This Research Note is my response in reacting to a communication sent to me
by Peter McNeall, by letter mailed on May 16, 1997 from his address in Houston,
Texas. Peter was the very first physicist to check the mathematics of my aether
theory. Many years ago, shortly after it was published, he drew my attention to
a minor error in the numerical derivation of the fine structure constant in my
1966 book *'The Theory of Gravitation'*. Since then I have heard from him
from time to time as he has revisited my theory and sought ways of modifying it
or even reconciling it with the relativistic physics of our modern age. His
message to me on this occasion raises a point which needs clarification. Hence
this open response.

Peter McNeall's note reads:

"In the magical world of matter and energy Einstein's famous equation E=Mc^{2}applies to particles of matter obeying relativistic mechanics. But our ether particles obey quasi-Newtonian mechanics, so E=Mc^{2}no longer necessarily holds true. The energy of a lattice particle is (2/3)e^{2}/b while its mass is only (1/3)e^{2}/bc^{2}, so it appears E=2Mc^{2}! The result possibly has support from Dirac's relativistic wave equation according to which an electron has a magnetic moment of 1 Bohr magneton, while its spin is only (1/2)[h/2(pi)]. It is just as if the inertial mass of the electron in the spin mode is only one half its normal translational mass - so once again we find E=2Mc^{2}! There is no doubt Aspden's theory is a challenge to one's sanity and self respect, as is quantum mechanics itself."

So here Peter McNeall is saying that there are inconsistencies in my theory, it being a fact that I have used a mass value of half the normal particle mass in formulating the centrifugal force acting on my aether lattice particles as they are active in their quantum jitter motion. However, the physics underlying this can easily be explained and justified.

I begin by saying that I certainly do not need 'support from Dirac's relativistic wave equation'. Whatever that equation has to offer to the world of physics and whatever inconsistencies it may produce, that is for its advocates to address. My concern is my own theory and it can stand firmly on its own foundations.

McNeall is wrong in saying that the aether lattice particle of my theory has
a mass-energy of half that given by the J. J. Thomson formula relating energy,
charge and charge radius. E=Mc^{2} is deduced from first principles in
my writings, dating from that 1966 publication mentioned above, and it holds
validly founded on the principle that a charge possessing electric field energy
E will respond in an accelerating field exactly so as to conserve energy and
thereby exhibit an inertial mass M given by that formula. However, the response
of a charged particle depends upon governing constraints and these can be
different where that particle is not able to move freely. Aether lattice
particles form part of a structured system having a microscopic quantum jitter
motion which is the primary motion. In contrast an electron moving freely in a
particle accelerator has only a minor quantum jitter component of motion and
that does not affect the derivation of the formula E=Mc^{2}.

The governing constraint in the case of aether lattice particles is the
synchronous phase-lock which holds between all those particles as they move
collectively in small quantized orbits so that the whole structure jitters in
harmony, there being one aether particle in each lattice site. Now, (see for
example pp. 72-73 of *'Physics Unified'*) once E=Mc^{2} has been
derived on a good physical foundation, onward progress from there to deduce the
formula for the so-called 'relativistic mass increase' is simple algebra plus
one assumption. The assumption is that energy is conserved and not radiated as
the speed increases. Einstein's theory is not involved. However, if the particle
in question is constrained to conform with phase-locked motion, albeit gaining
energy and speed in orbits of increased radius, then the particle mass cannot
change. Simple harmonic motion at a fixed frequency is a characteristic of there
being a linear restoring force rate governing radial displacement and an
invariant mass. The aether particle does not change its mass as the aether
absorbs energy! As a result, and even at speeds that are a significant fraction
of the speed of light, the mass remains constant and Newtonian mechanics are
applicable. Einstein's theory has no place here.

However, there is a very important element to all this which needs clarification. In my earlier writings I recognized that the aether lattice particles exhibited centrifugal effects as if they were only of half their normal mass. I justified that by noting that when a spherical particle is immersed in an incompressible fluid of equal mass density then the particle does respond inertially as if its mass is halved. This is a standard fact known in hydrodynamics. That is why I introduced the half mass factor in working out the formulae governing aether lattice dynamics. It gave perfect answers quantitatively and allowed derivation of the value of the fine structure constant to part per million conformity with its measured value.

My last book presenting the formal analysis on that subject dates from 1980
(*'Physics Unified'*) and progress thereafter has been reported in
published scientific papers. In the course of these developments I had struggled
relentlessly to derive from first principles what is known as the 'Neumann
Potential'. This is the stepping stone to understanding the physical basis of
the law of electrodynamics, though I knew the form of the latter from my earlier
work based on empirical analysis. In short, I had already (before 1959)
discovered the form of electrodynamic law that gave what was needed for
unification with the law of gravitation and it had empirical foundation, but my
ambition was to derive that law from first principles, starting with Coulomb's
law of force between electric charges. The Neumann potential had been the
starting point for deducing the applicable law of electrodynamics.

It was in my paper [1985g] that I introduced an account of Fechner's Hypothesis to lead into the derivation of the Neumann potential, but here I was adopting something that can be read in Clerk Maxwell's treatise. The starting point was a formula that can best be described as a 'mutual kinetic energy' term involving the square of the relative velocity as between the two interacting particles. Then, some three years on from there, I completed the link back to Coulomb's law as the starting point [1988a].

