| Effect of an Unequal Number of Doublets in a Three-ring Layered Configuration Giulio C. Cima (May 2010) |
In Part B of the Author’s “Effect of Charge Interaction on Baryon Rings
Configurations and Stability” (the Reference) it is shown that a proton model
consisting of a layered configuration of three concentric rings of 169 doublets with the
positive spare singlet located at the center of the middle ring is stable or will reach
stability if the rings have the same spin direction and 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.
It is also noted that the number of doublets in the rings has no effect on the stability of
the layered configuration as long as it is the same for all rings.
The purpose of this study is to determine the effect of an unequal number of doublets in
rings on the stability of the three-ring layered configuration.
Contents:
1: Force Interactions among Singlets of Two Concentric Rings
in the Same Plane
2: Force Interactions among Singlets of a Two-Ring Layered
Configuration
3: Force Interactions among Singlets of a Three-Ring Layered
Configuration
4: Force Interactions among Singlets of a Spinning Three-Ring
Layered Configuration
5: Proton Neutron Configurations Interchange
Configurations and Stability” (the Reference) it is shown that a proton model
consisting of a layered configuration of three concentric rings of 169 doublets with the
positive spare singlet located at the center of the middle ring is stable or will reach
stability if the rings have the same spin direction and 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.
It is also noted that the number of doublets in the rings has no effect on the stability of
the layered configuration as long as it is the same for all rings.
The purpose of this study is to determine the effect of an unequal number of doublets in
rings on the stability of the three-ring layered configuration.
Contents:
1: Force Interactions among Singlets of Two Concentric Rings
in the Same Plane
2: Force Interactions among Singlets of a Two-Ring Layered
Configuration
3: Force Interactions among Singlets of a Three-Ring Layered
Configuration
4: Force Interactions among Singlets of a Spinning Three-Ring
Layered Configuration
5: Proton Neutron Configurations Interchange
1: Force Interactions among Singlets of Two Concentric
Rings in the Same Plane
For two concentric rings in the same plane with d1 and d2 doublets there are 4(d1 d2)
force interactions. If d1 and d2 are both even or both odd then for each force interaction
between singlet s1 in ring 1 and singlet s2 in ring 2 there is an opposite interaction
between singlet s11 in ring 1 and singlet s21 in ring 2. Singlets s11 and s21 are
separated from s1 and s2 by an angular distance of 180 degrees. If the singlets in ring 1
are numbered from 1 to 2d1 and the singlets in ring 2 are numbered from 1 to 2d2 then:
s11 = s1 + d1
if s11 > 2d1 then s11 = s11 – 2d1
s21= s2 + d2
if s21 > 2d2 then s21 = s21 – 2d2
Since these are pairs of opposite forces, the resultant force of all interactions between
ring 1 and ring 2 is null. This is true regardless of the number of doublets in ring 1 and
ring 2.
If d1 and d2 are not both even or both odd then there are no pairs of opposite forces and
the resultant force of all interactions between ring 1 and ring 2 is not null. Examples are
shown in Table 1 which displays data for two rings with singlet 1 in ring 1 of opposite
charge in exact alignment to singlet 1 in ring 2.
Table 1
d1 d2 Fx [g cm/sec2] Fy [g cm/sec2] Result [g cm/sec2]
168 172 null null null
168 173 0.020679 -0.000119 0.02068
169 170 20,632,739,470 0.4194 20,632,739,470
169 171 null null null
170 171 20,754,460,913 0.421199 20,754,460,913
170 172 null null null
170 173 0.0071471 -0.0002464 0.0071513
Table 2 displays the reason for the behavior of even and odd numbers of doublets in
rings.
Table 2
Singlet number at cardinal points
doublets singlets 0 pi/2 pi 2pi/3
168 336 0 84 168 252
169 338 0 84.5 169 253.5
170 340 0 85 170 255
171 342 0 85.5 171 256.5
Rings with even number of doublets have a singlet located at each cardinal point. Rings
with odd number of doublets have a singlet located at 0 and pi cardinal points, and a
singlet located at half the singlets angular separation from pi/2 and 2pi/3 cardinal points.
