Ring Theory - a TOE

[mike@mlawrence.co.uk]

A Schematic Preon Model of Quarks and Leptons
Michael Jefferson Lawrence
(Currently Unaffiliated)
physics@mlawrence.co.uk
Dated: 4 August, 2008
Abstract
We consider a scheme in which all quarks and leptons are composites of only one type of fundamental object, with fundamental charges +1 and –1 differentiating particle from anti-particle. The concepts of mass, electric charge, spin, time, colour, and flavour acquire meaning only at the level of the composite systems. Gauge bosons, such as W± or gluons connect only composite states and are not fundamental and no Higgs particle or higher dimensions are necessary. The scheme accounts for several regularities of the observed pattern of quarks and leptons as well the apparent handedness of neutrino/anti-neutrinos and one possible mechanism underlying observed CP violation in Kaons. A new fundamental constant provides an indication that the charged leptons are not necessarily found in different flavours, but may be mass resonances of the same particle, composed of preons, which hints that the same may also be the case for the quarks and neutrinos. The dynamics provide a framework for the masses and magnetic moments of the quarks and leptons, including neutrino masses, and for the next level up, the protons and neutrons, as well as the possible composition of gluons. Group colour symmetries are given physical meaning and used to show that only 20 different mass sizes of symmetric stacks of 2 or 3 asymmetric composite particles may exist. The symmetric stacks, which are the next level of composite particles, all have integer or zero electric charge, and there are multiple isomers of all particles. The dynamics of the preons and composite particles are further explored and extended to show that charge and mass systems can be treated identically and that the expected charge and mass energies of atomic and planetary systems are recovered at low energies. The framework suggests a new energy that has not yet been proposed and that the combination of preon and anti-preon particles may form the underlying nature of space. The dynamics also suggest the location of quantum mechanical states within general relativistic systems, and how to avoid infinities, but many important questions remain unanswered.
PACS: 12.60.-i, 12.10.-g, 12.38.-t, 11.10.-z, 75.10.Jm, 04.60.-m

1. OUTLINE
The discovery of six flavours of quarks, each appearing in three colours, and the observation of six types of leptons, raises the possibility that these particles conceal some further substructure [1]. It is simply unlikely that 36 building blocks of matter are fundamental.

The observed similarity between quarks and leptons suggests that, if there is a substructure, both types of particles are constructed from the same basic entities. This is particularly indicated by the relationship between the electric charge quantisations for leptons and quarks. The neutrality of the Hydrogen atom reflects a mysterious connection between the charges of quarks and leptons. Such a connection would arise naturally if they consist of the same objects. A related empirical fact, which should be naturally explained by a successful scheme, is the vanishing sum of electric charges of quarks and leptons in each ‘generation’ (e.g. ne, e-, u, d and anti-partners). These arguments have been aired previously, with possibly the best known scheme relating to building blocks known as Rishons [2], and this paper makes use of those generic arguments.

Additional motivation for an underlying structure is offered by the observed pattern of ‘generations’ of quarks and leptons. Here we have two independent facts, both hinting at a common substructure: within each generation, quarks and leptons appear in an analogous way and each generation reproduces all the properties of its predecessors, except for the masses. It is possible to envisage some fundamental entities whose combinations create one generation of quarks and leptons, while the next generations may be simply higher order excitations of the same system or the same system with different separations between the same components.

Our final motivation is much more speculative. The use of one particle, together with its anti-particle, as the building blocks for quarks and leptons suggests that the combination or merger of this particle and its partner should form a more fundamental state of matter. This state of matter should be the lowest possible level, from which only these building block particles appear.

Several different arguments lead us to believe that any possible substructure may be observed only at extremely short distances and correspondingly large momenta. The well-known evidence for the ‘point-like’ behavior of leptons and quarks indicates that such a substructure must correspond to distances well below 10 –18m. The present accuracy of QED tests, the success of the Weinberg-Salam model, the approximate scaling of deep inelastic structure functions all indicate that leptons and quarks are ‘point-like’ at least down to 10 –18m.

If second generation fermions are excitations of the same bound system which forms the first-generation fermions, transitions such as m®e + g, s ®d + g might be allowed. The present upper limit on the rate for m®e + g indicates that the characteristic distances involved may actually be much smaller than 10 –18 m, and probably below 10 –26 m. The details of such calculations depend, of course, on the unknown dynamics. However, a stab at these dynamics will be made later in the paper. One implication is that m®e + g, s ®d + g is allowed, but not as excitations of bound systems.

Finally, if quarks and leptons are ‘made’ of the same objects, baryon and lepton number violations might be considered very likely. The present limit on the proton’s lifetime indicates that this can probably happen only at distances below 10 –31 m, or momenta somewhere above 10+15 GeV. Unification with gravity hints, of course, at the Planck mass, corresponding to distances around 10-35 m. A successful scheme should explain why baryon and lepton number violations do not occur, or occur at such high energies that they are infrequently observed.

Having realized that any substructure must involve distances that are many orders of magnitude below our present understanding and intuition, we should not exclude the possibility that the relevant dynamics is different to anything we have seen, so far. It would be premature to insist, for example, that presently established ideas of gauge theories are sufficient for fully explaining the interactions of the new hypothetical building blocks. In fact, the correct dynamics at very short distances may be radically different, and is likely to involve some entirely new principles. However, when viewed at present energies and distances, in which quarks, leptons and ordinary gauge bosons are ‘point-like’, it should somehow reproduce currently accepted theories such as SU(2) x U(1) and QCD.

Several authors [3] have already discussed possible substructures. All the published schemes, except rishons, generally have two common features: the fundamental building blocks were assigned either colour or flavour and the standard gauge bosons remain fundamental. Rishons introduced building blocks in which colour and flavour were generated through combinations of the fundamental building blocks and some of the gauge bosons are not fundamental. We wish to consider a scheme that differs from both these sets of ideas, in which none of the attributes of the quarks, leptons and bosons are truly fundamental, each being the overall outcome of the composites generated by the new building blocks.

2. MODEL
In a composite model of quarks and leptons, the fundamental electric charge would normally be expected to be one-third of the electron charge. In our composite model, the fundamental electric charge is ±1/6 of the charge on the electron. The generation of this electric charge is hypothesized to be by means of the spinning of the preon building blocks, called meons, about an axis parallel to their direction of motion as they travel. This hypothesis is necessary to enable the correct number of symmetries to be available when the meons are in combination. In order to avoid confusion with J = ½ spinning, which we say is linked to the rotation of the composite, the spinning of meons will in future be described as ‘twisting’. A positive meon twisting in a right hand screw direction as it travels is defined as generating +1/6 electron charge. A negative meon twisting in a left hand screw direction as it travels also generates +1/6 electron charge. This asymmetry in time component (since the direction of travel relative to an observer depends on their choice of time axis) might be thought to lead to paradoxes in observation. However, the nature of the twisting and the dynamics of the meons, which, as will be outlined later, travel in a loop each chasing the one in front, means that no such paradoxes arise.

In order to generate all possible observed electronic charge combinations for the leptons and quarks, it is necessary to have six meons. In order to balance the total value of the fundamental charges of the meons, each of ±1 adjusted Planck units of fundamental charge (adjusted in size as explained later), within the loop of six, there must be three of each sign of meon present in every loop.

To show the combinations possible, the letter M will be used to denote the positive meon and M the negative meon, the anti-partner of the positive meon. An M twisting RHS will be denoted M+. An M twisting LHS will be denoted M-. The + and – denote the sign of electric charge generated, of value 1/6 in every case. The change from ring to anti-ring, that is composite particle to anti-particle, involves only swapping the type of meon at every position, ie M to M and M to M. Such a change at each position, whilst keeping the twisting orientation the same, results in the generation of opposite charge at each position within a composite.

The only combinations possible, representing the loop in linear form starting at position 1, are:

(i) M+ M+ M+ M+ M+ M+ This is a loop of +1 electronic charge. We identify it as the positron e+. For an identical loop, but with swapped meons, each will generate charge –1/6 cq, giving a loop of total charge –1 cq and the loop is identified as the electron e-. The use of cq rather than q for electronic charge is explained later, but is to allow the systematic consideration of energies across both mass and charge systems.
(ii) M+ M- M+ M- M+ M- This is a loop of 0 electronic charge. We identify this as a neutrino. The swapping of meons still sums to zero charge and is identified as the anti-neutrino. As well as the + - + - + - shown, there are other isomers such as + + + - - - or + - + - - +. The definition of the neutrino is taken to be the M at position 1 generates +1/6 cq, so RHS for each meon. Each neutrino and anti-neutrino are thus composed of meons all twisting RHS, differentiated only by 60o of rotation when viewed as a loop. Symmetry predicts the existence of LHS n and n, the ramifications of which will bee explored later.
(iii) M+ M- M+ M+ M+ M+ This is a loop of +2/3 electronic charge. We identify it as the up quark. Swapping meons provides the anti-up quark. The position of the sole negative charge in the up quark loop can be on either the M or M meons, but in each case represents an SU(3) symmetry if we decide that the position of the charge within the loop and the identity of the meon, twisting negative charge, represents different cases of the same loop. This is a ‘colour’ type symmetry since each case, or state, is clearly degenerate . This suggests that ‘colour’, is actually a form of synchronization of the asymmetry of a loop. The loops contain meons that are each chasing the next in front and the presence of an asymmetric charge can be thought of as providing a timing signal. The initial suggestion is that only the appropriate combination of asymmetries (colours) will enable a composite made of a number of loops to be stable (colourless). This will be shown to be only partially the case later.
(iv) M+ M- M- M- M+ M- This is a loop of –1/3 electronic charge. We identify it as the down quark. Swapping meons provides the anti-down quark. The SU(3) symmetry is here again in each of the different isomers. As well as the + - - - + - shown, there are also isomers such as - - - - + + or + - - + - -. Although one might suspect that only one isomer would be ‘suitable’ for correct synchronization with, and when sandwiched between, two up quarks of opposite spin to form a ‘stack’ of loops that we would identify as a proton core, as will be shown later, all isomers can be found in multiple ring combinations that have overall symmetry of charges.

Also shown later is the result that all overall-symmetric ring combinations of 2, 3 or more rings (‘stacks’) have charges of only 0, ± N (N integer >= 1) electric charges, which shows that this type of symmetry probably underlies why fractional charges are not normally seen in nature.

Note that in each case above, if the orientation of the motion of the meons in the plane of the ring is assumed to be in one direction (eg rotating clockwise on the page defined as spin J + ½ ), the time reversal of the motion of the meons around the ring will lead to the production of opposite charge and the rings having J – ½ spin . So care is needed in the definition of a ring and its anti-partner. If the electron ring is defined as –1 cq and J + ½ , then the positron ring will be +1 cq J – ½ in a time-reversed definition of the electron’s anti-partner. In the cases described above, without time reversal but by switching meon identity only, the anti-partner to the electron –1 cq J + ½ will be the positron +1 cq J + ½ . We will continue with the latter definition of ring and anti-ring relationship. It will later be shown that, from symmetry considerations, the definition of what is the ring and what is the anti-ring has to be more precise on two counts.

Also note that the leptons have colour symmetry, but it is hidden in the ±1 cq charged loops because each SU(3) position is identical to the other two. There are no possible isomers of the ±1 electronic loops. There are isomers of the neutrino loops, such as + + + - - - and + + - - + +, the latter being SU(3) symmetric. So there is no underlying colour reason why certain isomers of the leptons should not be found inside nuclei, if colour is defined as synchronization ability plus SU(3) symmetry.

The above combinations represent the ONLY possible charge combinations of three M and three M meons. In the loops the order of the meons is always alternating from M to M to M etc and the fundamental masses of M and M are hypothesized to be equal and opposite, so that their interaction externally overall is zero, as will be shown later.

In the limit in which the number of M’s and M’s is conserved and equal, we have three additive relationships, where F represents fundamental charge, T fundamental mass (as explained later) and cq the electron charge:
n(M) – n(M) = 0T
n(M) – n(M) = 0F
n(M+) + n(M-) + n(M+) + n(M-) = 0q
So at the level of meons, matter and anti-matter should be equally abundant in the universe.

We would hypothesize, without yet going into the loop dynamics, that it is expected that the loops do not break, once formed, except at extreme energies. This means that electric charge, baryon and lepton numbers are conserved when loops are not broken. So there is no process under normal circumstances for proton decay and yet at large energies, or in extreme enough charge or gravitational fields, rings may be broken.

The relation between quark and lepton charges is natural in this scheme. The empirical observation concerning the vanishing sum of charges ne, e-, u, d and anti-partners is now explained by the assertion that there are equal numbers of +1/6 and –1/6 electron-charges across the whole generation (24 of each).

In each generation
n(M) – n(M) = 0T
n(M) – n(M) = 0F
n(+) – n(-) = 0q

The second and third generations of quarks and leptons are presumably constructed in an analogous way to the first generation, although, as will be shown later from considerations of magnetic moments for at least the charged leptons, the generations appear to be different mass resonances of the same loops. Each generation must contain the same sets of states, at higher energy values. What we suggest here is that it is the size of the loops (the radial distance to the center of the loop from each meon as well as the separation of each adjacent meon) that represents the energies of the loops, or their masses. So there are three sets of sizes that are preferred, for some reason, over all other sizes and these are the mass resonances. The alternative is that each loop attracts a stack of other loops with zero total charge and spin, and the mass of that stack adds to the mass of the initial loop to produce a second excitation level. It is unclear yet why there would be such stack quantisation, although the section on colour symmetries does show that there are very few different size mass stacks amongst the symmetric stacks composed of asymmetric loops.

3. DYNAMICS
The dynamics we propose are simple. That each meon has a specific fundamental mass size ±1 and that as it travels around the loop it has a specific momentum. If the fundamental mass size itself is the adjusted Planck mass Mo, and the masses sum to zero over the loop, in the same way as the fundamental charges, then the only remaining fundamental mass and charge energy effect observable will be in the momentum of each meon in the loop. The reason for the use of the adjusted Planck mass Mo is because the relationship between the Planck mass Mp , light speed c, the Planck length Lp and the Planck constant h is h/(2p) = Mp c Lp, whereas we require h = Mo c Lo, where Lo is the adjusted Planck length. So both the adjusted mass and length used here are a factor of (2p)½ larger than their Planck versions. The relationship between Qo and Mo is that cQo = (G)½ Mo and this is partially why cq is used instead of q for charge. In adjusted Planck units |Mo| = |Qo| = G = c = 1. For SI units there is a further factor of (10+7)½ required. The momentum of each meon in the loop is taken to be h for each meon at all times. So the observable feature of the loop will be the momentum of its constituent parts multiplied by the frequency of rotation, w, or hw.

