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

Here we will enter into the formal analysis of one of the most basic features of physics, the relationship between inertia and instantaneous action-at-a-distance.

Take an electric charge e, assume that it is accelerated under the influence of other electric charge and examine the physics of what happens. I ask you to accept as your starting point two hypotheses: (i) that the electric charge will not under any circumstances radiate any of its energy and (ii) that its electrical action at a distance, meaning its electrostatic field external to its body of charge, will only experience change as effects which propagate at infinite speed, that is virtually instantaneously.

If you have any formal training in physics, beyond high school standard that is, then you will know that both of these hypotheses are quite unacceptable to the orthodox professionally qualified physicist. I am therefore asking you to follow an argument of heresy just to see where it leads. You will be surprised at the result.

To ease your concern about what has just been suggested I refer to a remark which J S Bell, a recognized authority on quantum theory, made in speaking to a distinguished audience on the subject of action-at-a-distance in quantum mechanics. He said that Lorentz invariance has "become very problematic" and that "an ether would be the cheapest solution". [See the text of his lecture at p. 269 of v. 10 of Speculations in Science and Technology (1987)].

The unitary charge e is that we assign to the electron, but it could apply to any particle comprising such a unitary charge, whether of positive or negative polarity.

If we depict that charge in a figure, what will you draw? Will it be a point or perhaps a sphere or, as was once suggested to me by a Professor of Physics, a vector diagram denoting something called 'spin'?

Before we get into the detail of that, it is appropriate to summarize some background information, that of my background. As a university student back in 1946 I invested in the purchase of an academic textbook entitled

So, as my funds were scarce, when I say I 'invested' in that book, I meant it. I expected it to be of benefit to me.

Now at the time, being 18 years of age, I was not the least bit interested in Einstein's theory, but I was interested in electricity. That book meant a great deal to me when I made my way forward on the electrical front. It clarified the physics which in turn helped me in my more practical study of electrical technology. I may note here that the book had, indeed has, 432 pages, but, although entitled

I read all that and understood it, but it was of no immediate interest and it certainly had no utility so far as my career interests in electrical technology were concerned. However, in later years I came to realise that Einstein's theory had blocked the scope for initiatives aimed at advancing the technology that depended upon knowledge concerning the way in which the aether stores energy. In other words Einstein's theory was obstructing technological advance.

Of course, you will say that E = Mc

The reason, in simple terms, is that the facts of electron theory, of energy and the increase of energy and mass with speed were known from experiments performed in the late 19th century and before Einstein appeared on the scene.

This brings me then to page 15 in Wilson's book, where he reproduces a method devised by J J Thomson for explaining the Larmor radiation formula for the energy radiated by an accelerated electric charge. I shall in this Tutorial Note be working through the analysis involved, but I want you to know what Wilson stated on page 16 as he ended that analysis. It reads:

"Electromagnetic radiation is obtained in practice from electrical oscillations produced by the discharge of a condenser through a wire. In such cases, in which enormous numbers of electrons are involved the radiation obtained agrees with that calculated by electromagnetic theory. Radiation from single electrons has not been observed, and according to the Quantum Theory the electrons in atoms do not radiate when they are moving around orbits and so have an acceleration. The success of quantum theory makes it possible that the expression just obtained for the radiation of an electron is erroneous, and in fact that the equations of the electron theory are probably only true when the density of electricity us taken to be the average density over a large volume containing a large number of electrons and atomic nuclei."

So you see, here, by page 15 in a 432 page textbook directed at the serious student of physics as a precursor to research specialization in a particular field, Professor Wilson has revealed something that is surely extremely important and warrants very careful consideration. Why is it that the analysis by that J J Thomson method works for electricity in bulk, but not for the isolated electron? Surely physicists cannot hide behind the magic principles of Quantum Theory! Yet that is exactly what the full might of the academic physics establishment has done for most of this 20th century. They have ignored that problem which was assuredly presented in the 1937 edition of Professor Wilson's book, if not expressly stated in his first, 1928, edition.

