Partons Reloaded: A Philosophical Thought Experiment on the Divisibility of Elementary Particles

Gábor BihariDept. of Experimental Physics, University of Debrecen, Hungary

Abstract

The following thought experiment is based on two basic assumptions. One of them is that all fundamental particles – leptons, quarks and bosons – are composite systems, which are held together by a probably yet unknown interaction. The electric charge of the fermions – namely 0, 1/3e, 2/3e, 1e – suggest that the number of their constituents is probably three. We call these constituents as partons. This presumption is sufficient to reconstruct the known particle families, whereas the heavier counterparts of lighter particles can be interpreted as excited states.

The other basic assumption is that beside the complex numbers, the quaternion and octonion number systems are perhaps necessary for the perfect description of natural phenomena. We suppose that the three colour charges of the strong interaction and the well-known electromagnetic charge are in fact the three imaginary and the real part of one single quaternion number, a quaternion charge.

Based on these two assumptions, by the help of pure logic and some simple physical and mathematical formulas, we can reach several interesting conclusions. In a universe, where the above assumptions are true, the fermions are made of three, while the bosons are made of six partons. Indeed there is a possibility for the existence of a heavy scalar boson, made of twelve partons. By investigating the interactions of these composite particles we have to conclude, that these partons are probably the same particles we know now as gluons. Due to the quaternion nature of charges, and the non-commutativity of quaternions, the interactions of these partons cannot be described by the normal exchange mechanism. Instead of that we have to suppose the existence of a simultaneous multi-particle interaction mechanism, with a chiral nature. This latter mechanism necessitating the existence of the angular momentum of composite particles, the spin. Another consequence of this new interaction mechanism is, that in some particle processes, where the interaction is forced to change direction, the parities of particles are not conserved.

The partons seem to be very simple particles: they can be fully described by one single octonion number, an octonion charge. They have no mass, spin, or any other feature. Since partons have no rest mass, the composite particles gain their mass by the kinetic energy of their components. In this view the composite particles – fermions and bosons – are small packages of partons, in which enormous forces are bounding the high energy partons that move at the speed of light. Since the source of the mass of the composite particles can only be the kinetic energy of the massless constituents, in the world of such particles rest mass isn’t exist at all. The two components of matter are the energy of partons and the partons themselves – particles, that are characterized by a single number, a piece of information.

Such initial conditions are causing an apparent asymmetry in the amount of matter and antimatter, although this asymmetry is only ostensible, as the balance of quaternion charges shed a new light on the problem. Nevertheless, in the partonic world the reactions and decay modes of composite particles would be identical to that of the observed world. The self-organizing nature of particles by the manifesting forces can be followed to the formation of atomic nuclei and atoms. Nevertheless, the neutrinos – made of three gluons – would have only imaginary characteristics, making them to be the strangest members of the particle families.

The Partons

Back in the 1960's Richard Feynman suggested that some properties of the neutrons and protons could be explained very well, if we assume that they are not elementary particles, but indeed complex objects. His theory is known as the parton theory, as he named the smallest elements of matter as partons. As the soon appearing quark-theory of Gell-Mann and Zweig explained the same properties of the proton and the neutron in a more detailed form, giving insight to the inner structure of these particles, so Feynman’s theory was indeed more or less incorporated into the quark theory.

As the collision energy of particle accelerators quickly increased, a large number of new particles discovered. Although initially they were called elementary particles, the quickly establishing quark theory classified most of them into the groups of composite particles. The quark theory has shown that these particles, the hadrons are doublets and triplets of only a few kinds of quarks. The ground and excited states of these doublets and triplets create the diversity of mesons and baryons.

However, Feynman’s parton theory is not perfectly equal to the later quark-theory. In Feynman’s theory the hypothetical partons are the basic constituents of every hadron. The partons are the ultimate ingredients of these particles – thus, can’t be divided further – so they are not necessarily on the same level of fragmentation as the quarks. The basic assumption of our current thought experiment is that Feynman’s partons, the most elementary components of matter, are not the same as Gell-Mann’s quarks. Indeed all the known elementary particles, including the quarks and the leptons can be divided further. From now onwards, we use the word parton in this original sense: not as a collective word for quarks and gluons, but as the basic components of all particles, including the quarks themselves and the leptons.

Fig. 1: The fundamental particles as we know them recently.

The currently known elementary particles form four type-groups. The two groups of leptons are either electrically charged or neutral particles: the electron, the muon and the tau particles are charged, while the other group, the neutrinos are neutral. Also, there exist two groups of quarks, bearing 1/3 or 2/3 portion of the electric charge unit. The main assumption of our current thought experiment is that all those particles, which we recently believe to be elementary, are in fact composite structures, composed of the smaller partons. If we finally get a contradiction, the main assumption was erroneous, the quarks and leptons are probably elementary particles. While if we do not face a contradiction, our assumption can still be erroneous, but in this case the consequences of the theory are worth to be compared to the experimental reality.

First of all, after supposing that the known particles are not elementary, we have to find out, how many partons they are made of? The most logical answer is three, as all the known particles have 0, 1/3, 2/3, or 1 portion of the elementary electric charge. All these numbers are multiple values of 1/3: multiplied by 0, 1, 2 or

3. Thus, supposing that there are electrically charged and neutral partons – having 1/3 and 0 electric charges respectively – it is easy to build up the quarks and leptons by selecting triplets of charged or neutral partons. If we choose three charged partons, the result will be a particle with 1 electric charge unit. If we select two charged and a neutral parton, we get the 2/3 charged quarks. Two neutral and a charged parton build up the 1/3 charged quarks. And finally three neutral partons create the neutral leptons, the neutrinos.

The partonic triplets created so, are explaining the different electric charges of the particle types in the above manner. Of course, we have to deal with the other interactions of these particles. Regarding the strong nuclear interaction, as far as we know, three different charges exists, all of which have their opposite charge. The interaction works between all the three and the opposite charges as well. Based on similarities, the three charges are named after colours, Red, Green, Blue, abbreviated R, G, and B. Thus, the opposite charges can be notated as Ř, Ğ, B̆ - these are the anti-colours. As the mixing of red, green and blue light creates white colour, so the RGB charge combination will be neutral in terms of the strong interaction. In the same way, the combination of anti-colours, ŘĞ will also be neutral.B̆ Not only these colour triplets, but the colour-anti-colour pairs are also neutral, just as in the case of the true colours. Because of the similarities, sometimes the anti-colour charges are nominated as Cyan, Magenta and Yellow, C, M, Y – these colours also give white when all three are mixed, or in the case of Red-Cyan, Green-Magenta, Blue-Yellow pairs. Though, for practical reasons, we use now the ŘĞB̆ symbols for the anti-colour charges of the strong interaction.

To minimize the number of basic building-particles, let us suppose, that the electrically neutral partons are not involved in the strong interaction as well, thus only the electrically charged partons have colour charge. This is a reasonable supposition as the only neutral elementary particles, the neutrinos does not show any little sign, that they are somehow involved in the strong interaction. In this way we suppose that there are charged partons that are involved in strong and electromagnetic interactions, and there are neutral partons that are not involved in these interactions.

Even though, it seems to be logical to suppose that the neutral partons are not involved either in the strong and the electromagnetic interactions, this condition creates a problem. We have seen that the neutrinos presumably are the combinations of three neutral partons. As this triplet is formed by some kind of interaction, we have to suppose the existence of a new kind of interaction. Obviously, the interaction bounding the three neutral partons together can’t be the strong or electromagnetic interactions: we have just now supposed that the neutral partons are not involved in those interactions. Thus we have to suppose the existence of a new kind of interaction: let us call it just simply as X-interaction.

In fact, the next step in this line of thoughts is that, we have to suppose: the charged partons are also involved in this new kind of interaction. Let us see for example the 1/3 charged quarks. These quarks are made of two neutral and a charged parton. Such a mixture of charged and neutral partons could be held together only if the charged partons are also involved in the X-interaction. There is no other force that can bind the coloured partons to the neutral ones. The case of the 2/3 charged quarks are also supporting the idea. There should be an interaction holding together the triplets of the two charged and the neutral partons. Thus, the existence of the mixed particles, the quarks, that are supposedly contains neutral and charged partons as well, makes it inevitable that all the partons are involved in this X-interaction. Thus, we can say, the only possibility to bond the neutral partons to the charged ones is the X-interaction, that works between all kinds of partons, regardless of their electromagnetic or strong charges.

We know one more thing about the X-interaction beside its universality. As it works between three partons, it should be similar to the strong interaction regarding its charges. As the strong interaction has three colour charges, so the X-force, that bond the neutral partons together, have to have three charges and their opposite charge-pairs as well. Let us notate these charges with the I, J, K letters, while the anti-charges will be Ǐ, , Ǩ. All of our partons, either the electrically-strongly charged or the neutral ones both carry these charges ofJ ̆

the X-force, which now seem to be a main factor of the bonding of elementary particles. This interaction is completely independent of the other interactions and holds together all kind of partons regardless of their other charges.

Summarizing these thoughts, we had to suppose the existence of a “charged parton” which involved in the strong, electromagnetic and the supposed X-interactions. Also there should be a “neutral parton” that is

involved only in the X-interaction. At this point we don’t deal with the weak nuclear interaction – we are going to see the reason soon. Regarding the mass of the partons, at this stage of out thread it is reasonable to think that the neutral parton have a much smaller mass, than the charged parton. The neutral parton involved only in the supposed X-interaction, and due to this, it has a weaker interacting field than the charged one. The weaker field means less energy and thus probably smaller mass. On the other hand, the neutrinos also support the idea of the light neutral partons. The neutrinos – which composed of three neutral partons – have a very little mass, compared to the charged particles. And if the neutrinos have a small mass, than probably their building blocks, the neutral partons are also light particles.

The following table shows the characteristics of the supposed partons:

Table 1: The partons, the existence of which is supposed in this recent thought experiment.

Assembling composite particles

Thus, we have two kinds of basic particles, a charged and a neutral parton, as well as their anti-particles. What kind of structures can we assemble together, if we assume, that three partons can form a composite particle?

First of all, we can assemble three charged partons. If we choose R, G, B coloured partons, than the composite particle built of them will be white – that is, beyond the scale of its size, it will no longer participate in the strong interaction. Nevertheless the electric charges of the constituents are adding together, so the composite particle will have -1 electric charge. In terms of the interactions, this system corresponds to the electron and its heavier counterparts, the muon and the tau particle.

If we choose three charged anti-partons as building blocks, the ŘĞB̆ combination will also create a colour neutral, white composite particle with a +1 electric charge. White means in this case again, that this particle will not interact with other coloured – strongly interacting – particles at a long distance, e.g. larger distances than its own size. Thus, this particle corresponds to the anti-electron, the positron. The electron or the positron assembled so, expectedly will not have a large mass: even though they are composed of the heavier, charged partons, both the strong and the X-interactions are bounding together these partons. Due to the strongest possible bonds, the bounding energy reaching its maximum in this case, and this reduces the mass of the composite particle to a low value.

Let us choose now, as the second possibility, one neutral and two charged partons. They will build up a particle with -2/3 electric charge. Contrary to the previous case, this composite particle won’t be „white”: it won’t be neutral in terms of the strong interaction, as it will contain only two colours, one colour will be missing for the „whiteness”, the neutrality. For example if the two charged partons of the system have R and G colours, than the composite particle will miss the blue B colour to be colour-neutral, to be white. We can say

that it has an anti-blue effective colour charge, as a blue coloured particle could neutralise its colour-charge. In the same way, if the composite particle contains G and B colours, its effective colour charge will be anti-red: Ř. While in the case of R and B, the result will be anti-green: R+B = Ğ.1 From the point of view of the interactions, this composite particle corresponds to the anti-up quark and its heavier counterparts. The anti-up quark has -2/3 electric charge and can have Ř, Ğ, B̆ anti-colour charges.

It is easy to find the corresponding anti-particle of this composite particle, if we substitute the partons with the corresponding anti-partons. Two charged and a neutral anti-parton will create a +2/3 charged, R, G or B colour-charged composite particle: this might be the up-quark.

The next step is to create a composite particle out of one charged and two neutral partons. As the two neutral partons do not engage in strong and electromagnetic interactions, the charges of the composite particle will be the same as that of the charged parton. Thus the electric charge of the composite particle will be -1/3, and the possible colour charges are the usual R, G, and B. This triplet corresponds to the well-known down quark. Naturally, its anti-particle is made of one charged and two neutral anti-partons: This system would have +1/3 electric charge, while the possible colour charges are the same as that of the charged anti-parton, the three anti-colours: Ř, Ğ, B̆. This system obviously corresponds to the anti-down quark.

Table 2: The table shows the possible triplets of partons. The triplets of three colour charged and three neutral partons exist only in one combination, while the mixed triplets exist in three versions, in three different colour. It is apparent that the triplets well correspond to the known particles and antiparticles. Nevertheless, in the case of up quarks and neutrinos antipartons are forming the particle and partons are forming the antiparticle. This observation leads to the conclusion that matter and antimatter are indeed in perfect balance in nature.

1 Indeed, we will see later, that it is better to describe these combinations of charges with multiplication instead of addition.

The only system left, we can create from the partons is the triplet of three neutral partons. The result is a composite particle which will not be involved in the strong and electromagnetic interactions. Let us call it anti-neutrino, as we will see soon, while examining the reactions of our partonic particle systems that it corresponds to the anti-neutrino, not the „normal” neutrino. The neutrino will be the trio of the three neutral anti-partons. The case is similar to the second composite particle, the up quark, where the three partons created the anti-up quark and three anti-partons created the up-quark.2

Particle families

Of course, the list of the possible partonic triplets does not end our thought experiment. In fact it is only the beginning. The experiments have proved long ago that there not only one charged lepton exists, but the electron has two heavier “brothers”, the muon and the tau particle, which have almost identical properties as the electron, except for their mass. They are quite like “fat bros” of the electron. The same is true for the two families of the quarks. The up and down quarks also have two heavier counterparts, the charm and top, and the strange and bottom quarks, respectively. There are also not only one but three kinds of neutrino: beside the electron-neutrino, there are the muon- and tau-neutrinos.

As all kind of particles have two heavier counterparts – that is, all particle systems exist in three different forms – it is a natural thought to suppose that the heavier versions are some kind of higher energy excited states. Let us see for example the case of the electron. If it really consists of three parts, there should be some kind of interactions bounding the parts together. If these bounds exist, probably these bounds can be loosened to some extent as well: thus higher energy excited states can be created. If we suppose, that loosening of the bounds means at the same time increasing distance of the partons, our supposition have a simple geometric consequence. It is logical to assume, that in the ground state, the three part system form a simple equilateral triangle – we do not have any reason to think about other, asymmetric forms.3 If this system absorbs some kind of excitation energy, it is logical to suppose that the symmetry of the system breaks and one of the partons move away from the other two, as its bounds loosen. That is, the first excited state of the system is probably an elongated form, a long isosceles triangle, in which the loosened parton sits on the distant tip. It means, that not one, but two of the three bond have to be loosened by the excitation. If the system absorbs another portion of excitation energy, the third bond can also be loosened, thus the second excited state can form again an equilateral triangle, though, due to the loosened bounds, it is larger than the triangle of the ground state. If the bounds can’t be loosened further, as the next portion of absorbed energy breaks the bounds, than there are no other excited states of the system. It means in the case of the partonic triplets, that only one ground and two excited states exist, and so every composite particle has only two heavier counterparts and no other. Every type of particle have to have a ground state and two excited states: two easily decaying “resonances”.

There is an interesting result of these simple geometric considerations. We can predict in the case of this kind of three parton system that the relative energy – or we can say, the relative mass – difference of the ground and first excited states should be larger than that of the first and second excited states. The cause is simple: the first excitation weakens two bounds, while the second excitation weakens only one bound. Of course, this is a very simplified picture, but the experimental data supports this thought: in the case of the electron, the mass ratio of the first excited state, the muon and the ground state, the electron itself is m μ/me = 200, while the second/first state, the tau/muon mass ratio is only m τ/mμ = 17. The same applies to the first

2 One of the referees of this article has raised the attention of the author, that similar thoughts have already appeared in the 1970’s, when Haim Harari and Michael Shupe created the so called rishon model. Even though the author was not aware of the rishon model when writing the article, this recent thought experiment can be seen indeed as the extended version of the rishon model.3 In theory there could be a state, where only one bound is loosened: a flat isosceles triangle. But as we speak of a triangle, the length of the loosened bound can’t be longer than the sum of the two other bounds. Considering, that there is a huge difference between the weights of the different particle families, such a restriction does not seem to be plausible. It is more logical to suppose that the loosened bounds are much longer than the ground state bounds.

family of quarks, though in that case the bounds are different: the bounds of the charged partons are probably stronger than that of the neutral partons. The mass ratio of the up quark and the charm quark is about 500, while that of the charm and top quarks is 100. In the case of the second quark family the ratios are 20 and 40 respectively, which means that the proportions are in a reverse order. Thus, we can conclude that the different bonds of the strong and the X-interactions create a much complicated situation as it seemed for the first glimpse.

Fig. 2: The excitations of the hypothetical three parton system. Due to geometrical reasons, the formation of the first excited state weakens two bounds between the partons, while the formation of the second excited state loosens mainly one bound. This view is in good correlation with the number of generations and the mass ratios of the charged leptonic and the quark groups. We found no contradiction to the idea that these particles might be partonic triplet systems and the heavier counterparts of the light particles are only excited states.

Let us now examine the excited states of the quark systems. Of course, the hypothetical three-parton-system quarks also have the same kind of excited states as the charged leptons: a ground state and two heavier particles with identical properties except for the mass. But in the case of the quarks, the different bounds are causing different properties of the ground and excited states.