The symmetry of opposite interactions requires that the location of singlets at the
cardinal points be consistent between the two rings so that if one ring has an even
number of doublets, the other ring must also have an even number of doublets; or if a
ring has an odd number of doublets, the other ring must have an odd number of
doublets. The symmetry breaks down, however, if one ring has an even number of
doublets and the other ring has an odd number. That the symmetry is broken down
does not necessarily mean that the resultant force of all interaction cannot tend towards
zero, as it is the case when d1 = 168 and d2 = 173, and when d1 = 170 and d2 = 173 in
Table 1 above.
Rings in the Same Plane
For two concentric rings in the same plane with d1 and d2 doublets there are 4(d1 d2)
force interactions. If d1 and d2 are both even or both odd then for each force interaction
between singlet s1 in ring 1 and singlet s2 in ring 2 there is an opposite interaction
between singlet s11 in ring 1 and singlet s21 in ring 2. Singlets s11 and s21 are
separated from s1 and s2 by an angular distance of 180 degrees. If the singlets in ring 1
are numbered from 1 to 2d1 and the singlets in ring 2 are numbered from 1 to 2d2 then:
s11 = s1 + d1
if s11 > 2d1 then s11 = s11 – 2d1
s21= s2 + d2
if s21 > 2d2 then s21 = s21 – 2d2
Since these are pairs of opposite forces, the resultant force of all interactions between
ring 1 and ring 2 is null. This is true regardless of the number of doublets in ring 1 and
ring 2.
If d1 and d2 are not both even or both odd then there are no pairs of opposite forces and
the resultant force of all interactions between ring 1 and ring 2 is not null. Examples are
shown in Table 1 which displays data for two rings with singlet 1 in ring 1 of opposite
charge in exact alignment to singlet 1 in ring 2.
Table 1
d1 d2 Fx [g cm/sec2] Fy [g cm/sec2] Result [g cm/sec2]
168 172 null null null
168 173 0.020679 -0.000119 0.02068
169 170 20,632,739,470 0.4194 20,632,739,470
169 171 null null null
170 171 20,754,460,913 0.421199 20,754,460,913
170 172 null null null
170 173 0.0071471 -0.0002464 0.0071513
Table 2 displays the reason for the behavior of even and odd numbers of doublets in
rings.
Table 2
Singlet number at cardinal points
doublets singlets 0 pi/2 pi 2pi/3
168 336 0 84 168 252
169 338 0 84.5 169 253.5
170 340 0 85 170 255
171 342 0 85.5 171 256.5
Rings with even number of doublets have a singlet located at each cardinal point. Rings
with odd number of doublets have a singlet located at 0 and pi cardinal points, and a
singlet located at half the singlets angular separation from pi/2 and 2pi/3 cardinal points.
The symmetry of opposite interactions requires that the location of singlets at the
cardinal points be consistent between the two rings so that if one ring has an even
number of doublets, the other ring must also have an even number of doublets; or if a
ring has an odd number of doublets, the other ring must have an odd number of
doublets. The symmetry breaks down, however, if one ring has an even number of
doublets and the other ring has an odd number. That the symmetry is broken down
does not necessarily mean that the resultant force of all interaction cannot tend towards
zero, as it is the case when d1 = 168 and d2 = 173, and when d1 = 170 and d2 = 173 in
Table 1 above.
2: Force Interactions among Singlets of a Two-Ring Layered
Configuration
For two rings in a layered configuration with d1 and d2 doublets, if d1 and d2 are both
even or both odd then for each force interaction between a singlet in ring 1 and a singlet
in ring 2 there is an opposite interaction as shown in Section 1. Since these are pairs
of opposite forces, the resultant of the X and Y components of all interactions between
ring 1 and ring 2 is null. This is not true, however, for the vertical, or Z component as
shown in Table 3 which displays data for two layered rings separated by a gap equal to
the singlets separation distances of ring 1 and with facing singlets of opposite charges
in exact alignment.