Now when I came to focus on this particular problem, which I certainly did once I had my own Ph.D. as a qualification, I saw so clearly that the J J Thomson derivation of the energy radiated by the accelerated electron had not taken any account of the necessary electrical field producing that acceleration. It had just been assumed that somehow the electron was accelerated as if the statement "Let there be acceleration" was akin to God's biblical utterance: "Let there be light". Accordingly I set about incorporating the field that produces the acceleration to see how that affects the analysis. I had, incidentally, by the time I embarked on this task in 1954, convinced myself that there is an aether, a real aether, so I was beginning to rebel against the influence of Einstein's theory and was ready to challenge virtually anything that lacked true substance and a ring of truth.

We will first see the derivation of the radiation formula assuming no accelerating field is active and then correct the analysis by rectifying the assumptions involved.

Referring to Figure 1, consider an electron moving along a straight line AO with constant velocity v. At and near to O suppose the velocity changes abruptly to a constant velocity v' along OB. While the electron is moving along AO its electric field moves with it. At O where v changes it will begin to excite the electric field corresponding to velocity v' along OB, and at the time interval t later this new electric field will fill a sphere of radius ct. Here c is the assumed speed at which the change of field propagates radially from that point O. Outside the sphere the field will still be that due to the electron moving with velocity v along AO. The two fields will be separated by a layer of thickness c.dt containing the field excited by the electron during the short interval dt in which its velocity changed from v to v'. The layer moves out with the velocity c and it contains the wave produced by the change from v to v'.

The lines of force in the field outside the sphere of radius ct will radiate from the point O' on an extension of the line AO, where OO' is vt and the lines of force inside the sphere radiate from a point P on OB such that OP is v't. If we consider a line of force starting from P and making an angle θ with O'P, it will be displaced relatively to the parallel line outside the sphere by a distance (O'P)sinθ, and we may suppose these two lines are joined into a single line by a part lying in the layer of thickness c.dt. This requires a field component in the layer, in the plane containing O'P and parallel to the surface of the sphere, equal to:

At this stage we can introduce an acceleration term denoted (v'')/dt. This is the rate of acceleration f of the electron, v'' being the vector difference betrween v' and v. Note that O'P is (v'')t, so that the tangential field in the layer under consideration is:

The electric energy density in the wave region defined by that tangential field component in that field layer is 1/8π times the square of this field component and, based on Maxwell's theory, we suppose that there is an equal amount of magnetic field energy, so we can formulate the energy in the whole wave as:

This brings us to the formal classical derivation of the rate of energy radiation by an electron owing to its acceleration. However, we are going to question this result, because somehow electrons can be accelerated in an ongoing everlasting life within their abode inside an atom and there is no energy radiated unless the atom is excited by some quite dramatic external influence so as to drive the electron to an energy level by which it is forced into an unstable state.

Experiment says that electrons suffering the enormous rates of acceleration they experience within atoms do not radiate energy in a continuous emission process such as that implied by the above analysis.

Now, there are several points that we can make at this stage. Firstly, if the electric field could adjust to the electron's change of velocity instantaneously, as if c were infinite, then there would be no energy radiation and the problem would disappear. Secondly, there is an implicit assumption in the analysis based on c being finite, which is that the electric field can adjust instantaneously to the electron's change of position (as opposed to velocity). How else can we justify the assumption that the field lines all move bodily as a unit sharing the velocity of the electron? They ought otherwise to bend, the faster the electron, meaning that they should be distorted as a function of speed even though that speed is constant. So this second point actually obliges us to adopt the argument that c is infinite so far as the electrical action is concerned and that means no energy radiation.

Our third point arises if we now ask how the electron can be accelerated. Presumably the electric field interaction of another charge or group of charges in the environment of the electron is at work promoting that acceleration. That field must have a field intensity F which is equal to mf/e, where m is here the mass of the electron. This field acts in the direction of acceleration but will not affect the energy radiated except for its component in a direction common with that of the above-mentioned tangential field. In fact it will have such a component Fsinθ that is negative, because the tangential field lines emanating from the charge are stepped backwards in relation to the forward acceleration field direction.