There are two possible arguments against this simple dynamic system for the loops. Firstly that we have introduced a negative fundamental mass into play in order to have the sum of the fundamental masses equal to zero, and that negative mass is an ‘explosive’ subject. However, the negative fundamental mass that we introduce here has almost the exact opposite symmetry of the actions of existing electronic charge and of the hypothesized fundamental charge. Where like-charges repel and unlike attract, what we propose is that like-masses attract and unlike masses chase – the latter, in order to remain equidistant, equivalent to trying to remain at constant energy between the two meons. So negative fundamental masses attract other negative fundamental masses in the same way as positive fundamental masses attract other positive fundamental masses. The result in a loop, considering both fundamental charge and mass interactions, is that each meon chases the next meon in line, whilst fundamental charges and masses sum to zero over the loop. This leaves normally observable only the momenta of the meons as they rotate, for both charge and mass energies, the total electronic charge created by meon twisting and the shape/orientation of the loop, which will be explained below as giving rise to the J = ½ spin energy. Actually there are expected to be eight energies within a loop, each of which is equal and opposite to another energy. These energies will be explained later, but comprise Mo c2, Qoc c2, Mo v2, Qoc v2, qc, s, qc v2/(2p) and s v2/(2p), where s is possibly the cause of the strong force and equal in size to the electronic charge energy. Mo v2 is better known as mr c2, the mass of the ring or loop and Qoc v2 as ½ h (w), the J = ½ spin of the ring or loop. The extension of the dynamics into ring-ring interactions and beyond will be investigated later.

The second argument against the dynamics proposed is that the six meons, each with one h of momentum, is six times as large as we would expect for a particle whose energy should be hw, not 6 hw. However, although each meon has one h of momentum in the same sense around the loop, the M has +h and the M has –h momentum in a spin J + ½ loop, and vice versa in a spin J – ½ loop. So in both cases, the sum of the momenta of the meons due to fundamental mass or charge in a loop is zero. But the loop still contains momentum that drives each meon around the loop at frequency w. So to observe the loop ought to be to measure its frequency w and the angular momentum of its components h, providing an energy hw. However, it is not quite that simple, since the measurement requires the use of another loop. In the same way that the spin-orbit interaction of an electron in orbit around a proton gives rise to Thomas precession and the halving of the rate of spin (here rotation) by a factor of 2 from the normal external frame of reference, here the result is the same. But the rate of rotation is unchanged inside the loop. So the internal loop dynamics are all integer values, whilst the external frequency measurements are all ½ integer values.

The shape of the loop, as a donut-like structure, or ring, with moving components constrained in a flat plane gives a frame of reference to the interaction between observer and ring, either above or below the plane of the ring. The direction of rotation of the ring can be inferred from the combination of charge and direction of magnetic moment generated by the meons around the ring. The result is what we term J = ± ½ h spin momentum, and what this scheme hypothesizes as due to the rotation of the meons around the ring. The energy associated with this momentum is actually the same size in energy terms as shown by the ring as a whole in its momentum, which is the mass of the ring in the case of an electron or positron, independent of the electronic charge of the ring. The mass energy of the ring is hw, and the spin energy observed externally as ± ½ h w but is actually ±hw for the electron and positron, depending on the relative orientation of spin and direction of travel of the ring.

So the two energies due to the rotation of a ring are exactly the same size when measured internally, but appear different when measured externally. The mass mr c2 = hw for the ring cannot be different, with a ½ factor, because its gravitational effect is not dependent on any frequency measurement. What confuses is that two rings of equal mass and aligned parallel may have the attractive mass energy exactly balancing the repulsive spin J energy, but which is the ‘correct’ energy to use to infer the other? If the spin energy is presumed ‘correct’, then the mass energy of the ring will be deduced to be ½ hw. If the mass energy is presumed correct, then the spin J energy should be observed as hw. But neither is the case, as explained above. So the exact relationship between the mass of a particle and its spin energy has been ignored so far in physics, resulting in the spin J energy being considered only in terms of fractions of angular momentum h relative to other rings.

The masses of the other rings, the neutrinos and quarks, relative to their rotational frequencies w is not so easily apparent. We hypothesize that the electronic charge in some way mediates the size of the observed mass of an isolated ring as a fraction of the ring frequency. So the e/e have observed me = 1 hw, the n/n have mn = 0 hw, the u/u have mu = 2/3 hw and the d/d have md = 1/3 hw, and the same for all other generations. In each case w represents what the size of the ring would be if each ring had ± 1cq, and that is the ‘normal’ or preferred ring size for that fermion.

We further hypothesize that either rings in a stack of at least two rings show a mass equal to the size of the ring, regardless of charge, or that the charge of the adjacent ring/s or total stack charge influence the mass observed. In either case, the neutrino rings would have mass when in a stack, but not when totally isolated. This leads naturally to a very small observed mass for neutrinos when they are passing close by, within a certain ‘influence distance/angle’ or ‘id/a’, of other rings which do have mass when isolated. This is an ‘induced’ mass for the neutrino, which we suggest increases to 100% when in a stack. The rotational rates of the rings would not change, but the existence of those rates would be partially disclosed. Within the influence distance/angle, each ring probably interacts between component meons, rather than as composite rings. This is expected to be what allows neutrinos to be stacked in nucleons. The id/a is expected to be a function of the relative orientation of the planes of the interacting rings and their separation. The action is expected to be symmetric perpendicular to the plane of the rings but declining with distance/angle away from the axes of rotation of the rings.

So, in the preferred hypothesis, the relative sizes of the three generations can now be defined as three different frequencies of rotation of the same type of rings. Transition rates between generations will depend on the available energies that will increase or decrease the ring sizes to change one generation into another. As was suggested above, there may be more than just ring size at play, but the main feature is expected to be ring size. The possibilities of quantisation will be explored later.

The sign of observable mass of a ring is hypothesized to be positive for all rings when the observer is outside the id/a of the ring under observation. Inside the id/a, all J + ½ rings are defined as positive mass, and all J – ½ rings are defined as negative mass by an observer that could get inside the id/a, although we do not think this possible. On symmetry grounds the energies of the ring due to mass and J spin are equal and opposite. The observation of mass by external observers which involves the ring mass changing due to it’s relative orientation to the observer is not possible because of the id/a hypothesis. But other rings are affected appropriately inside their respective id/as. The ‘mass’ used here has similar properties to fundamental mass, but may not be the same.

Concerning the earlier mention of the potential paradox on the direction of observation of the meons twisting. In the frame of reference of the rings, the meons are twisting against space and continue to do so regardless of the relative velocity of any external observers. Such an observer may travel fast enough to make the apparent screw direction of the meon or ring reverse, but the meon does not change the sign of charge that it is producing. Also, since the rings are so small, the motion of the meons in a loop, both advancing and retiring on opposite sides simultaneously relative to any observer, does not allow any observer to experience a preferred direction of motion of a meon within a ring. All that can be observed normally is the frequency of rotation of the meons around the ring, the total electronic charge of the ring and the relative orientation of the plane of the ring to its direction of travel, with the spin J ± ½ apparent. The observer’s relative velocity will also change the apparent frequency w of the ring, but in the ring frame of reference, nothing has changed.

Along with the dynamics described above, come simple equations of motion for the meons in the ring. Each meon, and the ring as a whole, as shown above, has momentum

h = Mo vi ri (1)

where Mo is the adjusted Planck mass, vi the velocity around the loop and ri the radius of rotation. No differentiation between +/-h is required. The energy of each meon, and the ring, is given by

E = h wi = Mo vi2 = Y mr c2 (2)
where mr is the actual rest mass of the ring due to its size and, for isolated rings, Y = 1 for e/e, 0 for n/n, 2/3 for u/u and 1/3 for d/d and possibly Y is dependent on actual positioning of rings within a stack.

This gives predictions on the sizes of the rings, in a frame of reference in which the rings, but not the meons, are stationary with respect to an observer, such that the ring radius is given by

ri = (h2/(Mo mr c2))1/2 (3)

When mr = Mo, then ri = Lo, the adjusted Planck length and E = Mo c2, the adjusted Planck energy. So the isolated ring sizes for the charged leptons will be given simply as:

e- m = 0.510999 MeV r = 9.914538 x10 –24 m
m- m = 105.658 MeV r = 6.895 x 10 –25 m
t- m = 1776.99 MeV r = 1.68 x10 –25 m

These radii are in the range described above for excitations of first-generation fermions and are consistent with the upper limit on the rate for m®e + g .

Provided the isolated neutrinos are the same size as the electron ring in each generation, which would be a reasonable assumption for their maximum interaction together, the sizes of the neutrino generations should be:

ne m = 0 MeV r = 9.915 x10 –24 m
nm m = 0 MeV r = 6.895 x 10 –25 m
nt m = 0 MeV r = 1.68 x10 –25 m

However, as will be shown in the section on protons and neutrons, the neutrinos appear to have a slightly smaller size when in the nucleon stacks than their related charged leptons.

The quark generations are understood to be the following mass sizes, using 2005 Particle Data Group masses given in the MS-bar scheme [4], plus the Top quark mass from the Tevatron Electroweak Working Group [5], and will have corresponding radii using equation (3), if these sizes are correct:

u+ m = 1.5 – 4.0 MeV d- m = 4 – 8 MeV
c+ m = 1150 - 1350 MeV s- m = 80 - 130 MeV
t+ m = 170900 ± 1800 MeV b- m = 4100 - 4400 MeV
However, the framework predicts different sizes for each of the three quarks considered in this paper.

5. STACKS
We now look at the configuration of rings when they are not isolated. The most obvious configuration is to be stacked, like dishes ready to be washed. This also makes the calculation of magnetic moments easier because the orientations of the planes of the rings will all be the same and the sum of the magnetic moments of the component rings will be the total magnetic moment of the composite stack. To investigate how the rings may stack involves considering how asymmetric rings may be made to act symmetrically when in combination with other asymmetric rings in a stack. As will be shown below using the definitions set out for the isomers of each asymmetric ring, there are a total of 144 possible different orientations of the asymmetric rings, giving rise to a maximum of 1442 two-ring stacks and 1443 three-ring stacks. There is no need to consider longer stacks for symmetry because the only symmetries in the rings are 2, 3 or none. The latter ‘no symmetry’ rings will repeat with 3-fold symmetry of position, so if there have been no symmetric composites in 2 or 3 length stacks, there will be none at any longer lengths.

In the Appendix (A1) are listed the 144 possible asymmetric ring orientations for the asymmetric rings. Not included in the work on combinations are the symmetric electron/positron and symmetric neutrino/anti-neutrino, because for these all positions are symmetric and they are able to add to any stack and retain the stack symmetry. These symmetric leptons are designated S3 for symmetry.

When considering how rings interact it is necessary to define a system for systematic comparison of the positions of the ring components, the meons. We define a ring as six meons in the plane of the paper, with position 1 being the top left meon (imagine a hexagonal nut place flat on the paper, with two flat faces parallel to the top of the page.) and position 2, 3 etc following in order along the direction of travel of the meons. So the definition of a J+ ½ loop is when the meons are traveling clockwise when viewed from above the paper. One half of loops will have M at position 1, and the other half will have M at position 1. This will not affect the charge combinations possible, but will affect which rings can merge to form photons rather than remaining as unmerged bosons, for example.

We also need to define colours and symmetries. We define the meon at which point, or through which line, the asymmetry of the loop lies as being in some way coloured. Since there are three pairs of meons in each loop, there will be three-fold symmetries possible, rather than the six that might be expected just by considering what the possible charges are. Instead of considering the symmetry of charges on the M of each pair, and then on the M of each pair, we will consider the symmetries of charges at positions on the loop by swapping each M with M, which makes the combinatory work simpler because the underlying identity of the meon does not affect the symmetry of the ring, although it does affect what the overall combination of rings can be (eg photon or boson as mentioned).

For a loop (not an anti-loop) the colours are either green (when the asymmetry is on position 1), or red (when on position 3) or blue (when on position 5). For an up quark, with its sole –cq/6 as the point of asymmetry, this should be clear, so the ring can be defined as coloured g1, r3 or b5. But, as will be shown, the lines of asymmetry become more complex and can lie between meons. Here the asymmetric meon can be M or M at 1, 3 or 5 to give a coloured loop. This means that for a symmetric loop, with all charges the same at each point, there are two different but probably indistinguishable isomers, regardless of the colour positions, which may also be indistinguishable. This means that there are expected to be two identical electrons in existence, but effectively rotated by 60o relative to each other. Only if the two loops were created simultaneously, and one specific position tracked in each loop, could the 60o difference in orientation be theoretically observed. Even trying to merge the two isomeric rings together would not work, because the twisting of the meons is in the wrong sense to allow meons at the same point to merge. Instead of correctly twisting meon pairs, with opposite charges, that will merge to form a photon, these are unable to merge. They may however be able to stack, with alternating isomers, because the meon to meon attraction may overcome the charge to charge repulsion. But it will not be possible to say which isomer is which, only that they are different. So there are two types of electron, and two types of every different isomer of every fermion ring.

For the neutrino, the situation is more complex. As already seen above, the definition of the neutrino and anti-neutrino contains a 60o difference, although the reason is different. The neutrino also has the second isomeric neutrino rotated by 60o, but since there is no change of meon type, it is technically not an anti-neutrino that results, but a neutrino rotated through 60o. So whether an uncharged ring is either a neutrino rotated by 60o relative to its counterpart, or is the anti-neutrino to the counterpart, is not discernable to a new observer because they are precisely the same in layout and energy. In principle, for an observer watching from before the ring was rotated, the difference would be observable, because the rotated ring would try to un-rotate whereas the anti-neutrino would not.

In addition to defining colours, we need to define anti-colours. When the asymmetric meon, or symmetry line, of an anti-loop is at position 1, 3 or 5, these are defined as anti-green, ant-red and ant-blue. The anti-loop will be coloured g-1, r-3 or b-5. In this way, a loop and anti-loop rotating J + ½ will have opposite charges and opposite sign meons at each point 1 to 6, which will allow the formation of a colourless photon from a coloured loop and its anti-coloured anti-loop.

But symmetry shows that there will also be opposite colours shown by the meons at the opposite point on the loop, through which the line of symmetry also passes. So loops will be anti-coloured when the asymmetry positions are at g-4, r-6 and b-2, and anti-loops will be coloured with the symmetry line or meon positions at g4, r6 and b2.

The result is that for all loops there are 24 different combinations of point/line of symmetry (Each loop or anti-loop, M or M at 3 coloured or 3 anti-coloured positions) for J + ½ spin/rotation.