Table 3
d1 d2 Fx [g cm/sec2] Fy [g cm/sec2] Fz [g cm/sec2]
168 168 null null -1,360,057,833
168 169 666,827,775 -0.01356 0.006678
168 170 null null 0.004378
168 171 0.01158 0.0001074 0.002336
168 172 null null 0.001089
169 169 null null -1,368,153,440
169 170 670,785,235 -0.01365 0.006725
169 171 null null 0.004402
169 172 0.01163 0.0001067 0.002348
169 173 null null 0.001095
170 170 null null -1,376,249,049
170 171 674,742,695 -0.01371 0.006751
170 172 null null 0.004420
170 173 0.01169 0.0001066 0.002360
170 174 null null 0.001101
The gap between the two rings has the following effect:
1) Configurations with rings with equal number of doublets are stable and held
together by extraordinarily strong vertical (Fz) forces with null displacement (Fx
Fy) forces (see Reference).
2) Configurations with rings where the number of doublets differs by 1 are unstable
due to very small vertical (Fz) forces and strong displacement (Fx) forces causing
a lateral movement of the rings along the X axis.
3) All other configurations are unstable due to very small or null components of the
resultant forces.
Configuration
For two rings in a layered configuration with d1 and d2 doublets, if d1 and d2 are both
even or both odd then for each force interaction between a singlet in ring 1 and a singlet
in ring 2 there is an opposite interaction as shown in Section 1. Since these are pairs
of opposite forces, the resultant of the X and Y components of all interactions between
ring 1 and ring 2 is null. This is not true, however, for the vertical, or Z component as
shown in Table 3 which displays data for two layered rings separated by a gap equal to
the singlets separation distances of ring 1 and with facing singlets of opposite charges
in exact alignment.
Table 3
d1 d2 Fx [g cm/sec2] Fy [g cm/sec2] Fz [g cm/sec2]
168 168 null null -1,360,057,833
168 169 666,827,775 -0.01356 0.006678
168 170 null null 0.004378
168 171 0.01158 0.0001074 0.002336
168 172 null null 0.001089
169 169 null null -1,368,153,440
169 170 670,785,235 -0.01365 0.006725
169 171 null null 0.004402
169 172 0.01163 0.0001067 0.002348
169 173 null null 0.001095
170 170 null null -1,376,249,049
170 171 674,742,695 -0.01371 0.006751
170 172 null null 0.004420
170 173 0.01169 0.0001066 0.002360
170 174 null null 0.001101
The gap between the two rings has the following effect:
1) Configurations with rings with equal number of doublets are stable and held
together by extraordinarily strong vertical (Fz) forces with null displacement (Fx
Fy) forces (see Reference).
2) Configurations with rings where the number of doublets differs by 1 are unstable
due to very small vertical (Fz) forces and strong displacement (Fx) forces causing
a lateral movement of the rings along the X axis.
3) All other configurations are unstable due to very small or null components of the
resultant forces.
3: Force Interactions among Singlets of a Three-Ring
Layered Configuration
For a three-ring layered configuration with facing singlets of opposite charges in exact
alignment, the overall forces acting on either of the outer rings by the presence of the
middle ring are equal in magnitude but opposite in direction. In addition, it is also
necessary to consider the overall forces acting on either of the outer rings due to the
presence of the other outer ring. These forces are also equal in magnitude but opposite
in direction.
In Section 2 it is shown that the components of the overall force acting on ring 1 due
to the presence of ring 2 of a two-ring configuration of 169 doublets with rings
separated by a gap equal to the singlets separation distances and with facing singlets
of opposite charges in exact alignment are:
X component: Null
Y component: Null
Z component: -1,368,153,440 [g cm/sec2]
alfa direction: Null
beta direction: 270 [degrees]
(The direction of the overall force F acting on a ring 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).
In a three-ring layered configuration the components of the overall force acting on
outer ring 3 due to the presence of middle ring 2 have the same magnitudes of the
components shown above but opposite signs. The direction (beta) of the overall force
is also opposite to that shown above.
A stable two-ring layered configuration requires that the facing singlets be of opposite
charges in exact alignment. This means that in a stable three-ring configuration the
facing singlets of the two outer rings are of same charge in exact alignment.
