posted 09-04-2003 04:43 PM
Particle Structures
How rings form stacks
How stacks are photons, nucleons, pions and bosons
How electrons and muons switch identities
How magnetic moments arise
Why nuclei form
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Using a model of leptons and quarks, composed of singlets that move in a loop or ring, it is possible to interpret various experimental results in a new light. Particle structure is based on the stacking of rings composed of singlets. The forces holding planets, atoms and nuclei together are considered on an identical basis.
This chapter seeks to show, in a simple form, how the masses and magnetic moments may be related to their observed values and how the actions of charge and gravity vary between rings.
The intention is not precisely to arrive at all the known values of the parameters of all the known particles. It is only to give a flavour of how they may be achieved.
If it is accepted that the central feature of a proton is its two up quarks and one down quark, then it is necessary to explain how each quark holds the other in place. It was shown that the effect between adjacent rings is proportional to the difference in rotational frequencies between the rings. If the rings rotate at the same rate, in the same direction, then there is no frequency difference and the two rings would be in the same frame of reference and would see each other as stationary.
The same chapter also showed that in such a frame of reference the two rings would see the underlying masses of the singlets that composed the rings, and that such composite rings, made from equal numbers of positive and negative singlets, would have all their masses attractive or chasing gravitationally. So the force between two rings, due to mass, would be the square of the equivalent total mass of each ring, the Planck mass, Mo because of the many individual singlet-singlet interactions. In the stationary frame of reference there is no observable charge generated, and all the charges of the singlets sum to zero.
The two rings are thus bound together by gravity, and the maximum effect will be when all the rings in a stack have the same rotational rate. However they cannot all rotate in the same sense because they would form bosons and photons, in pairs of rings, which would break the stack up. So the sense of the rotation of the rings must alternate down the stack.
From symmetry considerations it can be taken that the two up quarks are each adjacent to the central down quark. The up quarks are rotating the same way and strongly attract each other. They would prefer to not have the down quark between them because their mutual attraction is far greater than either's' attraction for the down quark. So there must be two non-charged rings either side of the up quarks which act to retain the down quark in place. These can only be neutrinos. This stack of five rings is the proton 'core'.
In order to allow for interactions with other passing rings it is likely that there need also be two 'guard' rings adjacent to the core. These must be attracted to the up quarks, but may be dislodged if a passing ring has sufficient momentum. These seven rings are the base from which all larger particles are built, and are called collectively a proton.
The stack can enlarge by the addition of more rings at each end, but the basic property of the stack is the one frequency, or size, of ring. If the proton has a mass of 938.256 MeV, then each ring will represent one seventh of that mass, or 134.037 MeV.
This implies that there are four neutrinos, each of mass 134.037 MeV in the proton. This may seem strange since the neutrino is supposed to have a zero mass. However it is the case that the internally generated masses, due to the velocity of the singlets around the neutrino ring, totals zero, but the gravitational action of both positive and negative masses, between composites, is always attractive or chasing. So the massless neutrinos appear to have masses, and those masses are related to the physical size of the ring.
The quarks have fractional masses. Thus the up quark has a net, positive versus negative, mass of 89.3577 MeV whilst it appears to be 134.037 gravitationally, and the down quark similarly has a net mass of 44.679 MeV.
These figures are, of course, approximate since they do not distinguish between the difference in forces between each type of ring. Thus the ring sizes may be slightly different to 134.037 MeV in order to allow for some form of binding energy, but they will still be each the same size.
If one ring is now dislodged by a passing ring what can occur? That depends on what the passing ring is. The presumption is that there are only three other sizes of free ring, corresponding to the electron, muon and tau, each with their respective neutrinos. The ring sizes for the charmed, strange, top and bottom quarks are not free, and their stacks will have different ring sizes.
