TUTORIAL 17

TUTORIAL NOTE 17

Welcome to the Second 'Semester' of Ten Tutorial Notes, which teach the mathematical basis of Aether Science theory.

PARTICLES GALORE: HOW THEY ARE CREATED

I deferred the preparation of this Tutorial No. 17 until last by moving ahead to complete Tutorials No. 18, 19 and 20. My plan, as stated at the end of Tutorial No. 16, was to go into the details of how a myriad of fundamental particles are created based on principles already introduced elsewhere in these web pages. The essential key is reliance on a combination of conservation principles, including especially the notion that the actual volume of space occupied by the electric charges belonging to a transmuting system of fundamental particles is conserved. I have, however, decided to abbreviate this discourse and leave you, the reader, to glean that information from my published work elsewhere, notably in two papers included in my book Aether Science Papers, of periodical record also in university libraries which stock the Hadronic Journal [1986e] and [1986j]. Here, in Tutorial No. 17, I will only pursue the theme in a summary way.

Once it is understood that the vacuum medium is alive with activity as Nature tries to deploy its energy into the creation of a myriad of particle forms amongst which the proton and the electrons are the survivors, there are few secrets left that warrant our attention. To understand the creation of the proton is to understand its meson source, rooted as it is in the muon activity of the aether itself and with that comes the system of dynamic balance, the elusive background of gravitons which mediate in setting up the force of gravity. All this has already been discussed in our Tutorials and elsewhere in these web pages and the fundamental particle spectrum that we explore by our research into high energy particle physics is simply a product of the merger of gravitons, muons, protons and the like.

Here I will just remind you that J J Thomson's formula 2e²/3a is governing in defining the energy of a particle of charge e encapsulated in a sphere of radius a. The volume of space involved is proportional to a³ and the energy involved is proportional to 1/a, given that e is a universal unit of electric charge. So if you take a pair of particles of positive and negative charge polarity and say that they transmute into two pairs of particles (radii b and c) with overall charge volume conserved then energy is released and we have the condition that:
a³ = b³ + c³ ...... (1)
On the other hand, if the transmutation is one involving constant energy, rather than conservation of charge volume, then we can have action according to the following relationship:
2/3a = 2/3b - 1/(b+c) + 2/3c ....... (2) where two electric charges of opposite polarity, one of radius b and one of radius c, are in surface contact owing to their mutual electrostatic attraction. Of special interest is the case where a equals b, in which case we can have a particle and its antiparticle form changing, with no added energy or loss of energy, so as to remain intact in form whilst giving birth to a charged particle pair for which the charge radius c is double b.

A basic particle form can, therefore, given a little extra space, give birth to a secondary particle form having half the energy of the basic form. This comes together in a scenario where the vacuum, or aether, is alive with mu-meson forms which merge to become dimuon energy forms which in turn can shed those half-energy forms as muons. The proton comes into the picture once we examine how a proton can live in company with a dimuon. Just differentiate the right hand side of equation (2) with respect to c to establish the ratio between b and c when the overall energy has become mimimal with b constant. You will find that:
1/[b+c]² = 2/3c² ....... (3) and deduce that b is 0.22474c and this says that the heavier particle is 4.4496 times the lighter particle. If the latter is a dimuon of twice the energy of the muon, the latter being a little larger than 206 electron mass units, then can see how a proton emerges with a mass of 1836 electron units.

Having said that, I am now looking at equation (1) with a simple question in mind. The question is whether, just as there is a universal unit of electric charge e, there is a universal unit of space volume that that charge could occupy. This brings into mind the possibility that, since a will be a quite small radius, much smaller than the radius of the electron, there is a corresponding unit of energy, albeit one that is really enormous. The idea of a 'unit' is then not one to be seen as a building block but rather as a massive chunk of energy that might exist naturally and need to be chopped up to form particles of real matter.

My interest in this was aroused when I saw the connection with the problem of Fermat's Last Theorem. If there were a solution to equation (1) with a, b and c all integers, then I would have been encouraged to probe this subject further. However, given that no such solution exists, I see no point in that onward pursuit. I can say, however, that the notion of particles giving birth to other particles is implicit in a form of equation having multivalued solutions, even if they are not in integer form.

With equation (1) in mind imagine a pair of particles having the same charge radius a to be transmuted into two particle pairs of radius b and c, respectively. Now let b equal c and determine b in relation to a. It will be smaller. We are saying that therefore that two particles of the same energy, confined to a given overall volume of space, can transmute into a two pairs of charges of higher energy, given input of energy. You can see that b is smaller than a in the ratio of the cube root of one half, which means that the particle of radius b has a mass that is greater than that of radius a by the factor of the cube root of 2, that is some 26% heavier.

However, things are not that simple, at least for the normal hyperons in the proton to two-proton mass range, as we shall now see. One is of cpurse tempted to ask if Nature obliges us by generating particles, albeit short-lived, that support the abovwe proposition and its variants, given that different combinations of charge forms can be involved. The answer is affirmative and that is what I was referring to in introducing this Web page. I will end by quoting the examples listed in TABLE II of the second of those papers referenced above:

The Table has the form:

and the supporting description on p. 156 of the paper reads:

"A collective particle transformation is of special interest, where a three-particle cluster (e.g. two positive charges and one negative charge of like mass) involves pair annihilation with energy transfer elsewhere, followed by local adjustments with numerous other such clusters to conserve both energy and charge volume. The energy/volume ratio is then one-third that of the original particle form. From the Thomson formula this implies that the charge radius (inversely proportional to energy) has decreased by the factor fourth root of three. Such a process can occur in reverse as energy is forced into a particle system. there is an analogous process where pair annihilation occurs in the presence of other similar pairs, which then share the additional space. The factor involved is the fourth root of 2. this process, like the previous one, appears reversible. Indeed, the examples to be given relate only to the reverse process, because one of the particles is the proton and we have only evidence of synthesis of more massive particle forms.

These appear in the first two examples in Table II. The remainder of the data in the table shows how the simple transformation of a three-particle cluster to or from a single particle at constant volume builds the several hyperons listed. The delta hyperon (1235) forms the tau (1782), and this has lepton characteristics and can combine with the Q(211) quantum, the energy of two virtual muons, to form a state from which there is decay to the hyperon forms listed. As with the data in Table I, the dimuon unit seems to be a dominant feature."

To conclude, I have decided to rest my case concerning the production of the numerous high energy particle forms that are generated in the collisions occurring in particle accelerators. It suffices to let my published papers serve their role by sitting quietly on university library shelves and patiently awaiting any interest that may be shown by those who seek enlightenment.

Harold Aspden

To progress to the next Tutorial press:

Tutorial No. 18