The components of the overall force acting on ring 1 due to the presence of ring 3 of a
three-ring configuration of 169 doublets with gaps between rings equal to the singlets
separation distance and with facing singlets of opposite charges in exact alignment
are:
X component: Null
Y component: Null
Z component: 39,704,828 [g cm/sec2]
alfa direction: Null
beta direction: 90 [degrees]
The components of the overall force acting on outer ring 3 due to the presence of outer
ring 1 have the same magnitudes of the components shown above but opposite signs.
The direction (beta) of the overall force is also opposite to that shown above.
Using the middle ring as reference, the resultant forces on the outer rings and their
components and directions are:
Outer ring 1
Resultant force: 1,328,448,612 [g cm/sec2]
X component: Null
Y component: Null
Z component: -1,328,448,612 [g cm/sec2]
alfa direction: Null
beta direction: 270 [degrees]
Outer ring 3
Resultant force: 1,328,448,612 [g cm/sec2]
X component: Null
Y component: Null
Z component: 1,328,448,612 [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 no shift away from B due to the null 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.
Layered Configuration
For a three-ring layered configuration with facing singlets of opposite charges in exact
alignment, the overall forces acting on either of the outer rings by the presence of the
middle ring are equal in magnitude but opposite in direction. In addition, it is also
necessary to consider the overall forces acting on either of the outer rings due to the
presence of the other outer ring. These forces are also equal in magnitude but opposite
in direction.
In Section 2 it is shown that the components of the overall force acting on ring 1 due
to the presence of ring 2 of a two-ring configuration of 169 doublets with rings
separated by a gap equal to the singlets separation distances and with facing singlets
of opposite charges in exact alignment are:
X component: Null
Y component: Null
Z component: -1,368,153,440 [g cm/sec2]
alfa direction: Null
beta direction: 270 [degrees]
(The direction of the overall force F acting on a ring 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).
In a three-ring layered configuration the components of the overall force acting on
outer ring 3 due to the presence of middle ring 2 have the same magnitudes of the
components shown above but opposite signs. The direction (beta) of the overall force
is also opposite to that shown above.
A stable two-ring layered configuration requires that the facing singlets be of opposite
charges in exact alignment. This means that in a stable three-ring configuration the
facing singlets of the two outer rings are of same charge in exact alignment.
The components of the overall force acting on ring 1 due to the presence of ring 3 of a
three-ring configuration of 169 doublets with gaps between rings equal to the singlets
separation distance and with facing singlets of opposite charges in exact alignment
are:
X component: Null
Y component: Null
Z component: 39,704,828 [g cm/sec2]
alfa direction: Null
beta direction: 90 [degrees]
The components of the overall force acting on outer ring 3 due to the presence of outer
ring 1 have the same magnitudes of the components shown above but opposite signs.
The direction (beta) of the overall force is also opposite to that shown above.
Using the middle ring as reference, the resultant forces on the outer rings and their
components and directions are:
Outer ring 1
Resultant force: 1,328,448,612 [g cm/sec2]
X component: Null
Y component: Null
Z component: -1,328,448,612 [g cm/sec2]
alfa direction: Null
beta direction: 270 [degrees]
Outer ring 3
Resultant force: 1,328,448,612 [g cm/sec2]
X component: Null
Y component: Null
Z component: 1,328,448,612 [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 no shift away from B due to the null 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.
4: Force Interactions among Singlets of a Spinning Three-
Ring Layered Configuration
In Section 2 it was shown that two-ring layered configurations with no spin, with rings
with equal number of doublets and facing singlets of opposite charges in exact
alignment, and with rings separated by gaps equal to the singlets separation distance
are stable and are held together by extraordinarily strong vertical forces with null
displacement forces. If the number of doublets differs by one then the configurations
are unstable due to very small vertical forces and strong displacement forces causing a
lateral movement of the rings. All other configurations are unstable due to very small or
null components of the resultant forces.
The introduction of spin in a three-ring layered configuration has the following effect:
1) Rings with equal number of doublets have the same angular 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 (see Reference).