To consider the interaction of symmetry between J = + ½ and J = - ½ rotation loops we need to define how to achieve the change, the flipping over of the loop or ring, remembering that each change of planar orientation of the asymmetry of a ring is defined as a different colour/anti-colour. The simplest definition is that the loop should be flipped over through its line of symmetry, with the point of symmetry (if on a meon) kept at the same position number. But we need to define how we think that the asymmetries of a J + ½ loop interact with the asymmetries of a J – ½ loop. Our hypothesis is that they act exactly as if they were rotating in the same way rather than opposite ways, provided that the two loops are the same size. This is because, when the loops are the same size, the lines of asymmetry will coincide twice as often as the loops’ frequency, but will retain the same overall lines of asymmetry in the combination. After one rotation of each loop, the relative positions of the lines of asymmetry are unchanged, although they will have crossed after half a rotation. So whether the loops are rotating in the same way or opposite, in a stack of same-size loops, the lines of asymmetry of the combination will be retained. At the moment, we are not concerned with how long it takes to flip the ring – which will involve a change of relative phase – only the definition of the end result of a flip.

Although there are now 48 possible orientations for each loop, only 24 need be considered when combining with other loop orientations. However, it is still necessary when considering the combinations, to define ring and anti-ring in a systematic way. This means that we have to redefine for this consideration of symmetry what is currently considered the particle and which the anti-particle in our four quark and lepton rings. We have chosen that the ring is the positive charge variant and the anti-ring the negative charge variant. This simplifies the combinatorial work involved and allows summaries of what combinations are possible to be drawn on a consistent basis. So when discussing the combinatorial permutations of rings or loops, we mean e+, u+, d+ and n (latter is with +cq/6 on position 1, 3 and 5 for both M and M isomers). When discussing anti-rings or anti-loops we mean e-, u-, d- and n (latter is with +cq/6 on position 2, 4 and 6 for both M and M isomers). However, this definition is not used in any other considerations in this paper, it is used here solely to simplify the outcomes of stack combinations when considered from a colour perspective.

Considering what the loops actually are, it is obvious that the electron (S3) and symmetric n (Type n1, symmetry S3) are symmetric in all positions and will not change the symmetry of any other combinations of loops. So any combination of any coloured e+, e-, n1 and n1 will be possible with each other and with other loop stacks. Here the fact that they have S3 symmetry does not mean that they do not ‘feel the coloured force’ in current parlance, but that they do not affect the symmetry of an existing stack and so cannot be used for balancing asymmetric stacks in order to make them symmetric. But they can join any stack that is already symmetric or replace a symmetric loop that is already in a stack.

Looking at the asymmetric loops, there are a number of different symmetries present. The u+ are all A3 symmetric of the form - + + + + + (meaning the line of symmetry is on a meon, with 3 possible colour positions) and type U. The d+ of the form - + + - + + is defined as type D2 with symmetry A2, M2 (meaning that there are two lines of symmetry, one is 2 symmetric on a meon and one 3 symmetric between meons). The d+ of the form + - + + + - is type D1 and the symmetry is A2 only. The d-, type D3 is M3 only, being of form - - + + + + .

There are three neutrino isomers, n1 we have met, is S3 and of the form + - + - + -. The isomer n2 is + + - - - + and is A2 symmetric only. The isomer n3 is + + - - + - and is non-symmetric, called N0.

In forming the possible symmetric combinations, using 2 or more asymmetric rings, all the asymmetric rings have been included. For 2 ring combinations, starting from 144 total different asymmetric ring orientations (24 each for U, D1, D2, D3, n2 and n3) there are 144 * 144 = 20,736 possible outcomes. The Appendix (A1) shows the identities of each orientation of the asymmetric rings.

In considering the outcomes, it is necessary to look at the relationships between the colours and the relationships between the rings, rather than the actual colours or rings, in order to simplify the results. So instead of listing all possible outcomes of, for example, u+ g1 (A3) d- r3 (A3) u+ b5 (A3), we have converted to c1, c2 and c3 for the colours and X Y and Z for the rings. This means that the three two ring combinations u+ g1 (A3) u- g-1 (A3), u+ r3 (A3) u- r-3 (A3) and u+ b5 (A3) u- b-5 (A3), can be simplified into the one group X X- c1/c1- (A3 A3), where X represents a generic ring and X- its anti-ring. This has converted colour symmetries into group colour symmetries where it is the relationship between rings and colours that matters, rather than what the individual colours or rings themselves are.

The result is that there are only 16 different sets of 2 rings formed from asymmetric rings that are overall symmetric. There are examples listed in the Appendix (A2).

6. 2-RING COMBINATIONS
The Appendix (A3) gives some examples of 2 rings symmetric combinations. Considering both Appendices (A2) and (A3), it can be seen that there are many possible particles made from these 2-ring combinations. For example, photons made from u+ u- c1/c1- (A3 A3), n n c1/c1 (S3 S3) or e+ e- c1/c3 (S3 S3). Depending on the definition of pions and gluons, which will be covered later, there are pions or gluons made from n n c1-/c1 (N0 N0). Note that the outcomes are both colourless and coloured. So colour is not a sufficient definition to say what can exist as a stable entity and what cannot. The symmetry of the outcome defines what can exist as a combination, and that combination could be coloured in our use of that definition. Another combination could be called a Zeron, being d+ d- c1-/c1- (A2, M2 ; A2, M2) which has no overall charge and couldn’t be used to change a colour. All of the 2 ring combinations can occur in both J = 0 and J ± 1 spin varieties, so photons, pions and gluons may differ only by relative rotational directions.

Note that there are no charged 2 ring combinations possible using asymmetric rings, except u with d of the same charge. Other than this, a charged ring of ± N cq (N>=1) can only be achieved using the symmetric S3 leptons. The Appendix (A3) shows some examples of the many ‘different’ symmetric combinations of 2 symmetric leptons. In this framework, the symmetric rings are all the same energy, regardless of colour (phase), so there are really not that many different symmetric combinations using S3 rings.

7. 3-RING COMBINATIONS
The Appendix (A4) gives the complete list of 104 different symmetric combinations of 3 asymmetric rings out of the total possible of 27,648 symmetric outcomes, a small fraction of the 2,985,984 possible 3-ring colour combinations. These do not include symmetric 2-rings made from asymmetric rings with an added symmetric third S3 lepton, which are also possible combinations that make a symmetric 3-ring stack.

Note again that the charges of these symmetric combinations are 0, ± N cq (3>=N>=1) only. There are no fractionally charged symmetric 3 ring stacks. Again there are both colourless and coloured symmetric stacks. Similar to the 2 ring asymmetric combinations, which did not produce any charged outcomes without using same charge u with d or symmetric leptons, there are combinations such as n u- d- c1/c2-/c3- (N0 A3 A3) which has a charge of -1 cq. On it’s own, this stack cannot be a charged pion. It requires a symmetric n1 neutrino to be added to the stack and the spins to sum to zero in order to become a charged pion.

Another example is the colourless anti-proton core made from d+ u- u- c1/c2/c3 (A3 A3 A3), which is what would be expected from current definitions of colour. It does appear here, but so do coloured proton core outcomes like u+ u+ d- c1-/c1/c2 (A3 A3 M3). From symmetry, every coloured ring can be swapped in the stack for its coloured anti-ring partner and the same colour grouping of the stack will be symmetric.

What this implies is that there are limitations on the outputs of interactions between stacks (particles) set by the symmetries and colours of the input stacks (particles). If 2 A3 rings and 4 N0 rings go in to an interaction, then that is what has to come out – even if other stacks become involved, the symmetry of their component rings must be accounted for.

MASS
In considering the number of different possible symmetric 2 and 3 ring combinations, it becomes apparent that, if the order of rings in a stack does not matter and all the rings in the stacks are the same frequency, there are very few different total mass sizes of symmetric stack. The Appendix (A5) shows the only 14 different mass sizes for 3-ring combinations that are possible, under the assumption of order independence and constant stack size. This is an area that will be considered further at a later date, but does hint that together with the limitations on input/output symmetries, there are very few building blocks that can be used to make the ‘normal’ particle stacks, like protons, neutrons and bosons. Appendix (A6) shows examples of the only 6 different symmetric 2-ring mass sizes, under the same assumptions. Appendix (A7) shows the first few hundred of the total 27,648 combinations of 3 asymmetric rings that make symmetric stacks.

8. PARTICLE TYPES
Having looked at the symmetries of 2 and 3 ring combinations, it is apparent that the differences between particle types can depend on as little as the relative direction of spin of two rings. So single rings are fermions. Two ring combinations are bosons and can be spin J = 1 or J = 0 depending on relative spin components. The precise character of J+1 combinations depends on the identities of the two rings. If they are ring and anti-ring, then the combination will be a photon. If they are not ring and anti-ring, the combination will be a meson. J = 0 combinations of ring and anti-ring are massless measured inside id/as, but have 2 m when measured from outside, leading to the existence of ‘massless’ particles that have mass. J = 0 combinations that are not ring and anti-ring will have masses and will have non-zero J spin energies because although their spin h momentum values may cancel, the energy of those spins hw will not because the masses of the two rings are different. No J+1 boson can be massless because a J + ½ ring is positive mass for each ring, regardless of the identity of those rings.

3-ring combinations could be proton and neutron cores, J + 3/2 symmetric stacks or temporarily excited electrons with a photon stacked. Higher ring combinations are like engineering Lego, dependent on smaller symmetric stacks in combination.

9. BOSONS
We now proceed to discuss the role played by the usual gauge bosons. Since the fundamental unit of electric charge is 1/6, the W± cannot act between single meon states. In fact the simplest boson with the quantum numbers of W+ (Q=1, J=1) corresponds to a state where two quark rings are stacked side by side, rotating in the same sense (eg both spin J + ½), such as W+ = u+ + d+. That is not to say that the sum of the masses of the quarks will be the same as the mass of the W+ because the stacking of rings can be longer than just the two needed for the correct charge and spin. The stack could be 2, 4, 6 or any even number of rings longer than the minimum required two. An example of a pair of rings adding to the externally observable mass of the composite but not adding charge or spin, would be an electron and positron, with opposite spins. Here the mass (ring frequency) of the e- and e+ may be changed, if the interaction during the formation of the stack has provided sufficient energy, and they may have larger or smaller masses than expected. Despite the sign of mass of the electron and positron here being opposite inside the id/a, an external observer will see an additional mass equal to the positive sum of the two ring masses.

What this suggests is that the W (and Z) bosons are not carrier particles that mediate the weak nuclear force, but composites of quarks and leptons that have a specific preferred size, charge and spin overall. Since the motion of the meons around the ring represents the mass size of the rings, there is potentially no need for a Higgs boson, and the mass of the gauge bosons not being zero is no longer a problem if they do not carry any forces. As we have already seen, the equivalent of a Higgs particle could be any isolated ring that has mass, in that it induces mass into neutrinos when they are close by.

To show how the carrier of the electromagnetic force, the photon, fits into this interpretation it is necessary only to consider what the photon would look like, based on the dynamics discussed above. The photon would be a stack of electron and positron, both spinning the same way. From the dynamics, the stacks would have each meon in one ring chasing its anti-partner in the other ring externally, as well as simultaneously chasing around in its own ring internally. The result would look like a single ring of six merged M and M meons. If we assume that the merger of M and M meons results in a zero-fundamental-mass black hole, then the photon has no mass, although it has energy in the w rotational motion of the meons and canceling twisting energies since, in our definition, both rings will be J + ½ , they will both appear to have +m inside their id/as. If the force of chasing between meons were opposed by some background viscosity of the universe, then the result would be a maximum speed that the ring would accelerate to in transverse motion, the equivalent of terminal velocity of a falling object in air, which we call the speed of light, c.

For photons, as combinations of ring and anti-ring, it is those with symmetric lepton components that are more likely to remain broken apart in any interaction because the asymmetric rings would be unlikely to each find an appropriate partner to stack with. As the colour symmetry section showed, and from a consideration of weak interactions, it is likely that quark and anti-quark are able to form photons. Most observations will be of leptonic photons, but many interactions require quark photons to be present. Photons do not have to be carrier bosons, but could be just manifestations of the combinations of rings present.

What is certain in this interpretation of fermions, bosons and rings is that rings are not usually broken. If a m- decays into e-, n and n, then this interpretation says that the n and n were already present in the stack that represented that particular m- and will have taken away some of the w present in the original ring combination or were present close by, in the form of a zeron, and were hit by the m- and broken apart, taking the excess energy above that required by the incoming m- ring, now in the guise of an e- . It could be that a p-, composed of a stack of e- and n, added a n ring, resulting in a J ± ½ m- . Alternatively the p- could be d- and u- stacked, with an added n , to produce the m- , but in this case when broken apart there would be no e- exiting. So this interpretation does not allow W+ to convert ne® e+, d- ® u+, u- ® d+, or e- ® ne. What it does allow is these rings to be stack components of the composite W+, which can be separated into the various rings in that stack. The result is the same, but the process is different.


Because the interpretation of rings interacting in stacks uses synchronicity of asymmetry in the rings as the equivalent of the colour force, there is no need for gluons to act between quarks. Provided the asymmetry of each of the quarks present in the stack is appropriately synchronized to maintain the stability of the stack, the stack will be stable. But not needing gluons does not mean that they do not exist. There are examples in Appendices (2) and (3) of gluons, in the accepted terminology of coloured and anti-coloured particles, comprising n and n spinning opposite.

The phase of synchronization of a ring is physically similar to having different times for different synchronizations. Even though the frequency w of the ring may be the same, changing the phase of that frequency requires a fractional change in the transfer of h across rings, which is not possible because, for the meons to have the same hw all the time the transfer must be in multiples of 6h. So the phase of a ring, at a specific frequency and a specific orientation in space, is apparently fixed permanently when the ring is first formed and this is its preferred frame of reference in which it is ‘at rest’. Any difference is opposed by the ring and shows as an energy or phase difference. As will be shown later, the flipping of a ring involves a change in its phase with respect to an observer, with four flips required to return the ring to its original energy.

10. BEGINNINGS?
The formation of rings is beyond this paper, but a possible route may be sketched out, based on the merger of meons within a photon. If the initial state of the universe is just innumerable zero-fundamental-mass black holes, then splitting these apart would see chains of meons chasing each other, attaching onto their own tails as loops, and Darwinian loop breaking into the most stable length loops. Note that the formation of loops provides a frequency framework, and from a frequency can be obtained time. So the implication is that there could be no time before loops formed, and the basis of our time and observational framework is the loops, or rings.

Once loops have formed six-meon rings, it is possible that abrupt physical interactions caused them to inflate from their formation size (around the adjusted Planck energy at r = Lo, the adjusted Planck length as initial ring radius) to their current preferred sizes, with one preferred size or resonance for each of the three space-dimensions, representing different inflation rates in each dimension.

11. PROTONS AND NEUTRONS
In the ring framework, protons and neutrons are simply longer stacks than those encountered so far, containing an odd number of rings. The main assumption for a long stack is that most of the rings, or component composite short stacks, in the stack have the same ring radius. Only temporary replacement or additional rings could be of a slightly different size and that difference in size might be a measure of the stack lifetime.