If, for example, a muon-neutrino (nu) dislodges an outer proton neutrino (n1), the process will conserve both momentum and energy if the nu alters ring size to match the proton stack, and the n1 alters size to match the incoming ring. Thus the two neutrinos will have swapped sizes and identities without altering their total size or charge. This would appear to be the same as a glancing collision, except for any time delay.
If the incoming ring were, for example, an electron, then the n1 would take on the size of the electron to become an electron neutrino (ne), and the electron would match size with the proton stack. Because the electron generates the same mass as its size, rather than a fraction, like the quarks, it will have a mass of 134.037 MeV. So an incoming electron displaces a n1 from the stack, which appears as a ne. The proton stack now has total charge equal to zero, and any alteration in mass will be due to the difference in binding energy between the electron in the stack rather than the neutrino. The proton stack has become a neutron stack. The electron, with a preference for being as small a mass, or as large a ring, as possible will easily be replaced by an incoming ne, resulting in the neutron decaying into a proton plus a fast electron.
The proton core has not altered, and it will be shown later that the neutron stack cannot be two down quarks and one up quark in a similar stack. The basic building block for atomic matter is the proton stack.
Note that an identical neutron would result from a muon or tau as the incoming ring, because the rings sizes alter. The muon and tau are just larger mass, or smaller ring size, versions of the electron.
The process of altering an electron into a muon, or vice versa, can be seen along the lines of the stack dislodging process. An electron ring meeting a nu ring can take the momentum and energy of that ring and adjust its size to that of a muon, with the nu becoming a ne. However this is not the preferred mode because the electron, with its charge, prefers to be as small a mass, or as large a ring size, as possible - which also drives the electron out of the neutron eventually - and so the muon tends to use a ne to become an electron, called weak decay.
The way an electron can become a muon is more likely to occur through a photon, where an electron and positron, with sufficient energy - which directly governs the ring size - join together whilst rotating in the same sense to form a photon. The photon adjusts the two electron rings to be the same size, accelerates to light speed, passes near or collides with another ring and separates into two rings again. With sufficient initial energy the result will be a muon and anti-muon with small velocities.
Thus the charged Pion can be either a n1 and an electron or an anti-up quark and a down quark, or each of their anti-rings. The neutral Pion can be a n1 and a ne. The identity of a neutrino or anti-neutrino is of no consequence, in that they can both have either rotation direction, and their current labelling is incorrect. That labelling leads to different helical orientations of the neutrino and anti-neutrino which are not justified when the spin orientations of the singlets within the rings is understood.
When the charged Pion leaves the proton stack, or its immediate environment, and encounters the environment outside the nucleus, it changes its internal binding energy and can then separate as a muon and ne, or nu and electron - unless it is made from quarks, in which case it breaks up other stacks and hadrons will be observed. However there is very little gravitational attraction between two similar size rings rotating opposite, so a Pion made of quarks is unlikely, or exceptionally short lived. Thus the unbound state of the neutrino ring would seem to be the nu. This implies that the average binding energy per ring in the proton is about 28.378 MeV, and that the Pion's binding energy, or proximity-generated extra mass, is represented by the difference between twice-n1 and 134.972 MeV, or 133.102 MeV. The unbound Pion will then further separate into muon and ne or electron and nu, depending on which ring supplied the necessary binding energy.
The identification of induced mass and neutrino gravitational masses is not certain. The proximity, or closeness, of two rings tends to cause the rings to alter shape from a perfect circle. This effect has been discussed fully elsewhere and the resulting uncertainty in ring masses underlies quantum uncertainty. It may be that either the whole gravitational mass, or only the binding energy between rings, can be ascribed to the proximity of the neutrinos to other rings. The induced mass will be proportional only to the separation and size of the two rings and their relative rotational frequencies. In this picture it is possible that free neutrinos have zero gravitational mass, and that they only appear to have such attractive masses when in the presence of other rings (including other neutrino rings). Then the whole of a neutrino's gravitational mass could be described as binding energy. The maximum induced mass for any ring will be Mo, and such a ring must be stationary.