2) Configurations with rings where the number of doublets differs by one can be
represented as:
[d1 d2 d3]
[d1 d2 d2]
[d2 d1 d1]
[d1 d2 d1]
[d2 d1 d2]
Because of symmetry, the effect of spin is explored in detail below only on the last two
configurations, that is, configurations where the middle rings have either one more
doublet than the two outer rings [d1 d2 d1], or one less doublet [d2 d1 d2].
3) All other configurations are unstable regardless of spin.
Part A: Effect of Spin on [d1 d2 d1] Configuration
The chosen configuration is [169 170 169] doublets with facing singlets of opposite
charges in exact alignment at the time of formation, and with rings separated by gaps
equal to the singlets separation distance of ring 1 and 3 at the time of formation. The
rings characteristics are shown in Table 4 below:
Table 4
doublets 169
singlets 338
ring radius 8.3969676414255E-12 [cm]
singlets separation 1.56091550461828E-13 [cm]
angular separation 1.85893056426036E-02 [rad]
ring velocity 24959872368 [cm sec-1]
ring angular velocity 2.97248643007198E+21 [rad sec-1]
transit time 6.25378990953153E-24 [sec]
doublets 170
singlets 340
ring radius 8.44665138373317E-12 [cm]
singlets separation 1.56091531425011E-13 [cm]
angular separation 1.84799567858824E-02 [rad]
ring velocity 24959873716 [cm sec-1]
ring angular velocity 2.95500223480309E+21 [rad sec-1]
transit time 6.25378775292662E-24 [sec]
The singlets transit time is equal to singlets angular separation divided by ring angular
velocity.
For the two outer rings of 169 doublets, if the direction of the spin is the same then their
motion has no effect on the forces acting between them.
The effect of the spin on the forces acting between middle and outer rings is
determined by using the two outer rings as reference and the middle ring spinning at a
relative angular velocity of 1.7484E+19 [rad sec-1] with respect to the outer rings. This is
equal to a relative transit time of 1.057E-21 [sec].
Because of the nature of the model, time has to be in discrete increments of the relative
transit time: the smaller the increment the more accurate the results. The increment
chosen is 128th of the relative transit time.
The results are shown in Table 5 and in Figure 1 and Figure 2 below.
Table 5: XYZ displacements of outer rings
Ring Layered Configuration
In Section 2 it was shown that two-ring layered configurations with no spin, with rings
with equal number of doublets and facing singlets of opposite charges in exact
alignment, and with rings separated by gaps equal to the singlets separation distance
are stable and are held together by extraordinarily strong vertical forces with null
displacement forces. If the number of doublets differs by one then the configurations
are unstable due to very small vertical forces and strong displacement forces causing a
lateral movement of the rings. All other configurations are unstable due to very small or
null components of the resultant forces.
The introduction of spin in a three-ring layered configuration has the following effect:
1) Rings with equal number of doublets have the same angular 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 (see Reference).
2) Configurations with rings where the number of doublets differs by one can be
represented as:
[d1 d2 d3]
[d1 d2 d2]
[d2 d1 d1]
[d1 d2 d1]
[d2 d1 d2]
Because of symmetry, the effect of spin is explored in detail below only on the last two
configurations, that is, configurations where the middle rings have either one more
doublet than the two outer rings [d1 d2 d1], or one less doublet [d2 d1 d2].
3) All other configurations are unstable regardless of spin.
Part A: Effect of Spin on [d1 d2 d1] Configuration
The chosen configuration is [169 170 169] doublets with facing singlets of opposite
charges in exact alignment at the time of formation, and with rings separated by gaps
equal to the singlets separation distance of ring 1 and 3 at the time of formation. The
rings characteristics are shown in Table 4 below:
Table 4
doublets 169
singlets 338
ring radius 8.3969676414255E-12 [cm]
singlets separation 1.56091550461828E-13 [cm]
angular separation 1.85893056426036E-02 [rad]
ring velocity 24959872368 [cm sec-1]
ring angular velocity 2.97248643007198E+21 [rad sec-1]
transit time 6.25378990953153E-24 [sec]
doublets 170
singlets 340
ring radius 8.44665138373317E-12 [cm]
singlets separation 1.56091531425011E-13 [cm]
angular separation 1.84799567858824E-02 [rad]
ring velocity 24959873716 [cm sec-1]
ring angular velocity 2.95500223480309E+21 [rad sec-1]
transit time 6.25378775292662E-24 [sec]
The singlets transit time is equal to singlets angular separation divided by ring angular
velocity.