We can guess first of all, that our hypothetical ground state quarks will have a greater mass than that of the electron. The inner bounds of the partonic triplet electron are much stronger than that of the quark systems. The stronger bounds equals to greater bounding energy, thus smaller mass for the electron. In the electron system not only the X-interaction holds the three partons together but the strong interaction as well. The three charged partons of the electron system have RGB and IJK charges as well, which increases the bounding energy and probably decreases the mass of the system. Contrary to this, in the 2/3 charged quark system with two charged and one neutral parton, the main bounding force is the X-interaction. The X-interaction has all the three charges in the system, so the interaction works at its full power. As a secondary effect, the strong force can perhaps interact between the two charged partons of the quark as well, but for this, the quark probably has to be the part of a larger, colour neutral system, which complicates the situation further. Nevertheless, this effect of the strong force is only a secondary one, and its effect weaker than the strong interaction of the electron system. At that case all the three colours are appearing in the system, thus, the bounds are fully strengthened by the strong force. If we count the number of bounds differently for every interaction, in the electron system there are 6 bounds: 3 of the strong interaction, and 3 of the X-interaction. In the up quark system, there are 4 bounds: 1 of the strong interaction and 3 of the X-interaction. The bounds of the down quark system are even weaker: the charged parton of this system can interact by the strong force only with other composite objects, as with the two neutral partons of its own system it is impossible. Thus in this case only the X-force can create 3 bounds in the system.

The number of bounds and their relative strength suggest that even though the mass of the neutral parton is probably smaller than that of the charged parton, the mass of the three charged parton system, the electron can be quite low, due to the large bounding energy. The 2/3 charged up quark system contains a neutral parton which would reduce its mass, but the bounding energy is much lower, than that of the electron system, thus the ground state of this quark system supposedly heavier than the electron. The mass of the down quark system, with its three weak bounds can be the heaviest: although it has two neutral partons and a charged one, the low bounding energy does not reduce its mass as strongly as in the other cases.

Similar considerations can give a very low mass estimation for the neutrinos. These particles are made of three neutral partons. These partons have no other charge as the supposed IJK charge of the X- interaction, thus no any other interaction can cause repelling forces between the partons. The partons can be thus very close to each other, causing a considerably large bounding energy of the X-interaction and a very little physical size for the neutrino systems. As we supposed that the neutral partons have a lower mass than the charged ones, the system of three light neutral partons with considerably strong X-bounds can result in very low masses. Such neutrino systems can even have almost zero mass. Contrary for example to the electron system, where the three partons experiencing repelling electromagnetic forces: the residual mass of the system can’t be lower than what is equal of the energy of the electromagnetic field.4

To summarize the considerations about the masses of the ground states, we can say, that the three charged parton system and the three neutral parton system could have the smaller mass, while we can expect the masses of the mixed systems of charged and neutral partons to be higher. The system of the three charged partons have the strongest bounds, thus the bounding energy lowers its mass. The electromagnetic forces of the partons can limit the strength of the bounding forces, thus leaving some mass for the system. Without such limit, the system of the three neutral partons can have a very low mass, as the partons can be located very close to each other, strengthening the interactions to a very large bounding energy.

The masses of the mixed systems, the quarks are expectedly higher than that of the leptons. The strong force is probably not involved in the creation of the systems, as they are not colour neutral. If the quarks are part of a larger system, than the strong interaction can have an effect on the bonds between the partons, but it is only a secondary effect. The main binding force is the X-interaction, while the other interactions, the binding force of the strong interaction and the repelling force of the electromagnetic interaction are only causing a perturbation. In fact we could expect that the mass of the up quark is higher than that of the down quark: the repelling electromagnetism and the two heavier charged parton of the system causing higher mass. In reality this is not the case, which shows, that the interactions inside the partonic systems are in fact not as simple as the picture outlined here.

Besides the charges and masses of the fundamental particles, their lifespan is also a very important data. In fact, the lifespan of the heavier members of the particle groups can also support their interpretation as excited states. In the leptonic group, the lifetime of the electron is infinite as far as we can prove it. The half-life of its heavier brother, the muon is 2·10-6 sec, while the same data for the tau particle is 3·10-13 sec. It’s worth noticing that the half-life of the tau is almost exactly the square of that of the muon. This relation has a simple logic if we are facing here the first and the second excited states of a composite system. The first excited state of the system is a single, while the second excited state is a double excitation. The single excitation has a certain probability for de-excitation. If the excitation is doubled, the probability of de-excitation is the square of that of the single excitation. Thus it is a logical supposition that in such a system the probability of the decay of the double excitation will be roughly the same as the square of the decay probability for the single excitation.

The same phenomenon can be observed to some extent in other particle groups as well. In the case of the quarks, the relation of half-lives is not as simple as in the case of the leptons. We cannot examine free quarks, only those, which are bounded in hadrons. Thus, it is impossible to measure the lifespan of a quark directly: we can estimate it only by the half-lives of the mesons and baryons, which are containing the particle. Nevertheless, it is interesting to recognise that the first excited states of the basic up and down quarks, the strange and charm quarks create particles, which has a half-life of about 10 -10 sec. Of course, if the composite

4 This is one of the main paradoxes of particle physics: if the electron is an elementary particle, one might think it is a point-like object. But if it is not point-like, it has an exact size, than it has to have one end and another different one: so it has some kind of parts, it has to be a structure. Thus, it can’t be an elementary particle. But if it is point-like, we have difficulties to explain its angular and magnetic momentum: we have difficulties in explaining the rotation of a point.What is more, some experiments, like the measurement of the energy levels of the electrons stored in a Penning trap, suggest that the electron has a definite physical size, which can’t be less than 10 -22 m. The classical electrodynamics also has some problems with the size of the electron. If it is a point-like particle, than its field energy is infinite. If we choose a proper size, which fits to the field energy of the electron, than the magnitude of the magnetic momentum suggest that the electron is spinning with the speed of light at the equator of the particle. So there is plenty of controversy around the size of the electron.

particle contains not only one singly excited quark, but more, the life-span is even shorter. But if the composite particle contains only one strange or charm quark the half-life is falling mostly to the 10 -10 sec magnitude. In the case of the third family, the heaviest quarks, which we explain as the second excited state, the same data is usually 10-20 sec. Of course, there are exceptions, but most hadrons are following this rule.

For example, the proton with an uud (up-up-down) quark combination have two similar but heavier brother, the Σ+ and Σb

+ baryons with a uus (up-up-strange) and uub (up-up-bottom) quark structure. Their half-life is 8·10-11 sec and 6.8·10-23 sec respectively. The half-life of the Σb

+ is again the square of the half-life of the first excited state, the Σ+. As the decays of the baryons are usually complex processes and they can result different decay products, the connection is usually not as simple as this one. The different decay channels have different probabilities, and the more channels exist, the less is the half-life of the particle. But in most cases, we can observe half-lives in the 10-10 sec magnitude for the second family (first excitation) and 10 -20 sec magnitude for the third family (second excitation). Thus the “square correlation” works quite often in the case of the quarks as well.

The only particle type where one cannot observe such a relation between the lifespans, are the neutrinos. As far as we know, the different neutrinos can „decay” to each other freely: this is called the neutrino oscillation. If a muon neutrino is created in a certain process, soon it can be observed as an electron or tau neutrino, or again as a muon neutrino. It means that the „decay” of these particles is not usual: they can convert to each other continuously. In the traditional approach this procedure is a bit difficult to explain – while not impossible. But if our supposition is true and the different kinds of neutrinos are one and the same composite particle system in different energy states, the explanation becomes very simple. If the excited states of the neutrino system are very near to the ground level – that is the electron, muon and tau neutrinos have almost the same mass – than even a very weak influence can excite or de-excite the neutrino system. As the kinetic energy of the neutrinos is usually far larger than their rest mass, an imperceptibly weak scattering event can excite the neutrino to other states. As the neutrinos are travelling through matter, these scattering events are not changing the direction of the speed or the kinetic energy of the particle considerably. Thus, they are remaining mostly unobservable. But they can excite or de-excite the neutrino system very often – how often; it depends on the energy of the excited states. The only possibility to discriminate between this excitation process and the traditional neutrino oscillation approach is that, this excitation process is attributed to matter, while the neutrino oscillation process in theory occurs in empty space as well.

If the energy loss of the neutrino system, the de-excitation of neutrinos requires interaction with matter, that has an interesting consequence. We will see in the section on mediator bosons, that the partonic neutrino system is probably unable to create a photon to lose energy. Strange it may sound, if this is the case, the excited neutrino system alone is unable to lose its energy. Thus, without interaction with matter, the excited states can have an infinite lifespan, just as the ground state.

Particle Reactions

At this point, a question naturally arises: what are the consequences of the above results regarding the well-known particles of everyday matter?

The first and perhaps the most striking consequence of our previous thoughts, that in a world, where every particle is in fact a triplet of partons, there is no matter-antimatter asymmetry. The partons have negative charge, while the antipartons have positive electric charge, thus we do not have think about any asymmetry, as the electric charges are in perfect equilibrium in our universe, as far as we know. In the partonic world perfect equilibrium of electric charges would mean perfect symmetry of matter and antimatter. Thus, matter as we know it, contains the same amount of partons as antipartons. But how it is possible without annihilation?

Fig. 3: The left side of the picture shows the partonic composition of a hydrogen atom. The electron is made up of three charged partons. The larger proton contains three quarks, two up and one downs quarks. It is easy to recognise that the whole system consists of six partons and six antipartons and either the colour charges, either the electric charges are in equilibrium.

The right hand side of the picture shows the parton composition of the two most abundant neutral particles, a neutron and a neutrino. We can recognise the same equilibrium in this case as well. If the leptons and quarks are truly partonic systems, that would result a perfect matter-antimatter symmetry in the universe.

Easy to see for example, that a hydrogen atom consists of the same number of particles and antiparticles. The electron of the hydrogen atom composed of three charged partons, while the three quarks of the proton composed of nine particles: three partons form a down quark, while six anti-partons form the two up quarks. In other words, there are exactly the same number of particles and anti-particles in the system, and the colours and the electric charges are perfectly neutralizing each other. In this way the material of our universe is in fact an equal mixture of matter and antimatter, so the apparent matter-antimatter asymmetry in the world does not really exist. For there are the same number of protons in the world as electrons and we will see from the reaction mechanisms, that probably the same is true to the number of neutrons and neutrinos. Thus, we have the same number of partons and anti-partons in the universe. Of course an obvious question arises: why does the material of the universe not destroying itself by the annihilation of partons and anti-partons? The answer probably lies in the structural asymmetry of the partonic matter: the partons obviously can annihilate with each other only, if all of their charges are neutralizing each other. Otherwise it is impossible. In fact it can happen only in larger systems, that all the charges are finding their counterparts. To understand this problem, it is better to analyse some particle reactions, to see, how the partonic systems interact with each other.

First of all, let us see the best “guinea pig” of the particle physics, the neutron decay. In the decay process the neutron emits an electron and an electron antineutrino and in doing so, it converts itself to a proton. The process does not affect all the three quarks of the neutron, only one of them. One of the down quarks of the neutron converts itself to an up quark, and so the udd (up-down-down) quark system, the neutron, becomes a uud (up-up-down) system, a proton. The transforming quark itself emits the electron and the antineutrino. But how this process looks like on the partonic level?

As we have seen already, the transforming down quark consists of three partons: two neutral and a charged parton creates the 1/3 charged, coloured down quark. At the end of the process we have much more particles, three composite particles made of total nine partons. The three partons transformed into nine partons, obviously by creating six new particles, three parton-antiparton pairs. Thus more precisely, the initial state consists of three partons, the final stage consist of six partons and three antipartons. The six partons of the final stage must form the electron and the antineutrino, while the three anti-partons must form the up quark. Will they do so?

If the initial state was a single composite particle, that is a three parton system, while the final state is three composite particle, made of total nine partons and antipartons, it is a natural assumption that in the process six partons were created: three partons and their corresponding antipartons. The three parton-antiparton pairs are probably created along the three bonds of the original partonic triplet system – the down quark – as the system is disintegrating due to the dissolution and reorganization of bonds. The figure below shows the actual process. Let us choose for example for our disintegrating neutron a green up quark and a red

and a blue down quark. As previously, let us mark the coloured partons with the RGB letters, while their anti-parton counterparts with ŘĞB̆, and the neutral partons and anti-partons with just simply S and Š letters respectively, regardless of their IJK charges. With this notation, the green up quark composed of Ř Š partons,B̆ the red down quark of RSS, and the blue down quark has BSS partons. In the case of the figure, the blue down quark converts itself to a blue up quark. During the process, the BSS system falls apart and inside it, three parton-antiparton pairs are created, namely a neutral S-Š pair and two charged R-Ř and G-Ğ pairs. The only charged parton of the initial down quark, the B parton allies itself with the two newly formed charged R and G partons, thus creating a simple RGB system, the -1 charged electron. The newly formed neutral parton joins the two neutral partons of the original quark, forming an SSS system, an anti-neutrino. Only the three newly created anti-partons are left, and thus, they join each other into an ŘĞŠ system, namely an up quark, with a blue effective colour charge. The initial blue down quark thus transformed into a blue up quark, an electron and an antineutrino: BSS-1/3 + (S-Š + R-Ř + G-Ğ)0 = RGB-1 + SSS0 + ŘĞŠ+2/3 (the superscripts show the electric charge of the partonic systems.)

The example of the neutron decay shows us clearly, why is it logical to associate the system of the three neutral partons to the antineutrino, not the neutrino. The particle that created in the neutron decay, when it was discovered, was named antineutrino. The logic of this naming was that during the decay, the newly created electron is a lepton, so the other particle has to be an anti-lepton, to preserve the leptonic number. If the electron has a leptonic number 1, than the other particle should have -1: it has to be an antiparticle, an antineutrino.

Fig. 4: The decay of the neutron to a proton regarding their supposed partonic composition. The left hand side of the picture shows the partonic triplets of the neutron’s three quarks. Although the colours are continuously changing during the interactions, in this example the up quark is green: it contains an anti-red and an anti-blue anti-parton, which is in effect a makes a green colour charge, as it misses an anti-green anti-parton to be colour neutral.

The right hand side of the picture shows the blue down quark of the neutron to convert itself to an up quark. Inside the down quark, consisting of two neutral and a charged partons – in this case a blue parton – three new parton-antiparton pairs are created. The three neutral partons merge into an antineutrino, the three charged parton merge into an electron, while the remaining antipartons create the up-quark.

After the description of the partonic theory of the neutron decay, we can investigate other particle reactions, for example the opposite reaction, the transformation of the proton into a neutron. It is well known that the free neutrons decay to protons, but in bounded states the reaction can take the opposite direction as well. In a nuclear system it often happens, that a neutron has a much larger bounding energy than a proton, thus the opposite direction of the reaction is energetically favourable. In an unbounded state the decay of the neutron is favourable, as it releases energy, while in bounded states the direction of the reaction depends on the bounding energy of protons and neutrons. If the bounding energy of the neutron is about 1 MeV deeper than that of the proton, the proton can capture an electron and transforms to a neutron and a neutrino. In even deeper states the proton can decay without any external influences into a neutron, a positron and a neutrino. In both of the processes only one of the up quarks of the proton is involved: it transforms to a down quark.

In the case of the electron capture, the initial state consists of two composite particles, an electron and an up quark of the proton. In our thought experiment the up quark is a system of three antipartons – two charged and a neutral – while the electron is made of three charged partons. The final state is also comprised of two composite particles: a down quark and a neutrino, three partons and three antipartons respectively. Let us choose the colour of the quark as B. In this case the partonic composition of the initial up quark is ŘĞŠ+2/3 – a triplet of antipartons with an effective B colour and a +2/3 electric charge. The electron is an RGB -1

combination. It is clear that the two triplet systems almost completely annihilate each other: the R-Ř and the G-Ğ pairs annihilate, and what is left, is the Š neutral antiparton of the quark and the B parton of the electron. But along the disintegrating bonds and particles, new partons can be created by the released energy – we will see later the exact process. Two parton-antiparton pairs should be created, so again there will be three partons and three antipartons, to form two new composite particles. Of course, there is a possibility that two new charged parton pairs are created namely an R-Ř and a G-Ğ pairs, but this would lead again to an up quark and an electron, the same as the initial case. But if two neutral parton-antiparton pairs are created, the final state will be different from the initial. The Š neutral antiparton of the initial state can connect to the newly created neutral antipartons, thus forming an ŠŠŠ neutrino. The other two neutral partons can join the B parton, thus forming a BSS system, which is a blue down quark.5 The equation describing the process is: ŘĞŠ+2/3 + RGB-1 = Š0 + B-1/3 + (S-Š + S-Š)0 = ŠŠŠ0 + BSS-1/3.

Fig. 5: The picture shows the parton distribution in the process of the electron capture of the proton. On the left hand side of the picture the initial state can be seen: the RGB colour neutral particle is the electron, the larger black circle encircling the three quarks of the proton. Next to this, in the blue circle we can see the transforming blue up quark of the proton. The three partons of the electron are now inside the quark, just as the three original antipartons of the quark itself. The two charged pairs, the R-Ř and G-Ğ pairs are annihilating, and two new neutral pairs are created – S-Š + S-Š – as it can be seen on the next blue circle of the picture. The right side of the picture shows the final state of the process: the three neutral antipartons are forming a neutrino, leaving behind a blue down quark. The up-to-down quark transformation causes the proton to become a neutron.