Now, in the above calculation, we have squared the electric field intensity and we have not taken account of this field F. Let us do that. You will then find that there is a condition for which the resulting electric field energy density in the radiated wave is zero. In working this out we must only consider the components of energy density that amount to a wave disturbance, because we cannot suppose that any of the normal energy of that field F is radiated. The relevant factor in the energy calculation is:

The condition is that:

Now we have argued that there really can be no continuous radiation of energy by that discrete charge when accelerated, as we well know from quantum theory, so we know that this equation has to be valid. Yet if we put c as infinite to cater for that instantaneous action which assures that no energy is radiated through regions well remote from the sphere of influence of the accelerating field F, then that energy expression mc

What, therefore, the above equation does tell us is that the electron has a finite form, a spherical form containing the charge e, but that the finite speed c applies within that charge sphere, whereas the propagation speed outside the body of charge becomes infinite. We can then interpret the equation in the following way. Note that if we denote the radius of the electron charge as

In other words E = mc

So the situation you now confront is an electron that tells you that E= Mc

You will no doubt have many questions to raise in your effort to cast doubt upon my conclusion here, so I will raise some of those questions myself.

Firstly, where is that electric energy located. It amounts in fact to the electric field energy disposed outside that radius

Your next question then could be: "What about the wave radiation conveying energy through the body of that charge? How does that affect the above calculation?"

The answer to this is that it has all been worked out and is of published record on pages 82 and 83 of my book

So now we have understood that the electron and, indeed, any discrete particle of unitary charge will exhibit the property of inertia and a mass equal to E/c

Let me remind you of that comment by J S Bell. He was concerned with action-at-a-distance in quantum theory and felt that the answer, the 'cheapest solution' in the expenditure of scientific brainpower, was to revert to a belief in the aether.

We have introduced action-at-a-distance in saying that c could be infinite where c is the speed at which electric field action propagates in free space, meaning in space between discrete electric charge forms. So now we must face that question concerning magnetic fields.

First, however, we need to dispose of the minor question concerning c being the same in charges of different size. Here I can but appeal to an analogy with the known properties of gas. Compress a given quantity of gas into spheres of different size. The pressure will increase inversely as the volume decreases and the mass density will increase with the pressure, but the square of the speed of propagation of sound in those gases is proportional to the pressure divided by the density. It is the same whatever the volume taken up by that standard amount of gas. I do not see this as proof for the corresponding case of the electric charge, but it is suggestive that there could be some common factors governing the physical circumstances involved. Certainly, if the argument is restricted to conserved mass and energy, and volume is varied, energy density divided by mass density is independent of volume and we can infer from the physics of dimensional analysis that the speed parameter is independent of volume.

The question of magnetic field raises with it the question of what happens when groups of electrons are accelerated in unison. This is the situation in a radio antenna and we do know that energy is radiated, or rather shed, by such an antenna, radiation being a questionable term because it implies that the energy shed actually travels at the speed of light and there is nothing to confirm that that is the case. The answer to our magnetic field problem is found in the fundamental roots of the physics of electrodynamics.

Now already I have introduced you to this subject in Tutorial No. 3. If you seek further enlightenment then I refer you to my published paper 'Instantaneous Electrodynamic Potential with Retarded Energy Transfer' [1988a]. You need to work out the Neumann Potential starting from the Coulomb electric interaction as being an instantaneous interaction, but involving two electric charges that are in motion relative to one another. Once you have derived the Neumann Potential you can deduce the law of electrodynamics and from that you can go on to derive the familiar theory of the magnetic field.

That step of going from the Neumann Potential to the law of electrodynamics involves recognition of a role played by the aether, meaning charges in the aether reacting to disturbance.

