I propose next to turn my attention to a problem in physics, one well within the scope of the knowledge I gleaned from my school studies. This is a challenging question in Newtonian mechanics. One of the lessons of history is that one should not 'put the cart before the horse'. That lesson dates from the era before we discovered electricity. Electrical technology changed things around. We can now, if we wish, transport the horse using electrically powered vehicles.
When Newton enuciated his laws of motion he had no way of predicting the way in which electrodynamic forces would affect his dynamical findings in mechanics. Seen in retrospect, it is now evident that, in prescribing his third law, Newton has put the cart before the horse. The 'cart' is the assertion that action and reaction between any two particles are always in balance. The 'horse' is the rule, Newton's rule, which declares that when two particles emerge from a collision then, if there is no loss of energy, the receding particles have a relative velocity that is equal but opposite to their relative velocity at the moment just before impact.
Electrodynamics concerns electric charges in motion and the electric energy potential attributable to charge interaction is a function of the relative position of those electric charges. It is therefore a logical physical consequence that, to the extent that motion affects energy in a charge interaction, that energy must depend upon the square of the relative velocity. When we work out the square root of that energy at impact we find, as we know from simple mathematics, that there are two solutions, just as -1 or +1 is the square root of 1. Since all ponderable matter comprises nothing other than charged particles, this is really why two particles separate after collision with their relative velocities reversed.
Newton derived his 'rule' by declaring that action and reaction are equal and that energy is conserved in the collision between two particles. He could equally have deduced that if two colliding particles separate with their relative velocities reversed, then, assuming that energy is conserved, action and reaction are equal and opposite. The fact that the masses of the particles may be different does not affect this argument and so one might think that, since the answer comes out the same, it matters not whether the cart or the horse has the forward position.
However, imagine now that you, the reader, are sitting in a classroom, paying careful attention. The teacher aims to show why the principle of conservation of momentum applies to a body which is a conglomerate of numerous component particles, all in motion. The teacher explains that because the law of action and reaction governs how each and everyone of those particles interacts individually with each and every other such particle, then one can sum all the forces and their moments about any axis to prove that net momentum, whether angular or linear, is conserved and is independent of internal interactions within that conglomerate body. As a student you do not question this, because the teacher has ensured that the syllabus followed introduces you to the basics of mechanics before you learn anything about electromagnetism. However, what would be the scenario if the teacher made a mistake and did put the cart before the horse by teaching electrical principles before teaching mechanics?
You would have learnt that when an electrical charge is in motion in a magnetic field it experiences a force owing to that motion, a force directed at right angles to the motion. You would have learnt also that when an electric charge is in motion it sets up a circular magnetic field in a plane at right angles to its motion and centred on the axis of that motion. So, if two charges travel together at the same velocity, side-by-side, they will, by symmetry, set up a balanced action and reaction. However, what if these two charges are moving together but one is somewhat ahead of the other? Then those forces acting on the charges cannot be directed along the line drawn between them. They will be directed in opposite directions and have the same magnitude, but as they are not acting in a common line drawn between the charges they must cooperate to produce an out-of-balance couple.
So, armed with what you have been taught about the forces between electric charges in motion, you now come to learn about Newton's laws. The teacher says that action and reaction are equal and opposite between each particle of a pair in the conglomerate body and is about to go on from there to justify the principle of conservation of momentum for the body as a whole. You put your hand up and ask the obvious question. "What if the particles forming that body are electric particles? Will not that affect the assumption we are making about action and reaction being equal and opposite?"
Now, here, your teacher has a problem. If he or she is well read then what will come to mind is the rather complicated law of electrodynamics that was formulated by Ampere expressly to ensure that action and reaction are equal as between two electric charges in motion. However, the teacher knows that that force law is never used in practice. The Lorentz force law, which is supported by Einstein's theory, is the one we use, but what the teacher will most probably not know is that Lorentz's law has been disproved experimentally .
The question really at issue is whether that body could, owing to its internal electrodynamic interactions ever begin to rotate of its own accord or perhaps propel itself in a linear direction, without there being any applied external force. Your teacher will then, no doubt, insist that you must learn Newton's laws, which forbid that possibility. You, on the other hand, will still be asking yourself how Newton could command authority on the issue, even though he could not have taken account of the electrodynamic issue. Meanwhile, your teacher might later ponder the question of why Ampere bothered to formulate his law of electrodynamics if Newtonian law gave a sufficient explanation. I say, he or she might have such thoughts, but I know that, almost certainly, the thought will be that 'experience' shows that we can get by without worrying about such problems. Yet, I also know that we can, if we so choose, live through another century without understanding gravitation and its unifying link with electromagnetism.