The other possible process by which the proton can decay into a neutron is occurs when the neutron is much deeper bounded than the proton. In this case one of the up quarks of the proton emits a positron and a neutrino, while transforming into a down quark, thus the original proton (uud quarks) becomes a neutron (udd quarks). It perhaps needless to explain the process in detail, and we can just write down the partonic equation of the process (now starting with a green up quark): Ř ŠB̆ + (G-Ğ + S-Š + S-Š) = ŘĞB̆ + ŠŠŠ + GSS. It is easy to find out what kind of parton pairs are created in the process, as for the positron a Ğ is necessary for the initial ŘB̆ 5 The creation of two pairs of charged partons would return to the initial case, while two pairs of neutral partons are causing the proton-electron system to transform into a neutron-neutrino system. In theory it would be possible that a neutral and a charged pair are created, which would lead to the emerging of hadronic particles. Even though the energies involved in the process does not allow the creation of new hadronic particles, we are going to see later, that the process in fact starts with the creation of boson pairs, which are interacting with the transforming quark. But no boson can serve the process with neutral and coloured partons and antipartons at the same time, so the hadronic transformation is forbidden. The only possibility for the system is to stay in the proton-electron state or to transform to the neutron-neutrino state.

partons to be neutral, while the neutrino needs two new Š for the original one. Thus, it is very easy to create the describing equations for any particle reactions. The difficulty lies deeper, in the explanation, why and how these partons are created in the interactions.

Finally let us see a different kind of reaction, the decay of the most important meson, the pion or π-meson. There are two reasons why this process is interesting. Firstly, the mesons are two quark systems, bounded states of a quark and an antiquark, which are quite different from the three quark system baryons, as the above mentioned proton and neutron. The other reason is that the pion can be an interaction mediator boson between the most common baryons, the proton and the neutron, and its decay was the main reason, why it was necessary to suppose the existence of a new kind of interaction, the weak nuclear interaction.

For example the negative pion is a system of a down and an anti-up quark: π-1 = d-1/3 + û-2/3. As we can see on Table 2, both of these quarks are build up from partons and do not contain any antipartons. Although, the colours of the two quarks of the pion system are continuously changing, let us see a moment when the quarks are for example red and anti-red. In this case the down quark has RSS parton combination, while the anti-up quark has to have a GBS combination, so with its two charged parton this quark have an anti-red, Ř effective colour. Thus the negative pion has a very simple parton structure: RSS(R)-1/3 + GBS(Ř)-2/3.

There are two simple consequences of the above parton structure of the pion. One of them is explaining the decay of it: a very simple rearrangement of the partons concluding two leptons, a charged and a neutral one. RSS-1/3 + GBS-2/3 = RGB-1 + SSS0. It can be in effect an electron and an electron-antineutrino pair, or a muon and muon-antineutrino.6 It is an interesting question, whether a muon - electron-antineutrino pair or an electron – muon-antineutrino pair can be created as well? Let us return to this question later on. The experimental data says that muons and electrons are created almost in the same number in the decay of the negative pions.

The other consequence of this parton structure of the pion is a bit philosophical. This structure is having an RSS and a GBS sub-structure in it. In this system of six partons, we can find all the three RGB colours. Beside the three coloured partons, there are three neutral partons, obviously with the IJK charges of the X-interaction. It is again obvious that if we try to find a deeper bounded state of this system, we have to create triplets of colour-charged and neutral partons: RGB and SSS. But exactly this rearrangement is happening during the “decay” of the pion. And the reason why this shift takes place is again simple: the distance of the R and the GB partons are keeping their bounds in a high energy state. The forces try to keep the distance at the lowest possible, but these partons are part of different quarks, so the possibilities are limited. The bounds can hold the quarks together, but this is still a high energy state: the red down quark and the anti-red anti-up quark create a bounded state, nevertheless it is unstable. The partons will quickly rearrange themselves, so that the distance between the RGB and SSS partons will be the shortest possible, thus creating compact colour neutral particles: electrons or muons and neutrinos instead of coloured quarks.

Although the pion itself was also colour-neutral – just as the final products – but this larger particle means a much higher energy state, in a much more complicated structure. This shows us, why neither of the mesons is stable particle: their quark-antiquark structure always contains the necessary RGB or ŘĞB̆ colours in the two quarks, and so their rearrangement to a much lower energy state is always possible. The partons of the mesons can always create smaller leptons, and so, they will always decay to a charged and a neutral lepton.7 It means, no stable meson can exists, if our parton theory is true. The only possibility for the quarks to exist in a stable form is to create three quark systems, that is, baryons. In these systems, the colours of the quarks are neutralizing each other, but the rearrangement of the partons usually cannot create leptons. 8 Thus, the parton theory suggests: quarks can create stable baryons but mesons are always unstable.

6 The decay of the positive pion is very similar: ŘŠŠ + Ğ ŠB̆ = ŘĞB̆ + ŠŠŠ. The process is creating a positive muon and muon-neutrino pair or a positron and electron-neutrino pair.7 It is easy to recognise, that this statement is always true for charged mesons. The case of the neutral mesons is different: they do not have a simple quark structure. We will deal with their case later.8 In some rare cases the rearrangement of partons is theoretically possible in baryons as well. For example in the case of the Δ- and Δ++, the ddd and uuu quark structures are made of purely partons or anti-partons, and there is no obstacle in the way of regrouping. But these particles have a very short lifetime – about 10 -24 sec – so it is improbable, that we can experience their direct leptonic decay ever.

Fig. 6: The decay of the negative pion in the partonic approach: π- → e- + ῦe. It is in fact a very simple kind of rearrangement of particles. The negative pion is a bounded state of a down quark and an anti-up quark. In the case of the figure we show the quarks in red colour, but this is continuously changing as the quarks (and their partons) are changing their colour during interaction. The parton structure of the red down quark is RSS, while that of the anti-up quark is GBS – its effective colour charge is GB = Ř (The red circle surrounding the three partons of the red down quark shows its colour charge, while the dashed red line surrounding the partons of the up-antiquark shows its anti-red colour).

During the rearrangement of the particles, the charged and the neutral partons are forming new composite particles, namely a charged and a neutral lepton: RGB (electron or muon) SSS (antineutrino). As the creation of these more compact particles liberates a large amount of energy, the excited leptonic states, the muon and muon-antineutrino pairs are just as often formed as the ground state, the electron and electron antineutrino pair.

The Feynman diagram of the decay is on the right hand side of the figure.

Understanding the decay of the pion system is very useful, if we would like to understand the stability of matter in the partonic theory. The regrouping of the partons, constituting the two quarks of the charged pion is a quite slow procedure: it takes about 10-8 sec, although there is no natural law prevents its occurrence. The decay is only slow, because it is not a simple two particle reaction, but is a much more complex process, involving six partons of the pion. The 10 -8 sec seems to be a very quick process, but the characteristic time of the strong interaction is about 10-24 sec, which is 1016 times faster. The pion lives 1016 times longer as the time necessary for the interaction of its constituting quarks. But how much time is needed to the decay or rearrangement of more complex systems?

We could see previously, that the leptonic decay of the baryons is usually not possible. This means, that the partons of the baryons are unable to rearrange in such a way that they create leptons. Most of the baryons are decaying to the most common baryons, the proton and the neutron. We have seen previously that the neutron can decay to a proton and two leptons, but for this, new partons have to be created. Not surprisingly, this process is very slow, so the lifetime of the neutron is about 103 sec: an incredibly long time in the realm of particles. The question is, whether the final product of all baryonic decay, the proton is stable or not?

In fact we will find here some contradiction. The partonic structure of the proton for example (RSS) R-1/3 + (Ř ŠB̆ )G+2/3 + (ŘĞŠ)B+2/3, where the superscript shows the colour charge and the electric charge as well. In theory it is possible that these quarks react each other and by the annihilation of the R- Ř, and the two S-Š pairs, the remaining three partons are connecting into an ŘĞ system, that is a positron.B̆ 9 The only thing what we can say about this process, that even though at this point we can’t exclude it, it must be very slow. If the two quark system of the pion needed 1016 times longer time for the decay than the characteristic time of the interaction, 10-24 sec, than the three quark system of the proton needs at least 1016 times more time. The electric charge of the quarks can have an effect on the probabilities as well, increasing the lifespan of the proton further.

9 It is important to see, that this process is not the same as the above mentioned one, when the proton and an electron interact with each other. In that case only one of the quarks of the proton interacted with the electron and another baryon created in the process. The number of baryons did not change. While here we see the possibility of the complete disappearance of baryons converting themselves into leptons.

Nevertheless, the simple estimation for the half-life of the proton in this process would be 10 -24·1016·1016 = 108 sec, which is obviously not in tune with the reality. In fact this procedure, the proton’s decay to a positron would show the perfect matter-antimatter symmetry of our world, as the created positrons would annihilate with the same amount of electrons, and all matter would disappear. Obviously, this is not the case, the universe did not annihilate itself, as we are here to think and speak about protons. Thus, the stability of the proton is still a question. We have to investigate the interactions of the partons further.

Quaternion charges

Up till now, there are two kinds of partons, the existence of which we had to suppose. There should be a charged parton, with electric charge and three kinds of colour charge, and a neutral parton, which interacts with other particles only by the supposed X-interaction. So far, it seems these two kinds of partons were enough to create all the particles we know from the experiments.

Nevertheless, it is interesting to recognise, that the fraction electric charges and colour charges are always “go along”. The colour charged particles always have a fraction electric charge, while the opposite is true, all the particles having a fraction electric charge are also coloured. What is more, we have never seen neither colour charged particles, neither a fraction electric charge. We can recognise experimentally only those particles, which are colour-neutral, or white, and having a whole electric charge unit. All other particles are completely closed into the micro-world of the particles. Does this feature have a hidden cause, or it is just an occasional coincidence? Let us examine the possibility that this phenomenon in fact have a hidden cause, and these charges are in fact the different sides of the same coin. It should be a very special coin, with four sides, of which three is similar.

We know of such kind of “special coins”. In the 19 th century, the well-known Irish physicist, W. R. Hamilton discovered a special number system, the so called quaternions. He tried to broaden the boundaries of the complex numbers, and realised, that the only possibility for that is an algebraic system, where the numbers have four factors, a real and three imaginary parts. At that time the complex numbers were in use more and more in physics, but Hamilton tried to expand these two dimensional numbers to three dimension. He failed, and realized that the cause of his failure is that the extension of the complex numbers can’t be three dimensional, but four. The complex numbers are two dimensional, as they have two factors: the real part, the unit of which is 1, and the imaginary part, the unit of which is i, where i2 = -1. In the case of the four dimensional quaternions, the first factor is again real, and its unit is 1, while there are three different imaginary factors, i, j, k, the square of which are all -1 = i2 = j2 = k2, but it is also true, that i·j·k = -1. The system of the quaternion numbers is in fact the cross product of the complex numbers by themselves, and so, the multiplication of the quaternions is non-commutative: i·j ≠ j·i. Indeed this body of numbers can sustain very interesting results for us. One of the reasons why quantum mechanics have very uncommon features is that it proved: Nature indeed uses the complex numbers. Wave functions or forces can have an imaginary factor, which we can’t recognise directly, but it results in particles infiltrating through barriers, and so on. The experiments have shown long ago, that the imaginary part of the complex numbers is an existing thing. Nature uses it as it works, and by using them also in our calculations, we can track the strangest features of nature. Is it possible that nature uses the quaternions as well, when creating our world?

Perhaps yes. We can recognise that the electric charge and the colour charges of some particles are act like the units of the quaternion numbers. We can experience the effects of the colour charge, but we can’t directly measure its existence. No one could ever see a colour charged particle, just as the three imaginary parts of the quaternions are non-real numbers. They have only effects on the real part: multiplying them will give us -1, a real number. Exactly the same thing is happening with our coloured particles: if three coloured particles are connected together, the result will be a real electric charge, though the individual colour charges disappear as they merge into a white, colour neutral system. So the question arises: is it possible that the electric charge and the colour charges are in fact one and the same phenomenon? Are they just function the

same way as the real and the imaginary part of the quaternions? Can the charge of a particle be described by a single quaternion number?

Surely, if the analogy is perfect and the charges of the partons can be described by quaternion numbers, it has several consequences. For example, it would mean, that neither the partons nor the quarks have the theoretical fractional electric charge. In fact, they only have the well-known RGB colour charges, and only when they are joining together in a colour neutral particle, than the real part of the quaternion charge, the electric charge appears. Thus, the coloured particles have no electric charge at all, but the colour charge itself incorporating the possibility of the creation of an electric charge. Not a fraction, but an integer value. When the coloured particles neutralizing each other’s colours, this will create a unit of electric charge, not just simply a white, colour neutral object. Just exactly the same way as the real part of the quaternions is appearing. The imaginary units of the quaternions, the i, j, k numbers are themselves fully imaginary, without real part. But when they are multiplied, the real part appears: i·j·k = -1. Thus, even though, they are imaginary numbers, the i, j, k units are – due to the characteristics of the quaternions – incorporating the possibility to create a real number.

The existence of the quaternion charges would mean, that it is not just a simple coincidence, that only the coloured particles have fractional electric charge and vice versa. In this way no coloured particle has ever had any electric charge, but if they join together, they create one. In this case we are not just simply adding the colour charges together, but by multiplying them we create a new kind of charge. The multiplicative nature of charges is not a very strange idea.10 When counting the strength of an interaction between two charges, we have to multiply the charge values. The force, F between two charges, Q1 and Q2, is proportional to the Q1·Q2

product. The quaternion nature of charges would mean only that when examining the forces created by the interactions, instead of Q1·Q2, in theory we can write (R1·G1·B1)·(R2·G2·B2). As the multiplication of the quaternions are non-commutative, we have to multiply the colour charges in brackets first in the necessary order, thus the product will be anyway Q1·Q2, causing no change in the usual calculations of electromagnetic interactions.

Interactions

We have seen in the previous section that, if we don’t treat the electric charge and the colour charges of the strong interaction as separate properties, but as the real and imaginary parts of a single quaternion charge, it can provide simple explanations for the most basic phenomena related to elementary particles. The presumption of the existence of quaternion charges has a serious drawback, though. As a result of using quaternions, perhaps we have to change our view as how interactions work between the fundamental particles.

So far we perceived the interaction between two particles, as the exchange of mediator bosons between the two interacting particle. One of the interacting particles emits the mediator, which the other interacting particle absorbs, and the momentum exchanged in the process is responsible for the arising force between the particles. The interacting particles are fermions with a half integer spin, while the mediator particles are always bosons with an integer spin value.

We are now perhaps forced to change this simple picture: we have to assume, that there are three body interactions that affect all the three parties at the same time. This will be a very unusual idea, as usually in the case of three body interactions we handle the situation as three different two-body interactions. In the case of quaternions, it is impossible, as probably there are no two-body interaction exists: without the contribution of

10 In fact, we have already used the multiplicative nature of the colour charges as quaternion factors. When realising that two colour charges is equal in effect with the anti-colour of the third charge, we used the quaternion multiplication rule: R·G = (=-B)B̆ . Indeed, only some of the hypercomplex number systems like the quaternions have such equalities, so the nature of colour charges might directly suggest the usefulness of the quaternions in their case.

all the three imaginary charges the interaction does not result an interpretable final state. This is the result of the non-commutativity of the quaternions.

The supposition of this inseparable three body interaction – that is, the interaction of three bodies at the same time – may sounds strange, nevertheless this feature can be the origin of the spin of fundamental particles. The key for the solution of the problem is hidden in the properties of the quaternions. As we have seen, the multiplication of quaternions is non-commutative, that is, the result of the multiplication depends on the order of the factors. For example i·j = - j·i. This is why we are unable to interpret two body interactions: the result is controversial. In general, we can say, that in a multiplication of the units of quaternions every swap of units will change the sign of the result.

Hitherto we seem to create the elementary particles from the supposed partons without any problem. We have three colour charged partons: R, G, B, and their anti-coloured antipartons: Ř, Ğ, . If the threeB̆ different colour charged partons join together, they will create the electron: a -1 electrically charged particle with a spin and magnetic momentum. And if the three anti-coloured partons combine together, they will create the same way the positron, the antiparticle of the electron. If R, G, B are different imaginary quaternion units and Ř, Ğ, are their opposite: than the description of the events are simple: R·G·B = -1, and Ř·Ğ· = (-R)·(-G)·(-B̆ B̆B) = (-1)3·R·G·B = (-1)4 = +1

Nevertheless, our fine conception collapses in a moment, as we change the order of the imaginary charge units in the multiplications. The RGB combination results -1, while a single swap of the order to RBG for example results +1. This would mean that the electric charges of the particles are not definite. This is obviously not the case in our world, so the only way to avoid such ambiguity, is to determine the sequence of the interactions between the partons. Even though we do not know yet exactly what it means, we have to define the R>G>B>R>G>B sequence as the only possible way for the partons to interact. That is, the interactions of the partons have a definite direction: it is not mutual, not reciprocal between the partons. For example the R parton „interacts” with the G parton, but the G parton can never interact with the R parton, only with the B. At the same time, the B parton never interacts „backward” with the G parton, but can interact only with the R parton. And so on.

Thus, the simple identification of the colour charges as quaternion units have far reaching effects. A kind of rotational effect seems to be a built-in feature of the interactions. The effect of the interaction of the partons circles between them and can never turn backward. This is the only possibility to avoid the contradiction that arisen from using the quaternions. The effect can rotate in one direction only. It means that in the case of partonic triplet systems, the fermions, the constituting partons are not necessarily rotating, but at least the interaction holding the particle together must have a rotary nature.