In order to show why the proton and neutron stacks are composed in the way proposed here, it will first be necessary to list some of the underlying assumptions (all numbers used are 2006 CODATA recommended values):
1. The magnetic moment of a ring is composed of two parts – one due to charge and one due to mass. The formula will be detailed later, but the two parts in all free rings are both separately equal to a new fundamental constant of nature L = ½ (h q/ 2p). This is why the electron has g=2 (plus anomaly). It has 2L of the product of charge and momentum, which will be called ‘charge momentum’. L appears to be the more fundamental driver for ring actions, and through it mass and magnetic moment are exchanged as rings change flavour. By breaking down the actions of the rings in a stack into terms of L, the structure of the stack can be confirmed.
2. Electrons, in the form of muons, are present in the nucleon stacks. The small size of the electron is normally taken to preclude its presence in the nucleus. But as a muon, it has sufficient mass, although in the stack it seems to be 0.113 MeV lighter. As will be shown later, the new formulation of magnetic moment implies that the electron, muon and tau are actually the same ring, but at different sizes. So discussion of the electron should now be taken to include muon and tau flavours.
3. Neutrinos are present in the nucleon stacks. There is a difference between the mass shown by a neutrino in a stack and when isolated, even when the neutrino ring radius is the same. When completely isolated, the ring will be symmetric with no external charge field. When such a ring passes by another ring with a charge or mass, it will be slightly distorted. This distortion will be observed as a small mass and magnetic moment. So almost isolated neutrinos appear to have small masses because there are other rings generating mass and charge fields and, as mentioned earlier, all these other rings could be described as Higgs particles as far as the neutrinos are concerned. The size of those fields will affect the amount of neutrino mass observed. In the case where the neutrino is in a stack, the mass effect will be a maximum and the neutrino is likely to show a mass of 100% of its ring radius. So a neutrino ring of around the size of the muon would be allowable inside the nucleus. Since we require an odd number of rings in a nucleon stack, the closest match is nine rings in the proton, each of ring radius that generates a mass of (938.272 /9 ) MeV = 104.252 MeV. Different length stacks are possible, but the minimum is five rings for both the proton and the neutron.
4. In a similar way to the electron, muon and tau being resonances of the electron ring, so probably are the neutrinos. But they appear not to be limited to only three sizes. The neutrinos seem to act to add or subtract ring frequency in interactions between rings. Where this occurs within longer stacks, mass looks like it is conserved. Where this occurs in shorter stacks (2 rings), total mass will appear to change although the actual total energy of the interaction, as measured in terms of momenta and ring frequencies, will not change.
5. Quarks in a stack will show 100% of their ring radius. Quarks outside the stack are expected to show a fractional mass proportional to their charge.
6. The different energies within a ring have different actions. These will be explained more fully later, but initially it is only necessary to mention again that some energies act only inside a specific distance and relative angle between ring planes, the influence distance/angle, of another ring. For such distance/angle-limited energies, it is necessary that both rings are within a mutual influence distance/angle from each other before they will affect each other. One example of a distance/angle-limited energy is the J spin of a ring. Charge is not a distance/angle limited energy.
7. The mass energy of a ring is equal and opposite to the J spin energy of that ring. Once again, it will be explained later that all energies in a ring have equal and opposite size partners, although the actions of those energies may be different. The energy of J spin of a ring is ½ h multiplied by the ring frequency. Thomas precession halves the externally observed ring frequency, but that J spin energy is equal and opposite to the mass of the ring h w. So a ring that has a spin of J+ ½ in a ring framework has a positive mass. A ring with a spin of J – ½ has a negative mass. However, whether the mass is positive or negative is only actionable inside the ring’s id. Outside the id, all that is observed is a mass size. This asymmetry of action of mass energy leads to structure at small distances and lack of structure at large ones – the formation of quantum based structures like atoms at short distances and of gravity based ones at large distances. The sign of mass at small distances is what differentiates the sign of magnetic moment of neutrinos in a stack and what builds stacks with alternating J+ ½ and J – ½ rings.
8. Because the main ring stacks are the same size in both proton and neutron, the energies of interaction between rings from stack to stack will be the same regardless of the identity of the stacks themselves. So whether an up quark in a proton stack is interacting with a down quark in a neutron stack or a down quark in another proton stack is immaterial, although the separation and relative orientation will matter.

With these assumptions, it is now possible to consider the values of the masses and magnetic moments of the proton and neutron, and to extend these later into other particle stacks.

Consider the standard formula for the intrinsic magnetic moment me of a spin ½ free electron (not its orbital magnetic moment) of mass me

me = ½ ge (½ h q / (2 p me)) (4)

where ge = 2.0023193043622(15) and is known as the most accurate agreement between theory and experiment in physics. In the ring framework, the same value is composed of two parts, that due to charge and that due to mass. Since the main consideration is of the positively charged proton of spin J + ½ , the electron will be considered to be J + ½ also. The overall magnetic moment of the neutron is negative, whilst the charged proton is positive, so the rotation of meons around the electron in J + ½ spin orientation will be assumed to give rise to a negative magnetic moment due to their generated mass, which is the same orientation as the negative charge circulating. Rearranging the expression above for the magnetic moment, and using g = 2 + 2 Ae, where Ae is the anomalous part of the g value, gives

me me/ (2 + 2 Ae) = ½ ½ h q / (2 p) = ½ L (5)

where L is the charge momentum as mentioned earlier and is a new fundamental constant of nature, albeit a composite. If the magnetic moment is now split into its two constituent parts, due to charge cq and mass m, so that me = meq + mem ,the equation becomes

(meq + mem) me/ (2 + 2 Ae) = ½ L (6)

(meq + mem) me/ (1 + Ae) = 1 L (7)

meq me + mem me = (1 + Ae) L (8)

Now the assumption is that the 1 and Ae are specifically due to the charge and to the mass respectively, so the relationship can be recast as

meq me + mem me/ Ae = 2 L (9)

which implies that each part of the equation is equal to L separately and that meq =mem/ Ae, so that Ae is a measure of the relative strength of the magnetic moment due to mass versus that due to charge at a specific ring (mass) size.

Although we imply here that Ae is due to mass, it may be that the underlying cause is a factor of induced mass and the distorted shape of the ring when close to other rings. The asymmetry would change the area of the loop and thus its magnetic moment. The greater masses/smaller distances in a stack could plausibly allow different values of Ae to those when free. The implication is that when completely isolated, the ring might have no Ae. So the inducing of mass or Ae by rings on each other could involve the transfer of L between rings.

The above formula needs to be adjusted for the fractional charges of the quarks, but the same fractional adjustment of the charge and mass, as already assumed, leads to the same outcome, that each quark has 1 L from charge and 1 L from mass, although the signs may be different. This is explained later. The question for the neutrinos is whether the same applies. Without any charge, it must be the case that they only generate magnetic moment when they have a mass, which is when they have induced mass when free or at a maximum when they are in a stack. So neutrinos have only 1 L of charge momentum, due to their induced mass when free or when in a stack.

The further implication of the above formula is that regardless of the size of an isolated ring, the product of its mass and magnetic moment due to charge is always the same. So an electron ring that has its size changed will have a different magnetic moment due to its charge, basically due to the change in area that the meons orbit around. This means that the mass and intrinsic magnetic moment of a ring are simply two different ways of expressing the energy of rotation of the meons around a ring. So mass is not conserved in interactions, although the product of mass and magnetic moment, representing the momentum of the components of the ring, will be, and there must be a similar change in ring frequency in any other rings taking part in the interaction to cause that change in ring size. It may look like mass is conserved, but it is ring frequency that is conserved overall.

The discussion so far has looked at free rings, those not in a stack, which have integer L. However, as will be shown below, because of the sizes used for calculating the magnetic moments of stacks, the stacks look not have integer L, but a different multiplier. However, when considered in the right units, integer L is conserved when in stacks as well.

Returning to the proton, it is assumed that it is composed of 9 rings (although it is possible to be any odd integer greater than 3 in this framework), of which three are the udu quark core. So the starting assumption is that the J spins alternate down the stack, with udu core and all masses (ring radii) the same. The only rings that are not charged are the neutrinos n, so it must be they and the anti-neutrinos n that populate the remainder of the ring This will be shown as

p+ Stack Spin Ring Mass Total Magnetic moment
à J + ½ n +mn -mn
ß J - ½ n -mn +mn
à J + ½ n mn -mn
ß J - ½ n -mn +mn
à J + ½ u+ mu +mu
ß J - ½ d- -md +md
à J + ½ u+ mu +mu
ß J - ½ n -mn +mn
à J + ½ n mn -mn

The resulting summation leads to a stack with a total J + ½ , magnetic moment of 1.410606 x10-26 JT-1 and mass of 938.272 MeV. Note that no allowance has been made for binding energy in stacks. The presumption is that a stable stack contains rings at internal separations that are stable, requiring no energy to bind them in place. The formation or break up of stacks may require/release additional energy externally. This energy is provided by/to external rings from/to either their motion or change in ring frequencies.

The neutron, in contrast to the proton, has a larger mass and decays when free. So it can have a slightly dissimilar sized ring temporarily. It may be that the ring becomes semi-permanent when the neutron is constrained within the nucleus, but that should not change the size of the main components of the neutron stack. This means that the neutron cannot be a dud J + ½ quark stack, because it would then be exactly the same mass as the proton. This also becomes apparent when considering the magnetic moment of the down quark – in a stack of any length, the total magnetic moment of the J - ½ down quark is always positive and always the same sign as the J + ½ up quark. So a J + ½ dud core, with positive magnetic moment, will have a negative overall magnetic moment for the whole stack due to the mass generated component, but not the right size. A J – ½ dud core, with negative magnetic moment, will have a positive overall magnetic moment due to the mass generated component. The solution is to replace a neutrino in the proton stack by a electron/muon, with its mass slightly larger than the stack rings. This will be shown by

No Stack Spin Ring Mass Total Magnetic moment
à J + ½ e- +me -me
ß J - ½ n -mn +mn
à J + ½ n mn -mn
ß J - ½ n -mn +mn
à J + ½ u+ mu +mu
ß J - ½ d- -md +md
à J + ½ u+ mu +mu
ß J - ½ n -mn +mn
à J + ½ n mn -mn

The resulting summation leads to a stack with a total J + ½ , magnetic moment of –0.966236 x10-26 JT-1 and mass of 939.565 MeV. The solution to these two summations leads to the following properties of the rings in the proton and neutron stacks, in p+ units:

Spin Ring Mass Total ring m
à J + ½ e- +me +105.545 MeV me -2.666388 x10-26 JT-1
ß J - ½ n -mn -104.252 MeV mn -0.289546 x10-26 JT-1
à J + ½ n +mn +104.252 MeV mn -0.289546 x10-26 JT-1
ß J - ½ d- -md -104.252 MeV md +0.513758 x10-26 JT-1
ß J + ½ u+ +mu +104.252 MeV mu +1.317062 x10-26 JT-1
à J + ½ -q bare mq 0 (stack size) mq -2.409912 x10-26 JT-1

These are split as follows between the charge and mass components that generate the total magnetic moments of each different ring type above as follows, remembering that the bare cq figure given is at the stack size 104.252 MeV, whereas the electron/muon in the stack is at 105.545 MeV and generates a smaller magnetic moment due to both charge and mass than it would do if it were the stack size:

Spin Ring Mass-generated m Charge-generated m
à J + ½ e- +me mem -0.285999 x10-26 JT-1 meq -2.380389 x10-26 JT-1
ß J - ½ n -mn mnm -0.289546 x10-26 JT-1 mnq 0
à J + ½ n +mn mnm -0.289546 x10-26 JT-1 mnq 0
ß J - ½ d- -md mdm -0.289546 x10-26 JT-1 mdq +0.803304 x10-26 JT-1
ß J + ½ u+ +mu mum -0.289546 x10-26 JT-1 muq +1.606608 x10-26 JT-1

Although the masses are shown as positive and negative, that is only the case when observed within the id/a of the stack rings. Outside the stack, all masses appear the same sign and have the same actions in attracting each other.

To some extent, this may also explain some apparent asymmetry of action of what is termed the electro-weak force. The proton J + ½ stack is capped at both ends by J + ½ rings. This could be expected to influence the surrounding environment, favouring the replacement of the end rings over others in the stack. Those J + ½ end rings could only be replaced by appropriate symmetry neutrinos or electrons. So the preferential observation of J + ½ electrons is because that is the only ring type that would bind in replacement for the existing J + ½ neutrino, forming the neutron. It is likely to be much more difficult to dislodge another stack ring. However, as will be shown later, there are also other factors providing asymmetry of ring interactions.

If 3 n, 3 n, 2u and 1d are summed, to produce a proton, the result will have a mass of 938.272 MeV and a magnetic moment of +1.410606 x10-26 JT-1, which are the accepted values. Replacing a n with an e-/m- produces a neutron with mass of 939.565 MeV and magnetic moment of –0.966236 x10-26 JT-1, again the accepted values.

Looking at the possible fractional parts of the stack, the most obvious is the n J + ½ and n J – ½ pairing, which has zero charge, zero spin and zero mass observed from inside its id, and will have a zero mass when completely isolated outside the stack. This pairing looks like a gluon. Note that the udu core is capped at each end by the n J – ½ part of the gluon pair, with the same sign magnetic moment as the two up quarks.


12. UNITS
The size and magnetic moments of rings have to be understood in the right units. The magnetic moment units used when it is in the nucleus are p+ units. When outside the nucleus, e- or m- units are used. But the magnetic moments are the same, in that translation of one to the other involves only adjusting the mass used – equivalent to changing the units. This can be shown in the following equal magnetic moments, considering for the moment only free electron and muon rings:

2 L = me me /(1 + Ae) = mm mm /(1 + Am) (10)
= me meq + me mem / Ae = mm mmq + mm mmm / Am (11)

Following the arguments above,
L = me meq = mm mmq (12)
L = me mem / Ae = mm mmm / Am (13)
meq Ae / mem = mmq Am / mmm (14)

The first equation (12) shows that the charge momentum generated by a ring due to its charge depends on the size of the ring, that is its mass. It shows that a smaller mass ring (with a larger ring radius) will generate a larger magnetic moment, and that the two properties are inversely proportional – if the ring size changes, then the mass and magnetic moment due to charge also change in order to keep the charge momentum at L. The second equation (13) shows that the anomalous magnetic moments, described by (1 + Ax) are not constant because they depend on the magnetic moments generated by charge and mass at each specific size of ring. The third equation (14) shows the relationship between those variables for the electron and muon. These equations could be used to predict the magnetic moment of the tau, although only the magnetic moment of the charge part can be predicted accurately without knowing the anomalous factor At. Assuming At to be 0.00116592069(60), the same as the muon, with the tau mass at 1776.99 MeV provides a predicted magnetic moment for the Tau of 0.267 x10 –26 JT-1. The basic implication is that there is only one charged lepton ring, which occurs in three preferred sizes, which we call the electron, muon and tau.

