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


© Harold Aspden, 1999

If you have heard of Newton's Third Law you will know that any physical action is always balanced by an equal reaction. Put another way, if you build a machine and put in in an enclosure, the forces it generates by pushing on itself inside that box and pushing against the inside walls of that box can never cause that box to take off and fly into space. You can, of course, design the machine so that the box wobbles about, merely because you cause the centre of mass of the machine in the box to move one way while the centre of mass of the box moves the other way, but you will inevitably, according to Newton's Third Law, find that there will be no sustained lateral motion of the system however you operate the machine inside that box.

Such is the folklore of physics but I shall now resume a theme I began in Tutorial No. 3 concerning the law of electrodynamics, the law which governs how an electric charge e in motion at velocity v acts on an electric charge e' in motion at velocity v' and at a vector distance r from e. The physical factor here is the unseen 'something' that sits in the background as the frame of reference for those velocities v and v'. That 'something' is not a box, but it could be something one can push against, if only to set up that wobble, or jitter, perhaps the jitter motion that causes physicists to talk in terms of the Heisenberg Uncertainty Principle, a feature of quantum mechanics.

Now the empirical facts of electrodynamics, restricted as they are to measurements involving reactions on closed circuital electron currents, leave us in some doubt concerning the true law of electrodynamics. There are three alternative versions of the law that can be deduced by rigorous analysis combined with a chosen one of three assumptions. The assumptions are:
(a) That the two charges assert forces on one another that are completely balanced so as to set up no linear out-of-balance force and no turning couple.
(b) That the action between the two charges does not set up any linear out-of-balance force, but permits an out-of-balance as a couple that can turn the system as a whole.
(c) That the system will not permit a turning action solely owing to the interaction of the two charges but may develop an out-of-balance linear force.

Intuition may tell you to express favour for the first of these laws, which is the one formulated long ago by Ampere. However, that law is never used by physicists in their advancement of physical theory. Nor, indeed, is the second law, though it finds more favour in historical works than does the third of these possible laws, the latter being a version that has not been mentioned in scientific writings, except in the writings of this author, my goodself. So you will understand that I am now going to set about convincing you that this 'third law of electrodynamics', albeit one that defies Newton's Third Law, is the true law.

You may have heard of the Lorentz law, a law found acceptable by enthusiastic followers of Einstein's theory, but that is not a law that can be used to define action between two discrete charges in motion. If you apply it in that way you will soon see that it defies Newton's Third Law of Motion and on that basis I defy you to make it fit as a potential way forward for unifying the theory of gravitation and electrodynamics.

The Lorentz law, so far as it concerns electrodynamic interaction, is otherwise known as the Biot-Savart Law. Textbook authority on this subject is that of R A R Tricker 'Early Electrodynamics: the First Law of Circulation', published by Pergamon Press in 1965. On page 44 he writes concerning this law:
Newton's law of action and reaction is, thus, not obeyed between the elements, and it is to this that many elementary difficulties in using the Biot-Savart formula are due.

Gravitation does satisfy the law that action balances reaction. So what we really need is a law which, regardless of the relative disposition in space of two interacting electric charges in motion, can account for a balanced force acting directly between them, even if one has to impose constraints on the direction of those charge motion vectors v and v', as by saying that they are always mutually parallel for the case where they relate to gravity.

The first law, Ampere's law, does not work because the force between the charges varies according to their spatial orientation and is not strictly one reducing to the inverse square of separation distance form.

The second law, has a form proportional to:
(v'.r)v + (v.r)v' - (v.v')r ...........(1)
where the notation (v.r) is a scalar product of the two vectors, meaning that it is the product of the modulus or amplitude of v and of r as multiplied by the cosine of their angular separation. The expression has to be multiplied by the product of the two charges involved, divided by the speed of light squared to convert them into currents in a free space environment of unit dielectric constant, and further divided by the cube of the separation distance corresponding to the vector r. This law will always satisfy the condition for linear force balance. The reason is that interchange of v and v' and reversal of the vector r will give a force equal and opposite to that represented by (1).

However, if you consider this, you will see that in this case there is normally an out of balance couple tending to turn the two-charge system.

The third law, on the other hand, has the form:
(v'.r)v - (v.r)v' - (v.v')r ...........(2)

Here, if you interchange v and v' and reverse r, you will see that, as before, the last term does not produce any out-of-balance force but yet, in the general case there is a net linear force acting on the system as a whole. However, no turning couple is developed because that net force is:
2[(v'.r)v - (v.r)v'] ...........(3)

This is a linear out-of-balance force but it produces no turning action because each charge experiences half of that force of the form defined in equation (3) plus one acting between them through their centre of gravity, assuming they both have the same mass. In this latter statement resides a fascinating research issue, but it is one that does not affect our extension of these ideas to the problem of gravity, but has certain technological implications affecting plasma discharges involving heavy ions and electron interaction.

