting of three rings of 168 doublets in an equilateral triangular
configuration with rings lying in the same plane and separated by gaps equal to twice the separation distance
between singlets. The model has the following characteristics: the direction of the spin is the same for all rings; all
singlets are in exact alignment; and the singlets facing each other across the gap are of the same charge. The
positive spare singlet is located at the center of the triangle.
Using that model, the study shows that the triangular configuration is unstable. After an initial collapsing period,
the rings break away from the center of the configuration and continue with that motion indefinitely. The gaps
between rings will reach twice their initial value in about 4E-20 seconds after the time of formation of the rings.
If the model is modified so that the rings are separated by gaps with values near or equal to the singlets
separation distance, the triangular configuration, after a collapsing period, still breaks away from its center and
continues with that motion indefinitely.
Part B: Layered Configuration
The subject is a model of the proton consisting of a layered three-ring configuration with rings of 169 doublets.
The centers of the rings are on a line of length equal to twice the gap between rings which is equal to the
separation distance between singlets. The direction of the spin is the same for all rings. The positive spare singlet
is located at the center of the middle ring.
Using that model, the study shows that the layered configuration is stable, or will reach stability, if at the time of
formation the facing rings of the configuration are separated by a gap that is less than or equal to a threshold
value which is dependent on the alignment of the singlets in one ring with respect to the singlets in the facing
ring. The stability is reached by a shift in the position of the rings towards exact alignment of opposite charges as
the gap between the rings is reduced from the threshold value to the singlets separation distance. If the gap
between two facing rings is greater than the threshold value then the rings may break away from each other and
continue with that motion indefinitely.
It is important to notice that the stability of the layered configuration depends only on the rings having an equal
number of doublets and the same spin direction, and on the condition that at the time of formation the rings are at
a distance that is less than a threshold value of about ten times the singlets separation distance. The number of
doublets in the rings has no effect on the stability of the layered configuration.
In addition, the doublets identification uncertainty for a three-ring layered configuration with rings of equal
number of doublets spinning in the same direction presented in Section B2 is at its maximum when the rings
have singlets of opposite charges in exact alignment. Under that condition, doublets in the configuration lose
their identity and the whole configuration becomes a homogeneous spinning entity bound together by
extraordinarily strong forces. Should this entity be breached by stronger forces then the result would
be a burst of high energy gamma rays, neutrinos, and undetectable Z helixes.
Appendix: Part A Tables
=======================================================================================
Copyright © 2009 Giulio. C. Cima All Rights Reserved
=======================================================================================
Copyright © 2009 Giulio. C. Cima All Rights Reserved
=======================================================================================
B6: Effect of Forces on a Layered Configuration
If the three rings A, B, and C of a layered configuration have an equal number of doublets, have the same spin
direction, and the facing singlets are in exact alignment, then the overall forces acting on positive target singlets
in either of the outer rings by the presence of the middle ring are equal in magnitude and direction to the forces
acting on negative target singlets.
If the middle ring has a spare singlet located at its center, then the magnitudes and directions of the overall forces
acting on positive and negative target singlets in the outer rings are not equal.
In Section B3 it is shown (see Appendix Table 3) that the resultant force acting on outer ring A due to the
presence of middle ring B of a proton model with facing singlets of opposite charges in exact alignment is:
Resultant force: 1,368,184,378 [g cm/sec2]
X component: Null
Y component: 9,200,979 [g cm/sec2]
Z component: -1,368,153,439 [g cm/sec2]
alfa direction: 90 [degrees]
beta direction: 270.39 [degrees]
The components of the resultant force acting on outer ring C due to the presence of middle ring B have the same
magnitudes of the components shown above but opposite signs. The directions of the resultant force are also
opposite to those shown above.
In addition to the forces acting on the outer rings due to the presence of the middle ring it is necessary to
consider the forces acting on either of the outer rings due to the presence of the other outer ring.
A stable two-ring layered configuration requires that the facing singlets be of opposite charges in exact alignment
(see Section B4). This means that in a stable three-ring layered configuration the two outer rings have facing
singlets of same charge in exact alignment.
Appendix Table 7 displays the forces acting on a positive target singlet in outer ring A from the first ten and the
last ten singlets in outer ring C of a proton model with facing singlets of opposite charges in exact alignment. The
gap between the two outer rings is twice the singlets separation distance.