Teachers are supposed to know the answers to such questions but this is a subject they never mastered. In later life, after leaving school, one sees, if one bothers to look, that this same problem has remained an active issue without ever being resolved. It remains unresolved, but teachers, even those who lecture on physics at university, do not go out of their way to draw this scientific inconsistency to the attention of their students. Indeed, one sometimes sees evidence of an even worse scenario, where the problem is recognized but the teacher assumes that it has all be solved by Einstein's theory, notwithstanding the fact that Einstein struggled to his dying day to forge that unifying link that could bring electrodynamics and gravitation together.
Newton was concerned about the force of gravity and, to this day, scientists of the highest calibre still strive to find that connection between gravitation and electrodynamics. They occasionally hear of claims by individual 'crackpot' researchers who assert that they can build electrical or magnetic machines which deliver more power output that input. This is contrary to Newton's laws, because action and reaction are always said to be equal and opposite. Yet the Lorentz force law which was 'confirmed' by Einstein's theory is a law which, as applied between two electrical particles in motion, does not itself conform with that law of action and reaction. It is here that we see the farce that underlies all attempts to merge Einstein's gravitational theory and electromagnetism into a common unified field system. Indeed, there is something wrong deep down in the foundations of the problem. The true law of electrodynamics, one which does conform with gravitational theory, is the subject of reference , but see also the sixth of the appended papers.
Scientists declare that when the forces predicted by the Lorentz force law are integrated for a complete system then the overall result is a balanced action and reaction. However, they are not then dealing with basic principles as applied to discrete interactions between elements of matter but are asserting overriding constraints of their own choosing and this amounts to insisting that Newtonian philosophy has the last word.
One could say "So be it" if the hoped-for unification of the gravitational field and the electrodynamic field was already an established fact, but it is not. Also one cannot escape being left with that dominating problem of wondering about the attractive forces involved in the formation of the stars and how energy ever converged into matter to create it in the first place and set things in motion.
If there were a force out-of-balance, a possible breach of the principle of conservation of linear momentum that could occur under certain very special and exceptional circumstances, then one could see a way forward and make some sense out of the current nonsense which is limiting our field of enquiry. Once the aether yields energy so it must assert force on matter. Newton would say that that is an `externally applied' force, but yet it could be a force developed within matter, inasmuch as aether fills all space, even the space between the electrons in atoms.
So here is another rather subtle point that gets glossed over in the teaching of physics. In this situation, the teachers close ranks and refuse to refer to the aether. It does not exist, because Einstein's theory does not require it! It does not exist because it was thought to regulate the finite speed of light but experiment shows that the speed of light in vacuo is referenced on something sharing the Earth's translational motion through space, though not the Earth's rotation. So, assuming that the aether moves through the Earth, there can be no aether!
Well, that is hardly logical. Indeed, it is as illogical as an argument which says that we think there are green men on Earth, but we can find no green men, so there are no men on our green Earth!
There is, indeed, an aether, if only defined as that which feeds energy to sustain the creation of matter, and one can be sure that much of what now remains unexplained in physics has its explanation rooted in that mysterious aether which physicists have turned away from. To say otherwise and declare that the aether does not exist is like knowing that all the answers are in a textbook but refusing to open the book because to read such a book goes against one's principles.
The aether is an energetic medium which reacts to actions set up by the flow of electric current in wires. It is like a bank that accepts money on deposit. It accepts and disperses the energy we label as that stored by magnetic induction. It disperses that energy just as a bank uses money on deposit by dispersing it to borrowers, but it has reserves of energy just as the bank has reserves of money, and the aether allows us to withdraw on demand the energy we have put on deposit. Take away the aether and you take away the whole basis of magnetic induction in electrical technology. It is like taking away the banking system and letting money float around freely in the community. Scientists have adopted a way of interpreting electrical phenomena by supposing that electric particles in matter, migrant photons and the mysterious neutrinos are all that one needs to consider. In that philosophy, however, there is no creative source yielding new charges and nowhere to give energy a resting place when the particles are eventually annihilated.
Now, it may seem to the reader that, in challenging the foundations of Newtonian mechanics by bringing in my concerns about electrodynamic interactions, I am mischievously trying to shake the very foundations of physics. I am not, but I am intent on moving forward and solving the unification problem and to do this I must insist on the adoption of the correct formulation of the law of electrodynamics.
To advance to that I will presently, in the pages ahead, make a quantum leap, a leap that takes me back to the physics of my last school year, some 51 years ago, when I heard about the Bohr model of the atom. The reader will see from such reminder of one's schooling and pre-university education that I am deliberately stressing how easy it is to see where science has gone off track. We need to be very sure of the basics of our subject and look very closely at the groundwork on which we later build.
There is now ample evidence which confirms my own long standing conviction that if the mass ratio as between two interacting electric charges in motion is not unity, as it has been for all the chosen experiments giving us the basic empirical foundations of the subject, then the law of action and reaction can be breached .