These notes teach the mathematical basis of Aether Science theory


© Harold Aspden, 1997
The Role of the Muon

The most fascinating question in physics is that of Creation, whether one has in mind the stars and planets or their offspring, including mankind or the fundamental particles from which we and the universe are formed. The primary challenge is to explain how protons with their attendant electrons are created. Then one needs to explain gravity so as to provide the reason why the stars formed, but neither of these perplexing problems can be resolved without accepting that there is an aether which is the active agent in these creation processes.

In these tutorials I have done my best to summarize in a concise way my perception of the aether that is ever at work in keeping our universe alive. The universe can never die unless it expands to the point where it can find space for all of its energy in a state of rest in a dormant condition where it will have cooled to the point where all charge motion in the aether has stopped. However, that cannot happen because, as we have seen, that involves a negative energy potential in the aether charge interaction and the combination of aether plus universe can never have an overall energy that is negative. The universe can perhaps develop sporadic events in regions where temporary overheating carries the underlying structure of the aether charge through, as it were, its 'Curie temperature' and causes it to lose its gravitational action in those regions.

As we have seen, the force of gravity is an electromagnetic force but one that is tuned to develop interactions only at the resonant frequency of the aether itself, which happens to be the Compton electron frequency. So it comes as no surprise to find that the aether can create electrons. However, the aether is a sea of energy in the form of 'heavy electrons', those mu-mesons we call muons, which exist in opposite polarity charge pairs, and this provides a bombardment of all sectors of space at that aether frequency, as those muons move around, expanding, annihilating, and reappearing elsewhere in their initially contracted form.

When energy is dispersed in the normal way, as by radiation from a star, it is eventually absorbed by that rhythmic aether motion of the quons as they expand their orbits to bring that energy into their rhythmic dance at that Compton electron frequency. This alters the equilibrium of the aether machine and gives scope for the muons to create matter in the form of protons along with the attendant electrons, namely hydrogen atoms and so matter as we know it. The energy cycle is regenerative because energy is conserved. It has nowhere to go other than into the aether system, but the aether seeks to reestablish its equilibrium by shedding that energy at the first opportunity. The muon activity provides that opportunity by bombarding the quons and so, from time to time, everywhere in space, protons are created along with the electrons and that is why the dimuon energy quantum of 412.6658 electron rest-mass energy units features in the proton creation process. Our task in this tutorial is to explain that process and so complete the account presented in Tutorial No. 8.

Now, when a muon hits a target quon of opposite charge polarity its energy merges with that of the muon and it takes a while before what is produced decays into something that has at least some quasi-stability. Meanwhile that quon target volume, meaning the space occupied by the quon charge, can also serve as a target space for capturing other muons. This is a statistical process and only very occasionally will the situation develop for a particular target quon that allows a truly stable particle product to emerge. By that is meant our proton and its electron.

So our task is that of finding the algorithm governing this process and there has to be something special about it that can explain why the proton is the unique end product capturing virtually all of the energy involved.

I may add here that it took me 30 years to discover the algorithm after I had seen how the aether works and obtained the formula for the fine-structure constant. The dimuon energy quantum emerged after 10 years but yet it took still another 20 years to arrive at the formulation now to be presented. So, please, do give some thought here to the wonders of Nature as involved in proton creation.

You must first learn your Ps and Qs, by which I mean the way in which a particle of energy P can give birth to a particle Q when seeded with an electric charge of opposite polarity. Take a charge +e of energy P, so that the charge has a radius 2e2/3P, as given by the J.J. Thomson formula. Then bring a charge -e into contact. The latter could be that of a muon. Let this merging of particles develop but keep each unitary charge intact and separated in its own charge sphere, but with those two spheres having surface contact. Let us denote the radii of the spheres a and b, respectively. Now note that there will be a negative interaction component of energy in this system as given by e2/(a+b), whereas the self-energy of each charge will be that given by the J.J. Thomson formula.

The parent particle of energy P will now be assumed to shed energy or consume more energy, as required, until it reaches a state where its offspring is ready to be born. That state is one of minimal overall energy, meaning that, if a has remained constant, b has adjusted so that the sum of the three energy components is a minimum. You will see that b must then have a unique value in terms of a. What is that value?

To formulate this let a/b=x and write the energy equation as:

E = (e2/a)[2/3 + (2/3)x - x/(1+x)]
Now find Emin by differentiating with respect to x:
dE/dx = (e2/a)[2/3 - 1/(1+x)2]
Equating this to zero gives:
x = (3/2)1/2 - 1
We can put this value of x into the energy equation to find Emin, but note that, by knowing x, we have found the energy the offspring would have if separated intact from the parent. It is simply:
Q = P[(3/2)1/2 - 1] = 0.224744871P

So here is what I meant by learning the Ps and Qs, because if the value of P is 1836.1523 then the value of Q is 412.6658 and you will recognize these as the proton and virtual dimuon masses in electron units as discussed in Tutorial No. 8. We have derived the first of the relationships which we brought into that earlier tutorial.