This progress following my 1980 book has clarified that issue of the mass-halving feature of the centrifugal force of the aether particle, as I now explain. The Fechner hypothesis, as I interpret it in modern terms, requires that what we see as a charge e moving at velocity v is really a charge e moving at velocity v/2 towards a pair of charges e and -e located in the forward field, with the -e charge of that pair moving at velocity -v/2. When the two moving charges meet they annihilate one another and so leave the remaining charge e in a position forward of the original charge e. This action repeats as the energy shed to the aether by the charge pair annihilation regenerates a new charge pair in the field ahead of that charge e and so there is, in effect, a motion of charge e seemingly at the speed v. The reason for this curious state of affairs is apparent when we consider two separate charges moving along in spaced relationship, each at their own speed. To work out the mutual electrodynamic potential as between the two charges one finds that four interactions need to be added. It then works out, basing the analysis on a formula involving the square of relative velocities, that the resulting potential reduces precisely to the empirically-founded Neumann potential.

So far as concerns the subject raised by McNeall, we can now explain how mass
can be different for the centrifugal force of the aether particle. Firstly,
concerning the electron advancing through space at speed v with the assistance
of electron-positron pair creation and annihilation, there are two masses m
moving in opposite directions at speed v/2. If the path they follow is an arc of
a certain curvature radius R, their combined centrifugal force consists of two
components m(v/2)^{2}/R. This, however, is only half of the force we
know to be applicable to a mass m moving at speed v. It is here that my gravity
theory comes to the fore. Every mass m has a counterpart 'ghost' mass m linked
to it and providing the dynamic balance in that quantum jitter which underlies
the motion of all matter. For motion freely through space, that 'ghost' mass,
which is itself seated in a charged particle system, has to tag along and so the
overall centrifugal force has to be doubled. This results in the standard
formula mv^{2}/R.

Now, had that electron not been in free motion but was simply tracking around an orbit of radius r in its quantum jitter motion, that added 'ghost' mass is not moving as if seated with the electron. Instead, it is positioned in juxtaposition on the other side of the orbit, because it provides the dynamic balance. It is at the other end of the restoring force that opposes the centrifugal forces set up by both the electron and its 'ghost'. In other words the centrifugal force formula can, correctly, be written as if the particle has half its true mass.

This is why the aether lattice particle exhibits a mass that is only half
that given by the formula E=Mc^{2}, but only in respect of its
centrifugal inertial response in its confined quantum jitter orbit.

If Peter McNeall regards this as a challenge to one's sanity, then may I say that a mind that keeps to one track as we advance in physics is likely to get confused when reaching the buffers at the end of the journey. When twos and halves creep into comparisons between theory and experiment, then it needs a little double vision to make sense of what one sees. However, there has to be an answer, if one is on the right track. The routes followed by Einstein and Dirac cannot be right, given that my theory is already well past many of the stations that they could not reach.

As a footnote, I can but say that delving into the physics of the aether is
not an exercise that can be fitted into the tight logical picture that we have
formed from observations on the behaviour of normal matter. It may be that
physicists can imagine 'superstrings' and 'worm holes' in a microscopic
sub-world of empty space, but that will not give the precise numerical answers
that have emerged as a check on my more mundane vision of the aether world. The
aether particles formed into a simple cubic structure and held displaced
collectively so as not to be at positions of negative potential, thanks to
centrifugal action set up by motion in orbits which define the Planck quantum of
action, tell us enough, without getting into 'worm holes'. I will never know
what it is that accounts for that charge pair-creation activity in space, but
explaining that has not been my challenge. I have sought simply to decipher the
coded version of Nature that is locked into the numbers representing the
dimensionless physical constants, particularly those involving G, h, e, c and
M/m, the proton-electron mass ratio. I had to do this using a physical model of
the structure of the aether, because numerology alone leads one nowhere.
However, the twos and halves, such as discussed above, though simple numerically
have been equally challenging.

Some readers, those familiar with the wave properties of electrons, will wonder how what is said above fits in with the diffraction and the de Broglie wave length properties of an electron. Well, it is beyond the scope of this Research Note to get into the problems of the interplay of photons and the electron as the electron travels at speed through the aether. As these Web pages expand I shall be providing a full account of this relationship, building from what is said in Chapter 4 of my book

This shows how four photon spin units involving a 3x3x3 array of aether lattice particles cooperate in setting up standing waves at the de Broglie wavelength. The unit of priming energy associated with the combined spins of these four photon components is the energy involved in the annihilation or creation of an electron. The rate of spin is a function of the speed of an associated electron and the change of spin energy equals the kinetic energy of the electron. However, these photons have a transient existence as the system characterizing the electron alternates between a state in which the electron exists in company with these photon units and states in which it is not moving in the electromagnetic reference frame but has the company of one or more electron-positron pairs, which have the kind of motion described above in this Research Note. The Physics Letters paper just referenced concerns also the way in which electron-positron pairs are involved in setting up the wave properties which account for neutron diffraction. Indeed, just as the electron alternates between states, so the neutron alternates continuously between its four states, as illustrated in Table I of the Hadronic Journal paper referenced as [1986d] in the abstracts included in these Web pages. Although the electron and the neutron have state transitions that differ considerably owing to their entirely different compositions, the photon activities associated with their motion through the aether are identical in character, resulting in their respective de Broglie wavelengths being similar except for the different mass values involved.