It is thus possible to now identify the n1 as a bound nu, which also points to the nu in the Pion as having the size and energy of the n1. The same argument cannot be made for bound and unbound quarks, since they cannot appear unbound, or free, at any time. So there will be only one mass for each type of quark.
A similar line of thought will lead to the sizes of the n2 and n3 neutrinos in the second and third quark generation stacks. Their sizes will represent the nu plus the binding energy for that size of ring.
The result will be only three sizes of free neutrino, and three sizes of bound neutrino, any of which can alter size to become any other in a process involving the rings.
There are only three sizes of free electron - the electron, muon and tau, each of which can become the other in a suitable ring process, and three sizes of bound electron in the three different quark stacks.
There are only three different sizes of quark stack. The repetition of three different sizes leads to the possibility of a relationship to three different periods of universal expansion, or something similar.
The end result is that there are only four different rings - the electron, neutrino, up and down quarks. Each has three different sizes when bound, but the leptons also have three extra unbound sizes.
Magnetic Moments
Using the net masses of the rings it is possible to arrive at the magnetic moments of stacks such as the proton and neutron, and then longer stacks.
The net mass of the proton (the sum of the masses generated by the rings, rather than the sum of the ring sizes - which would be the total mass of the proton) will be 759.541 MeV, and its rotating charges will sum to 5/3 Qe. The net mass of the neutron, where the electron (mass 0.511) replaces one of the n1 (mass 134.037 MeV) and the extra binding energy must be included, will be 626.798 MeV. These two figures provide the nuclear magnetic moment, in a stack, of Qe to be 4.70585 NM, and the moment of a unit of mass of size 7.686645 x10-31 kg to be -2.867 x10-3 NM.
The down quark represents 17.7 % of the proton's mass per total moment of 759.4 MeV, and the up quarks will be double that at 35.3 %. Each ring represents 1/7 of the total momentum within the proton stack, since each ring has momentum equal to Planck's constant. The value of the rotation of the ring, called 'spin ± ½' is the same regardless of the size of the ring, or the net mass of that ring.
The stack neutrinos(n1) represent 70.6 % of the net mass of the proton, and if these were allowed in some way to become loose, could represent a form of dark matter particle. With quark matter approximately ¼ of this amount (17.6 % of the net total), the remaining fraction must be free electrons, neutrinos and other rings. The amount of mass not seen (total less net) in the proton is 2/ 7 of the total mass of the proton.
Using the above figures it is possible to arrive at masses and moments that closely approximate the observed values for the stable particles. The match would be closer if the precise attribution of binding energies could be made between each type of ring. However, the basic mode of stacking and binding has been shown.
It is interesting to note that the mass differences between different mesons tends to correspond to the sizes of the up and down quarks, muon, twice-muon, n1 and twice-n1. Given the limited sizes available to the rings this should not be surprising.
The most surprising feature of all is the gravitational mass apparent for the neutrinos. That it is necessary is made clear by the need for any more than three rings in the proton stack. The replacement, rather than addition, of an electron in the formation of a neutron, plus the loss of a neutrino, rather than addition of an anti-neutrino, in the same process hints at the extra rings. The small mass difference between the proton and neutron limits the possible relative sizes of the quarks, and the need for maximum effect between rings implies the same size rings in a stack. All of these lead inexorably to the recognition of the necessity of the neutrino's masses as being observable.
The same effect has been seen in photons, where the electron and positron, although of opposite mass type, are both gravitationally affected in the same, attractive or chasing fashion. Thus neutrinos will also be bent by close passage past stars and planets, with the effect proportional to the physical size of the neutrino, as well as its distance from the star or planet.
From the masses of the quarks arrived at earlier it can be seen that it is not possible for a neutron to be composed of two down quarks and one up quark, the overall mass may be the same, if the binding energy is apposite, but the magnetic moment will differ due to the different number of charges rotating in the quarks.