So, ignoring now that electrical field F introduced in the above analysis, suppose, because we have two charges that are interacting, that you work out the energy radiation formula at a distance well removed from the source and replace e by 2e. You will get the propagating field energy density as being proportional to (2e)

It means that electromagnetic waves are set up by the oscillation of electric current and its effect in setting up magnetic fields which disturb the aether and, being 'magnetic', they represent energy in transit from a photon source to a region of photon absorption, energy which is pooled with the energy sea of the aether. Yes, those oscillations of aether energy imply aether charge displacement and waves which are local oscillations as between electric displacement energy and kinetic (magnetic) energy. The action complies with Maxwell's theory but only if that theory is modified to put the electric and magnetic field oscillations into quadrature time phase, meaning that as one rises to its maximum the other falls to its zero state. That way, the energy is conserved and does not travel at the finite speed c, which is the wave velocity.

The standard teaching concerning electromagnetic waves requires you to believe that the electric and magnetic fields, though in space quadrature, meaning one oscillates from right to left as the other oscillates up and down, both reaching their maxima and minima together. That forces energy dissipation. It is a feature governing the operation of most radio antennae, but, though its effect is to shed energy quite effectively, it is not the best way of exciting electromagnetic waves that have to travel long distances. I can but refer here to the Gieskieng antenna experiments, the subject of the Appendix to Lecture No. 10 in these web pages.

Note that if you discharge a capacitor through a straight wire the surge of current will develop an induced back-EMF as the energy is absorbed into the magnetic field, where it is stored. However, the current involved surges through the resistance of the wire causing some loss and, further, because that current is not in time-phase quadrature with the EMF applied by that capacitor it forces a condition in which the aether finds itself at odds with itself because it wants to sustain a natural oscillation as between the electric and magnetic disturbance. Accordingly it takes on board energy which it then finds a way of rejecting as heat adding to its entropy. There is a phase angle between the antenna EMF and the current and this is dealt with in theory by asserting that it accounts for radiation resistance, the theoretical assumption being that all the energy injected into the oscillations of those electromagnetic waves is carried away at the speed of light.

All this means that we have theory which scientists are happy with, theory which says that electromagnetic waves radiate energy but yet that requires photons to convey that energy, theory which denies action-at-a-distance, but yet conflicts with what experimental evidence concerning quantum theory tells us by implying what amounts to superluminal speed of communication. So my argument is that if one really looks deeply into the case put by H A Wilson concerning the radiation of energy by the accelerated electron, one can see scope for correcting errors implanted in that theory. I suggest that there is no such thing as energy radiation at the speed of light, given that what travels at the speed of light, if tangible in energy terms, must have infinite mass, so posing an impossible scenario. I suggest instead that waves, as travelling disturbances of energy already in the aether, will involve the forward and backward low speed displacement of aether energy, while the wave itself, meaning the surface envelope of that aether energy travels at that high but finite speed c.

I further suggest that, whereas in that J J Thomson method of deriving the Larmor energy radiation formula, Wilson added magnetic field energy in amounts equal to the electric field energy, basing his argument on the assumption that electric field energy is forcibly propagated and that it develops Maxwell-type waves, the fact is that current oscillations in an antenna set up a propagating magnetic wave oscillation which deploys aether energy, as from a standing reserve of energy in the space through which the wave travels, but into a compliant local electrical field oscillation in time-phase quadrature.

The aether is essential and action-at-a-distance in the Coulomb gauge is equally essential. The consequences technologically could be that we have already been missing opportunities in exploiting new types of antenna for radio communication, if not opportunities to tap energy from the sea of aether energy that is omnipresent. I note that the latter was deemed feasible long ago by Tesla, but will not enlarge on that theme. I see the Gieskieng research as warranting scrutiny and have stated my case on that in that above-referenced Appendix to Lecture No. 10.

There will be many who happen to read this Tutorial Note who will stand ready to defend what they have been taught about radio communication. They know that an antenna has a radiation resistance and see the calculation of that resistance in their textbooks. They are well aware that so much is already known about radio communication that it seems foolhardy to suggest that there is a startling gap in that spectrum of knowledge. However, all they really know for certain is that they inject energy into an antenna to excite its current oscillations and that somehow the signals generated are detected by radio antennae elsewhere. The electromagnetic waves are real and they suffer attenuation with distance travelled much as is expected from the theory taught in those textbooks, though when physicists get into the act and start talking about photons carrying the energy then the picture gets a little hazy. So where have things gone wrong?