Now, the problem with this is that it tells us how, given that the parent proton exists already, we may create that dimuon energy quantum, but our picture of creation requires that things work the other way around. We want to know how protons are created from those virtual muons that populate empty space. Of course, having discovered the astounding numerical factor that accounts for the proton/electron mass ratio so precisely, it was appropriate to publish that finding and that was done in 1975 by reference [1975a]. However, so far as this author was concerned that was only a stepping stone to finding the real answer. It took another 10 years from that point.

The onward step involved regarding the parent particle as a charge having the dimuon energy and developing its own offspring according to the above formulation. Then, before the offspring separates, that entity is deemed to be bombarded by muons until the statistical event occurs that allows the offspring to be born whilst leaving a parent proton with its still unborn new offspring, after which the first offspring, being an energy misfit in the stable particle world, is gobbled up by the proton and its unborn to cause a miscarriage, the end result of which is simply the solitary proton.

In this way the proton can be created by the muon activity of the aether, but only if the numbers can come out right in conserving energy in the two separate steps in this process.

Now the remarkable feature of what has just been proposed is the fact that there is a unique solution to the scenario described. First let us write an equation to portray the process:

nEmu + (kEmu: z)min = (P: kEmu)min + z = P
Here we are saying the k muons of energy Emu come together to form an electrically neutral entity which develops by first shedding some energy to settle in a minimal energy state in which the unborn offspring of energy z appears. Then n more muons bombard that entity and pool their energy to create a parent charge of energy P with an unborn offspring, that is in fact the parent of the original target entity, shedding a charge of energy z in the process. This is followed by that charge of energy z being recaptured, by chance encounter, by the main parent body of neutral charge to create that solitary end product, the proton of energy P.

For this to occur k must be an even integer and n must be an odd integer and the question is whether we can find any such integer combinations that assure energy balance across the two equation signs in the above formulation. Let us begin the search. We start by first evaluating that Emin factor. I will let you, the reader, make a start by first showing that when that value for x is put into the equation for minimal energy of the parent plus offspring combination it gives the factor (61/2-3/2), meaning that Pmin, for example, is 0.949489742P.

Next we will restate the energy equation involving n and k in the form:

nEmu + (61/2-3/2)kEmu = (61/2-3/2)P + ([3/2]1/2 - 1)Emu = P
Now, again, I leave you to do some checking to find n and k solutions to this double equation. There are four unknowns and only two equations, but we are only interested in the ratio between P and the muon energy Emu so that reduces the unknowns to three. There is therefore no certain solution to the two equations that can be found by routine mathematics. If, however, we simply say that k has to equal 2 because we can expect the simplest solution to arise from the simple pairing and merger of the two muons of opposite polarity, then we can use mathematics to find a solution for n, but it would seem to be a miracle if that solution turned out to be an integer! Yet, indeed Nature does deliver that miracle, because there is a solution with n equal to 7.

So P has the value (4+2(6)1/2)Emu or (2+(6)1/2)(2Emu) or (2+(6)1/2)Q and you can verify that, with Emu as half of Q, that is half of 412.6658, we obtain P as 1836.152.

We can here end our quest to explain the creation of the proton, but if you ask how it is that physicists tell us that protons appear to comprise three quarks, then you open another chapter of enquiry and I need to explain how that can be accommodated by this aether theory. The point to keep in mind here is that we are discussing the fundamentals of creation and not the ultimate states of matter. You see, these unitary charge particles find comfort in merging together in groups of three or four components and then flipping between alternative states that are possible in such groupings. This is conducive to stability and so long as energy is conserved notwithstanding a fluctuation about a mean condition then real matter forms exhibit such conditions. You will see more on this subject in my Lectures and other writings in these Web pages and in what I have published in book form and in the scientific periodicals.

Taon creation and Gravity

Now, to move on, we need to come to the question of how protons get involved in the creation of taons. One aspect of this story is told in my paper [1986j]. Its gist is as follows. If charges group together in clusters and by an exchange process they contrive to share their energy in a reduced space then they can develop into hybrid forms. Such clusters are never alone. There are always numerous other such clusters not too far away, but things can happen where, local to a cluster, there is conservation of energy as space occupied by charge locally contracts by the local annihilation of charge pairs.

Now, to give examples, suppose that a group of three particles of the same family, one of negative and two of positive charge, suffer charge pair annihilation and the vacated space closes locally. We are left with three times the energy for one unit of charge volume. Note I am here working in the E-frame, the matter frame, and there is no need to conserve the energy to charge volume ratio in this frame as there is in the G-frame, where the gravity conditions prevail. Put three units of energy in a sphere of charge where one unit of energy existed before and the J. J. Thomson formula poses a problem. However, if there are numerous particles all trying to cope with this same problem and we can allow them to form more of the same new particle family so that each requires less space, then that triple energy condition can be accommodated in the same overall space as before.

Check this by considering the two equations below. The first represents conservation of charge volume, N being the initial number of particles and N' the final number of new particles. The second equation represents energy. The radius r of the charges of the new particle family is expressed in units of the radius of the initial particle family.