This kind of rotary effect requires a completely new kind of mechanism for the interactions. The mechanism of the strong interaction hitherto imagined as that of any other interaction, regardless of its six charges: by the exchange of mediator bosons. For example when a green and a blue particle interact, one of them emits a mediator boson, while the other absorbs it. The boson is a gluon, which have two colours at the same time. For example the green particle emits a green-antiblue gluon, and so, it becomes blue itself: the emission of the green colour charge neutralising it, while the emission of antiblue colour, makes it blue. The other particle absorbs the gluon and so, the particle, originally blue, becomes green: the original blue colour neutralised by the gluon’s antiblue colour, and the incoming green colour creates the new green colour charge of the particle.

Fig. 7: The figure shows the conventional view of the exchange mechanism of the strong interaction. The blue quark emits a blue-antigreen gluon and thus, becoming green. The green quark absorbs the gluon and thus becoming blue. In this way all the three colours are preserved, but the RGB order has changed. If the quaternion charges exist, this mechanism would lead to contradiction: the mechanism changes the electric charge of the composite particle without any external influence, just by changing the RGB order.

Unfortunately, the conventional view of the mechanism of the strong interaction, indeed have very unfavourable features, that are incompatible with the quaternion charges. First of all, during the interchanging of gluons two of the three particles have the same colour, and there is also a two-coloured particle in the system. It means that the RGB colour combination of the triplet system is temporarily disrupted. In the above example, during the interaction, an RGG parton combination and a BĞ gluon is present in the system. Indeed, this situation is unexplainable from the viewpoint of the quaternions: the RGG combination is still imaginary, thus it does not result in a real electric charge. Also, the two colour charges of the gluon just simply have no sense: if a gluon, for example have blue-antigreen colours, its effective colour charge would depend on the order of the colours: the BĞ or ĞB orders gives opposite products.

Another problem of the conventional process is that as a result of the interchanging of the gluon, the G and B coloured particles changed places. The original RGB order changed to RBG, which means that the electric charge of the particle changed from -1 to +1. This is obviously not possible, so if we want to suppose the existence of quaternion charges, we need to find another mechanism, which changes the colours of the partons exactly at the same time, so all the three colours are in a perfect balance in the system at any time. Another requirement of the mechanism is that, it should preserve the RGB order during the process.

In theory, there can be such a mechanism. Let us imagine the three different coloured partons in a triplet system for example in a counter-clockwise RGB order. Although the conventional view of the strong interaction is based on two coloured gluons, we have seen that it is impossible if quaternion charges are exist. So let us suppose that our gluons have only one colour. In this case, there are six types of gluons: red, green, blue, and the anti-coloured antired, antigreen and antiblue ones. The letters r, g, b and ř, ğ, will denote them. In fact, ifb̆ not the partons themselves, but the field between them, will emit gluon-antigluon pairs, exactly that will happen, what was needed for us. For example, the field between the R and G partons generates a red gluon antigluon pair (r-ř), the field between the G and B partons generates a green gluon-antigluon pair (g-ğ), and the field between the B and R partons generates a blue pair (b- ). The R parton meets two gluons: an ř from oneb̆ side, and a b from the other side. As it absorbs them, the previously R parton becomes B, in a similar way, as a two coloured gluon would change its colour. The G parton has an r and a ğ gluon at its side – thus, it becomes R, as it absorbs them. The same way the B parton becomes a G parton as it absorbs a and a g gluon. Placingb̆ the particles of the process in a line row, the partons of the (R – ř-r – G – ğ-g – B – -b – R) line absorbs theb̆ gluons on their both sides. Due to this process, the RGB parton order becomes BRG, but the multiplication of the imaginary charges will give the same result, a -1 electric charge. As the process continues, the BRG order changes to GBR and finally back to the initial version, RGB.

For the first glimpse, it seems as if a kind of a “gluon-vortex” would spiral in the partonic triplets. This gluon-vortex is made of colour-anticolour gluon pairs and while the gluons are spiralling in one direction, the antigluons are turning to the opposite direction. Their movement have a definite direction and they never turn backwards. This kind of mechanism creates not only the forces of the interaction, but it ensures the direction of the interaction as well. The only thing what is necessary for the process is, that the field between the partons should emit the gluons, and the partons should attract and absorb the proper gluons. Namely, the red parton must attract and absorb only the anti-red and green gluons, the green parton must attract the anti-green and blue gluons, while the blue parton must attract the anti-blue and red gluons only.

There is a philosophical problem with this mechanism though. Is it possible for a parton to lose its colour? Can a coloured parton be colourless? If not, we have to suppose, that the gluons are reaching the parton at the same time. In the conventional view of the strong interaction, this problem does not appear, as in that theory there are two-coloured gluons, so every particle changing its colour by absorbing one single two-coloured

gluon. Contrary to this, in the case of the quaternion interaction, the parton has to absorb two gluons at the same time to change colour.

But how is it possible, that these gluons are generated and absorbed simultaneously, exactly at the same time? In physics the supposition of simultaneous events are usually difficult to explain and tend to cause difficulties. If two events have some kind of connection than usually they cannot be contemporaneous. One is happening after the other as one of them is the cause of the other, or at least has an effect on the other. As every effect travels through space with the speed of light or slower, if there is any connection between two events, they cannot happen at the same time. If they are simultaneous, they have no connection. There is only one possibility against this rule: if the two events are happening not only at the same time, but also, at the same place in space. This is the only exact, physically acceptable solution of the simultaneity problem. In everyday life we can call two connected event simultaneous, even though they are really not: the effect can travel with the speed of light so we may not see any time difference. But there is in fact some delay between the events. If the two events are happening really at the same time, they must happen at the same place as well, if they are connected events.

What does it mean in our case? We have supposed, that the creation of the three gluon pairs are happening at the same time, otherwise the quaternion multiplication rules does not give interpretable results. So, if the events must happen at the same time, than they must happen at the same place as well. The gluon pairs are generated at the same time and at the same place. Thus, the above mentioned gluon-vortex of the three gluon pairs is generated in one single point. The gluons of the vortex, which mediates the interaction created simultaneously in a point inside the partonic triplet and absorbed also simultaneously in the partons. Indeed, these three gluon-antigluon pairs, this gluon vortex is forming as a single object and it behaves as a single particle.

What kind of particle can it be? Let us see its characteristic properties: perhaps it can lead us to further conclusions. First of all, it is a virtual particle when it appears in the strongly interacting systems. Its gluons are probably not interacting with each other: if this is the case, we do not have to deal with its spin and electromagnetic field inside the partonic triplet system, inside a complex particle. In this case the gluons are just created and absorbed inside the three-parton system, and their wave functions are probably so extended that they indeed overlapping each other, thus the simultaneous creation and absorption is a very simple process.

Nevertheless, if this quasi-particle, this gluon-vortex gets some energy, the wave functions of the gluons will have smaller wavelength, thus they overlapping nature damaged. If this quasi-particle gets enough energy, the wavelength of the gluons can be small enough for the wave-functions to be separate from each other. In this case they can interact with each other and they can probably leave the partonic system, which created it.

What are the properties of this liberated particle, which leaves the prison of the partonic triplet? First of all, it is obviously a boson: three of the coloured gluons are creating a spin of ½, while the other three antigluons are creating also a spin of ½. Even though, the interactions are rotating to opposite directions, the gluons and the antigluons are creating spins of the same direction. The interactions are turning to opposite directions but they have opposite charges as well: it means the quaternion multiplication rules give spins of the same direction. Thus, the particle is a boson with an integer spin of 1.

What kind of field this particle has? Of course, it has electromagnetic field. The rotation of the colour charged gluons create some electromagnetic field, while the anti-gluons are creating an electric field which has opposite direction than the other. The quaternion nature of the colour charges ensures this. We can’t simply say that these electromagnetic fields will compensate each other as we do not know, whether they are added in the proper phase. Indeed their interference probably creating an alternating electromagnetic field.

We may think that this mediator boson will participate in the strong interaction, though it quite probably not. Even though as a virtual quasi-particle it is the mediator of the strong interaction, as it leaves the coloured partonic systems, it cannot interact with the partonic systems from outside any more. Its gluons are interacting with each other only, and they can interact again with other particles by the strong interaction only if they are close enough to a partonic system – close means in this case the size of the partonic systems themselves. Indeed, this boson has to be absorbed back to a coloured triplet system and lose its energy to interact again

with other coloured particles. It is simple: if this boson is in the inside of a fermion, it is the mediator boson of the strong interaction. But in a larger scale, as a free, real particle, it will not be involved in the strong interaction: looking from larger distance it is colour neutral.

To summarize these thoughts: this new particle is made of six gluons, or more exactly three gluons and three antigluons, so, it is the antiparticle of itself. With the necessary energy, matter can emit this particle, but probably it can be created in vacuum as well, in pairs. It is a boson, with an integer 1 spin unit. In large scale it is not involved in the strong interaction, although it has probably an alternating electromagnetic field, which means that it interacts electromagnetically in a large scale.

These properties are perfectly fitting to a particle: the photon. At the same time, we can state that there isn’t any other particle, which have any similar properties. So the gluon-vortex of our thread is probably one of the most ordinary particles: the imaginary colour charges of the three gluon-antigluon pairs create a real photon. They form a quaternion particle in this way: the group of imaginary gluons, plus the real part of their interaction, the vibrating electromagnetic field.11

Fig. 8: If we would like to illustrate somehow the gluon structure of the photon, a possible representation is the two intertwined triangles above. The three coloured gluons and the three anti-coloured antigluons can be depicted in triangles, which represent their probable geometric position. The centres of the two triangles are the same point, as all the gluons are created in that same point. As the gluons and their antigluons burst to opposite directions, the red, green and blue gluons are on the opposite angles of the triangles. So the six particles and their two triangles are forming a six pointed star in the above manner. This figure can be seen as the representation of the imaginary parts – the RGB and ŘĞ charges – of the photon. “In operation” theseB̆ gluons and their triangles are rotating in order to create the real part of the photon, the alternating electromagnetic field, and the spin of the particle.

11 If this is true, we would be wrong to say, we have never seen a gluon: we can see nothing else but gluons, as the photons of the light themselves are made of gluons. Indeed, it is a big problem of the Standard Model that theory predicts the existence of particles made of purely gluons without any quarks, though none of the known particles could be linked to this prediction.

Fig. 9: If the gluons that are mediating the interaction between the partons are crated at the same time in the same point, it is logical to assume, that in that point a source of the virtual gluons, a mediator boson can be found. This boson, made up virtual particles, mediates the simultaneous interaction between the partons. The wave functions of the gluons of the boson are large enough to be present everywhere in the system, making the simultaneous reactions possible. The Feynman diagram of the process can be seen on the left hand side of the picture: the gluons are represented by the arrows pointing outwards of the mid-point, while the antigluons are the arrows pointing inwards. The gluons and antigluons are bursting into opposite directions, but they need some deflection to be absorbed.

Even though the emission and the absorption of several gluons must happen simultaneously, the diagram can be interpreted, as if only one gluon would travel across the partons changing their colour continuously. What is more, if we consider that two gluons absorbed by the same parton at once, we get back the conventional view of the strong interaction with the two-coloured gluons: red-antigreen, green-antiblue, blue-antired gluons. The result of the process is the rotating and colour changing interaction, as presented in the right side of the picture.

It may be interesting to note, that the left side diagram with the three coloured partons and the boson, made of six gluons is in fact shows the inner structure of the electron.

However, there are some properties of the photon, which did not appear in our thread yet, but still, they are very important. Supposing that the above gluon-vortex mediator boson of the strong interaction is the same as the photon, we should take into consideration all the other properties of the photon as well. For example, the photon travels – obviously – with the speed of light, its rest mass is zero, and its energy and mass can vary freely, it can take any value. The zero rest mass and the speed are of course not independent, but are consequences of each other. The question is, whether the gluon-vortex boson of the above thread can possess these properties of the photon?

In theory, it is possible. The first and most important criterion is that the gluons have to have a zero mass, just as the photon. And if the mass of the gluons is zero, the gluon-vortex they create can gain some mass only by the interaction – the energy of the field they create can have some mass. Though, in this case, the starting of interaction is starting the movement of the photon as well, as the photon has only motion mass. Thus, we can say, the photon has mass only if it is moving: if their parts interact, than it starts to move, and so it has energy and mass. In fact, this is perfectly in tune with our previous thoughts that the gluons are not interacting with each other if they are in the core of a partonic triplet system. They interact there only with the partons of the system. They behave there as virtual particles: the gluons are created from the vacuum without mass and energy and so, they are not interacting with each other.

The fact that the photon’s mass and energy can be of any value means, that its interacting gluons does not have discrete energy values. We know that the free-moving particles can have any energy values, but it is somewhat surprising that the gluons of the photon, while interacting with each other, can have arbitrary energies. We have accustomed to the situation, that during interaction, the particles can only have discrete energy levels. Though, the case of the photon is anyway very special, as we do not know any other case, when the starting of interaction means that the particle immediately burst out with the speed of light. We may think that these two phenomena – the continuous energy levels and the only possible discrete speed – are related, as only the photon shows these properties.

Another philosophical problem develops along the wave-particle duality. Every of our experience suggest that the strong interaction have a very short range. We have supposed previously, that the partons of the electron system are held together by this interaction, but out of the system, the force is no longer observable. The largest distance, where it can have an observable effect is the size of the proton and neutron, the coloured quark systems: the order of 10-15 m. There is no reason to assume, that the gluons which are forming the photon, are moving apart to a larger distance than this. Nevertheless, the photon can have a much larger electromagnetic field. Does this mean that the photon has a kind of a nucleus? That is, the photon has an inner core, wherein the coloured gluons are interacting with each other, and these six small gluons are creating a much broader field? Or another possibility is true, that the gluons of the low energy photons are having large

but overlapping wave-functions? And so, their coloured field is experienced on a large scale as an electromagnetic field, and only the smallest objects, much below 10 -15 m size can experience the true coloured nature of its field? Does it mean that the electromagnetic field of the photon have a fine structure, below 10 -15

m, made of strong colour fields?Beyond the structure of the photon, we must pay attention on the machinery that gives birth to it. In the

previous example it happens through the interaction of three coloured partons. As we have seen on Fig. 9, the gluons are travelling through the space between the three coloured partons. We can see the procedure in a normal way, when time goes to one direction: in this case the gluons are created in the middle of this space and after following a curved track, pairs of these gluons are absorbed by the partons, thus changing their colour. But there is another interpretation of the figure: only one gluon travels around between the partons and it is just mediating their colour change, as it brings a new colour and brings away their original colour. But regardless of the interpretation, we have to find an explanation, as to why the tracks of the gluons are curving to the same direction, while travelling from one parton to another.

Indeed, one can recognise that the path of the gluons between the three partons is basically the same as the track of a simple harmonic oscillator in a rotating reference frame. That is, the picture we can see on Fig. 9 is nothing but a summation of the movement of an oscillator and a rotator. It is simply a particle, which oscillates in a system that itself rotating. The question arises immediately, whether, the oscillating gluon is rotating as well, or the three parton system is rotating and the gluons are only oscillating in the middle? As a matter of fact, we can state only that the rotation is relative: the triangle of the three partons seems to be rotating relative to the oscillating gluons.

The most important conclusion of this observation is that the mechanism of the interaction we had to suppose works only, if there is rotation in the system. No matter whether the gluons are rotating in the middle, forming a rotating boson or the frame of the three partons is rotating. They must rotate relative to each other to make the interaction possible. This means, that the interaction of the quaternion charges must create spin, or it just simply does not work. The existence of the spin can be a consequence of the quaternion mechanism. Without the spin, this mechanism of the interaction cannot exist. Thus, the existence of the spin is not an option for the particles, but a “must have”. If the quaternion charges and the quaternion mechanism of the interaction is existing, all composite particles have to have spin. So the partons themselves do not have spin, but all particles they create, will have spin.12

The Weak Interaction

We have seen till now, that if partons exist in the form we supposed, we can easily reconstruct the structure of every fundamental particle, their decay modes and reactions. Although the limited possibilities of this current article do not allow us to examine every reaction or decay mode of every particle, the author have done thorough research in this topic and found no contradiction. So, let us say, regarding the particle reactions the parton theory is perfectly in tune with the experimental data.

We also have seen already, that a new kind of correlation can exist between the strong and the electromagnetic interactions: the quaternion charge, which requires a new interaction mechanism as well. But this interaction mechanism can explain not only the appearance of spin and the question of the fraction electric charges, but reveal a connection between the gluons and the photon as well. Meanwhile, we could have the

12 Indeed, this situation suggests that the partons may have no electric charge. If they are rotating and having an electric charge, they can radiate energy. Even though the partonic systems have discrete energies, the excited states could lose energy. As we have not observed any kind of decay of muons or tau particles to electrons by the emission of photons, the individual partons probably do not have electric charges. This is supporting the view, that the partons only have colour charges, and they are creating the electric charge of a complex system as the real part of their imaginary charges.

comforting feeling, that we did not encounter any particle process, in which particles are created without the proper antiparticle. We have seen that particles appear only in pairs, or even in sextets: every colour and anticolour created the same time in one single process. In the next sessions indeed, we will see, that this is a universal rule: not even pairs are created in any process, only sextets with all existing charges.

Thus, we do not have to face with any philosophical problems, like particles giving birth to other particles, which were not existing in the parent particle before. That is, a particle flies off somewhere, where it wasn’t previously there. For example, the partonic approach of the pion decay is a very simple rearrangement of constituents: all parts of the decay products, the electron and the neutrino were inside the pion before. Or the case of the photon: it is there inside the charged particles, as a kind of gluon-vortex. When an electron-positron pair is annihilated, the photons are just released from the annihilating systems. By gaining energy, the virtual gluon-vortices become two real photons.

