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


© Harold Aspden, 1999

There was a time when people worshipped the Sun. Their reasons must have had some scientific foundation, just as today's astronomers and cosmologists seek a deeper wisdom by gazing into the heavens. However, in their wisdom, the modern priesthood of science is dedicated to the worship of what has come to be called four-space, in the version according to the Gospel of Einstein. About Time is the name of a book authored by Paul Davies, an ardent believer in the Einstein myth. Paul Davies was a critic who in the 1972 period reviewed my book Modern Aether Science (1972) by saying it was "Physics of Fairyland". He may perhaps have been less scathing had he been called upon to review the book The Einstein Myth and the Ives Papers - subtitle: 'A Counter-Revolution in Physics', (Editors: Dean Turner and Richard Hazelett), published in 1979 by the Devin-Adair Company, Old Greenwich, Connecticut. I quote from page 33 of that work:
"To make complete sense out of the existence and behavior of matter and energy in space, we need to be able to understand not only how the ethereal laws work, but why they work."
I can only suppose that the very mention of the word 'aether' has, on Paul Davies, much the same effect as waving a red flag at a bull. He has, in his 1995 book About Time, captioned 'Einstein's Unfinished Revolution', at least mentioned the aether by waving it "Goodbye" on page 49 of that work. He relies on the popular belief that the Michelson-Morley experiment proved the non-existence of an aether, even though Einstein's picture of 'space-time' is a picture of an aether seen through spectacles having distorted lenses.

Having got that introduction off my mind I will now focus on my task of teaching you why it is that certain particles have longer lifetimes, the faster they travel. I have chosen this topic for two reasons. The theme of 'time dilation' is the science fiction idea that Paul Davies exploits in applying Einstein's theory to build an imaginary picture of past and future cosmic events. It is also intimately related to the primary point which I see mentioned as support for Einstein's theory in a book Imagination and the Growth of Science, which its author, Professor A M. Taylor, presented to me many years ago. Professor Taylor, now deceased, was a social acquaintance, both of us living in Chilworth, on the outskirts of Southampton in England, a mile of so from the University of Southampton. The book was dated February, 1966 and was a record of the Tallman Lectures of 1964-65 which he had delivered at Bowdoin College, New Brunswick, Maine, U.S.A.

Had you attended those lectures you would have heard Professor Taylor's praise for Einstein's theory, punctuated with a few cautionary remarks, but I will here direct my attention first to the topic stressed as the most important. Professor Taylor states:
The most convincing of all experimental support for the special theory of relativity are the facts of nuclear fission and fusion. From the theory it follows that the energy E associated with any mass m is mc2, and as c (the velocity of light) is very large, the energy released when mass, even a very small mass, is annihilated is very great.

Taylor then goes on to explain how, in 1939, a group of scientists in Germany discovered the fission of uranium and how, in the light of that knowledge, Einstein felt it his duty to warn President Roosevelt that the atomic bomb was a possibility.

That, however, is history, history which can be set alongside the 1904 assertions by J H Jeans in the journal Nature telling the world that the energy which powered stars came from the transmutation of mass into energy, the annihilation of protons, though in those days Jeans referred to the proton as a 'positive electron'. The proton had yet to be discovered. Indeed, in 1904 Einstein had yet to be 'discovered'!

Certainly I do not share the awe which E=Mc2 has earned for Einstein's memory, simply because it is the obvious product of classical electron theory, as I have discussed in considerable detail in Tutorial No. 12. So let us turn to the 'time dilation' issue, which is not a feature of classical electron theory.

Professor Taylor writes at some length about the 'space traveller' problem and relativistic time dilation. He explains how there is often discussion of a paradox concerning two twins, one who travels and one who stays at home, leading to the belief that if Einstein's theory is correct then those twins must be seen as having different ages when reunited. He declares this to be an erroneous conclusion because the predictions of Einstein's Special Theory of Relativity do not apply to circumstances where there is acceleration and that twin who travels away for a while only to return eventually cannot do that without accelerating a decelerating at some stage in his travels. It seems that the travelling twin winds his clock backwards when accelerating and forwards when decelerating so as to keep the right time when he comes back down to earth. If this leaves you reeling mentally, then share the feeling. I can only express my sorrow for professors of physics who have to explain their subject in such a confusing way. To be sure I feel that no professor of physics can say, with honesty, that time dilation has a logical explanation, except for it nurturing flights of fancy into the dream world of virtual images of space-time.