The resultant force acting on outer ring A due to the presence of outer ring C of a proton model with facing
singlets of opposite charges in exact alignment is:
Resultant force: 39,709,809 [g cm/sec2]
X component: Null
Y component: -628,971 [g cm/sec2]
Z component: 39,704,828 [g cm/sec2]
alfa direction: 270 [degrees]
beta direction: 90.91 [degrees]
The components of the resultant force acting on outer ring C due to the presence of outer ring A have the same
magnitudes of the components shown above but opposite signs. The direction (beta) of the resultant force is
also opposite to that shown above.
Using the middle ring as reference, the net resultant forces on the outer rings and their components and
directions are:
Outer ring A
Net resultant force: 1,328,476,267 [g cm/sec2]
X component: Null
Y component: 8,572,008 [g cm/sec2]
Z component: -1,328,448,611 [g cm/sec2]
alfa direction: Null
beta direction: 270 [degrees]
Outer ring C
Net resultant force: 1,328,476,267 [g cm/sec2]
X component: Null
Y component: -8,572,008 [g cm/sec2]
Z component: 1,328,448,611 [g cm/sec2]
alfa direction: Null
beta direction: 90 [degrees]
The very strong Z components of the resultant forces tend to move the outer rings towards the middle ring. There
is a slight shift away from B due to the Y component, and no lateral shift due to the null X component. The two
outer rings are strongly attracted to the middle ring and are held to it at a distance equal to the singlets separation.
If the three rings A, B, and C of a layered configuration have an equal number of doublets, have the same spin
direction, and the facing singlets are in exact alignment, then the overall forces acting on positive target singlets
in either of the outer rings by the presence of the middle ring are equal in magnitude and direction to the forces
acting on negative target singlets.
If the middle ring has a spare singlet located at its center, then the magnitudes and directions of the overall forces
acting on positive and negative target singlets in the outer rings are not equal.
In Section B3 it is shown (see Appendix Table 3) that the resultant force acting on outer ring A due to the
presence of middle ring B of a proton model with facing singlets of opposite charges in exact alignment is:
Resultant force: 1,368,184,378 [g cm/sec2]
X component: Null
Y component: 9,200,979 [g cm/sec2]
Z component: -1,368,153,439 [g cm/sec2]
alfa direction: 90 [degrees]
beta direction: 270.39 [degrees]
The components of the resultant force acting on outer ring C due to the presence of middle ring B have the same
magnitudes of the components shown above but opposite signs. The directions of the resultant force are also
opposite to those shown above.
In addition to the forces acting on the outer rings due to the presence of the middle ring it is necessary to
consider the forces acting on either of the outer rings due to the presence of the other outer ring.
A stable two-ring layered configuration requires that the facing singlets be of opposite charges in exact alignment
(see Section B4). This means that in a stable three-ring layered configuration the two outer rings have facing
singlets of same charge in exact alignment.
Appendix Table 7 displays the forces acting on a positive target singlet in outer ring A from the first ten and the
last ten singlets in outer ring C of a proton model with facing singlets of opposite charges in exact alignment. The
gap between the two outer rings is twice the singlets separation distance.
The resultant force acting on outer ring A due to the presence of outer ring C of a proton model with facing
singlets of opposite charges in exact alignment is:
Resultant force: 39,709,809 [g cm/sec2]
X component: Null
Y component: -628,971 [g cm/sec2]
Z component: 39,704,828 [g cm/sec2]
alfa direction: 270 [degrees]
beta direction: 90.91 [degrees]
The components of the resultant force acting on outer ring C due to the presence of outer ring A have the same
magnitudes of the components shown above but opposite signs. The direction (beta) of the resultant force is
also opposite to that shown above.
Using the middle ring as reference, the net resultant forces on the outer rings and their components and
directions are:
Outer ring A
Net resultant force: 1,328,476,267 [g cm/sec2]
X component: Null
Y component: 8,572,008 [g cm/sec2]
Z component: -1,328,448,611 [g cm/sec2]
alfa direction: Null
beta direction: 270 [degrees]
Outer ring C
Net resultant force: 1,328,476,267 [g cm/sec2]
X component: Null
Y component: -8,572,008 [g cm/sec2]
Z component: 1,328,448,611 [g cm/sec2]
alfa direction: Null
beta direction: 90 [degrees]
The very strong Z components of the resultant forces tend to move the outer rings towards the middle ring. There
is a slight shift away from B due to the Y component, and no lateral shift due to the null X component. The two
outer rings are strongly attracted to the middle ring and are held to it at a distance equal to the singlets separation.
Appendix: Part B Tables