The situation for a stack looks different. Considering the situation for a muon in the stack and when free. The mass when free will be mmf = 105.658 MeV and when stacked mms = 105.545 MeV. The charge magnetic moment in each case will be mmqf = -4.485218 x10-26 JT-1 and mmqs = -2.380389 x10-26 JT-1, the latter as calculated using the relationships given above with the muon total magnetic moment of 4.490448 x10-26 JT-1. The ratio between the two charge magnetic moments is 0.530719 as quoted, but even adjusted to be for the same size ring is 0.537301. This suggests that the charge momentum of a ring in a stack is not L, as for a free ring, but will be 0.537301 L when the ring is the same size in both environments. However, as will be shown below, if each ring is considered in its own units, each charge magnetic moment in a ring will be shown to be L.

The situation for the mass-generated magnetic moments is similar, in that the two effects appear different in each environment. The mass generated moment for the free muon mmmf is -0.005236 x10-26 JT-1 and for the stack electron/muon mmms is -0.289546 x10-26 JT-1. The simple ratio between these values is 54.627 and the mass-adjusted ratio 55.304 with neither corresponding to any known ratio. Again, this is only a unit problem and if each ring is considered in its own units, each product of mass and magnetic moment in a ring will be shown to be L.

In order to understand the units, it is necessary to define the sign of L in a ring. In the case of the free J + ½ electron, both the mass and charge components of magnetic moment must be negative, so this sets the sign of each L in the ring to be negative as well. The formula to be used in the free environment, subscript ‘f’, to find the L value of a ring is

Lrf = mrf (mrqf qr /qr) +/- mrf (mrmf/Arf) (15)

where the ‘r’ subscript denotes ‘ring’ rather than the identity of the ring and the other variables follow the use seen earlier. The use of qr/qr is to show only that the fractional charges of some rings has been taken into account. The formula to be used in the proton stack environment, subscript ‘s’, is

Lrs = mrs [(mrqs qr /{ Rrs qr}) +/- mrs (mrms/(Ars{mp/mrs})] [mp/mrs] (16)

where [mp/mrs] represents the factor needed to translate the L value from stack units (generally the proton mp) into units of the ring under consideration and Rrs is the ring magnetic moment to nuclear magneton ratio of a ring in a stack.

Considering the free and stacked muon as an example, the two formulae can be used to find relationships between the charge and mass parts of the L components.

L = mrf (mrqf qr /qr) = mrs [(mrqs qr /{ Rrs qr}) (17)
L = mrf (mrmf/Arf) = mrs (mrms/(Ars{mp/mrs})] [mp/mrs] (18)
Rrs = mrs mrqs / (mrf mrqf) (19)
Ars /Arf = mrs mrms/( mrf mrmf) (20)

For the muon, using those variables already calculated above or taken from 2006 CODATA,
mp = 938.272 MeV
mmf = 105.658 MeV
mmqf = -4.485218 x10-26 JT-1
Amf = 0.0011659208
mms = 105.545 MeV
mmqs = -2.380389 x10-26 JT-1
mmmf = 0.005229 x10 –26 JT-1

the following values can be extracted:
Ams = 0.063696
mmms = 0.285999 x10 –26 JT-1
Rms = 4.712991

The ratio
mmqs/ Rms = mmms /(Ams{mp/mms}) = 0.505078 x10 –26 JT-1 = L / mp (21)

which is exactly the same as contained in the magnetic moment to nuclear magneton ratios of the proton and neuron, as given below and using their relevant magnetic moments, in p+ units. Thus

1.410606 x10 –26 JT-1/ 2.792847 = -0.966235 x10 –26 JT-1/-1.913043
= 0.505078 x10 –26 JT-1 (22)

For the neutrino and quarks, the relative variable values are
Rns = 4.712911
Rus = 4.712911
Rds = 4.712911
Ans = 0.063697
Aus = 0.063697
Ads = 0.063697
muf = mus 2/3 = 70.363 MeV
mdf = mds1/3 = 35.182 MeV
muqf = 6.818558 x10-26 JT
mdqf = -13.637115 x10-26 JT

What the extracted values say is that, on the assumption that each ring has ± L from each of the charge and mass contributions in a stack, the both the charge magnetic moment and mass-generated magnetic moment to R ratios of each ring are the same as the overall stack magnetic moment to nuclear magneton ratio. This ratio would be 1 in Planck units if the particle sizes were the adjusted Planck mass.

It is not possible to separate out the mxmf/Axf term for the quarks without knowing either their anomalous or total magnetic moments, but it is expected that the anomalous contribution will be small.

It is now possible to consider the values of L in a stack, based on the assumptions above and using ‘L’ to represent the charge momentum of a stack in multiples of L. For a neutron stack the split and total values of L (in each ring’s own units) are:

No Stack Ring L(charge) L(mass) L(total)
à J + ½ e- -1 -1 -2
ß J - ½ n 0 +1 +1
à J + ½ n 0 -1 -1
ß J - ½ n 0 +1 +1
à J + ½ u+ +1 -1 0
ß J - ½ d- +1 +1 +2
à J + ½ u+ +1 -1 0
ß J - ½ n 0 +1 +1
à J + ½ n 0 -1 -1
Totals +2 -1 +1

The values for a proton are similar, exchanging the muon for neutrino, and the totals are L(charge) = +3 L, L(mass) = -1 L and L(total) = +2 L. The total L(mass) is the same in both cases, because the electron has the same L(mass) value as the neutrino it replaces and all rings have the same L(mass) value in both stacks. By siting a proton J + ½ and a neutron J - ½ adjacent, the total L content of the two will be +2L –1L = +1L. This may be the way nucleon cores build up, by reducing the overall value of L to a minimum at each stage.

Note that the simple formula for the magnetic moment of a proton or neutron leads to the confusing suggestion that the value of L is different. Using

Mp+ mp+ = L fp+ and Mno mno = L fno (23)

implies that fp+ = 2.792847 L for the proton and fno = -1.915679 L (in No units) and fno = -1.913043 L ( in p+ units). However, these ‘g/2 values’ assume that the proton and neutron are not composites with different weighting for each component part and are consequently too simplistic. As has been shown, these values represent the unitised composites of the L values of the stacks, which can only be understood by separating them apart into charge and mass generated parts.

13. PIONS AND KAONS
In order to understand the stacks that form, the definitions of what actually are pions and kaons, for example, need to be widened. The framework proposed here does not suggest that a kaon is a specific set of rings in a stack, but that it is a stack whose external properties are constant whilst the components in the stack may vary. So, considering three related particles, the pion, kaon and eta, the framework would suggest that, although they have similar properties (apart from masses and the strange content of the kaon), the pion is composed of 2 or 4 rings, and the kaon and eta of 8 rings. So different particles are formed by extending the size of a stack.

To produce pion masses within 1/8 % of the actual observed values, it is necessary to propose that the stack neutrinos, for example, have a slightly different size when in a pion stack to that in a proton/neutron stack, and that there are other neutrino size resonances, the smallest called a ‘third-neutrino’, nt because its resonance is at one-third the mass of the new stack neutrino nn. This is not outside the framework that is being used in the paper because it is also proposed that quarks and anti-quarks form photons and it is the break up of these photons that provides the mass resonances that differentiate the flavours of the quarks. In the same way that it was shown that electron, muon and tau leptons appear to be all the same ring, but at different mass/magnetic moment resonances, the same is proposed for the quarks. So the basic particle stacks, composed of two rings, are expected to appear in sizes corresponding to their quark content following the interaction of quark-photons with other stacks. In order to produce a strange and anti-strange quark for interactions requires a photon that is composed of a down and anti-down quark that have been given enough energy, in terms of increased frequency, to become locked at the higher resonance of strange quarks. The decay of the strange particles in subsequent interactions could be via reformation of the strange photon or via the loss of frequency by the strange quarks, transforming rotational frequency into greater frequencies or velocities in other rings, reverting to their original base down quark/anti-quark status.

In the following section, the use of neutrino should be taken to include anti-neutrino where necessary, for instance in the case of forming a gluon from a neutrino and anti-neutrino, where the use of ‘2 neutrinos’ is shorthand.

In addition to the third-neutrino mentioned above, there are other proposed sizes of rings in pion, kaon and eta stacks. These are 101.233 MeV (nn only), 67.489 MeV (u, d, e and n), 69.785 MeV (n, u and d), 33.744 MeV (the third-neutrino size, nt only) and 105.658 MeV (m free mass). Note that 67.489 and 33.744 are 1/3 and 2/3 resonances of the new stack size 101.233.

In the case of the pions, the p ± is expected to be composed of a muon at size 105.658 MeV plus a contra-rotating third-neutrino nt at size 33.744 MeV producing total mass 139.402 MeV, only 0.168 MeV smaller than observed. The p o is expected to be nn at mass 101.233 MeV plus contra-rotating nt, producing a total mass of 134.977 MeV, as observed, or 4 nt , with two rotating in each sense, giving rise to two photons on break up, which is the main decay mode. The four third-neutrinos stack has the same mass of 134.977 MeV as the two different neutrinos stack.

It is only possible to produce the correct values using quarks if the pions are treated as stacks where each ring is the same size. The implication would be that every ring would have a mass of 69.785 MeV in a charged pion stack and 67.489 MeV in a neutral pion stack. So there are multiple different ways to obtain what is called a pion using either 2 or 4 rings in a stack.

It is necessary to differentiate these short stacks into two groups, the pions and gluons. The pions, it is suggested, are composed of at least one charged ring and the gluons of only uncharged rings. So the neutral pion may be a stack of up quark and anti-up quark, each at size 67.489 MeV, or electron and positron, or down quark and anti-down quark, all at that same size. The charged pion may be a stack of up and anti-down quarks or anti-up and down quarks each at 69.785 MeV or a muon plus third-neutrino. When the stack breaks up, the ring frequencies (masses) become redistributed differently between the rings in the stack and the interaction.

The gluons are grouped in sizes using the possible neutrino resonances mentioned above. The four different gluons used to build the pion, kaon and eta are two third-neutrinos totalling 67.489 MeV, four third-neutrinos totalling 134.977 MeV, two 69.785 MeV neutrinos totalling 139.570 MeV and a mix of one neutrino at 67.489 MeV and one at 69.785 MeV totalling 137.27 MeV.

The eta and kaon stacks are presumed to be 8 rings long, composed of 4 short two-ring stacks. These stacks could be pions or gluons. The actual make up of the stack influences the outcome of the decay of that stack. But the make up of the stack changes as other rings interact with the stack as they travel. So a stack that starts as a 3 pion plus one gluon stack may interact with external rings to become a 2 pion plus 2 gluon stack. Because the sizes of the gluons and pions in each stack are generally the same (excepting only one temporary different component), the observable masses of the stacks are the same regardless of the identity of the ‘components’. But whether the decay products can be identified is expected to depend on the break up of the components made from charged rings.

The eta is also expected to be 8 rings, or 4 components, in length, but here each could be of mixed size 137.27 MeV, totalling 549.1 MeV, close to the observed value of 548.8 MeV. The components could be mixed gluons or mixed quark/anti-quark pairs. The maximum decay sees 3 pions and the minimum one pion, so in this framework the other components would be gluons.

The kaon is more complicated, but a consistent size of 155.9± 0.3 MeV for the strange quark is achieved when the neutral kaon is composed of 2 small components of 67.489 MeV, one large component of 139.570 MeV and the strange component (down plus anti-strange or vice versa) at 223.1 MeV. Assuming the down quark in the strange component is of size 67.489 MeV produces the strange mass at 155.6 MeV. Considering the charged kaon as two small components of 67.489 MeV, one medium component of 134.977 MeV and the strange component (up and anti-strange or vice versa) produces the mass of the latter at 223.7 MeV. Assuming the mass of the up quark is the same as the down quark in the neutral kaon (the same assumption as for the two quarks in the proton/neutron stack) produces the strange mass at 156.2 MeV. The average strange mass is 155.9 MeV as mentioned. This is almost exactly 50% larger than the proton stack size, which is the mass of the down quark in that stack.

Parity violation, using this framework, can be hypothesised to be simply down to the difficulty of observing the break up of the gluons from the stack, and the continual changing of the identities of the stack components. Here the difference between KoL and KoS may be only how many pions are in the Ko stack when observed. Only on decay is it likely that the charged components of the stack can be identified, but they could have been different immediately before decay. An example of each Ko stack would be:

KoL Stack Spin Ring Mass (MeV) KoS Stack Spin Ring Mass (MeV)
à J + ½ n 33.744 à J + ½ n 33.744
ß J - ½ n 33.744 ß J - ½ n 33.744
à J + ½ e- 33.744 à J + ½ n 33.744
ß J - ½ e+ 33.744 ß J - ½ n 33.744
à J + ½ e- 69.785 à J + ½ e- 69.785
ß J - ½ e+ 69.785 ß J - ½ e+ 69.785
à J + ½ s+ 155.9 à J + ½ s+ 155.9
ß J - ½ d- 67.489 ß J - ½ d- 67.489
Total J = 0 3 po 497.935 Total J = 0 2 po 497.935

The formation of other particles is expected to occur along similar lines, with different length stacks but using roughly similar stack and stack-resonance sized-rings.

14. ASYMMETRY
There are a number of sources of asymmetry. The first is in the charge momentum L of the rings. Using the relationship between the total L content and the contributions due to charge and mass respectively as Lt = Lq + Lm, rings can now be seen to form three distinct sets of L, regardless of J ± ½ values. Rings with negative charge have ± 2 L. Rings with positive charge have 0L. Rings with no charge have ± 1L.

In the negatively charged rings, the sign of Lm is always the same as that of Lq, so the result is always the maximum value of ± 2L. In the positively charged rings, the signs of Lm and Lq are always opposed, so always sum to zero. The neutral rings take the value of Lm only, and are thus always ± 1L .

So there is a built-in asymmetry in the nature of rings, which, although it could be considered as charge-driven, is probably driven by the existence of the mass-generated magnetic moment. This may strongly influence which sort of environment dominates in nature. Protons and neutrons could be considered as ways of hiding the zero L rings within stacks that have caps of 1 or 2 L, and themselves have overall total values of 1 or 2 L. But the formation of these stacks leads to positive charge domination in the environment where J + ½ spin characterises the end caps of the stacks. The negatively charged anti-up quarks do not need to be shielded because they have ± 2L, so the drive to form negatively charged stacks is not present. Similarly, the presence of free positrons is not favourable because they have zero L. So these factors may be what drives the preferred existence of positively charged and neutral stacks alongside free negatively charged rings, in a positive mass J + ½ environment.