However, Professor Taylor presents the evidence. On pp. 34-35 of his book he writes:
For one-way travellers the relativistic time dilation has been confirmed by observations on cosmic rays. When they enter the atmosphere of our earth these rays from outer space may, on colliding with molecules of air, produce short-lived particles called mesons. These travel towards the surface of the earth with a speed nearly that of light. However, they decay rapidly and the duration of their brief existence is accurately known. Because we know where they are formed, and because we know their speed, the time required for their journey from their place of origin to our recording instruments on the surface of the earth can be calculated. This turns out to be fifteen times longer than their life! Yet they most certainly live long enough to reach the earth and there operate the recorder. The paradox is solved if the Lorentz transformations be applied to the problem. The mesons are travelling fast, and the consequent time dilation of their time-scale is great enough to expand their life sufficiently for them to survive the journey. ... This indeed is an Alice-in-Wonderland state of affairs and you may think that scientific imagination has got the better of sanity. Maybe! It is just one example out of many others that the behaviour of small high-speed particles must not be judged by the rules of everyday human life.

Well I do accept that the fact that Einstein can sustain stable motion on his bicycle, the better, the faster he goes, is not the kind of everyday experience one can connect with high energy particle behaviour. Equally, however, I cannot see how a 'Lorentz transformation' explains anything concerning particle stability. I can concur that what is described as 'time dilation' is an 'Alice-in-Wonderland' state of affairs and that means that Einstein's theory is the 'Physics of Fairyland', rather than my interpretation of the physics in terms of an aether.

So I shall present my explanation of so-called 'time dilation' or rather longer particle lifetime in terms of aether theory. I picture an aether as being the seat of quantum-electrodynamic action, meaning energy fluctuations and electric charge pair-creation and annihilation, all ongoing unseen in the background of the space we inhabit.

Along comes a meson travelling at high speed. It has a physical form. It is not a point charge, but a real 'something' that presents a target for a hit in the shooting range where energy fluctuations occur sporadically, like shells doing their killing work by bursting on a battlefield destroying antiparticle pairs of charges, only to find that Nature has its methods of reincarnation as those antiparticle pairs are created anew. If the meson were at rest in that sea of activity, meaning relatively at rest, given that whatever that background consists of it must have its own frame of reference, then suppose the chance of a hit is such that the meson has a lifetime To. However, the meson is moving. Suppose that in reality it 'jumps' suddenly, as from A to B in steps, or, as an equivalent scenario, it vanishes at A to reappear at B a little while later, so as to seem to be in constant motion as viewed statistically. Owing to its motion it possesses, say, E/Eo times as much energy as the rest-mass energy Eo of the meson.

I now have in mind the possibility of vacuum fluctuations concerning charge pair creation and annihilation, space conservation, meaning the space taken up by the electric charge of the particles and charge parity conservation. I see this as meaning that in any period T the meson has to flip between three different states. Our problem has to be formulated in terms of three simultaneous equations.

The states are deemed to be one in which the meson sits alone at rest for a period t1, one for a period t2 where it exists in its rest state and has an entourage of meson pairs created from the vacuum energy fluctuations, and one where the meson sits alone but has compacted into its contracted form all of the energy E this being for time t3 in that period T.

Now during the periods t1 and t2 the meson is subject to its normal chance of experiencing a hit and so a hit confined to these periods means a decay lifetime Tv of:
Tv = ToT/(t1 + t2) ....... (2)

During the period t2 if any of the virtual mesons in the entourage is hit this merely initiates pair annihilation and time t2 shortens as the meson adopts one of its other states.

The three relevant equations are, first, the time apportionment equation:
t1 + t2 + t3 = T ........ (3)
Next, the space volume equation:
t1 + (2N+1)t2 + (Eo/E)3t3 = T ........ (4)
and then the energy equation:
t1Eo + (2N+1)t2Eo + t3E = TE ........ (5)

This assumes that N virtual meson charge pairs feature in the quantum electrodynamic scenario of that t2 period.

Note that the J J Thomson formula for the energy of a electric charge tells us that its radius is inversely proportional to its energy, which means that its volume, is inversely proportional to its energy, thereby explaining that:
term in equation (4).