For the two outer rings of 169 doublets, if the direction of the spin is the same then their
motion has no effect on the forces acting between them.
The effect of the spin on the forces acting between middle and outer rings is
determined by using the two outer rings as reference and the middle ring spinning at a
relative angular velocity of 1.7484E+19 [rad sec-1] with respect to the outer rings. This is
equal to a relative transit time of 1.057E-21 [sec].
Because of the nature of the model, time has to be in discrete increments of the relative
transit time: the smaller the increment the more accurate the results. The increment
chosen is 128th of the relative transit time.
The results are shown in Table 5 and in Figure 1 and Figure 2 below.
Table 5: XYZ displacements of outer rings
| Figure 1: XY displacements of outer rings |
| Figure 2: XZ displacements of outer rings |
Table 5 shows the XYZ displacements of the outer rings for every eight time
increments (Ctr). At the 56th time increment (4.62E-22 seconds after the time of
formation) the vertical dZ displacement of the outer rings from the middle ring is about
ten times the initial gap between the rings. At that time, the lateral dX displacement of
the outer rings from the middle ring is 70.1% of the radius of the middle ring. The lateral
dY displacement can be ignored.
This shifting and expanding motion will continue indefinitely.
increments (Ctr). At the 56th time increment (4.62E-22 seconds after the time of
formation) the vertical dZ displacement of the outer rings from the middle ring is about
ten times the initial gap between the rings. At that time, the lateral dX displacement of
the outer rings from the middle ring is 70.1% of the radius of the middle ring. The lateral
dY displacement can be ignored.
This shifting and expanding motion will continue indefinitely.
Part B: Effect of Spin on [d2 d1 d2] Configuration
The chosen configuration is [170 169 170] doublets with facing singlets of opposite
charges in exact alignment at the time of formation, and with rings separated by gaps
equal to the singlets separation distance of ring 2 at the time of formation. The rings
characteristics are shown in Table 4.
For the two outer rings of 170 doublets, if the direction of the spin is the same then
their motion has no effect on the forces acting between them.
The effect of the spin on the forces acting between middle and outer rings is
determined by using the two outer rings as reference and the middle ring spinning at a
relative angular velocity of 1.7484E+19 [rad sec-1] with respect to the outer rings. This
is equal to a relative transit time of 1.0632E-21 [sec]. The time increment is 128th of the
relative transit time.
The results are shown in Table 6 and in Figure 3 and Figure 4 below.
Table 6: XYZ displacements of outer rings
The chosen configuration is [170 169 170] doublets with facing singlets of opposite
charges in exact alignment at the time of formation, and with rings separated by gaps
equal to the singlets separation distance of ring 2 at the time of formation. The rings
characteristics are shown in Table 4.
For the two outer rings of 170 doublets, if the direction of the spin is the same then
their motion has no effect on the forces acting between them.
The effect of the spin on the forces acting between middle and outer rings is
determined by using the two outer rings as reference and the middle ring spinning at a
relative angular velocity of 1.7484E+19 [rad sec-1] with respect to the outer rings. This
is equal to a relative transit time of 1.0632E-21 [sec]. The time increment is 128th of the
relative transit time.
The results are shown in Table 6 and in Figure 3 and Figure 4 below.
Table 6: XYZ displacements of outer rings
| Figure 3: XY displacements of outer rings |
| Figure 4: XZ displacements of outer rings |
Table 6 shows the XYZ displacements of the outer rings for every eight time
increments (Ctr). At the 50th time increment (4.15E-22 seconds after the time of
formation) the vertical dZ displacement of the outer rings from the middle ring is about
ten times the initial gap between the rings. At that time, the lateral dX displacement of
the outer rings from the middle ring is 57.8% of the radius of the middle ring. The
lateral dY displacement can be ignored.