Where the rings are completely isolated, and the assumption is that Lm = 0, the charged rings will all have ± 1 L and there is no charge preference in the local environment.

A second source of asymmetry is in the neutrino. The definition of the neutrino has been as M on position 1 in a J + ½ ring. The n has been defined as M on position 1 also in a J + ½ ring. Both of these have all meons twisting RHS. But from symmetry, there can also be n and n with all meons twisting LHS. Considering only the S3 symmetric isomers of the neutrinos discussed previously in relation to colour symmetries (other neutrino isomers will have the same effect described below, but to a lesser extent) we can label the RHS as na and the LHS as nb. It is obvious from previous discussion that only

na (J + ½) + na (J + ½) = g (J + 1) (24)
nb (J + ½) + nb (J + ½) = g (J + 1) (25)
na (J + ½) + na (+60o) (J + ½) = g (J + 1) (26)
nb (J + ½) + nb (+60o) (J + ½) = g (J + 1) (27)

When considering how na and nb travel, there is a difference. Using the general assumption that rings prefer to travel symmetrically with their planes of rotation perpendicular to their direction of travel, with the axis of rotation aligned along the direction on travel, the difference between na and nb is in the relative orientation of meon twisting versus direction of travel.

In na and na , with both J + ½ providing a LHS for the ring as a whole along the direction of travel, each meon is twisting with ‘front’ face inner section in opposition to the direction of travel. In the nb and nb , that inner section is twisting in the same sense as the direction of travel. This asymmetry of twisting-to-travel ( ‘ttt’) direction might have different effects in rings. If space were thought of like a screw thread along which a ring is travelling, an inner motion in the same direction of travel might be expected to help travel more than an opposing motion. The question is whether there is a difference between the inner and outer effects.

If there is a difference, then there will be a preferred ttt direction and a preferred type of na in motion. The non-preferred type would probably be locked away in lower velocity stacks. So there is a possible split in which types of neutrino are free and which in stacks, and a difference in their properties.

For the nb and nb , with J + ½ as LHS for the ring again, the inner/outer ttt effects are reversed, with inner edges moving in the same direction as the direction of travel. So the preferred type of nb in motion will be reversed from that for the na. For the J – ½ nb and nb, the ring travel is RHS and the inner and outer effects are reversed, with the outer edges moving in the same direction as the direction of travel, similar to the J + ½ na and na. The sets of possible variations are:

Neutrino type Spin Meon twist Ring screw inner effect outer effect set identity
na and na J + ½ RHS LHS oppose same A
nb and nb J + ½ LHS LHS same oppose B
na and na J - ½ RHS RHS same oppose C
nb and nb J - ½ LHS RHS oppose same D

So the identities of the neutrino sets which prefer to be in motion would be either A and D or B and C, depending on which of the inner or outer effects dominates the other. If the preference for motion were assumed to be as for set A, then A and D would be the two neutrino sets seen preferentially in motion. If now these sets based on na and nb were redefined in terms of n1 and n2 as follows

Neutrino type Spin Meon twist Ring screw inner effect outer effect set identity
n1 J + ½ RHS LHS oppose same A
n1 J - ½ LHS RHS oppose same D
n2 J + ½ LHS LHS same oppose B
n2 J - ½ RHS RHS same oppose C

then it would appear that a travelling neutrino would only be LHS and an anti-neutrino only RHS, although that would be to misidentify n1 as na and na and n2 as nb and nb. Similarly, the misidentification of n2 in stacks would suggest that only neutrinos were J + ½ and only anti-neutrinos J – ½. But in each case, what is neutrino and what anti-neutrino depends on very small differences. It would appear in both cases that it is the neutrinos that have J + ½ and LHS motion, with the anti-neutrinos having J – ½ and RHS motion.

The stack rings, if set B were to generate –1L, would suggest that set C generates +1 L, as expected. But for both to have -mm implies that it may be the inner/outer difference that defines the sign of induced mass and thus magnetic moment in the stack. The set preferences could also drive the environment to be one in which negative magnetic moment coupled with positive mass occurs in stacks.

What this suggests is that the identification of neutrino and anti-neutrino is open to further experimental observation to try to confirm that there are differences, as well as preferential identity sets in motion or stacks. But the framework suggested here is consistent with the magnetic moment framework above and the observed asymmetry in what are currently defined as neutrino/anti-neutrinos. In this framework, there is still symmetry in the rings – it is the identification of n and n that breaks the symmetry.

Further consideration of how loops first formed can provide another view on aspects of asymmetry. If a straight chain of six meons, all twisting in the same RHS sense with respect to its direction of travel along the line of the chain, is considered, constrained on a plane, it is apparent that a loop could be formed by the leading meon turning either to the left or right to join onto its own tail. If the chain swings right and forms a loop/ring, it will be a J + ½ ring and identified as a neutrino. If the chain swings left and forms a loop/ring, it will be a J – ½ ring and also identified as a neutrino. The difference is that the J + ½ neutrino has its meons twisting inner edge into the plane, whilst the J – ½ neutrino has its meons twisting outer edge into the plane. Any asymmetry in the preference of motion would be expected to affect which direction the resulting rings started to travel immediately after formation. If the preference is as has been assumed above, set A for motion (the two examples here are both na neutrinos), then the J + ½ neutrino would be expect to move upwards away from the plane, forming a LHS ring. The J – ½ neutrino would be expected to move preferentially downwards from the plane, again forming a LHS ring. But whether the rings are neutrinos or anti-neutrinos depends on the identity of the first meon in the chain, if that is defined as position 1.

If the chain were instead composed of LHS twisting meons, then the outcome would be preferred RHS neutrino/anti-neutrinos in motion in this framework. But with the definition used here, it is not the direction of twist that changes particle to anti-particle – although it does have that effect – but the swapping of M for M.

The energies of the newly formed loops/rings must be the same until they start their motion away from the plane, which breaks the symmetry. Flipping a ring over involves changing the J + ½ to J – ½ and the mass from positive to negative, as observed inside the id/a. It might be expected that to flip twice would restore the original ring, but the process of flipping requires time. If the phase change during the flipping process described earlier involves a change of h/2 of rotational equivalent, then the twice-flipped ring will be out of phase by h of rotation. This phase difference is equivalent to an energy difference and a second double flip will be required so that the ring will be 2h different to its original phase – which will return the meons to their original orientations, but rotated by 120o (due to the 6h of momentum in total in the ring) and currently not observable. The double flip effectively moves the M onto the M positions and vice versa and the second double flip is like moving the ring to a colour symmetric position of equal energy, but with each M back on the M positions.

Finally, considering asymmetry in photons, given all the different combinations considered for rings and their J spins, even with preferences for motion of some rings over others, there does not seem to be any reason why photons should not appear in both J + 1 and J – 1 variants. When considering the temporary excitation of electrons in ZEMP states, a J + ½ electron, which is positive mass, requires a positive mass J + 1 photon to boost it. Similarly a J – ½ electron requires a J – 1 photon to boost it. Possibly the excitation tends to excite the J + ½ ones preferentially. The alternative is that the positive charge, positive mass environment favours J + 1 positive mass photons, which are preferentially measured using J + ½ electrons. It is interesting to ask what would be the result of stacking a J - ½ electron with a J – ½ positron. Logically it should be a J – 1 photon. So fundamentally there does not seem to be any asymmetry in the anticipated existence of both J +1 and J -1 photons, except for the positive mass environment preferring positive J spin.

15. ENERGIES
So far the energies of the meons and rings have been skated over, with just sufficient information given to lead the arguments along. Now it is worth explaining all the energies contained within a ring, and how they are presumed to work. This section uses Planck units where c =1 PU of velocity, h = 1 PU of angular momentum and cq is the electrostatic charge e (written as cq not q, in order to match the mass energy treatment as shown later) equal to (a/(2p))½ cQo charge, where Qo is the Planck charge of 4.7013 x10-18 C with a the fine structure constant. Adjusted Planck units are used for mass and length. To convert to SI units, each time cq appears in a formula, the cq appearance must be divided by (G 10+7) ½ and other variables should be multiplied by the SI value of the appropriate PU variable, so that the mass of the electron me is 1.669753 x10-23 APU of mass and 9.109382 x10-31 kg in SI units, having been multiplied by the adjusted Planck mass 5.455526 x10-8 kg. Here v is the velocity of a meon around the ring when the ring is in a non-rotating stationary frame of reference.

There are expected to be 8 energies in a ring as follows:
1. Mo c2 the mass-energy of a meon. Can be positive (M) or negative (M) to define which type of meon is involved. Same types attract, opposites chase to maintain separation. Acts symmetrically in all directions.
2. Qoc c2 the charge-energy of a meon. Defined in this way to permit direct comparison with mass energy. Can be positive (cQ+) or negative (cQ-) to define which type of meon is involved. Same types repel and different attract. Acts symmetrically in all directions. Equal and opposite to the mass-energy of the meon (M+ equal and opposite to cQ+ within a positive meon, M- and cQ- in a negative meon)
3. Mo t2 = s c2 /6 the twisting mass-energy of a spinning meon, t the angular frequency or rate of twist in units of c. Can be positive or negative depending on screw orientation with respect to direction of travel inside the ring. Axis of spin always directed along direction of travel and meon always in motion with respect to a non-rotating centre of universe frame of reference (because the sum of all energies is zero in all rings, all points are valid centres of the universe) The same size for all meons and possibly responsible for the strong force acting between rings in nucleon stacks. Acts perpendicular to the plane of the ring, symmetrically falling off over distance/angle until the influence distance/angle is reached. Not a chasing energy. Same signs attract, unlike repel.
4. Qoc t2 = qc c2 /6 the twisting charge-energy of a spinning meon, can be positive or negative depending on screw orientation with respect to direction of travel. The same size for all meons and responsible for one-sixth the electronic charge. Acts symmetrically in all directions. Equal and opposite in size to the twisting mass energy of a spinning meon, but only equal in action when meons or rings suitably aligned and adjacent.
5. Mo v2 = Mr c2 the mass-energy of a meon and of the ring, equal to the motional energy, as explained later, of each meon travelling at v. Can be positive or negative, depending on meon sign, but always sum to zero over a ring. Acts symmetrically in all directions. It is necessary to choose an orientation from which to measure the rotational rate of the ring as positive, so that the mass of the ring will interact with other rings as if it were positive mass. The positive mass orientation has been chosen to be when the ring is observed to spin J + ½ . Inside the influence distance, this orientation will be apparent, but outside this distance, the sign of mass will not be distinguishable and all will act as if positive.
6. Qoc v2 the spin-energy of a meon and of the ring, equal to J+1 or J-1 depending on orientation of observation, but observed size reduced by ½ due to Thomas precession. This energy is equal and opposite to the mass-energy of the ring, with J + ½ observed being equal and opposite to +mr c2 the mass of the ring. Acts perpendicular to the plane of the ring, symmetrically falling off over distance/angle until the influence distance/angle is reached. Usually measured in terms of ± ½ h, but is actually the energy ± hw of the ring.
7. qc v2 F /(2p) the intrinsic magnetic moment-energy of a free ring, when F=1, due to the motion of its charge, but observed size reduced by ½ due to Thomas precession. Depends on overall charge of ring. Acts perpendicular to the plane of the ring, symmetrically falling off over distance/angle until the influence distance/angle is reached. Can be positive or negative depending on orientation of observation. May be altered when in a stack, when F is not equal to 1.
8. [Mo t2] v2 f /(2p) = [Mr c2] t2 f /(2p) = s v2 f /(2p) the intrinsic twisting moment-energy of a ring, due to the motion of its twisting energy, but reduced by a factor f depending on whether the ring is free or in a stack. Depends on overall mass of ring. Acts symmetrically in all directions, symmetrically falling off over distance/angle until the influence distance/angle is reached. Can be positive or negative depending on orientation of observation. Equal and opposite to the intrinsic magnetic moment energy due to charge motion, but only equal in action when rings suitably aligned and adjacent. The factor f may be a geometric construct dependent on the relative areas of the rings or meons on which the energy acts within the influence distance.

16. HOW ENERGIES INTERACT
The use of the phrase ‘sum to zero’ above has been a simplification. The actual interaction of energies required in order to keep the rings internally stable is not a summation of energies, but a product of fields of the form (1 – Gm/(r c2)) and (1- Nqc /(r c2) for mass and charge respectively. This is explained later in terms of clock rate changes in energy fields. Initially this will be considered for meon-meon interactions, but later it will be shown that the same mode of interaction can be used successfully to describe energies of interaction within atoms and between planets.

17. MEON – MEON INTERACTIONS
1. Mass Mo c2 and Charge Qoc c2 Using the numbering system set out when considering the colour framework, if the meon at position 1 in a ring, which is rotating clockwise in the direction of higher position numbers, is an M, then it will have a mass of +Mo and charge of +cQo. It’s charge will repel the meons at positions 3 and 5 and will attract those at 2, 4 and 6. It’s mass will attract the masses of the meons at positions 3 and 5, and will try to balance the meons’ mass interactions at positions 2, 4 and 6. Specifically, because it is charge-attracted by meon 4, it will equally mass-repel. For meon 2, meon 1 is charge-attracted but meon 2 is moving away from meon 1, so it will try to catch up – will be attracted. For meon 6, meon 1 is charge-attracted but meon 6 is moving towards meon 1, so it will try to move away – it will be repelled. In field terms, using eg M2 = G Mo/(r c2) and Q2 = Qoc c2 /(r c2) for meon 2, the energy-squared of meon 1 due to Mo and cQo energies is represented by

E2M(1)(MQ) = Qoc c2 Mo c2[(1–Q2)(1-Q4)(1-Q6)(1–M2) (1–M3) ( 1–M5)]/[(1–Q3) (1–Q5) (1–M4) (1 -M6)] (28)
= Q oc c2 Mo c2 (1–Q2)(1–M2) (29)

because in each case cQx = Mx in size. The energies of each of the other meons is identically the same, being directed towards the meon next in line in front of it as it travels around the ring. The (1-Qx) or (1-Mx) in the numerator equates to attraction whilst in the denominator represents repulsion.. So the energy of each meon in a ring of ring radius ri and frequency wi due to Mo and Qo energies, in terms of mass, is

EM(1) = Mo c2(1–M2) = Mo c2 – G Mo Mo /ri (30)
= Mo c2 - hwi (31)

directed towards the next meon in front. The Mo c2 part is the rest-mass energy of the meon itself, so the energy in action is only hwi, as discussed earlier. For each positive meon, hwi will be negative and for each negative meon, hwi will be positive, summing to zero over the ring but still ensuring rotation of the ring. No consideration given here to the effects of relativity on the energies discussed so far because the meons themselves are not affected by time since they have no framework within which to observe regular repeating events. Time becomes important at the ring level, where the rotation of the meons around the ring provides a timing signal for rings. This will be shown below when considering ring-ring energies.