An important issue have not been addressed yet. Namely, it is the question of the X-interaction – the existence of which we had to suppose previously, to find the agent which bound the neutral partons together. We have seen that the existence of mixed composite particles – the quarks – which comprise either charged or neutral partons, suggest, that the X-interaction works between the coloured and neutral partons as well. In the case of the colour charged partons, this interaction works “in the background” in a less conspicuous manner, as in that case the strong interaction got the leading role. It is only the existence of the quarks, made of coloured and neutral partons, that proves the functioning of the X-interaction in the case of coloured objects as well. This means, that the X-interaction is universal, it works between all types of particles.

Having a closer look at the X-interaction, what clearly appears is that it works between three particles, just as the strong interaction. Supposing that the X-interaction is functioning in the same manner as the strong interaction, the three interacting particle would mean, that the X-interaction also has three charges and their anti-charges. We have notated the X-charges with the I, J, K letters, and the anti-charges with the Ǐ, , Ǩ letters.J ̆ In fact we could repeat almost the same thoughts in the same vein like before, in the case of the strong interaction. Of course, we are not going to repeat every thought, but will find only the analogies and draw the conclusions.

Firstly, if we think about the three colour charges of the strong interaction as the imaginary parts of one single quaternion charge, we have to do the same in the case of the I, J, K charges. We can never see the effect of these charges on a macroscopic scale, as these charges are closed into the interior of partonic systems. Although there are partonic triplets that have a colour charge – the quarks – there are no triplets with residual X-charge. In the case of the X-interaction, all charges are closed into the triplets, so all triplets are X-neutral. In the case of the neutrinos and quarks, all the three I, J, K charges must be present in the system to hold the composite particle together. In the case of the electron type particles, the charged leptons, it is not necessary, that all the X-charges are present in a particle, as the strong interaction holds the partons together anyway. But if X-charged electrons would exist, that would mean there are different kinds of electrons, that form more complex, two or three part systems, just as the quarks form mesons and baryons. As we have never seen anything like that, we can conclude, that the X-charges are closed in the partonic triplet systems in every case. Thus, every parton has an X-charge and the partonic triplet systems, the fermions never have X-charge, as the X-charges of the three partons are always neutralizing each-other.

Regarding the mechanism of the X-interaction, we can conclude, that the X-interaction probably works in a similar manner as the strong interaction: it has three imaginary charges that interacts the same way as the colour charges of the strong interaction. In that case the three imaginary charges together created a real electric charge. We have never experienced directly the existence of colour charges as they are closed in the particle systems, and we can experience only the effect of the electric charge on macroscopic scale. The same can be the case with the X-interaction: it is closed into the particle systems, so we cannot observe the I, J, K charges directly. Nevertheless, when neutralizing each other, they create a kind of charge that can be observed outside of the particle systems. We can observe the real part of the X-interaction as some kind of an interaction between the well-known particles: electrons, neutrinos, quarks.

We know of this interaction – the real part of the X-interaction – that every particle, which made of partons are involved in that. Thus, all fermions and perhaps some bosons as well, are interacting in this way.

Also, it is obvious, that this kind of interaction can be observed in the most direct way with the examination of the neutrinos, as the neutral partons of the neutrinos are not involved in any other interaction, only the X-interaction. So any effect, which can be observed in neutrino interactions, is indeed the effect of the real part of the X-interaction – the remnant of the X-interaction outside of the neutrino system.

It is the most basic feature of the neutrinos that they interact with other particles in a very weak manner. We do not know whether they have rest mass at all, so it is possible, that not even the gravitational field have an effect on them. Not considering the gravitational force, the neutrinos are involved in one interaction only, the weak nuclear force. So this force is the only candidate for the residual of the X-interaction that reaches out of the partonic triplet systems. According to our current knowledge, every known particle is involved in the weak interaction, and it is indeed the weak interaction, by which the neutrinos are created and annihilated in matter.

So we do not have to think too much of what could be the remnant of the X-interaction outside of the composite particles: we just now concluded that the neutrinos are interacting with other particles only by the weak interaction. That is, the charge, which is created by the I, J, K charges of the X-interaction, when they are neutralizing each other, is the weak charge itself. Or perhaps, we can say, that the X-interaction is the quaternion version of the weak interaction. The X-interaction is the extended version of the weak interaction. Thus, we had to realize, that the weak interaction is not that simple kind of effect, which only causes the decay of several particles. Instead of a simple effect it is indeed a four dimensional interaction that have several kind of charges, and it works in a much more complicated manner as we thought earlier. What we have seen till now, is just a one dimensional projection of a complex, four dimensional process. The same way as the shadow of a tree is not a tree, but a projection of its real, complex existence.

In fact, there is a significant difference between the electric charge created by the R, G, B charges of the strong interaction and the weak charge created by the I, J, K charges of the X-interaction (or eXtended-weak-interaction). The effect of the electric charge reaches to infinity, and this feature is related to the fact that the photon, the mediator particle of the electromagnetic interaction, has a zero rest mass and infinite lifetime. The mediator bosons of the weak interaction have a very large mass, thus, as virtual particles they cannot exist for a long time, and they do not reach far from the particle that emitted them. The characteristic time of their existence is about 10-24 s, during which the mass uncertainty of the particle is large enough to ensure its virtual existence. This time interval is equal to about 10 -15 m distance, counting with the speed of light. This is the region where the weak interaction can have on effect on particles. Needless to say, this is the cause we experience this interaction mostly by decay processes: during a decay event, every necessary particle is within the reach of the interaction. While for a particle reaction to be guided by the weak interaction, the particles have to be closer than the above distance – which happens obviously quite rarely, except for the case of the nucleus, where there could be dozens of particles within the necessary distance.

But what kinds of particles are mediating the known weak interaction? As far as we know, there are three particles that can mediate the weak nuclear force, the neutral Z0 and the two charged W bosons: W- and W+. For now, it seems, the Z0 particle is interesting, as it is usually called a kind of “heavy” photon, as it is quite similar to that particle. It is neutral, just as the photon, although it is not involved in the electromagnetic interaction at all. It is a tell-tale sign, that the Z0 has also integer spin, while it does not have any magnetic moment at all, so if we try to construct the inner structure of the Z0 boson, we cannot use any charged gluons. What is more, the antiparticle of the Z0 boson is itself, which is also the case for the photon. Perhaps we can say that in the form of the Z0 boson we have found the mediator particle of the X-interaction, the four dimensional extension of the weak interaction.

If there is almost perfect analogy exist between the strong-electromagnetic and the X-weak interactions, than the structure of the Z boson must be similar to that of the photon. The photon, as we have seen, is made of six gluons, which are all different: red, green, blue, and antired, antigreen and antiblue gluons. The X-interaction has to be mediated by gluons which does not have colour-charges, but X-charges: the above mentioned I, J, K charges. Let us call these particles for now X-gluons. There must be six different X-gluons, which we can denote with their X-charges: i, j, k and ǐ, , ǩj ̆ . Similarly to the strong interaction, the X-interaction is mediated probably by a kind of gluon vortex, although in this case the vortex is made of six X-gluons and not

coloured gluons. If any effect removes this vortex from the inner parts of a particle system, it can appear as a neutral boson. It will not have electric charge, as neither of its components had electric or colour charges. Although it is involved in weak interactions, it does not have weak charge, as it is double neutral: neutral by the i, j, k and by the ǐ, , ǩ charges as well. These two groups are creating opposite weak charges that arej ̆ neutralizing each other, but by their rotation they can cause similar alternating weak field, just as the electromagnetic field of the photon. And as this particle is made of x-gluons and x-antigluons, and contains all kinds of x-gluons, it is obviously its own antiparticle: any x-gluon finds its antiparticle within the boson itself. Indeed, this six-gluon complex is a good candidate for the Z0 boson. We can state, that our theoretical Z0 boson, and the experimentally observed one have basically the same parameters.

Fig. 10: As an analogy of the photon, we could create the model of the Z boson, the mediator boson of the weak interaction. It is composed of six x-gluons, all is colour neutral, but x-charged: i, j, k and ǐ, , ǩ.j ̆

The mediator bosons

We have seen in the previous sessions that all fermions, with a spin of ½ are made of three partons and the interactions that hold together these fermions are mediated by bosons which are made of six gluons. The colour charged gluons are creating the photon, while the x-charged gluons are creating the Z0 boson, which is similar in several features to the photon. But the charts of the elementary particles are showing two more bosons: the W- and W+ particles.

For the first glimpse, it seems that the mediator role of the W bosons is only apparent. These particles are formed only in the decay of composite particles that are made of quarks. For example during the decay of the neutron, one of the down quarks emits a W- particle, and while emitting it, it transforms into an up quark: d -1/3

→ W- + u+2/3. In a very short time interval, the W- boson decays into an electron and an antineutrino: W - → e- + ν̃e. The resulting two particles in our thought experiment are composed of six partons, while in the case of the W bosons, we would suppose, they are composed of six gluons, just as the photon and the Z boson. Nevertheless, even if not gluons, the W bosons can be made of six partons: the result will be a boson, with a spin of 1, and very similar properties to that of the other bosons. And as the electron was made of RGB, the antineutrino was made of SSS partons, we can conclude, that the W - boson is quite probably made of the same particles as its decay products: RGBSSS. In this way we do not need to suppose the creation of any particle during the decay of the W- boson. The decay process is a simple rearrangement of the constituents: RGBSSS → RGB + SSS.

The RGBSSS partonic structure of the W boson can account for several characteristics of the particle. The RGB partons are responsible for the creation of its negative electric charge and for its magnetic moment. The RGB and the IJK charges are creating two units of weak charge.13 Also, the RGB and the SSS partons are both

13 Indeed, it is not obvious, that the two weak charges of the W bosons have the same or opposite signs. In the former case the W bosons have 2 units of weak charge, in the latter case, the bosons have 0 weak charge. The decay modes of the W bosons, however clarifies the situation: they can decay into leptons and quarks as well. It means that for example the partons of the negative W- boson have only IJK x-charges and none of them has Ǐ Ǩ charges. In this way not only the RJ ̆ iGjBk + SiSjSk (charged and neutral leptons) decay mode is possible, but the mixed mode that produces quarks either: R iGjSk + SiSjBk

creating ½ spin as well, which are added together and so, the particle have an integer spin of 1. The same reasoning is true of course for the W+ particle: it is made of six antipartons, namely ŘĞ ŠŠŠ. It is also decayingB̆ quickly to a positron and a neutrino: ŘĞ + ŠŠŠ. And the partonic structure of the WB̆ + is obviously showing that it is the antiparticle of the W-.

There is only a little bit of strangeness, a little bit of asymmetry in this picture. We have a nice chart of the elementary particles: the fermions are made of three coloured and neutral partons, the mediator bosons are made of six gluons, while the two W bosons are again made of six partons. But isn’t it strange? We have the photon, made of six coloured gluons. We have to Z boson made of six colour neutral x-gluons. And while we could expect mixed bosons, made of coloured and x-gluons, instead, we get bosons, which are made of coloured and x-charged partons, not gluons. What is more, if we look at the constituents – the partons and the gluons – we can recognise that indeed, the list of partons and the list of gluons are virtually the same. We have three RGB coloured partons and three IJK charged neutral partons, and their antiparticles with ŘĞ and Ǐ ǨB̆ J ̆ charges. The list of gluons is the same: there are coloured gluons with r, g, b and ř, ğ, charges, that areb̆ building up the photon and there are the X-interacting gluons: i, j, k and ǐ, , ǩj ̆ . All partons have their counterpart in the list of gluons. The only difference is that, according to our previous assumption the partons are massive particles, while the gluons have no rest mass. In fact, if we neglect the presumption that the partons have mass, we can conclude, that the partons are indeed the same particles as the gluons. There are just simply no differences between them. In this case we do not have to construct two tables for the constituents of fundamental particles, but only one: the table of the six colour charged and the six x-charged partons. And in this case we can recognize perfect symmetry in the chart of fundamental particles: three partons are creating the fermions and six partons are creating the bosons. Though, the case of the photon obviously shows: the constituents of these particles have no rest mass. They can gain their mass only from their interactions.

Fig. 11: The partonic composition of mediator bosons. The equal role and structure of the photon and Z0

boson – made of gluons – and the W- and W+ bosons, which are made of partons, suggest, that the partons and gluons are the same particles.

Indeed, the supposition that the partons and the gluons are the same particles, make it easier to explain the decay processes of the bosons. The “decay” of the photon becomes a very clear and obvious process: if the photon has enough energy, it can split into an electron-positron pair. If the partons and the gluons are identical particles, than the photon is made of the same partons as an electron-positron pair. The photon contains the RGBŘĞ partons, and if it splits, the partons regrouping to an RGB electron and an ŘĞ positron. Naturally,B̆ B̆ energy and momentum have to be conserved in the process, so this “decay” cannot happen at any energy, but over 1,022 MeV, in the presence of matter the photon can undergo this “decay” process.

The case of the W bosons is a bit more complicated. It is known, that the W - boson at low energies split into an electron and an antineutrino – this process is happening during the second step of the neutron decay. But the heavier counterparts of the electron, the muon and the tau particles have the same partonic composition in the partonic theory: RGB. So it is an obvious step to expect, that at higher energies muon and muon-antineutrino pairs or tau and tau-antineutrino pairs can be created during the decay of the W - boson. But

(antiblue û + blue d quarks) for example. If the IJK and Ǐ Ǩ charges would mix in the W bosons, that could produce decayJ ̆ products with mixed charges also: IJǨ and Ǐ K for example, which makes their interaction impossible. Thus, the hadronicJ ̆ decay mode of the W bosons proves that they must have two sets of IJK charges.

is it possible, that sometimes not the proper kind of neutrino appears in the process? For example a muon and an electron-antineutrino appears, or a tau particle along with a muon-antineutrino?

The answer lies in the structure of the parent particles, the W bosons. In the neutron decay the W boson have a low energy, thus it can decay only to an electron and an antineutrino, as there is no energy for the creation of heavier particles. Even in this process, it is difficult to explain, why only electron-antineutrinos are created, as the muon or tau-antineutrinos have similarly low masses, thus the energy is enough for their creation. But apparently, only electron-neutrinos are created along with electrons, just as muon-antineutrinos are accompany muons and so on. Although it is difficult to detect neutrinos, there is no sign of free interchange of neutrinos in their creation.

Simple geometric considerations can answer this problem. The W bosons, just as any other mediator particle are made of six partons. If the boson is created in a low energy process, the structure of the six partons is expected to be symmetrical. There is no reason to think that the structure of the boson is distorted, so the partons of the boson are situated in the vertices of a regular hexagon. This means, when the W boson split into a lepton and a neutrino, the partons of the two particles are expected to form equilateral triangles. There is no reason to think that while the RGB partons are created in ground state, thus forming an electron, the neutral partons are forming a distorted triangle, which equals to a higher energy neutrino, a muon or a tau-antineutrino. In other words, at low energies there is no trace of the distorted form of an excited state. At low energies only electron and electron-antineutrinos can be created.

Nevertheless, if the W boson is created in a high energy process, one cannot expect that this high energy does not have an effect on the form of the W particle. Indeed, at sufficiently high energy the particle can have elongated vibrational states, and these states can decay into elongated decay products: that is, muons and muon-antineutrinos. It is reasonable to think that if the excited states of the fermions have an elongated shape, than the same is true for the bosons as well. And so, it is logical to assume that the elongated state will decay to elongated products.

Along with the leptonic decay modes, the W bosons can decay to other particles as well. The W bosons can decay to quarks, and at sufficiently high energies these quarks can create showers of mesons and hadrons. Indeed, above the energy of the muon creation, but below the energy of the tau creation, the decay of the W boson can result several kinds of particles, made of quarks. The most frequent product is the π meson. The partonic composition of the W- boson is RGBSSS. If this six partons split into RGB and SSS triplets, that would result in the leptonic decay modes. But if the partons are distributed into mixed triplets, that will result quarks: for example the RGS and BSS split will result an anti-blue up quark and a blue down quark. This pair of quarks is itself a π- meson, though due to the conservation of momentum and angular momentum, every decay event must produce at least two products. Thus, these two quarks will move apart and so will create at least two more quarks. Due to this, the minimal hadronic decay of the W boson will result in two pions. Of course, at higher energies, the number of the quarks created is increasing, thus producing showers of hadronic material. And of course, the higher energies can result in excited states of the W boson itself, so the split of the six partons can create excited quarks, charm or strange quarks as well.

Fig. 12: The figure shows two possible decay mode of the excited state of the W - boson. The left hand side picture shows the leptonic decay mode of the excited state, which result in the birth of a muon and a muon-

antineutrino. Previously, we have assumed that the muon is the excited and deformed state of the electron, and the same is true for the neutrinos. Thus, it is a logical expectation, that the muons and muon neutrinos are created from the excited states of the W boson. Even though the creation of excited neutrinos along with the ground state of the electron is not forbidden, due to geometric considerations it must be quite improbable.

The picture on the right shows the case, when the W boson decays in a fission-like process. In this case the former order of the RGB and IJK triplets are disappearing and the split forming mixed triplets, quarks. As the bounds of the strong force torn apart, this process needs obviously high energies. If the quarks are created in the ground state, the fission of the W boson creates a down and an up antiquark. The quarks can be created in excited states as well, which result in a strange quark and a charm antiquark. As these quarks move apart, they create showers of hadronic material.

It is interesting to note, that the direction of the X-interaction can change in the decay process. The right half of the figure shows that before the decay the direction of the interaction is anti-clockwise. During the low energy process, the boson split into two leptons, in which the direction of the interaction is clockwise. During the fission process, the direction of the interaction does not change. So in leptonic decays the direction of the interaction reversed, while in hadronic decay, the direction conserved. Indeed this can be the main difference between the leptonic and hadronic decay modes, which affect the parity of the particles.