Thus, allowing for anti-particles, the one singlet forms the building block from which the two leptons and two quarks can be made. These in turn combine to make all the particles observable in the universe. In our positive-mass positive-energy dominated environment the basic atomic building block is the proton, u d u, but in the opposite environment the same block will be the anti-proton, u- d- u-. Given that any ring is as likely to form as any other, there must also be somewhere for a neutron-like d u d or d- u- d- particle to exist. These may also be considered as candidates for dark matter since, from symmetry, if all visible matter is composed of proton or anti-proton cores, there must be an identical amount of neutron cored matter in the universe. Such matter will not be as active as proton cored matter since its stable state would be neutrally charged, with any charged variant (due to an electron or positron replacing a neutrino in the stack) would decay quickly, as free neutrons do in proton cored environments.
Such matter would tend to group and clump together under the action of gravity since most of the resultant particles would be electrically neutral, but there would be no electrostatic energy available to fuel the formation of nuclear fusion and thus main sequence stars. The most likely result would be a spectrum of stellar black holes and weak neutron stars, but without the significant gaseous surroundings normally required to ensure observation.
Different stack sizes can intermingle to form mixed stack particles, like the Kaons. The complexity of the resulting binding energies between different rings in various sizes is beyond this simplified explanation.
Strong forces
Now that the ring sizes within a stack have been shown to be more likely to be the same, and that a proton and neutron both enjoy the same rotational frequency, it is apparent that the forces between any two nucleons in a nucleus will be virtually identical. This is due to the similar number of rings, and only small difference in mass. It has nothing to do with any charge on the nucleons because that is not seen in a frame of reference in which the rings are stationary. The enlargement of a nucleus depends only, at least initially, on how to contain more nucleons within a constant, or marginally increased, volume.
There must be some separation or distance of one ring from another ring at which the influence, or knowledge, of their respective frames of reference must fail. Outside this distance one ring will see any other ring as a mass and charge, without being able directly to compare frequencies. This could be likened to being aware of a deflection of space-time nearby, but unable to discern what is causing the deflection. If the analogy is extended slightly, it could be that the rotation of each ring is hidden within the depression of space-time. The faster rotating the ring, the larger the observable mass and the deeper the depression, but the shorter the view to the ring's horizon. Outside the horizon all that can be discerned is the net effect of charge and mass. Inside the horizon the actual components can be individually distinguished and the different frames of reference compared.
There are thus three different situations that need to be considered.
1. Both rings are separated by a distance greater than the influence distance (Id) of either. Each ring will perceive the other as having charge and mass. However neither will be able to determine what is causing the charge or mass, only that they exist. The two will move under the influence of both charge and gravity as if they were point sources. This is the normal interpretation used for particles.
2. One particle lies within the influence of the other, and yet is outside its own Id Here one ring can discern the frequency of the other, and its constituents, but the reverse is not the case. The forces on each ring will be different, dependent on the frame of reference used. This is consistent with the underlying action of the singlets, although the sizes of force at the lower levels takes only one value. At the ring level, with eight different basic rings, and many combinations of stack size and binding energy, there are likely to be many different sizes of force between rings.
For the outer, and necessarily smaller mass, ring (e.g. an electron) the inner ring (a proton, and effectively, because of the smaller horizon due to the greater depression, acting as if it were one ring) can be seen to have charge and mass and frequency. Thus the electron will look at its own frame of reference, in which it has mass Mo and no observable charge, and will feel a force of
Fe = G Mo |{½ h Wp + ½ h We}| / d2(1)
where d is the separation of the two particles and Wp and We are the respective rotational frequencies of the proton and electron. Since the proton is composed of seven rings of size 134.037 MeV there must be allowance made for the relative direction of rotation of each ring. Thus for a spin + ½ electron and a spin + ½ proton the equation becomes
Fe = G Mo [ |{ 4 ½ h Wn + ½ h We}|
+ |{ 3 ½ h Wn - ½ h We}| ] / d2(2)
where Wn is the frequency of the n1 neutrino in the proton stack. This equates to
Fe = G Mo { Lt ½ h Wn} / d2(3)
where Lt is a factor dependent on the number and size of rings present. In this case Lt will be approximately 7.