2. s c2 /6 and qc c2 /6 The same argument holds for qc and s, which are counterparts to cQo and Mo respectively, except that there is no chasing component. Since all the meons are in the plane of the ring, within the ring the strength of s and its direction mean that it’s actions are equal and opposite to those of q. It is only outside the ring that s has it’s asymmetric action, perpendicular to the plane of the ring. So the energy-squared of meon 1 due to s and qc, using q1 = q c /(6 r c2) and s1 = G s /(6 r c2), and using an electron ring, will be

E2M(1)(sq) = {qc c2 G-½ /6} {s c2/6} [(1–s2)(1–s3)(1–s4)( 1–s5)( (1 -s6)]/[(1–q2)(1–q3)(1-q4)(1–q5)(1-q6)] (32)
= qc c2 G-½ s c2 /36 (33)
so that the ring is stable, the attractive and repulsive energies having cancelled out, with each meon having twisting mass energy equal to EM(1)(sq) = s c2 /6.

For an up quark, the energies will be individually different in whether they are attractive or repulsive, but overall they will give the same result. If the single asymmetric negative charge is on meon 2, the energy-squared for meon 1 will be

E2M(1)(sq) = {qc c2 /6} {s c2/6} [(1–q2)(1–s3)(1–s4)( 1–s5)( (1 -s6)]/[(1–s2)(1–q3)(1-q4)(1–q5)(1-q6)] (34)
= qc c2 s c2 /36 (35)

and each meon will have the same twisting mass-energy EM(1)(sq) = s c2 /6 as in the electron ring. This is the same for all rings internally. It is only when the s and cq energies of different ring types are considered externally that relative orientation and distance between rings need to be taken into account for s-s and cq-cq interactions. Here again, time is not included internally and relativity does not affect the energies involved. All rings are stable at all sizes.

The other four energies are not internal meon-meon energies, but are constructs due to the motion of the first four energies at velocity v around the ring. Although each meon has mr c2 and Qo c v2 individually, the internal effect is the same as for s and cq in that the two energies balance across the ring. These energies become important only outside the ring because in the frame of reference of the ring there is never any relative velocity between meons – except when changing ring frequency. So the v related energies only exist in external frames of reference, where the relative velocities of observers can change the observed v of the meons (although this doesn’t change the actual v with respect to the stationary ring frame of reference).

As has been detailed, for each energy of a meon, there is an equal and opposite energy. So, in an isolated ring, there should be no overall energy. However, the different ways in which the energies work, and the separation/alignment/presence of external rings makes the ring appear to have energy – but it is only the differences in actions of the energies at work. The isolated neutrino shows this. There is a rotational rate, but no observable mass until induced by other rings. It is the imbalance of external effects that looks like the ring has energy.

18. RING – RING INTERACTIONS
Using the same product of fields formulation, now adjusted for the effects of observation from different moving reference frames since the rings have timing signals, the mass and charge energies can be calculated for ring-ring interactions. For simplicity, the situation will be considered to be one where a ring and a central particle, a stack of rings, are outside their mutual id, so that only charge and mass energies act. These two energies cannot be treated exactly as before, in terms of energy-squared multiplication, because they are different in origination and size. So after an individual product of fields formulation, the resulting energies will be either added or subtracted depending on whether the energies are attractive or repulsive.

The system considered is, for simplicity, only one moving ring of mass m and charge cq and one stationary particle of opposite charge Ncq and mass Mp. The use of radius r is a simplification, since for orbitals the motions could be ellipses. But elliptical motion does not change the principal energy levels considered here. As explained later, 3-vector notation should be used, rather than 4-vector notation, but additionally this has been simplified to scalar notation because directionality is not an issue for energy levels and the only forces considered are radially inwards towards, or outwards from, a stationary central particle.

The use of m within the equations is also a simplification, since the reduced mass Um = m Mp/(m + Mp) is more correct in considering energy levels. However the equations would then become very messy, and the values of v and r do not in any case change in the frame of reference of a stationary central particle, which is what is used in this paper – stationary with respect to the universe.

Also used for simplification, 1/(1 – v2/c2) ½ = g when v here is the orbital velocity of the ring around the central particle and each energy formula has dimensions of mc2 or cqc2.
So the total mass-related energy of the ring Emt will be

Emt = g m c2 (1 – GMp/rc2) (36)

= mc2 [g – g GMp/rc2)] (37)

= mc2 [ (1 + { g -1}) – {GMp/rc2}(1 + { g -1}) ] (38)

so that, defining the following

ERM = mc2 rest mass energy (39)

EKE = mc2{ g -1} » ½ mv2 kinetic energy (40)

EPE = GMpm/r mass potential energy (41)

ESPE = [GMpm/r] { g -1} mass orbit interaction (42)

The total mass-related energy of the ring is now

Emt = ERM + EKE - EPE - ESPE (43)

We need to define a new energy, EME the motional energy, where EME = m v2, so that the energy can now be given as

Emt = mc2 [ (1 + {{g -1}-v2/c2}) – {GMp/rc2}[{1-v2/c2} +{ g -1}]] (44)
= ERM + (EKE - EME) + (EME - EPE) - ESPE (45)

Similarly for the charge energy, the energy of the ring Eqt will be

Eqt = g cqc2 (1 – Nqc/rc2) (46)

Defining the same set of energies as for mass-related break out

ERQ = cq c2 rest-charge energy (47)

EKQ = cqc2{ g -1} » ½ cqv2 charge kinetic energy (48)

EMQ = cq v2 charge motional energy (49)

EPQ = Nq2 c2/r charge potential energy (50)

ESPQ = [N q2 c2/r] { g -1} spin orbit interaction (51)

The total charge energy of the ring is now

Eqt = ERQ + (EMQ - EPQ) + (EKQ - EMQ) - ESPQ (52)

The introduction of a motional energy is not arbitrary. It represents the normal force equation for two orbiting particles multiplied by their separation. Usually this is not regarded as the ‘energy’ of the system. Instead the factor of ½ mv2 is considered to be the energy and is called the kinetic energy of the system. However, as seen in the Hydrogen atom, that energy is negative. By introducing motional energy, the result is that the term (EKE - EME) in a mass-energy only system is negative, approximately – ½ mv2 and the term (EME - EPE) becomes equal to zero in all such stable orbits. This latter point is crucial, because it defines the energy levels for quantum systems when considering systems with both mass and charge energies.

Now the two energies can be combined to consider the whole energy of the system. If the system is considered to be electron and proton, then both mass and charge actions will be attractive, so the energies need to be added, giving a total energy Ett of

Ett = g [mc2 ( 1- GMp/rc2) + cq c2 (1 – Nqc/rc2)] (53)

= mc2 [ (1 + {{ g -1}-v2/c2}) – {GMp/rc2}({1-v2/c2} + { g -1}) ] +
cqc2 [ (1 + {{ g -1}-v2/c2}) – {Ncq/rc2}({1-v2/c2} + { g -1}) ] (54)


= ERM + (EME - EPE) + (EKE - EME) - ESPE +

ERQ + (EMQ - EPQ) + (EKQ - EMQ) - ESPQ (55)

Because v here has to be the same in each case, since the system has both charge and mass energies, the definition of the zero energy of position and motion states, each a ‘ZEMP’, here will be that the energy of a stable orbital state with principal quantum number n, ESOn, is

ESOn = EMEn - (EPEn + EPQn) = <ZEMPn> = 0 (56)

What has been implicitly lost is the charge motional energy in the balance of motional versus potential energies. In the two-energy system, the velocity v is different to that in either one-energy system and the charge motional energy is absorbed by that change in velocity.

By gathering together some of the energies in a different way, we can define two composite energies that represent the energies which are usually observed in such a system. Firstly the orbital energy EORn is not given by just the kinetic energy, but is given by

EORn = (EKEn-EMEn) - ESPEn - ESPQn (57)

= mc2 [ -vn2/c2 + (g n –1){1 + vn2/c2 }] (58)

which is the energy associated with the relativistic Dirac energy levels of a one electron Hydrogen atom [6], ignoring all quantum numbers except principal quantum number n, usually presented in simplified form as

E » - ½ m vn2 [ 1 + vn2{1 – ¾ }] (59)

Secondly the magnetic energy EqR is given by

EqR = (EKQn – EMQn) = (g – 1 – v2/c2) cqc2 (60)

which is the energy associated with the magnetic moment me since

EqR » -½ cqv2 = -me c w (61)

in the same way that EOR represents the energy associated with the angular momentum (apart from the inclusion of ESPQ as part of EOR).

So the total energy of the particle in a stable orbit is given at all n states precisely by

Ett = ERM + ERQ + EOR + EqR + <ZEMP> (62)

= mc2 + cqc2 + mc2 [ -vn2/c2 + (g n –1){1 + vn2/c2 }] + (g n – 1 – vn2/c2) cqc2
+ <ZEMP> (63)
= rest-mass energy + rest charge energy + Dirac energy states
+ magnetic moment energy + QM states (64)

This is a pleasing result, the derivation of which has given some clarity to the relationships between different energies within the total energy.

A ZEMP can be described exactly now, for a two-energy attractive electron-particle system with relative velocity vn at orbital radius rn, as

<ZEMPn> = me (vn/n) (rnn2) wn - (GMpme/rn + q2 c2/rn) = 0 (65)

This is the basis of quantum mechanics, where nh/(2p) = me vn rn. This should be compared with the dynamics of the meons in a ring where h = Mo vi ri from above.

In stimulated emission, it is possible temporarily to increase the energy of an electron in a ZEMP orbital by stacking a photon with appropriate energy on the electron being excited. The photon thus stacked will demerge into electron and positron, but the electron cannot long stay in the new orbital because it has energy above zero. It must emit the photon in order to return to zero energy and the original ZEMP state. In order to permanently change the ZEMP state of an electron requires the change of both motional and potential energy equally, changing the balance of those energies but keeping the sum at zero.

19. RELATIVITY
Earlier it was skipped over why the 4-vector notation was not being used here, in what is supposed to be a relativistic treatment. When considering the special relativistic derivation of energy [7], no account is taken of the presence of a gravitational field. Even standard relativistic treatments [8] simply add in gravitational potential fields. The Dirac equation extended for electromagnetic fields does the same and ignores gravity completely [9]. The move to curved geodesics and curved space time, the Geometric Formulation (GMF), overcomes these simplifications, but loses understanding because it deals with four dimensions in general and complex terms and describes a path over time, without initial conditions, rather than energy levels at any specific time [10].

This paper started the consideration of ring-ring interaction energies by simply defining the relativistic mass in product of fields formulation for gravity, followed by extension to charge, but with the GMF ontology of space-time EKE = (g -1) mc2 [11]. Now the formulation of special relativity in an inertial frame of reference (IFR) needs to be considered to see how the effect of a gravity or mass field might enter.

If a standard special relativity system is considered, there is an IFR within which there is a flat stationary mirror off which a light beam is bounced. The stationary observer sees the beam reflected back directly. The moving observer sees an angle between the incident and reflected beams. The result is time dilation of the moving reference frame containing the moving observer.

To correctly include the effect of gravitation, it is necessary only to replace the flat mirror by a large spherical mass with a mirrored surface, the observers by very small mass clocks and to constrain the distance between the observers and the surface of the large mass to be so small that the gravitational field is constant over the distance that the light beam travels. This is the equivalent of speeding up the clock in this specific location by (1- GMp/rc2)-1 [12]. This is identical to reducing the energy of any particle at that point by (1-GMp/rc2).

Although strictly this system is not an IFR, if the distances over which the event occurs are small enough that the gravitational field does not change (using a ‘short light beam’, called a limited general relativistic or LGR system), then that field acts only as a constant extra energy for the whole system comprising the mirror surface, light beam and the observers, and will not change the relationships between the observers and light beam, beyond providing a constant multiplication factor. In the case of a stable circular or spherical orbit, where r is constant, this extends the applicability to the whole of that orbital path.

It could thus be argued that the 3-vector form (simplified into scalar notation) used here is appropriate, rather than the normal 4-vector form used in relativistic dynamics, because the clock adjustments used in the fields method in equations (36) and (46) above act to eliminate the curvature of space-time due to mass or charge energy, to the extent of the system under consideration.

However, the short light beam argument means that LGR only applies to systems within which the fields can be considered to be unchanged, over the system, and at a specific time. Appropriate systems include all stable orbits, so planets and electrons are covered. But the development of non-stable orbit systems requires the fields to change over time, which is precisely what GR does so well, although for gravitational fields only, but in which there are no stable orbits and so no ZEMPs. So GR in its 4 vector form cannot ever include charge-bound QM states, whereas LGR includes QM states, but not development over time. This would seem to imply that there should be some way of combining LGR and GR in a meta-formula that would describe both instantaneous energies and development of states over time.

In a one-energy only situation, such as a planetary system, the equation used is the first mass-energy one

Emt = mc2 [ (1 + {{g -1}-v2/c2}) – {GMp/rc2}({1-v2/c2} + {g -1}) ] (66)
= ERM + (EKE - EME) + (EME - EPE) - ESPE (67)
where
ESPE = [GMpm/r] {g -1} (68)

is the mass orbit interaction energy that has never been proposed. It is similar to the spin orbit interaction in a charge field. The size of ESPE is such that it would have produced acceleration towards the Sun, at the distances at which Pioneer spacecraft have been moving for the last few years, of 1.5 x10-13ms-2. This compares with the anomalous acceleration observed for the Pioneers of 8.7 x10-8ms-2 [13]. The effect is too small to measure currently and cannot be used to explain the anomaly.

The maximum effect of ESPE on the orbit of Mercury would be observable in an extra excess precession of perihelion, above that provided by GR, that would be approximately 0”.11 (seconds of arc/century). This is a large fraction of the 0”.14 representing the current level of accuracy of measurement, and it represents 75% of the difference between the GR prediction (42”.98 ± ”.04) and the current central observation (43”.13 ± 0”.14) of the excess advance [14]. Adding this maximum extra factor would make the GR plus LGR central prediction of excess advance 43”.09 ± ”.15, providing a closer agreement between prediction and observation.

20. GENERALISATION PRODUCT OF FIELDS METHOD
In order to calculate the effects of charge and gravity on a particle by other particles, the generalised version of the total energy Ett must be used. The moving particle’s apparent rest-mass and rest-charge energies are adjusted identically for velocity fields and differently for gravitational and charge fields, giving

Ett = mc2 {[ P g k ( 1- GMk/rkc2)] [ P g i ( 1- GMi/ric2)] [ P g j ( 1- GMj/rjc2)]}

+ cq c2 {[ P g i( 1 – cNiq/ric2)] /[ P g j(1 – cNjq/rjc2)]} + <ZEMPn> (69)

where P g k ( 1- GMk/rkc2) is the total gravitational field acting on the particle due to the distribution of uncharged masses Mk generating a gravitational field at distances rk from the particle under consideration and moving at relative velocity vk. P g i ( 1-cNiq/ric2) is the total field of the attractive charge distribution of the i particles and P g j (1 - cNjq/rjc2) the total field of the repulsive charge distribution of the j particles and Mi and Mj are those particles' respective masses. Each product is defined to include all particles from i=1, j=1 and k=1 to the maximum number of particles present i, j and k respectively. The charges do not have to be coincident with any central particle.