We have an almost full picture regarding the composite particles that can be built of partons. There are triplets, that are made of partons and triplets made of antipartons. While there are no triplets with mixed composition, which contain partons and antipartons as well, as the mechanism of the interactions does not allow it. In that case the charges of the partons could not interact with each other, as there won’t be any direction which is sufficient for starting the interaction. Neither clockwise, neither anti-clockwise direction does not give an unequivocal result for the multiplication of the charges. This means that only those triplets can exist, which are made of purely partons, or purely antipartons, but never in a mixed state. The result is the basic four fermions of our table of fundamental particles: the electron, the up and down quarks, and the neutrino. As all of them have antiparticles and two excited states, so the table of fermions contains twelve particles and twelve antiparticles.

In a similar way, the table of bosons contains four particles. One of them is made of coloured partons and antipartons and another is made of neutral partons and antipartons: the photon and the Z0 boson. There is another particle, which is made of only partons – three coloured and three neutral: the W -. Its counterpart is the W+ which is made of only antipartons: again three coloured and three neutral. In theory, there could be a sextet, made of three coloured partons and three neutral antipartons, and its antiparticle made of coloured antipartons and neutral partons.14 But in this case again, just as in the case of the fermions, the direction of the X-interaction would be ambiguous. Also, the decay of these particles could result mixed fermions, which we have just seen, can’t exist. Thus, we have only four bosons, and probably no other combination of six partons can create a new particle.

There is an interesting feature of our bosons though. The W- and W+ bosons are the antiparticles of each other, and together they contain all the partons that we supposed to exist. There are three coloured partons and three coloured antipartons in the table of partons, and also three neutral partons and three neutral antipartons. These are all together twelve partons. All of them are present in either the W - or the W+ bosons. What is more, these are also present either in the photon and the Z0 boson. This obviously means, that in theory, these bosons can transform into each other in a reaction: γ0 + Z0 = W- + W+. Both end of the equation contains all existing partons. But this thread leads us to the supposition, that there can be a transition state, in which the two W bosons, or the photon and the Z unite before transforming into the other outcome. This would mean the existence of a super boson, which made of twelve different partons – in fact all kind of partons that are existing in the table of partons are present in that super boson.

14 With some restrictions, these particles may exist. To avoid mixed fermions, these bosons could decay only to a charged and neutral lepton, never to quarks. Such W’ bosons would product electron-neutrino pairs for example, while during the decay of the „normal” W bosons, there is an antineutrino appearing along with the electron.

The question immediately arising along with the possible existence of this super boson: is it the only one of its kind? The answer is not as simple as we would think. Of course, there is only one combination of the twelve partons, if the combination contains all the partons, without repetition. But these particles in theory can create different states. Two possible states can be expressed most simply as the bounded states of the two W bosons. The two W bosons have integer unit of spin. But in a bounded state these can eliminate each other, or they can be added together. So if we see the super boson as the bounded state of W bosons, they can, in theory create a 0 spin state and a 2 spin state. At this point it seems, we can’t decide, whether all the two states exist, for this we have to examine the interaction of the partons in more details.

Indeed, the name super boson fits very well to this particle. As it contains all possible partons, this boson is the particle of all possibilities. It interacts with every other particle, fermions and bosons as well. It can split into two W bosons and also into a photon and a Z boson. Thus, there is no particle, which can pass by it undisturbed.

Even though, at this point we do not have any explanation on the creation of rest mass of particles, we can easily estimate the mass of this super boson, by a simple trick. We know already the mass of the W bosons, and we can think of this super boson as a bound state of two W bosons. As the mass of the W bosons is 80 GeV/c2, we can estimate the mass of the super boson is somewhere between 160-80 GeV/c2. Although we don’t know any exact data for the possible bounding energy of the two W bosons, the bounding energy probably reduces the mass of the two.

Although this super boson does not have any connection to the theoretical Higgs boson, there isn’t any other candidate for this super boson, except for the one, that was found recently at CERN. In the expected mass range, between 160-80 GeV/c2, there is no any other particle, than the one discovered and identified as the theoretical Higgs particle. At least the experimental data accumulated in the past few years about this particle is not contradicting our suppositions. For example, the mass of the newly found boson is 125 GeV/c 2, and its most frequent decay mode is the split into a pair of W bosons.

With the supposition of this super boson, we reached the end of the list of composite particles. There are no other combinations of partons left. Thus, if we create a chart of the particles taking a role in our thought experiment, in the first row, we have to place the parton/gluon, the fundamental building block of all composite particles. In the second row, we have to place the basic fermions, the ground states of the possible partonic triplets. The third row contains the bosons: the photon, the Z and the two W bosons. And finally the fourth and last row contains only one particle, the super boson.

Fig. 13: The chart of fundamental particles in our thought experiment. Even though it is not written in the chart, there is a possibility that excited states of bosons are exist in nature, as for now unknown particles. These must be almost identical with the above bosons, having only larger mass and perhaps larger spin, e.g. the possible s=2 state of the super boson.

There is a far reaching consequence of the above conclusion. At the end of a logical train of thoughts, we reached the conclusion that the fundamental particles we know may built of the same universal building blocks: the massless partons or gluons. Indeed there is only one way for a massless particle to gain mass: if it gains kinetic energy. This kinetic energy will appear as the mass of the composite particle system, according to the well-known Einstein equation: E = m·c2. This means that the composite particles are containing such partons that are moving with the speed of light – as every other particle that does not have rest mass – nevertheless, they are bounded into the composite systems by enormous forces. And if the premises of our thought experiment is true, than indeed, all the particles of our world, every matter in the universe is made of particles, which are basically massless, but are always moving with the speed of light, bounded in small packages. Which means, that there is no rest mass at all in our world: it is just simply non-existing. If our suppositions are true, every mass we see in the universe is nothing else but pure energy.

Charge conservation

It seems, in the vertical direction we reached the end of our thought experiment as we created the last particle, the super boson. In the horizontal direction we have several unanswered questions left behind, though. Regarding the mechanism of the interactions, we have seen previously, that there are two basic kinds of interaction, the strong and the X-interactions working between the partons. These have RGB and IJK charges and their opposite charges as well. The electromagnetic and the weak interactions, the effect of which we experience in our experiments are the “one dimensional” projections of these more complex interactions. The two quaternion charges are linking these interactions and their one dimensional projections: the RGB and IJK charges are imaginary, while the electromagnetic and weak charges are the real parts of these charges. The

nature of the quaternion algebra causes that the interaction works as a kind of merry-go-round: it is rounding between the interacting particles, thus creating the spin.

Until now, we have neglected a serious problem of this mechanism. How these interactions can function in partonic groups, whose number of particles is not divisible with three? That is, we have seen that they work in fermions, which have three partons, and bosons with six or twelve partons. But what about the other numbers, like 2, 4, 5? To mention the most obvious cases, the neutron contains four coloured partons altogether. The proton has five coloured partons. And the number 2: how the interactions can start to work if a parton-antiparton pair is created?

Let us see the simplest possibility first: the interaction of two partons. Is it possible for two partons to interact, and so, to create particle system? If a parton-antiparton pair is created, can they join together to form a more or less stable composite particle? We have to turn to the quaternions to answer the question.

We saw, that three differently coloured partons can join together, creating a colour neutral RGB particle, which will have a negative electric charge, while the corresponding antipartons are also creating a colour neutral, but positive charged particle. However, the creation of an R-Ř pair for example does not give a clear result regarding the electric charge of the particle – the same is the case with the X-interacting I-Ǐ pairs for example and the resulting weak charge. If we just simply apply the multiplication rules of quaternions i·(-i) = j·(-j) = k·(-k) = +1 but changing the order gives an opposite result: (-i)·i = (-j)·j = (-k)·k = -1. It seems, if nature chooses a direction in which two imaginary charges can interact each other, that will result the same kind of charge. Thus, if nature prefers one direction, all parton-antiparton pairs would create negative charges. Or if it prefers the other direction, all pairs would create only positive charges.

Here we encountered a fundamental contradiction. If we suppose the existence of quaternion charges, than the creation of parton-antiparton pairs causing serious problems. If the partons are created in larger groups, the problem disappears, as the RGB and ŘĞ charges, or the X-charges can create neutral triplets, andB̆ the problem does not arise. But the creation of individual pairs would cause the accumulation of positive or negative charges, depending on, what direction nature chooses for the interaction. Our universe would inflate enormously due to the accumulation of only one kind of electric charge. The problem is not directly the creation of imaginary charges: they are neutralizing each other during creation, R + Ř = 0. But if these imaginary charges can interact, and thus create electric charge, that would redraw the picture of our universe.

The answer of this problem is probably the simplest answer. We have never experienced any sign of the accumulation of electric charges in large scales in the universe, which probably means, that partons are never created in pairs. And as a consequence of this, no particle exists, that is made of a pair of parton and antiparton. If a pair of parton and antiparton is created in some process, at the same time other particles must be created as well, to maintain the balance of the universe. That is, in the case of imaginary charges, a blue–antiblue pair is not balanced at all. All colours and anticolours should be created at the same time to preserve the charge balance. In this case the laboratory balance has not only two arms, but six: all of them have to hold the same amount of particles.

We might add: this result is not surprising at all. After all, the interaction of the quaternion charges needs a circle to start, and two points are obviously not enough to define a circle. At least three is necessary. Two-parton-systems do not exist, just simply because two point is not enough to define a circle. It needs at least one more point. But three particles are impossible to create at one time as the particles must be created along with their antiparticles. The particles must be created in pairs, while to define their interaction circle they need to be at least three. Very simple mathematical problem: the lowest common multiple of 2 and 3 is 6. At least six partons have to be created at one time, to save the order of the universe from the quaternion charges.

Needless to say, these six parton systems are the bosons, we have examined previously. Photons can be created from the vacuum at any time: they contain three partons and three antipartons, and their charges are completely neutralizing each other. Z0 bosons can appear also at any time in a massless, virtual form: the three colour neutral parton-antiparton pair also neutralizing the x-charges appearing in the bundle. The W bosons can be created in pairs only, as they are not neutral alone: in this case twelve partons are created at one time. Is it possible, that the nature is so munificent, that every time twelve partons are created? In this case every process would start with the creation of a super boson, which than split to a W boson pair, or a photon and Z

pair. The virtual particles can appear and disappear at any time, and only those portions of them are used, which is necessary for an allowed reaction.

This simple logic leads us to the conclusion that even though the composite particles are made of three or six partons, they can never be created alone. Even though a three parton system can be colour neutral, it can be created only with its antiparticle counterpart. In the case of the electron and the neutrinos, the particle triplets can freely leave the place of the creation, as they are fully neutral, regarding the RGB and IJK charges as well. But the case of the quarks is different. Even though their IJK charges are neutralized in the interior of the particle, the strong charges are not neutralized. The quarks must be a component of a more complex particle system, just to neutralize their colour charges. Or in other words, the existence of the quarks is allowed only because they are parts of more complex systems. They are always created as parts of a more complex system, with at least two quarks and never less. Thus single quarks can’t exist, unlike electrons or neutrinos.

As we know already, the quarks can form two kinds of systems. They create complex particles like the mesons, quark-antiquark systems that are containing six partons, while the baryons are made of three quarks with nine partons. For example the proton contains two up and a down quark, while the neutron has two down and an up quark. Their partonic structure is for example RSS(R)-Ř Š(G)-ŘĞŠ(B) and RSS(R)-GSS(G)-ŘĞŠ(B) – inB̆ the brackets we find the effective colour charges of quarks. Of course, we could index these partons with their x-charges as well, like RiSjSk, but for now, it is unnecessary, as they are neutralizing each other even in the quarks, and are rotating continuously in the system independently of the colour charges.

What is the situation with the mesons? In the case of the charged mesons, the situation is simple. They are made of a quark and an antiquark, but in such a way, that in fact they are made of either partons or antipartons purely, but never both of them. The partons never mix with antipartons in the charged mesons. Their electric charge obviously shows this: the negative ones contain three coloured partons, while the positive ones contain three antipartons beside the other neutral ones. Other options are excluded. For example the positive π+ meson is made of an up quark and a down antiquark. As we have seen above the up quarks are consist of antipartons, just as the down antiquarks. Their partonic composition is ŘĞŠ- ŠŠ – if for example theyB̆ have blue-antiblue colours. Thus everything is fine, the three coloured antipartons can interact with each other and they create the positive charge: ŘĞ = +1. The antiparticles of these antipartons are sitting somewhere inB̆ the universe in a negative pion or in an electron, so the world will be nice round and neutral. The electrically charged mesons don’t raise any problems for us, as their three coloured partons are creating the electric charges in the expected manner.

The case of the neutral mesons is more problematic. Let us imagine the meson which is made of a down quark and a down antiquark. Its partonic composition would be RSS-ŘŠŠ – if we choose their colour to be red-antired for example. And the world would collapse, as here exactly that parton-antiparton pair appears in one single meson, which we tried to avoid previously. The two coloured partons are unable to create their interaction and if they succeed somehow, it is not known, what kind of electric charge they could create. Nevertheless, it seems we are lucky: such meson, such pair of quarks does not exist in nature.

Even though, common sense would dictate, that quarks and their own antiquarks can interact and so they create mesons, this is not the case. The experts of this field have long ago realised, that the neutral mesons produce a strange phenomenon, the so called quark mixing. The main point of this phenomenon is that the neutral mesons are not simply the pairs of a quark and an antiquark, but superpositions of such states. The neutral π0 meson, the simplest case of this quark mixing, is a state of a down quark-down antiquark pair, combined with an up quark-up antiquark pair: (dđ-uû). In terms of the partons, this combination is the RSS-ŘŠŠ – GBS-Ğ Š structure – which indeed contains all existing partons. In this way either the colour charges areB̆ neutralized in the RGB and ŘĞ triplets, either the x-charges in the other six colour neutral partons.B̆

Fig. 14: The schematic picture shows the quark mixing phenomenon of the neutral π0 meson. The state is a combination of an up-antiup (left) and a down-antidown (right) quark pairs.

The same quark mixing phenomenon appears in the case of the vast majority of the neutral mesons. Sometimes not only two but three states are combined: the η0 meson for example is made of the superposition of the (uû+dđ-2sŝ) quark states, while its „brother”, the ἠ0 is made of the (uû+dđ+sŝ) superposition. In these mesons 18 and 24 partons create the perfect balance of imaginary charges. There are some heavy mesons though, which appear to be simple quark-antiquark pairs. Nevertheless, it is possible, that these are also superpositions of different quark-antiquark pairs. The cause of the apparent lack of quark mixing is that, we do not notice the effect of the lighter quark-antiquark pairs along with the dominant heavy quarks in the superposition.15

It seems, that the creation of parton-antiparton pairs are quite limited process. The creation of single pairs is forbidden, and only three pairs of partons can appear at a time. Even the existence of parton-antiparton pairs are forbidden, and the mesons which would contain such a pair creating the quark mixing phenomenon to avoid the appearance of such pairs. We can conclude from this, that every process in the particles realm mediated by partonic sextet bosons, that is, the mediator bosons. Shortly: no pair creation allowed, only mediator bosons can be created from vacuum.

Previously, as we examined the reactions and decays of particles, we did not take the participation of any mediator bosons into account. But now, as their importance became clear, we have to describe every process in the particles’ world, every reaction, decay and creation of particles by considering the role of the mediator bosons. We have seen for example previously the decay of the neutron to a proton, electron and antineutrino. This process is indeed the transformation of a down quark into an up quark. At that time we needed only two coloured and a neutral parton-antiparton pair to describe the process. But now, we know that is impossible: we have to count with the emergence of three coloured and three neutral parton pairs to preserve the balance of charges and also, to fulfil the needs of the process.

Indeed, the transformation of the down quark into an up quark with the help of the bosons is similar as before, and giving the same results. If we had a red down quark, RSS, and we add the three coloured and three neutral parton pairs, as a result all the partons of the original quark annihilate, and the remaining partons are creating a new up quark and a W- boson. As there is a W- boson in the final state, we can suppose that the partons are first creating a W--W+ boson pair, and the W+ will react with the down quark, while the remaining W- boson will create the other two decay products, the electron and the antineutrino. RSS (down) + (SSSRGB (W-) + ŘĞ ŠŠŠ (WB̆ +)) = RGBSSS (W-) + Ğ Š (up). So the process consist the following steps: B̆

- the creation of a virtual super boson (6 parton pair)- the decay of the super boson into a W boson pair- merging of the W+ boson into the down quark, and so creating an up quark- decay of the W- boson into an electron and an antineutrino

15 After all, it is not a surprise: the top and bottom quarks are several thousand times heavier than the up and down quarks, thus, they have an overwhelming effect on a meson structure. As the mesons of the heavy quarks are at the same time very short lived, the detailed examination of these resonances is a difficult task.

Fig. 15: The transformation of the down quark into an up quark by the mediation of W bosons. The positive member of the W boson pair stays in the down quark and transforms it to an up quark. The negative W boson leaves the quark and almost immediately decays to an electron and an antineutrino. If the down quark was part of a neutron, than this transformation leads to the decay of the neutron.

This transformation of the down quark into an up quark is important now only because a similar process leads to the mixing of the different quark states to produce a neutral meson. For example the neutral π 0 meson can be created either in the down-antidown or in the up-antiup state, though soon it becomes the combination of these states, without any external influence. How so? Indeed, in a very simple manner. We have just seen, that the down quarks can transform into up quarks by the help of the W bosons. A down quark-antiquark pair can be transformed into an up quark-antiquark pair by a virtual W boson pair. The positive W + boson transforms the down quark into an up quark, while the negative W - boson transforms the down antiquark into an up antiquark. Another view of the same process is that the down quark emits a W - boson and so becomes an up quark and the released W- boson transforms the down antiquark into an up antiquark. It is indeed the same procedure, and the final result is that the down quark-antiquark pair transforms itself into an up quark-antiquark pair without any external influence. By the effect of virtual W boson pairs, the quark flavours can change freely, if both the quark and the corresponding antiquark are present. Down quarks into up quarks and vice versa. This is the way the neutral mesons are simply solving the problem of colour-neutralness, by mixing the flavours of the quarks with the help of the mediating bosons.