For the proton (s+½) and electron (s+½), Lt = ( 7 nu + Me)
For the proton (s+½) and electron (s -½), Lt = ( 7 nu - Me)
The force on the electron, in its own frame of reference, will be independent of any charge. However the force, from the proton's viewpoint, will be
Fp = {Qe Qe c2 + G Mp Me } / d2(4)
which is dominated by the charge component. Thus the electron will be held mostly by the charge attraction of the proton. The effect of the charge cannot be 'switched on' at a certain distance, but must be graduated. The different forces in the two frames of reference cause no problems at this level because the greater force dominates by so much, and will cause the proton the follow the path defined by that force. It is as if the reasoning for the existence of atoms is turned on its head.
Imagine a distribution of electrons in space, such that all were separated by distances greater than their Ids. Each could be considered to be in the outer shell of an atom, or free, with n = 2p and momentum h. At this separation each would see the other as having only mass and charge, but no frequency. The overall effect on any specific electron would average zero, for an infinitely large distribution, although a finite distribution would undergo expansion away from the central point. If the electron were travelling at the correct velocity for its free status, a /2p c, then for zero average effect it must move in an orbit about some point. If a proton is now inserted at each such point, for all the electrons, then the electron will be attracted gravitationally to that point whilst being held in place by the mutual repulsion of all of the other electrons.
The proton at each point must now follow a path that is defined by the force on it due to its partner electron. However, the electron has an average motion of zero, and so the proton need do nothing but remain at that central point. For a faster moving electron it will be necessary to reduce the size of the orbit in order to maintain the same distribution density throughout space.
Thus atoms can be built up from the outside inwards. This would imply that there must be an implicit link between the distribution density and the charge on the two rings, or alternatively, that the actual distribution density leads to the measurement of electrostatic charge to be the size observed, or vice versa.
3. Both rings are within the influence of each other.
Here each ring can see the internal constituents of the other ring, and the other ring's frequency as well as its charge and mass. In this case, each ring sees itself as uncharged and stationary, and will experience a force of
Fr = G Mo |{½ h W1 + ½ h W2]| / d2(5)
where W1 and W2 represent the ring frequencies. This is the same force as experienced by the outer ring before, and now both rings will feel the same force. The maximum force will depend on the relative rotation direction, as well as the ring sizes.
For similar size rings the maximum force, Ms, will be when they are both rotating in the same sense, and the minimum will be zero when they are rotating opposite. The absolute maximum force, Ma, will be when each ring is rotating at maximum frequency, Wo.
For different size rings, the maximum force, Md, will be when they are as different to each other as possible. Thus one is rotating at Wo whilst the other rotates at just above zero, but not at zero. Here Md = Ma >= Ms. The minimum will be as the ring sizes approach each other.
So the overall picture for interactions begins with point-like charges and masses, and equal forces in both reference frames, and ends with rotation (spin) dependent, charge independent, forces, equal in both frames, having gone through a stage where the forces in each frame of reference are different.
The neutron, being a stack of similar size rings to the proton stack, will feel the much the same gravitational, or rotational, forces as the proton, and will have a similar influence distance. However it will not be held in place by the electrons, but by the action of the ring rotations (masses) of the other rings in the other nucleons.
Influence Distance
So what is the influence distance, what could it be? It must be greater than the distance across the largest natural atom for the electrons in the outer shell, so that those electrons will be inside each other's Id, and will not see each other's charge. Then for the electron,
Id = 2 n2 ao (6)
where ao is the n = 1 orbital radius for an electron around a proton. Thus the electrons will not see the charges of any other electrons, or the nucleons, within their orbit or influence distance. However eventually the outer electrons in a large atom will always be outside the Id of the inner electrons. The outer electrons will thus continue to be repelled by the inner electrons, and this will set another upper limit to the size of any atom.