N = N'r3
3N = N'/r
Divide one equation by the other to eliminate N and N' and you can see that 1/r becomes the fourth root of 3, meaning that each new particle has a mass that is that much greater than that of the initial particle.

Next, consider a different scenario, one where the initial particle form finds that it has to absorb more energy and it does this by dividing its existing charge volume into three separate spheres as a newly-induced charge pair appears in the two new spheres whilst the charge in the original sphere contracts to match the energy of the newcomers. Here the new particles have a mass which is simply the cube root of 3 times their original mass.

Now, if both of these processes can occur in tandem, you can see how an initial particle form can transmute into one that has more energy or more mass by a factor that is the fourth root of 3 times the third root of 3 larger. This is 3 raised to the power 7/12, which is a factor of 1.898107 and if we multiply this by the proton mass in electron units, namely 1836.152, we get 3485.21 electron mass units, which is 1781 MeV. This identifies the taon and I have now, to this stage, shown you how one can derive the relationships I used in Tutorial No. 8 to derive G, the constant of gravitation.

The processes just discussed are part of a family of processes involved in meson creation, as listed in the paper I referenced above under reference [1986j]. However, I must disclose to you some misgivings that I have on this derivation of taon mass so far as concerns the evaluation of G. I asked myself how it is that the taons could appear in the G-frame, that is on the graviton side of the dynamic balance. We know there are taons amongst the particles of matter that put in a fleeting presence owing to their short-lived existence, but that does not give us assurance when it comes to accepting that taons feature as the primary particle in the G-frame. They must be regenerated constantly to assure the action of gravity and it does not seem right that those graviton-type taons should be produced as part of the material world that we witness as a meson generation chain.

So, let us go back to the drawing board, as it were, and think again. Maybe we have encountered one of the several coincidental features of Nature that tend to crop up so regularly in this theory. The point here is that Nature will allow particles to live longer if they have companions of the same family close by or if they have association with other such families that have nearly the same rest-mass. If they live longer they are detected more easily and they are given a name, but it is a fact of Nature that the spectrum of particles that can be created is enormous and so, to appear long enough to be noticed, there will be some that are similar enough to be given the same name but yet which can appear by two quite separate processes.

I must therefore now argue my case for the taon rather differently. I suggest that we should look again at that muon activity which creates the proton and imagine the same activity as occurring in the G-frame. We have seen how those z particles that are created momentarily get recaptured to allow the proton to materialize, but you can be sure that, owing to their very large volume compared with the gravitons, they will exhibit an enormous gravitational influence if they survive for long in the G-frame. They will find it more expedient to join up in pairs, suffer mutual annihilation and exit the scene. This will leave us with those (P:kEmu)min quanta which are electrically neutral.

Now suppose that these quanta, which are themselves misfits in the gravity scene, also suffer instability because of their enormous gravitational interaction. Though electrically neutral they will soon come together to merge their energy and, in finding that their charge components come into close proximity and exist in pairs, we can be sure there will be some annihilation and ejection of charge to leave the bulk of the energy concentrated in a single charged particle. I am tempted to suggest that three of the four charges form an electron-positron cluster of 1.875 electron energy units and quit the scene after reducing the energy of the residual state by that amount. I do not wish to justify that 1.875 quantity at this time, but note that its basis is of record elsewhere, for example on page 154 of that same reference [1986j]. It is the rest-mass energy of an in-line cluster of three leptons, two of one polarity and one of the other in the middle, with the three units of self-energy offset by the appropriate negative potential energy of their mutual interactions.

With this in mind let us now evaluate that residual energy quantum. The value of each of the two component energy quanta is the rest-mass energy of the proton reduced by the factor [3/2)1/2-1)]2 or 0.9494897 times 1836.152 in electron units. This is 1743.407. Twice this is 3486.814 but if 1.875 is energy carried away by the three-charge electron-positron cluster then the residual charged particle has a mass 3484.939 electron units. You can see that this is very close to that taon mass deduced above for meson activity in the E-frame.

Reverting now to the calculation of G and noting the fact that we have derived the graviton/taon mass ratio as being 1.452627, its inverse being 0.688407, I tabulate below the significant figures applicable to the taon, graviton and G computation, using the formula given in Tutorial No. 8.

		   Taon		Graviton     G
		   3484		5060.95	   6.687
		3484.9395	5062.32	   6.672
		   3485	        5062.41    6.671
		   3486         5063.86    6.656

You can see that the taon energy just derived by assuming that a pseudo proton creation process is at work in the G-frame gives a value of G that compares well with experimental findings. I must, therefore, in the light of this result, see the proton creation process as the key to the creation of gravitons and taons in the G-frame and as the essential basis for the value of the constant of gravitation. The measured value of G is 6.67259(83)x10-8 in c.g.s. units.

I now end this Tutorial No. 9, having accomplished my task of showing you how to derive G, the constant of gravitation by pure theory. To those who have read through these nine Tutorial Lessons and who lecture on physics in a university, I suggest that much of what I have presented in these tutorials should be incorporated in your teaching curriculum. It is not history, as I hope you may realize if you now glance through the concluding Tutorial No. 10.

To progress to the next Tutorial press:

Tutorial No. 10