Fig. 16: The quark mixing process as it actually takes place in the neutral π0 meson: without any outer effect, the quarks of the meson can oscillate between the dđ and uû states, by the exchange of virtual W boson pairs.

Summarizing the process: the interaction of the quarks creates a virtual W boson pair – there isn’t any obstacle of this event as the W bosons are the antiparticles of each other. Then, by absorbing the W + boson, the down quark transforms into an up quark, while the W - boson is absorbed by the down antiquark and so it becomes an up antiquark. The reverse process can take place of course, by absorbing the other member of the W boson pair. Thus, absorbing one of the W bosons change the flavour of the quark, while absorbing the other one transforms the quark back to its original form. Due to the interaction of the quarks, the W boson pairs are continuously present in the system, so the neutral π0 meson will naturally be the superposition of the two states: dđ-uû.

It is interesting to note, that the emission and absorption of the W bosons are not necessarily simultaneous, so the dû + W+ and the uđ + W- states can also be formed in the neutral π0 meson. These are indeed identical to the π- + W+ and π+ + W- states. As these are colour neutral and also electrically neutral states, they are helping to interpret, how the electrically neutral state of π0 meson can be formed. In the case of the dđ-uû mixed state of the neutral π0 meson, the solution of the problem is a bit difficult. It would be problematic to interpret, how the partons of these states interact, and it would be difficult to prove that these states are present in the system at any time simultaneously. But the interpretation of the neutral π 0 meson as the mixed state of π- + W+ and π+ + W-, allow us to avoid any complicated explanation. It is simply obvious that the superposition of these states is creating an electrically neutral meson.

There are three important consequences of these thoughts about the interaction of quarks in mesons. They are important especially because after the recognition of such rules, we can use them in the examination of other kinds of quark-quark interactions. That is, the recognition of these consequences is helping to understand the interactions taking place in baryons, the three quark systems.

One of the main consequences of the previous thoughts is that single gluons are non-existing, so they cannot be the mediating agents in the interaction of quarks. The reason is simple. We have seen that, if we suppose the existence of quaternion charges that will contradict to the emergence of single partons or even single parton pairs. Only partonic sextets can be created from the vacuum to avoid ambiguity and to preserve the charge balance of our universe. Thus only the creation of photons, Z bosons and W boson pairs are allowed – of course, only if quaternion charges exist. But previously we have seen that the partons and gluons are quite probably identical particles. And this means, that the existence of quaternion charges are contradictory to the existence of single gluons. So, if we suppose the existence of quaternion charges, no individual gluons can exist, and all interactions are mediated by bosons – partonic sextets – instead of individual gluons.

The other important consequence is the connection between the existence of the quaternion charges and the quark mixing procedure. We have seen that, if quaternion charges exist, than parton pairs cannot exist, and so, the neutral mesons cannot exist in a simple quark-antiquark form. Though, due to the interaction of quarks by the W bosons, the quark mixing phenomenon immediately occurs, that saves the neutral mesons from disappearance. Thus, the existence of quaternion charges makes it inevitable, that the neutral mesons are all superpositions of different states. And indeed, the quark mixing phenomenon really exists in nature. Of course, the existence of quark mixing does not necessarily mean, that quaternion charges are existing. But makes it reasonable, as we do not know any other cause, why the quark mixing phenomenon is necessary for nature.

The third interesting consequence of the previous thoughts is that the interaction through the bosons does not necessarily changes the colour of quarks. Sometimes it changes the flavour of quarks instead. We have seen, in the case of the neutral π0 meson, that the quarks can interact through the W boson exchange, which does not affect the colour, but changes the flavour: the u quark becomes d, and vice versa. Thus, we can conclude, that the interaction through the mediation of a photon can change the colour of the particles, but through the mediation of W bosons the flavour of the quarks are changing. In the charged mesons probably the former, colour changing mechanism dominates, while in the case of neutral mesons, the flavour changing interaction is possible only.

Let us now examine the structure of the baryons. The baryons are always made of three quarks with different colour charges. As we just concluded, the existence of quaternion charges is contradicting to the existence of individual gluons. Thus, in the partonic world, where interactions prefer the existence of

quaternion charges, we have to forget about individual gluons. We have to choose a boson to interpret the interaction between the quarks of a baryon.

Quite probably, the mediator boson in the case of the baryons is not the Z boson. Even though this boson is important in the formation of quarks as the mediator of the X-interaction, but probably do not play an important role in the interaction of the coloured quarks themselves. It is quite probable that those bosons are important in this case, which contains coloured partons: namely the photon and the W bosons.

We have seen previously that the interaction through the mediation of photons needs 3 coloured partons. Other numbers are giving ambiguous results. So if a baryon contains 3 or 6 coloured partons, the mediating boson can be the photon. Indeed there are such baryons, in which there are three or six partons. The problem in the case of such baryons, that they contain three identical quarks. Due to the Pauli principle, identical quarks cannot occupy the same state in the baryon. Two of them can be in different spin state on the ground level, but the third one must be on a higher energy level to avoid contradiction to the Pauli principle. Thus, such baryons never exist in a low energy state: they are always unstable, short lived particles. Such are, for example the two delta particles, the Δ++, consisting of three up quarks, and the Δ - made of three down quarks. Needless to say, the former contains six coloured antipartons, while the later contains three coloured partons in the three down quarks.

Much more interesting is the case of the nucleons, the proton and the neutron. In their case the mediation of photons is possible, but difficult to describe, as they contain both coloured partons and antipartons as well, 5 in the proton and 4 in the neutron in total. These numbers make the interaction through photons ambiguous: the direction of interaction is not specified. Perhaps, photons can create some kind of interaction between the partons – especially in the proton, where there are all the three anti-colours appearing – but surely it cannot create the main force that hold the quarks together. If we rule out the existence of individual gluons and the role of photons and Z bosons in the baryonic structure having secondary importance, the only possibility left is that the interaction between the quarks is mediated by the W bosons.

Let us see for example the case of the proton first. The proton consists of two up and a down quark. Its partonic composition is for example RSS(R)-Ř Š(G)-ŘĞŠ(B) – where the down quark is red, and the two upB̆ quarks are green and blue. We have seen previously, that if an up quark emits a W+ boson, it becomes a down quark: u+2/3 = d-1/3 + W+. Of course, the opposite is true, if the down quark absorbs a W+ boson, it becomes an up quark. This means, that this two procedure causes the interacting two quarks to exchange their flavours. If an up and a down quark interact, the up quark emits a W+ boson and becomes a down quark, while the down quark absorbs the W+ boson and becomes an up quark. The two quarks seem to be changed place with the exchange of the W bosons. Of course, the down quark can also start the interaction by emitting a W - boson, which the up quark absorbs, and so on.

This thread of thoughts suggests that there can be a flavour changing interaction working between the quarks of a nucleon. And if quaternion charges are real, than there isn’t any other possibility for their interaction. But in fact, there is no need for any other interaction, as in effect, this process is the same as the classical view of the interaction of quarks. What is happening during the process? The quarks are changing flavour. But in this procedure the colour of the quarks are not changing. That is, if a red down quark emits a W -

boson, it becomes a red up quark. If a blue up quark absorbs the same W - boson, it becomes a blue down quark. It is easy to follow it on partonic level: RSS(red down) = RGBSSS (W -) + Ğ Š(red up), and then ŘĞŠ (blueB̆ up) + RGBSSS (W-) = BSS (blue down). As the W bosons are colour neutral, it is obvious though that the colours of the quarks are not changing during the emission and absorption.

The proton comprises three quarks, two ups and a down. When starting the interaction, the down quark can emit a W- boson, thus becoming an up quark. At this moment there are three up quarks in the system and a W- boson. In fact this state is equal to a virtual delta baryon plus a W boson system: Δ++ + W-. Also, the two up quarks can initiate the interaction by emitting a W+ boson. If one of them do so, than there are two down quarks, an up quark and a W boson is in the system. That is virtually a neutron and a W+ boson system. It is indeed interesting, as the exchange of W bosons is not that kind of rotating interaction as we have seen before in the case of quaternion charges of the electron, but the traditional particle exchange interaction. And as the red down quark becomes red up quark and the blue up quark becomes blue down quark, we experience it as if

some kind of colour exchanging interaction would take place: dr + ub → db + ur. Indeed, it is impossible to distinguish what have changed, the colour or the flavour of the quarks. Thus, the exchange of the W bosons are in effect the same kind of interaction what was traditionally viewed as the cause of the strong interaction, through the exchange of two-coloured gluons.

The case of the neutron is very similar to that of the proton. It consists of two down quarks and an up quark: udd. If the up quark initiates the interaction, it emits a W+ boson and as it becomes a down quark, the neutron becomes a system of three down quarks and a W+ boson: that is a virtual Δ- + W+ boson system. If one of the down quarks initiates the interaction, it emits a W - boson and while becoming an up quark, the system becomes a sum of uud quarks and a W- boson: a virtual proton and W- boson system.

Now, it is easy to determine the electric charges of these systems, which are forming during the interaction, mediated by the W bosons. The proton can be a virtual system of a Δ++ and a W- boson. The electric charge of these particles is determined by the strong interaction through their quaternion charges. Thus the proton must have a positive unit electric charge. Also the proton could be a virtual neutron - W + boson pair, which suggest that the neutron is neutral and again, the proton have positive charge.

The neutron, the ddu quark system can be a virtual Δ - + W+ boson system. As these particles have a determined electric charge by the interaction of their colour charges, the neutron must be neutral. And as the same ddu system can transform into a duu quark system and a W- boson, that is a proton and a W-, which again proves, that the neutron is neutral. No matter which particle or superposition we examine, we do not find any contradiction in this scheme. The interaction mediated by the W bosons between the quarks, give a clear picture of its mechanism and the electric charges of the composite particles, the baryons.

However, we have to make clear, that the W boson field, that makes the interaction of the quarks possible, quickly disappear outside of the quark systems. The half-life of the W bosons is about 3·10 -25 sec, which means, that even with the speed of light, they can reach 10-16 m distance during this time. Even if a proportion of them can reach slightly larger distances, as this life-span is a statistical value, one cannot expect that they reach more than the diameter of a baryon. The diameter of the nucleons for example is 8·10 -16 m, which means, that it is highly improbable, that the W boson field of the quarks have any effect outside of a nucleon. This probably means, that the W boson field that works at smaller distances than the distance of the nucleons in atomic nuclei, does not have any significant effect on the nuclear forces. The nuclear scale is just too large for the W field – it remains in the close proximity of the quarks.

Even though we have excluded previously that any other bosons than the W bosons can mediate the interaction between the quarks of the nucleons, it does not mean, that the other bosons – namely the photon and the Z – have no effect at all on the quark systems. The main interaction that bound the quarks together is probably mediated by the W bosons, but the other bosons can cause perturbations in this interaction. If the main interaction bounds the quarks together and thus, they are close to each other, the other bosons can create weaker interactions, perturbing the main interaction.

For example in the case of the Δ++ particle – the uuu quark system – the possibility of photon mediated interaction is obvious, as in the three u quarks, there are six coloured antipartons, that can interact by their colour charges with photons. Similarly, is the case of the Δ -, the three d quarks are containing three differently coloured partons, one in each quark, so the strong interaction can again work. The case of the nucleons is slightly different, as in their case the numbers of coloured particles are not divisible with 3. The proton contains four coloured antipartons and a coloured parton, while in the case of the neutron there are two coloured antipartons and two coloured partons in the system. Obviously, the coloured particles of the neutron cannot interact by photons: this situation is just as ambiguous as in the case of the neutral mesons. Nevertheless, in the case of the proton there are always present three differently coloured antipartons in the system. Thus, in the proton, photons can mediate an additional interaction between the partons.16

16 Indeed, this additional interaction can be the cause for the slight mass difference between the proton and the neutron. One would expect, that the neutron has a lower mass than the proton as in the traditional theory the charges of the quarks of the neutron are neutralizing each other, and so, they create a deeper bounded state, than the proton with the repelling force of its inner parts. In our recent thread, the quarks have no electric charge, and the proton is the more deeply bounded state.

Another perturbation can be caused by the Z bosons. In terms of the X-interaction and the Z boson, the quarks and baryons are much more symmetric systems, than in terms of the strong interaction. All partons have IJK charges and all antipartons have the opposite charges, regardless of their colour charges. Thus, every quark contains all the three X-charges or anti-charges. These charges are interacting mainly inside the quarks, but theoretically it is possible, that the partons of different quarks interact with each other. For example, an I and a J charge of a quark can interact with a K charge of another quark. As the quarks are probably much smaller than the distance between the quarks, this interaction is much weaker than the one inside the quarks. For the above mentioned I and J charges the K charge of their own quark is much nearer than the K charge of the other quark. Though, such an interaction can have an effect on the formation and inner interactions of the baryons.

The conclusion we can reach by these thoughts is that the main source of the force between the quarks is the interaction mediated by the W bosons. Due to their mixed composition, the W bosons can mediate the strong and the X interactions as well. In the case of the quarks, we excluded either the mediation of individual gluons, either the photons as the source of their attractive force – of course, only if quaternion charges are existing. The only possibility left for the quarks, is a flavour changing interaction by the exchange of W bosons, which in effect have no difference of the usual view of the strong interaction: a colour changing interaction by the exchange of two-coloured gluons. This main interaction can be perturbed by two other effects: the strong interaction between the coloured partons of the quarks by the mediation of photons, and a similar effect of the X-charges by the exchange of Z bosons.

The last thought that may be of interest, regarding the quark systems, is a simple point on the structure of the W bosons and the charged π mesons. We have to notice that the partonic compositions of the W bosons are the same as the composition of the charged π mesons:

RGBSSS (W-) = RSS (d) + GBS(û) (= π-)ŘĞ ŠŠŠ (WB̆ +) = ŘŠŠ (đ) + Ğ Š (u) (= πB̆ +)

According to the traditional view of the strong interaction, the interaction between the quarks is mediated by individual gluons, while the interaction between the quark systems, the baryons is mediated by π mesons. Instead, we have now another possibility: the quarks are interacting through the exchange of W bosons – made of gluons – inside the baryons. While outside the baryons, the π mesons are mediating the interactions, which have the same partonic composition as the W bosons. This means, that the meson field that the baryons are creating around themselves, is in fact the modified version of the W boson field inside the baryons. The W bosons have a very short lifespan, but even the virtual W bosons can decay to mesons with a quite large probability. Thus, the W field, which decomposes at the border of the baryons, is continued outside the baryons as a meson field. This means, that indeed, the interacting field of those quarks, which imprisoned inside the baryons, can escape the borders of this prison. So the quarks of the baryons can form even more complex systems than the baryons and mesons: the atomic nuclei.17

17 The main difference between the hypothetical W boson field of the quarks and the π meson field of the nucleons is the spin of these mediator particles. The W bosons have a spin of 1, while the same value for the π mesons is 0. This means that the W bosons cannot transform simply to π mesons. Only W+-W- pairs can transform into π+-π- pairs. But this obstacle does not avoid the W boson field to transform easily to a π meson field as both of them are made of particle-antiparticle pairs.Even though it would be a comfortable idea, to suppose, that the W field is responsible for the attraction of the nucleons in atomic nuclei, there is a simple reason, why it cannot be true. The simplest nucleus, the deuteron is the bounded state of a proton and a neutron. This system has an integer spin of 1, which means that the spins of the neutron and proton are aligned to the same direction. Owing to the spin addition rules, in this case only those bosons can mediate the interaction, which has zero spin, for example the π mesons.

Parity

We haven’t pay attention yet about the parity of particles. That is, what happens with the particle systems, if there is a flip in the sign of the spatial coordinates of the particles? It is not a surprise, that in the case of the fermionic systems, which are made of three partons, the wave functions of the particles will be anti-symmetric. A flip in the sign of the coordinates would flip the direction of the interaction between the partons. It is not possible though, as the direction of the interaction have to be the same as before to preserve the sign of charges. So the flip of the sign of the coordinates will cause a flip in the sign of the wave function as well. Thus, the partonic triplets, the fermions are anti-symmetric. This is basically due to the chiral nature of the interaction, which was reduced from the supposition on the existence of quaternion charges.

What is the situation with the bosons? The case of the photon and the Z boson is simple. They have three imaginary charges and the three opposite charges as well: RGB-ŘĞ for the photon and IJK-Ǐ Ǩ for the Z boson.B̆ J ̆ The interaction of the partons is independent of the interaction of the antipartons. As we have concluded previously, the direction of interaction is opposite for partons and antipartons, so they create integer spin of 1 for the mediator bosons. This means, that a flip in the sign of the coordinates will cause a flip of the spin, but not in the sign of the wave function. There are two different directions of interaction and there are two partonic triplets in the system before and after the sign shift as well. Thus, the photon and the Z boson have symmetric wave functions and therefore, their parity is positive.