This shifting and expanding motion will continue indefinitely.
increments (Ctr). At the 50th time increment (4.15E-22 seconds after the time of
formation) the vertical dZ displacement of the outer rings from the middle ring is about
ten times the initial gap between the rings. At that time, the lateral dX displacement of
the outer rings from the middle ring is 57.8% of the radius of the middle ring. The
lateral dY displacement can be ignored.
This shifting and expanding motion will continue indefinitely.
5: Proton Neutron Configurations Interchange
The rings of a stable three-ring layered spinning configuration must have an equal
number of doublets. Given the rest mass of the proton of 938.318 MeV, the relativistic
mass of the doublet of 1.8451 MeV (Section 2 of Reference), and that of the spare
singlet of 0.511 MeV, then the only possible configuration of a proton model is [169,
169+Z, 169] for a total relativistic mass of 935.977 MeV (Part B of Reference). 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 [+Z] is located at the center of the
middle ring.
Because of the proton neutron configuration interchange presented below, the
neutron, with a rest mass of 939.611 MeV, has the unstable model configuration [169
170 169] for a total of 937.311 MeV. 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 of the outer rings. The direction of the spin is the same for all rings.
The dynamics of the proton neutron configuration interchange is given by:
[169 170 169] <----> [169 169+Z 169] [–Z*]
That is, a doublet [+Z –Z*] of the middle ring of a neutron configuration splits into its
singlets components [+Z] and [–Z*] reducing the doublets of the middle ring to 169.
The [+Z] singlet moves to the center of the ring as the spare singlet thus changing a
neutron configuration to that of a proton’s. The [–Z*] singlet is released and
immediately captured by the closest proton configuration. The process is then
reversed with the [–Z*] singlet combining with the proton spare singlet [+Z] to form a
doublet [+Z –Z*] which is added to the middle ring to increase the number of
doublets to 170.
This interaction guarantees the stability of neutrons when in close proximity to
protons as long as the number of neutrons does not exceed the number of protons,
and as long as the time of the interchange is within the threshold time of 4.62E-22
seconds which is the time when the vertical displacement of the outer rings from the
middle ring of the neutron configuration is about ten times the gap between the rings
at the time of formation (Section 4).
The rings of a stable three-ring layered spinning configuration must have an equal
number of doublets. Given the rest mass of the proton of 938.318 MeV, the relativistic
mass of the doublet of 1.8451 MeV (Section 2 of Reference), and that of the spare
singlet of 0.511 MeV, then the only possible configuration of a proton model is [169,
169+Z, 169] for a total relativistic mass of 935.977 MeV (Part B of Reference). 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 [+Z] is located at the center of the
middle ring.
Because of the proton neutron configuration interchange presented below, the
neutron, with a rest mass of 939.611 MeV, has the unstable model configuration [169
170 169] for a total of 937.311 MeV. 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 of the outer rings. The direction of the spin is the same for all rings.
The dynamics of the proton neutron configuration interchange is given by:
[169 170 169] <----> [169 169+Z 169] [–Z*]
That is, a doublet [+Z –Z*] of the middle ring of a neutron configuration splits into its
singlets components [+Z] and [–Z*] reducing the doublets of the middle ring to 169.
The [+Z] singlet moves to the center of the ring as the spare singlet thus changing a
neutron configuration to that of a proton’s. The [–Z*] singlet is released and
immediately captured by the closest proton configuration. The process is then
reversed with the [–Z*] singlet combining with the proton spare singlet [+Z] to form a
doublet [+Z –Z*] which is added to the middle ring to increase the number of
doublets to 170.
This interaction guarantees the stability of neutrons when in close proximity to
protons as long as the number of neutrons does not exceed the number of protons,
and as long as the time of the interchange is within the threshold time of 4.62E-22
seconds which is the time when the vertical displacement of the outer rings from the
middle ring of the neutron configuration is about ten times the gap between the rings
at the time of formation (Section 4).