The answer is found in an analogy with message communication using a homing pigeon. You can send messages from A to B by writing notes and having them carried by the homing pigeon. There are two ways of doing this. You can put the pigeon in a cage and ship the cage by regular transport so as to convey that pigeon with its message from A to B or you can release the pigeon at A and give it an initial 'nudge' to let it fly free and naturally in finding its way by flying from from A to B. The situation with radio waves is only slightly different. Our forebears designed a transit route which effectively puts your message in what I will term a 'Maxwell cage' and forces the transportation of that cage from A to B. Their research caused them to misinterpret that initial 'nudge' as being something that had to be sustained during the whole transmission from A to B.

Nature has a natural way of conveying those messages, but the scientist seeks to force his will on that process by insisting that the 'cage' travels as well. It is just a question of whether the energy needed to initiate the wave has to travel at the speed of the wave or whether it cannot keep up and so is dispersed in the early stages of the journey.

Clerk Maxwell introduced us to displacement currents and devised what my Cambridge University Professor, E. B. Moullin, described as 'Maxwell's Hypothesis', namely the notion that electric currents can only flow in closed circuits and those displacement currents in the aether duly keep faith with that requirement.

Once an electromagnetic wave is well clear of its transmitting source it relies solely on those displacement currents as we know from the four equations defining Maxwell's proposition:

-(μ/c)dH/dt = curl E

div E = 0

div B = 0

The significance of the symbols used in these equations is well known so I shall not define each such term. These equations literally 'force' the message to convey energy with it at the speed of light, but that is mere 'hypothesis'. Had the equations been formulated in a symmetrical form, symmetry being a theme blessed by many a physicist, then they would have the form:

-j(μ/c)dH/dt = curl E

div E = 0

div B = 0

Remember here that the whole concept of of magnetic field H is only notional. H is something invented to provide a link between two systems that convey electric charge and so involve currents acting on currents. The -1 connection that applies to real currents in the real inductive circuits of the matter form is no warranty that the displacement current at a point in free space has to partner another current to define that -1 term. Physically, if what is meant by E

So if you adhere to the conventional philosophy concerning radio waves then you are probably living in a state of ignorance, not knowing how energy really travels at the speed of light or what happens to that energy when waves crash into each other as they move in opposite directions. You are not destined then to research the problem of how two such waves crashing into each other sustain their frequency characteristic as they emerge, nor will you be able to discover how a very sparse population of pseudo-matter, Nature's ongoing attempts to shed energy in free space to create protons and electrons, will progressively reduce the wave frequency as a function of distance travelled. So you will not then see how this explains the cosmical phenomenon called the 'redshift' and you will be destined to think that the universe is expanding from a point in the seat of a lengendary 'Big Bang'. In short, bearing in mind that very nearly everything we know about outer space depends upon the interpretation of the physics of electromagnetic radio waves, your defective knowledge on that subject has aided and abetted in the distortion of the true physical picture of our universe.

Take note, if you are an old 'student', that this is all because you were misled into thinking that an accelerated electron radiates its energy! If you are a young student then take heart and learn more from these Tutorial Notes so that you can help me in my ongoing quest to discover the truths of these issues. Remember, some physicists are still struggling to solve a problem they have with the electron, namely the 'fact', as they see it, that the electron appears to have mass but no volume. They say that more money is needed to build bigger and better particle accelerators so that they can solve such problems, but I suggest that reading a few old textbooks, such as that by H. A. Wilson, reading them in a questioning way, might provide answers that can ease much of that pressure to justify more and more research expenditure.

My primary object in this Tutorial No. 12 has been to introduce you to the fact that E=Mc

I urge you not to be impressed by Einstein's theory, simply because you think that the physics of E=Mc