For the nucleons, there are only two parameters that need be set. Firstly that each nucleon must have the same velocity within the nucleus. This is vital to ensure that the ring sizes in each of the stacks are the same. Each ring expands or contracts from its stationary size to accommodate the external velocity that it has. If the ring sizes were different, then so too would the forces between different rings in different stacks. Thus it must be the case that all nucleons have the same velocity, independent of any quantum number. The second parameter is that of momentum. It must be the case that each nucleon has the same total momentum as any other nucleon. Thus
m Mo vc rRs = n h / 2p = {Me Mo} {a c / n} {je Rs}
= {Lt Mn Mo} {c / 2p} {jpRs} (7)
where je and jp refer to the orbital radii of the electron and proton respectively, and the velocity of all nucleons is taken to be c / 2p , the same as their free (n= 2p) velocity, and independent of n. This leads to the following equation, in Planck units, for the radius of orbit of any nucleon
jp = n / { Lt Mn} = n 3.26403 x10+19 Rs(8)
= n 1.32226 x10-15 m
where Mn = 134.037 MeV, and Lt = 6.99619 (approximately 7 due to the seven rings). The smallest nucleus will thus be when n = 1, and the largest at n = 2p, at which point the nucleons have momentum h and can be as easily free as bound. At this larger radius, the influence distance for a nucleon, using the minimum requirement as before, will give
Id (nucleon) = 2 jp (max) = 4 p 1.32226 x10-15 m
= 1.6616 x10-14 m(9)
So that every nucleon will be within the influence range of every other nucleon, but no orbital electrons will be within range. The maximum radius of a nucleus, constrained by n = 2p for free nucleons, will be half of this at
jmax = 8.308 x10-15 m(10)
To obtain an estimate of the forces, or energies, at these respective distances requires only to insert the relevant parameters. If Uranium 92U233 is used as an example and a relatively energetic proton (20 MeV), firstly for the maximum repulsive effect of the charge between one proton and the nucleus.
Echarge = - 92 G {a / 2p} Mo2 / 2 jmax
= - 1.277 x10-12 J = - 7.973 MeV(11)
Here the separation represents the distance from the incoming proton to the outer nucleon, since at this point the proton will experience all the nucleons as outside its influence distance. As the proton approaches past this distance it will gradually envelope the nucleons in the nucleus, within its own Id, and the number of repulsing charges will decrease to zero.
Since the energy here is a factor of two too small it would indicate that it may be that the proton needs to envelope all of the nucleons in order to change their effect from charge to mass. This would alter the separation, from the proton to the centre of the nucleus, to just jmax, and would raise the maximum repulsive energy to - 15.946 MeV. If the influence radius of the whole nucleus is considered, it will be found to be 1/233 of Id for an n = 1 nucleon. Thus the alteration may take place over that last distance of 5.675 x10-18 m.
The maximum attractive force will be when the proton has reached the centre of the nucleus. The separation will be approximately zero, but the shape of the nucleus and random effects should ensure that the force at the centre never becomes infinite. In order to reproduce the attractive energy of 45 MeV the distance of closest approach to the centre of the nucleus by a 20 MeV proton would come from
45 MeV = G [ 25 233 Mo {Lt Mn + 20 MeV}] / jx(12)
where 25 is the number of attractive actions between similarly rotating rings in two nucleons. (4 x 4 + 3 x 3 = 25). This results in
jx = 5.022 x10-30 m(13)
which is fairly near the centre. So between these two distances the force goes from repulsive to attractive maximums. Higher energy protons will result in either higher maximum attractive energies or larger separations for the same maximum energy. The greatest binding energy, paradoxically, is when the proton has zero incoming energy. Here it will have precisely the same size and frequency rings as the nucleons and will be attracted by the same size forces that bind the nucleus together - it will be caught, and will become a nucleon. However the incoming proton requires at least 15 MeV of energy to overcome the initial nuclear repulsion.