The key point of interest with the gravity issue in mind is that the expression in equation (3) reduces to zero if the interacting charges move parallel and v is equal to v'. There is no such case or equation (1) and (2) given that the separation vector r can have any direction. We then find that our third law of electrodynamics is ideally suited to delivering an explanation of the force of gravity as an electrodynamic interaction. We must look to gravitation being an effect as between charges having a mutually parallel component of motion.

That is my case in support of that third law, my law of electrodynamics, and I can bring to bear supporting evidence from plasma discharge research.

I will now just extend this analysis to show you how to interpret the law of electrodynamics when it is applied to an interaction where at least one of the interacting elements is a closed current circuit. It is then a question of integrating the force. This may sound complicated but it is really quite a simple task. That circuit will have two segments between the same distance radii r and r+dr drawn from a point at which a charge e' in the other interacting element is located. Owing to the current in those segments that charge will be acted upon by two force components. The current element in one of those segments is the scalar product (i.dr) and in the other element it is also (i.dr) with dr reversed, meaning that the two cancel one another. Note that the current i times an elemental distance measured along the circuit path s is equivalent to (ev/c) times ds, but ds resolved in that radial direction from the point where e' is located is dr and so we can justify this simple result, namely that the integration will tell us that the closed current circuit interaction will cancel that middle term in equations (1) and (2).

This leaves in both cases a scalar product vector notation corresponding to the contracted vector product version that defines the Lorentz force law. So what I am saying here is that the Lorentz force law works for the electron current situation in which at least one of the interacting components is a closed circuit flow of current. The Lorentz force is meaningless if applied to the problem of the interaction of two discrete moving charge elements.

The physics community has been very stupid in not waking up to this situation long ago and I say that unashamedly. I am quite appalled at the ignorance that has been displayed in this matter, given that the form of law stated in equation (1) is in Clerk Maxwell's treatise and is reproduced in the above vector notation in E T Whittaker's History of the Theories of Aether and Electricity, which is where I first saw it in the 1950s when I began to develop my own aether theory.

Surely those who opted to support Einstein's theory should have realised its failings on the issue of electrodynamics, especially as they could not go forward on their quest of field unification aimed at linking gravitation and electrodyamics. They were committed to follow the Lorentz flag and so their battleground became little more that an imagined sea of windmills as they became the Don Quixote's of the future history of physics.

There is nothing wrong with a law of electrodynamics that tolerates an out-of-balance linear force, if Nature uses that law in its special mode where action does balance reaction, as for the gravitational action arising from the interplay of graviton charges all moving in regular parallel motion. The out-of-balance linear force in the more general case tells us that the aether can, as appropriate and when called upon, assert forces on matter. This is something it must do in absorbing energy, the energy we shed into space as entropy, and in disgorging energy to create electrons, positrons, protons etc.

Students of physics must come to see this as the right way forward. We face enormous problems ahead on the energy front and we cannot afford to remain trapped in the space-time web woven by Albert Einstein. I have, in Tutorial No. 12, explained why we do not need Einstein's theory to adhere to the E=Mc2 formula. The transmutation of matter and energy was discussed as the energy source of stars in the journal Nature in 1904, before anyone had heard of Einstein. You cannot transmute energy and mass without bringing into the equation the square of a speed. J J Thomson knew that the only speed that limited the mass of the electron was the speed of light. So, where, I ask, did Einstein make a contribution to energy science? I know the history of the subject, but I remain bewildered and I want to see the world put to rights on this question of electrodynamics, its role in gravitation and the prospects we face in anticipating a new energy revolution.

I end this Tutorial Note by saying:
"The time has come to 'react' and then 'act'. The time has come to reverse the course of events in physics and put 'reaction' before 'action', keeping in mind that they are not always of equal strength. React against Einstein's theory and act to take new energy science forward. The time has come to open your minds on the prospect of tapping energy from the aether, by first learning how the aether regulates energy deployment in the physical world, be it via ferromagnetism, aether spin or by anomalous forces asserted by non-electron plasma discharges. That law of electrodynamics with its implications and pointer to an environment populated by electric charges moving in ever parallel harmonious motion is the launch platform and the point from which to begin you journey. I wish you well and will be pleased if I see that you overtake me in this venture."

Harold Aspden

To progress to the next Tutorial press:

Tutorial No. 14