The same is true for the W bosons, although the mechanism of the interaction enables an interesting feature of these bosons: in some cases the W bosons do not preserve parity. The W bosons have three strong colour charges and six X-charges – two packs of IJK charges – which mean that the situation can be more complicated as before. The three colour charges are creating an interaction between the coloured partons, just as before. But the six X-charges can create interaction in two different directions. As it could be seen on the right side of Fig. 12, the six X-charges are in the following order: IJKIJK. There is a possibility that all the six X-charges are interacting in one row as they obviously cannot interact independent of each other. There exists another possibility, that the six charges are forming two triangular interactions, but in this case the interactions find the IJK order of the charges in the other direction. The formation of two triangular interactions would lead to the disintegration of the boson, as there is no force that bonds together the two triangles, so in some cases the decay of the W bosons can be parity violating processes.

This possibility is interesting only because in some decay modes of the W bosons the direction of the interaction is conserved, while in the other, the direction turns to the opposite. As it can be seen on Fig. 12, during the leptonic decay, the hexagonal interaction of the X-charges, which involves all the six charges, dissolves. Instead of that, two triangular interactions are formed with an opposite direction. On the other hand, during the hadronic decay – the fission of the W boson – the direction of the X-interaction is preserved. The two triangular interactions that forms after the decay, inherits the direction of the hexagonal interaction. Thus, we can conclude that, in the hadronic decay modes of the W bosons the parity of the system is preserved, while in the other situation, during the leptonic decay, the parity of the system changes.

To examine the decay further, we have to pay attention on the plane of the original boson – that is, the plane where the partons of the boson are situated. Regarding the leptonic decay, we have no reason to think, that the planes of the decay products are not parallel to the plane of the original hexagonal system. As the hexagon splits into two triangles, the triangles are inheriting the plane of the original hexagon. The forces, which repelling the decay products are quite probably perpendicular to this plane, so during this decay mode, the products have a parallel velocity and spin vectors. The spin is obviously perpendicular to the plane of the partons, while the two repelling triangular planes developing a velocity that is also perpendicular to the planes. In the case of the charged decay product, the electromagnetic interactions with matter turn the spin of the particle easily and quickly to other directions.18 In the case of the neutrinos though, the lack of frequent

18 In fact, it is simple to prove that the spin and velocity vectors of the charged lepton product are also parallel. The spin of the original W boson is 1, and the two decay products have a spin of ½, which means that the spin of both products are pointing to the same direction as the original spin of the boson. Observing that the spin and velocity vectors of the neutrinos are parallel, due to the preservation of momentum, the spin and velocity of the charged lepton must be also

interactions preserves the original situation. According to experimental data, the neutrinos always have parallel spin and velocity vectors, which is perfectly in tune with our current thread.

Neutrino experiments have already shown that the spin and velocity vectors of neutrinos are antiparallel, pointing to opposite directions, while that of the antineutrinos are always parallel. It is often said, that the neutrino is “left handed”, because, when the left thumb shows the direction of the velocity, the other fingers of the left hand are showing the direction of the “spinning” of the neutrino. In the same way, the anti-neutrino is “right handed”: if the thumb of the right hand shows the direction of movement, the other fingers of the right hand are turning to the direction of the spinning of the anti-neutrino. In fact, this observation unveils the direction of the X-interaction: in the case of the neutrino, which is made of antipartons, this direction is clockwise, while in the case of the antineutrino, made of partons, the course is counter-clockwise. In both cases, the other direction is just simply forbidden by the quaternion multiplication rule.

Contrary to the leptonic decay, during the hadronic decay of the W bosons, a much less symmetric situation occurs. In this case the split between the two parts of the boson, a fission process create deformed products, so we cannot even guess any correlation between the original plane of the boson and the direction of the repelling forces by which the products gaining their velocity. Thus, in hadronic decay modes, the velocity and spin vectors are not linked to each other.

Fig. 17: In a system consisting of six partons, the course of interaction can turn into the opposite direction. The figure shows the partonic structure of the W- boson. If the two packs of IJK charges are exchanged in a hexagonal system, involving all the six X-charges, the direction of the interaction is counter-clockwise. However, if the interaction of the three coloured and three colour neutral partons takes place separately, in two triangular systems, the IJK sequence can be formed only clockwise. The hadronic decay of the W boson inherits the direction of the hexagonal interaction, while the leptonic decay inherits the direction of the triangular version.

Regarding the inner interactions, the W bosons have a kin: the electron. Just as in the case of the W bosons, the partons of the electron also have all colour and X-charges. It means that both interactions – the strong and the X-interactions – are working inside the electron. The question arises, whether the two interactions are independent of each other or not? Are they revolving around the partonic triplet in the same direction or perhaps the opposite to each other? The later possibility would be a bit strange, as in this case the spin created by the strong interaction would be opposite to the one created by the X-interaction. Even though it sounds strange, we cannot obviously exclude this possibility. It would mean that the particle has two different spins, but they are appearing separately during strong-electromagnetic or X-weak interactions. But does nature allow such duality? Or we can reword the question in another way: is it possible that there are two kinds of electrons? In one kind, the direction of the two interactions is the same, while in the other the directions are different.

The question indeed answered long time ago. One of the experiments about the violation of parity was conducted at the end of the ‘50s. In that experiment, the decay of 60Co nuclei was examined, while the sample

parallel.

of 60Co was cooled near to 0Ko and was placed to a strong magnetic field. The result of the experiment was that the electrons produced during the decay do not have a symmetric spatial distribution. The electrons appeared with a much higher probability in the direction opposite to the direction of the magnetic field, than the direction parallel to it. This means that, if the spin of the 60Co nuclei are directed by the magnetic field, and the thermal movement of the nuclei are reduced, than the decay favoured only one direction. It is interesting from our perspective because the magnetic field that set the spin of the nuclei, have an effect only on the electric charge and the magnetic moment of the particles, due to the strong-electromagnetic interaction. The decay process is in turn controlled by the weak interaction. The result of the experiment has shown that, setting the direction of the strong-electromagnetic interaction will set the direction of the X-weak interaction as well. This means, that the direction of the strong and the X-interactions are not independent of each other. Or to word the answer in the way we asked the question: there are no two kinds of electron, only one. The direction of the interactions and the spin is completely determined.

Indeed, there are several other experiments have conducted in the last decades, which proved that parity is quite often not conserved in weak interactions. Most of them include either electrons or W bosons, which suggests, that the above thoughts can be repeated about the directions of interactions and the change in the direction of interaction during the decay processes of bosons. Other experiments have shown already, that the CP violation can also occur: in this case the charge is also flipped along with the space coordinates. The violation of CP in some cases is even simpler to explain, using the parton model and the quaternion charges. As we have seen, the electric charge is not determined simply by the presence of colour charges, but the initiation of interaction in the allowed direction is also necessary for that. The flip of charge in some cases causing immediately the flip of space coordinates as well, and so, another flip in the coordinates gives back the original values. Thus the violation of parity or combined parities can have an easy explanation due to the existence of quaternion charges.

Without any detailed analysis of these experiments about the violation of parity, we can draw an important conclusion. We have seen that, the directions of the two chiral interactions are depending on each other. If both interactions are working in a particle, they have the same direction, even though this process is breaking fundamental symmetries of our world.19 The violation of fundamental symmetries can lead us to an important conclusion. The CPT (charge-parity-time) invariance does not exist: observing a phenomenon in nature does not mean, that the flip in the sign of spatial dimensions, electric charge and time result us a phenomenon, which can be observed also in nature.

This violation of symmetries follows from the fact, that the direction of the two interactions is the same, to create definite charges and spin for all composite particles. But if the two quaternion charges are not independent of each other, than the supposition arises: they are perhaps not two, but one single quality. One charge, which can be described by an eight digit number, an octonion. In other words, the dependency of the two quaternion charges means, that they can be united into one single octonion charge to successfully describe their nature.

Beyond the realm of quaternions, there is a system of numbers, which nature perhaps also uses when creating our world: the octonions.20 These numbers are comprising one real and seven imaginary parts. Though, the seven imaginary parts does not have equal role and importance. The fifth part has a special role in the number. The base of the fifth part is created from the multiplication of the 6 th-8th imaginary parts, just as the real part is created from the multiplication of the 2nd-4th parts. The two halves of the octonion number, which are indeed two quaternions, yet interdependent: the multiplication rules between the purely imaginary second quaternion and the other half, containing the real part ensuring that the second quaternion have an effect on the first one, and finally on the real part as well.19 Previously we left open the question, whether the three partons or the central virtual boson is rotating in a fermionic system. Obviously, if the three partons are rotating, the two interactions will experience the same course for the rotation: the same spin. In the case of the rotating bosons, there is no such limitation; the bosons can rotate in different directions independently. Thus, the observation, that both interactions are circling in the same direction suggest, that the three valence partons are rotating in the system, not the central bosons.20 There are no other, larger system of numbers beyond the octonions, which include the real, complex, quaternion and octonion numbers.

The structure of the octonion algebra is indeed corresponds to the mechanism of interactions. The fully imaginary quaternion fits to the X-weak interaction: the IJK charges are the sixth, seventh and eighth imaginary part of the octonion charge. The multiplication of these charges results the weak charge, which is the fifth imaginary part. This makes sense of the fact, that we cannot observe the weak charge directly in our experiments: it is trapped in the realm of the particles, and only the indirect results of this interaction can be observed. From a point of view, it behaves like the electric charge, but it does not have a macroscopic field. Indeed, using the octonions to describe the charges of a particle, the weak charge is just as imaginary as the IJK and RGB charges: it is impossible to observe it in the macroscopic world. But this weak charge has an effect on the RGB imaginary charges, as they are part of the same octonion charge. And through this effect, finally the seven imaginary charges are creating the only charge that can be observed on the macroscopic scale, the electric charge. If the weak charge is denoted with W and the electric charge with Q as usual, the octonion charge of a particle could be designated as Q-RGB-W-IJK. In this number Q is the only real part, all the others are imaginary, and so their square is equal to -1. With this notation, a coloured parton, for example a green parton with a J charge can be described with the (0,0,1,0,0,0,1,0) number. A colour neutral parton with an I x-charge can be (0,0,0,0,0,1,0,0). A composite particle, for example an electron could be described by a simple equation: (0,1,0,0,0,1,0,0) · (0,0,1,0,0,0,1,0) · (0,0,0,1,0,0,0,1) = (1,0,0,0,1,0,0,0).

One of the most essential features of the octonion algebra is that the multiplication neither commutes nor associative. Multiplication was not commuting in the quaternion algebra as well – thus i·j ǂ j·i – which has several consequences, if again quaternion charges are existing. For example the result of this non-commuting nature of quaternions was that the partonic interactions have a direction and so the composite particles must have a spin to create their inner interactions that holds the particle together. Another result was the uninterpretable nature of the parton-antiparton pair creation, and so the statement that only composite bosons can mediate interactions.

In the octonion algebra, the multiplication is not even associative, and therefore A·(B·C) ǂ (A·B)·C. In practice it means for example, that even though the partonic composition of the W - boson and the π- meson is the same, but the different order of partons result completely different particles, and they are both different from the final result, the electron-antineutrino pair that is created during the decay of them. The boson is created by the (RSGSBS) order, the π meson by the (RSS)·(GBS) equation, that finally result the stable (RGB) + (SSS), electron + antineutrino state. The course of the interactions can turn to the opposite and this can result in a long half-life, for example in the case of the π meson.

In fact, the multiplication of the octonions is a quite complicated procedure: it is described by an 8 by 8 matrix. Fortunately it isn’t only complicated for us, but for nature as well. The more complicated the multiplication, the larger half live the composite particle has. Sometimes the equations that nature has to solve are so complicated, that some particles have very long half-lives. It is obvious for example, that an R charge can eliminate an Ř charge, but an RI composite charge is not eliminated by a ŘǨ charge. In the case of the proton for example, the equation that nature has to solve needs several bosons, so the combination of charges are quite large. And thus, the lightest baryon, the proton must have a very long half-life.

The appearance of the octonion charges shed a new light on the role of the previously mentioned super boson. In fact, whenever there are colour and x-charges are present in a system, we have to suppose that the system is creating super bosons for initiating the interactions. Of course, the super boson can decay to other bosons in the process: H0 = γ + Z0 or H0 = W- + W+, and so, we may perhaps recognise only the effect of the latter, the effect of the two bosons after the split. It does not mean, though, that the former super boson was not present in the system. This thought does not affect much our previous thread, but add a more exact view on the procedures we have seen. For example in the case of the neutral π0 meson, the superposition of the đd and ûu states is simply created by the super boson, either by itself alone, or by its decay into a W boson pair.

It is only the neutrino and the Z0 boson, which are “handicapped” from this point of view: they don’t necessarily create H0 super bosons, by their interactions. This restriction means that, the neutrinos are unable to create either W bosons or photons, and so, they can interact only by the heavy Z bosons. The consequence of this “handicap” is that the neutrinos cannot lose their energy by emitting a photon, and unable to interact from a long distance, as the virtual Z bosons can reach very short distances. This feature makes them quite

unique: the heavier neutrinos are just as stable as the electron-neutrino, as these higher energy states are unable to loose energy. It can only happen, when the neutrinos are interacting with other particles and so the neutrinos can oscillate between the states only by interacting with matter. This interaction nevertheless is very weak, as the neutrinos have only imaginary charges and the Z boson field they create very short ranged. The neutrinos can interact with other particles virtually only by hitting them. This feature and not the weakness of the interaction is the cause of the very low cross section of the neutrino reactions. Indeed, the X-weak interaction is not weak at all: it is bounding the fundamental particles together. Though, as the neutrinos do not have a real charge and real field, they can interact only on a length scale, where the imaginary charges and fields can have an effect: on the scale, where the effect of different partons can be observed differently. As the cross section of the neutrino reactions is about 10 -42 m2, we can conclude, that the area of the partonic systems might be about the same order of magnitude. And if it is true, the diameter of neutrinos, electrons and quarks is about 10-21 m.

Conclusions

Let us summarize the results of our thought experiment. We first hypothesized, that all the elementary particles we know are in fact consist of three more basic particles, named for now partons. Then, we supposed that the charges and the interactions of these charges can be described by quaternion numbers. The colour charges of the strong interaction and the electric charge are united into a single quaternion charge, where the electric charge is the real, the colour charges are the imaginary parts. Another quaternion charge is made of the three imaginary charges of the X-interaction – that presumably holds together all kinds of partons to create composite particles – while the real part of this second quaternion is the weak charge.

The interactions that these quaternion charges are creating, cannot work in the way we traditionally imagine an interaction, by the exchange of virtual particles. These quaternion charges are creating chiral interactions, which can work only if the constituents have a rotation. In this case the central part of a partonic triplet continuously creates virtual mediating bosons, which are annihilated at the rotating partonic ring. The mediator bosons created in the middle of the partonic triplets, are the well-known vector bosons: the photon, made of six coloured partons, the Z, consisting of six colour neutral, x-charged partons, while the W bosons are composite particles made of coloured and colour neutral partons.

As we reached the conclusion, that the photon and the Z boson must be made of six gluons, while the W bosons consist six partons, it was a logical step to suppose, that the partons are the same particles as the gluons. This idea results a simple structure for the chart of the elementary particles: the fermions are partonic triplets and their excited states, while the bosons are partonic sextets. At this point, a possibility of a super boson arisen. In theory it is possible, that all the partons can join together and create a super boson with zero or 2 spin value.

This is one of the main successes of this recent thought experiment that, it creates such groups of composite particles that perfectly fit to the picture we recently know of the fundamental particles. The triplet structure gives us the possibility for a neutral and an electrically charged lepton, and two kinds of quarks with colour charges. As they are composite particles, they can have excited states, having larger mass, than the ground state. And so, the description of the fermionic groups is in tune with the experimental reality. Similarly, the group of the partonic sextets fits to the known vector bosons, which are mediating the interactions. The partonic sextets of our thought experiment have the same characteristics as the real bosons and they have the same reactions as well. And finally, we had to suppose the existence of a heavy scalar boson, which interact with any other particle: this is quite similar to the boson that was identified as the Higgs particle.

An interesting effect of these results is that, the particles the existence of which we supposed are utterly simple. The partons or gluons, which are building up the other composite particles, do not have mass. They do not have spin, or any other characteristic property. They have only charges – possibilities to join an interaction. Indeed, they can be described with a little piece of information, an eight digit number, in which only the 1, 0, -1

values can appear. All the other properties of the composite particles are appearing due to the interaction of these partons.

Another valuable feature of the partonic description of particles is that, we do not have to rely heavily on the help of the particle creating and annihilating operators. This description reduces the need for a philosophically cumbersome methodology, in which particles can transform into each other, without having any common component before. Without the partons, we have to assume, that particles can disappear, than appear again in another form, or they can give birth to completely new particles. These procedures can easily described by the groups of particle generating and annihilating operators. But these mathematical tools cannot substitute the physical understanding, how particles appear or disappear, or form other particles. The partonic description can help to solve this philosophical problem. All particle reactions can be interpreted as simple realignment of the constituting partons and interacting bosons, which are already present as an initial condition. In this way, neutrinos and electrons, protons and neutrons are not created by abstract mathematical operators, but by other particles. Only the perfectly symmetric groups of partons, the super boson, and the photon and the Z boson can be created from the vacuum, and these are the cause for all particle transformations.

Nevertheless, we must add that, the partonic description of the fundamental particles is only a thought experiment and not an elaborated theory; an algebraic approach, which can easily collapse under further scrutiny. Even though we didn’t have to face with irreducible contradictions yet, it is not a detailed mathematical description, and so, it has several boundaries. For example, we did not deal with the problem of the mass of the particles, what kind of process can give mass for the systems of otherwise massless particles. Detailed mathematical description of the interactions and the forces created by them is also inevitable to predict such phenomena, which can be checked experimentally. Nonetheless, such a thought experiment can be thought provoking, and thus, it can contribute for more precisely elaborated theories to describe the world of the elementary particles.

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