The nucleons are held by the action of gravity between individual rings in the nucleon stacks. Since the rings have the same physical size, they will appear to be stationary to a similar rotation ring in any other nucleon stack. This is why the zero incoming energy proton is so strongly attracted to other nucleons. However any extra energy, no matter how slight, relative to the existing nucleons, breaks that strong attraction down into a differential-frequency effect. The formula goes from
Fn = G Mo Mo / d2
to Fn = G Mo |{½ h W1 + ½ h W2]| / d2 (14)
where W1 and W2 are the respective ring sizes of the incoming and existing nucleon rings respectively. The incoming nucleon's rings alter to accommodate the total energy that the ring possesses. For a 20 MeV proton the rings in its stack will be of smaller radius unless it is in motion, and it must be in motion in order to maintain internal and external conservation of momentum. For the constituent rings with observable mass there is one preferred size, when at rest or in motion. Any extra energy must be absorbed by a ring's external motion. In this way the heating of a gas acts to reduce the ring size of, for example, an electron. The electron opposes this by translating the extra energy into external motion, and spreading the excess amongst as many other rings as possible - a form of utilitarianism amongst rings. The temperature of a gas, above the stationary frame of reference of a ring, can thus be directly gauged by measurement of the translational velocity that the components with mass possess, or by the measurement of the rotational frequency of the massless components - the neutrinos and photons. Where the 'temperature' of any ring with mass is less than the stationary rest mass energy of the largest ring (the electron) i.e. where any ring is larger than the electron ring, it requires energy to become a stationary electron. Thus such 'weak' rings will remain inside low frequency photons until they gain sufficient energy, for example, in a collision with a higher energy, or frequency, ring.
So when an incoming proton, with any velocity, meets a nucleus it may temporarily become stationary, but will still not feel the Planck mass attraction of the other nucleons unless the extra momentum and energy have been spread equally throughout the whole nucleus. Only then will it become bound. The redistribution of momentum and energy within a nucleus is likely to occur faster for higher energy incoming photons, which are also the least likely to become stationary for long enough to bind. There should be a humped probability curve for binding against incoming energy, with an anomalous peak at the low end. Random variations due to thermal motions will disguise the peak, but it should become clearer as the temperature of the existing nucleons, and the energy of the incoming proton, are lowered.
In all the above the neutron can be used in place of the proton because of the similar size of the ring stack in each. The charge, or lack of it, is irrelevant when considering nucleon-nucleon interactions.
Conclusion
Nearly 60 % by mass of the basic atomic building blocks, protons and neutrons, is composed of supposedly massless neutrinos. Experiments to detect neutrinos should not rely only on the Cherenkov radiation of a fast moving particle being due to a muon or electron. Electric fields should also help establish the identity of incident particles. However, this does not preclude the neutrino interacting with an electron and promoting it to become a muon. But its direction of travel, based on this indirect measure, should not be too heavily relied upon, especially with regard to the gravitational lens effect on neutrinos.
The sizes of the four secondary building blocks can be tabulated as follows, with the 2 and 3 bound states being left open for further study.
Size - meV
free
bound
1
2
3
1
2
3
electron
0.511
105.659
1784.2
134.037
?
?
neutrino
0.511
105.659
1784.2
134.037
?
?
up quark
-
-
-
89.358
?
?
down qrk
-
-
-
44.679
?
?
These are the only available masses from which to construct larger particles and stacks. Note that the bound states of the leptons only represent the same rings with larger binding energies.
When the technology for studying neutrinos has progressed to the stage achieved by current optical telescopes, it should be possible to observe gravitational lensing of neutrinos by the Sun and distant galaxies, with results consistent with the limited varieties of size of neutrino outlined in this paper.
The Bohr model of the atom is flawed at its most base level, disregarding its non-relativistic treatment of the kinetic energy of the electrons. How could any particle in a stable orbit, with no net force on it, have any amount of total energy other than zero?
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