Comparing this with the current treatment of fields, using a system with no overall charge (i = j = 0), all particles under consideration stationary (gk=1) and each GMk/rkc2<<1, the energy of a mass m will be

Ett = mc2 [ P g k ( 1- GMk/rkc2)] (70)

» mc2 [1 - S (GMk/rkc2)] (71)

which, excluding the rest mass energy, gives

E (grav) » - S GMkm/rk (72)

which is the accepted treatment of the gravitational action of Mk masses at separation rk from a particle m. Thus the treatment proposed here gives the accepted treatment at low gravitational fields and velocities, but applies at all gravitational and charge fields and velocities.

There are limitations to be applied to rings in order to limit the maximum energy of a ring due to its relative velocity, or to limit the maximum size of a charge or mass field, with respect to an observer. Initially these are taken to apply only to one ring in motion with respect to a second particle that is generating charge and gravitational fields. These limits do not apply to the energies or charges of composite bodies like planets when considered as a whole, but will to their individual ring components. There are only three assumptions underlying these limits, which are:

1 The maximum observable mass energy of any ring in empty space due to its velocity relative to an observer is the adjusted Planck energy
Eo = mc2/(1-v2/c2)½ = Mo c2 (73)
Where m is the rest mass of the ring, v its velocity relative to an observer, c the speed of light and Mo is the adjusted Planck mass. This limit sets a maximum velocity vLGR(m) with respect to any observer that any ring can be observed to travel at as

vLGR(m) = c (1 – m2/Mo2) ½ (74)

The rest mass of the ring is the mass or size that it has in a frame of reference in which it is stationary. Were there any rings with rest mass equal to the adjusted Planck mass, they would not be able to be observed to move with respect to any observer.

2 The maximum gravitational moment due to any ring interacting with a particle is less than unity
1 > GMx/rc2 (75)

where G is the gravitational constant, Mx represents the total mass energy of the particle generating the gravitational field and r the separation of the test ring from the gravitational field-generating particle. This implies that a ring cannot get close enough to a particle for the gravitational field to exceed unity.

3 The maximum charge moment due to any ring is less than unity
1 > cNkq/rkc2 (76)

for any charged particle k at a separation rk of the test ring from the charge field-generating particle. The fields of attractively charged particles have the same effect as attractive gravitational fields, whereas repulsively charged particles have the opposite effect, as described earlier in equation (69).

With these three limitations the energies of any interaction can never reach an infinite value, regardless of how many masses are present.

21. QUANTUM MECHANICS
Using the equation

<ZEMPn> = EMEn – (EPEn + EPQn) = 0 (77)

= m (vn/n) (rnn2) wn - (GMpm/rn + q2 c2/rn) = 0 (78)

the energy of each state n sums to zero for motion and potential energy. Changes between each state n1 and n2 alter vn and rn for the orbiting particle, the size of balanced motional and potential energies, plus the other energies in the system. The absorption or emission of a photon, corresponding to a change in work, changes the ZEMP balance and the internal energy levels if the system as a whole changes with the arrival of the photon. If it does not change, the photon will only stack temporarily because it changes the energy of the electron away from zero, which it needs to be in order to remain within a ZEMP.

In every ZEMP the clock rate is the same, even though the clock effects of the external fields are present in the motional and potential energies, each contributing to one side of the balance of energies. Only when a photon is absorbed or emitted from outside the system will the external environment impact, in that the energy of the photon will appear higher or lower depending on the underlying motion of the particle/system relative to the observer. But when considering the ZEMP energy states in the frame of reference of the system itself, the external motion will not affect them.

The equation for ZEMPn is an expression of QM energy levels, although classically the gravitational potential energy is usually ignored, and represents the quantisation of energy states. The energy of motion of the particle is positive, as required.

The quantisation really can be seen to arise from these ZEMPn, states which set all stable orbits at the same total energy, so that to have different variable values, meaning different v and r, for the energy levels requires that ZEMPn be composed of multipliers which balance out across the whole equation, leaving the sum as zero, as well as retaining the appropriate angular momentum and v = rw for the particle. The lowest multiplier possible is n acting on the components in the way given in ZEMPn.

The ‘spookiness’ of QM can be construed as arising because the specific internal ZEMP state of the particle in the orbital, due to motion and position, has no energy. A particle having zero sum of energy due to motion and position can be anywhere within an orbital, provided only that those energies sum to zero. And provided there are no emissions or absorptions, the particle does not need any energy to move from one part of the orbital to any other part of that orbital. It may be this aspect that enables apparent superposition, where a particle appears to exist at all points of the orbital simultaneously, and that gives rise to spookiness.

22. CONCLUSIONS
Certain aspects of the standard model become clear in this interpretation, and there are obvious benefits:
(i) Since all rings are composed of 3 M and 3 M, there can only be single fermions with electronic charge ±1, ±2/3, ±1/3 and 0 and J= ±1/2, although stacks may replicate these.
(ii) Particles with J> |1/2| are composites with stacked rings.
(iii) Colour is a manifestation of phase difference between rings at the same rotation rates, both internally as degenerate states and externally in providing a balance of asymmetries.
(iv) Mass is the product of rotational frequency and motional momentum of the ring components, mediated either by the total electronic charge of the ring when isolated from a stack or by proximate neighbours, when in a stack.
(v) The fine structure constant, a , as the constant underlying electronic charge q, represents a standard rate of spinning of meons, here described as a function of t.
(vi) Three generations represent different ring sizes of the same particles.
(vii) Carrier particles do not have to be carriers and may only be transient composites.
(viii) No Higgs particle is required to generate mass.
(ix) The ring sizes may have been fixed by inflation.
(x) The observation of only the photon J+1 suggests that it is the use of ‘normal’ rings (i.e. e- J + ½ electrons) for observation that preferentially shows only half the actual entities present.
(xi) The requirement for synchronization infers that all rings within a stack, other than any temporary additions or replacements, should have the same frequency.
(xii) One possible solution to CP violation is that the KL and KS kaons are different in terms of their pion and gluon content, but are identical in terms of overall number of these components, but that the identity of those components changes as the stacks travel .
(xiii) The combination of M and M in photon rings looks like the underlying state of space before M and M were initially separated to start chain formation.
(xiv) No higher dimensions are necessary than the three observed and time is a construct of the rings once formed.
(xv) Neutrino oscillation is natural in this framework, with size resonances representing simply larger or smaller versions of the neutrino ring.
(xvi) Quantum mechanics is shown to lie at the zero energy of motion and position states of a relativistic framework.
(xvii) The ring framework, with three underlying assumptions, ensures that no ring can exceed the adjusted Planck energy and so no infinities are possible anywhere.

Needless to say, we have major difficulties, even with a fairly simple dynamical explanation.
(i) Quark confinement here represents only rings that can be synchronized.
(ii) Do the asymmetric rings that cannot find suitable partners to synchronize with form unquantised ‘lumps’ of matter that cannot easily interact with symmetric rings? Could they be dark matter?
(iii) The mass spectrum of quarks and leptons remains unexplained, beyond accepting that three different inflation rates set preferred sizes.
(iv) Why the isolated mass of the quarks and leptons should be a product of ring frequency and charge is not clear.
(v) The masses of the u, d and s quarks calculated here are not those expected using the MS quark mass scheme.

We conclude by returning to our original list of motivations. The scheme proposed here is extremely economical. It suggests that all of matter consists of only one fundamental entity, which is itself present as particle and anti-particle, and this underlies the existence of space. The related quantisation of quark and lepton charges is explained, the content of each generation appears naturally and the similarity between generations is obtained. The concepts of mass, electric charge, spin, time, colour, and flavour acquire meaning only at the level of the composite systems. The dynamics proposed may not be convincing, but does lead to some simple relationships that may yet be open to investigation, including the size of the rings.

REFERENCES

1 For an earlier consideration of a substructure, see e.g.: J. C. Pati and A. Salam, Phys. Rev. DlO (1974) 275; H. Terazawa, Y. Chikashige and K. Akama, Phys. Rev. D15 (1977) 480; S. L. Glashow, Harvard Preprint HLJTP-77/A005; Y. Ne'eman, Phys. Lett. 82B (1979) 69; G. 't Hooft, Proceedings of the Einstein Centennial Symposium, Jerusalem (1979). The fundamental building blocks in these papers are called, respectively, prequarks (or preons), subquarks, maons, alphons and quinks.
2 For a review see e.g., H. Harari, Phys. Reports 42C (1978) 235.
3 Recent publications include: V. N. Yershov, Focus on Boson Research, Ed. A.V.Ling, Nova Science Publishers (Hauppauge NY), 2006, 131-181 arXiv:physics/0301034v2 [physics.gen-ph] ; V. N. Yershov, Physica D 226 (2007) 136-143 DOI: 10.1016/j.physd.2006.11.009 arXiv:physics/0603054v2 [physics.gen-ph] ; Sundance Osland Bilson-Thompson, arXiv:hep-ph/0503213v2 ; Sundance O. Bilson-Thompson, Fotini Markopoulou, Lee Smolin, arXiv:hep-th/0603022v2
4 Particle Data Group: hyyp://pdg.lbl.gov/2005/listings/qxxx.html
5 Tevatron Electroweak Working Group: http://arxiv.org/abs/hep-ex/0603039
6 R. M Eisberg, Fundamentals of Modern Physics (John Wiley & Sons, Inc., New York, 1961), p356
7 Einstein, Albert Annalen der Physik 17: 891-921.
8 R. M Eisberg, Fundamentals of Modern Physics (John Wiley & Sons, Inc., New York, 1961), p35
9 R. M Eisberg, Fundamentals of Modern Physics (John Wiley & Sons, Inc., New York, 1961), p356
10 M. V. Berry, Principles of Cosmology and Gravitation (Institute of Physics Publishing, Bristol and Philadelphia, 1993), p47 – 53
11 Gary Oas, “On the abuse and use of relativistic mass”, http://arxiv.org/abs/physics/0504110 v221 October 2005
12 M. V. Berry, Principles of Cosmology and Gravitation (Institute of Physics Publishing, Bristol and Philadelphia, 1993), p46
13 J. R. Brownstein and J. W. Moffat, Class. Quantum Grav. 23 (2006) 3427-3436 (Preprint gr-qc/0511026)
14 Anderson J. D. at al: Recent Developments in Solar-System Tests of General Relativity. Proc. Sixth Marcel Grossmann Meetin. Worls Scientific, Singapore (1992)

[mike@mlawrence.co.uk]

Apologies, but the equations didn't come out very well above. I should have attached the file as a pdf. Also the short version didn't post. For the pdf, please go to www.pbtsm.co.uk and click on Preon Model. I'll repeat the short version that didn't get put up.

Ring Theory in a Nutshell

Assume the universe is composed only of Planck unit-sized volumes of nothing; but that each unit volume is separable into preon particle and anti-particle of equal and opposite Planck charges and Planck masses. Assume that like charges repel, unlike attract and that like masses attract and unlike chase to maintain separation and energy. Assume that as unit volumes are separated out, each preon starts spinning at the same rate.
Chasing will cause the formation of chains of alternating particle and anti-particle, each chasing the one in front and chased by the one behind. Chains will eventually form loops as heads catch tails. A loop of six is the strongest configuration, which will break any other sized loop and will become the only size existing. Time starts when loops form and a loop of six is called a ring. Formation of rings at the Planck energy/Planck radius followed by physical interaction between rings could have expanded the rings to their present sizes very quickly, called inflation, without external motion of those rings.
If the orientation of the spinning axis of each preon is aligned with the chasing preon, there are only eight different electrostatic charge combinations possible for a ring of six preons when the preon spinning energy has a value of ± 1/6 qc3. The eight combinations represent the quarks and leptons. The rotational energy of the rings is currently called ‘spin ½ ‘ and is shown by the angular momentum h of each preon multiplied by the observational Thomas precession factor ½ , the ring frequency currently being ignored. The same internal energy is the ‘mass’ of the ring, being h multiplied by the frequency at which the ring rotates w. For each preon h = M v r inside the ring.
The constant ½ hq/(2p) is the same for all charged rings, due to charge and mass separately and shows that the muon and tau leptons are simply larger mass, smaller ring radius, electrons. The same is the case for families or ‘flavours’ of all rings.
The generation of magnetic moment due to both charge and mass enables a simple framework for the respective masses and magnetic moments of the proton and neutron.
The positioning of ± 1/6 q charges within the rings leads to symmetries. All charged leptons and some neutrinos are symmetric or ‘colourless’. All other rings are asymmetric, mostly with 3 and 2 fold asymmetries ie have ‘colour’. Stacking rings can balances out asymmetries between some rings, giving rise to 2 and 3 ring stack combinations that are overall symmetric or colourless. These combinations are always integer or zero electronic charge. Symmetric rings contain 3 fold symmetries, even though they are hidden, so electron and neutrino rings can exist in stacks. All isomers of each different ring have the same energy if they are the same ring radius.
A photon is a stack of particle and anti-particle ring, rotating in the same sense, where each preon has merged with its partner in the opposite ring to reform the original unit volume of space. Longer stacks include the proton and neutron of 9 rings and the stack framework enables the KL and KS to be the same mass and yet have different parities.
There are eight energies that exist within a ring, with four due to charge and four to mass that balance each other. Of each, two are due to the size of the preon and its spinning frequency and the other two due to these and the velocity of the preon around the ring. The measurement of the preon velocity (ring frequency) by external observers is what drives relativity.
In order for all rings to be stable, regardless of the different energies present, the energy of a body due to the presence of charge and mass must be increased or reduced using a ‘field’ formula on a product basis, not a summation of potentials, which also eliminates infinities. Identical treatment of mass and charge energies in this way leads to all the accepted energies of particle systems from atomic to planetary. The introduction of the concept of ‘motional’ energy enables the formation of zero energy of motion and position states (ZEMPs) where QM energy levels are replicated as one side of each ZEMP. Without energy, there is no time related to these states even though they exist within a relativistic energy framework.
As can be seen, the concepts of particle mass, electric charge, particle spin, time, colour, and flavour acquire meaning only at the level of the composite systems. For a ring, of observed mass mr composed of preons of mass ± Mo each traveling at velocity v inside the ring, Er = mr c2 = Mo v2.


Mike