Now assuming that the energy E is large compared with the rest mass energy, say that 15 times larger mentioned by Professor Taylor, then that volume is quite negligible so far as its contribution to equation (5) is concerned. One can then expect the meson to escape decay in the time t3 period and this allows us to deduce from equations (2), (3), (4) and (5) that:
Tv = (E/Eo)To ......... (6)

which tells us that the meson moving at high speed will survive for a longer period than its normal lifetime, that period being greater by a factor equal to the energy increase factor.

To verify this for the high speed condition note that equation (4) reduces to:
t1 + (2N+1)t2 = T ........ (7)
and equation (5) becomes:
t1 + (2N+1)t2 = (T - t3)E/Eo = (t1 + t2)E/Eo ........ (8)

This equations (7) and (8) are equal and so they tell us that T/(t1+t2) is E/Eo. Now, if the muon moving at speed escapes decay for the period t3 in time T its lifetime is increased with speed in proportion to the expression we have just derived, so confirming equation (6).

Now, without using Einstein's theory, we have shown in Tutorial No. 12 that E = Mc2 and on this basis the momentum of such a particle moving at velocity v is given by:
momentum = Ev/c2
so the kinetic energy of the particle is this energy E minus the rest mass energy Eo and this tells us that the kinetic energy is given by:
(M - Mo)c2

If a force F acts on such a particle in the direction in which it is moving, then assuming no loss of energy by radiation or otherwise, we have:
vF.dt = dE = d(Mc2) = v.d(momentum)
so that:
v.d(momentum) = c2.dM
which means that, since:
momentum = Mv
(momentum)d(momentum) = c2M.dM

Integrating this gives:
(momentum)2 = c2M2 + constant
and from this, since the momentum is zero when M is equal to the rest mass Mo:
(momentum)2 = c2(M2 - Mo2) = M2v2

This gives:
M = Mo/[1 - (v/c)]1/2
and so:
E = Eo/[1 - (v/c)]1/2 ....... (9)

From equations (6) and (9) we see that the lifetime of our meson moving at speed v is given by:
Tv = To/[1 - (v/c)]1/2
in compliance with the formula for time dilation, even though there is no time dilation involved.

I find it hard to belief that anyone could still believe in Einstein's theory after working through this argument, bearing in mind that it relies on quantum electrodynamic principles and quantum electrodynamics has an indisputable claim to much of the territory concerning the physics of the vacuum state. However, if you need further argument to convince you then I urge you to consider that approximation I made in neglecting that chance of meson decay during time t3. It will have the effect of reducing the lifetime of the meson slightly below the 'relativistic' value, but particularly over the range close to the speed at which lifetime is doubled.

My analysis of this says that there should be a reduction of as much as 6.25 per cent over this critical range. However, when I scan the reports of measurements of meson lifetimes I find that those reporting such measurements avoid reporting data over that range. They prefer the high energy scenario where the results obtained come closer to the relativistic value. Even so, at such high energy levels, there is always a discrepancy, one sometimes obscured by the stated precision of the measurement, but a discrepancy nevertheless.

So, if you wish to read what I have published on that subject, you should first look up my paper at pages 307 to 311 in Lett. Nuovo Cimento, v. 37 (1983) [1983f] and then the later paper [1983g] at pp. 206-210 in volume 38 of that same periodical. The latter paper was entitled Meson Lifetime Dilation as a Test for Special Relativity.

As you will gather, Special Relativity fails that test! Time dilation, as such, is complete nonsense! What sense, I ask you, can there be in applying Einstein's theory to the task of explaining why mesons have longer lifetime, the faster the travel, owing to the notion of time dilating, when physicists making such assertions do not know what it is that determines the lifetime of a meson which they see as being at rest? How can they know that the state of motion and the added energy does not affect the stability of that meson?

If they argue the meson is at rest as seen in its own frame which moves with it then does it have any added energy that is seen in that moving frame? If not, then where does the energy added in getting the meson to move faster actually go? Is that added energy something imagined by the observer in the frame initially occupied by that meson?

I leave you to ponder that and to search for your own answers, but it may help if I now, in my next tutorial, Tutorial No. 15, show you how to derive theoretically the lifetime of the mu-meson at rest. I have not published this derivation in any of my peer reviewed scientific papers, but I did include it in my 1980 book Physics Unified. It warrants an airing in these web pages and I hope you will find it interesting.

Harold Aspden

To progress to the next Tutorial press:

Tutorial No. 15