INTRODUCTION
In this Essay we shall see how easy it is to explain why iron, nickel and cobalt are ferromagnetic. This is a physics exercise which really should be included in all of the principal textbooks on magnetism, because without it students are left mystified by the mention of 'exchange forces' and the 'Pauli exclusion principle', with no real understanding of what is so special about iron, nickel and cobalt.
In summary, the state of ferromagnetism is a condition of least energy arising from the contest between the attractive forces set up by electrodynamic interaction of the orbital motion of atomic electrons in the 3d state, which move in synchrony, and the accompanying repulsion caused by electrostatic interaction. The 3d electron state is one where the electrons have an orbital motion that is quantized as 2 Bohr magnetons, equivalent to the condition n=2 in the Bohr theory of the atom. Ferromagnetism can only appear in a material having crystal form and only occurs where that material is strong enough to withstand the out-of-balance stresses set up by the above contest between those two forces. Loss of ferromagnetism will occur when temperature increases to the level where the cohesion of the atoms forming those crystals is weakened sufficiently. This occurs at the Curie temperature, before the substance melts. Phase changes in the crystal structure can also affect the ferromagnetic condition.
To explain why iron, for example, is ferromagnetic, all we need to do is to calculate the stresses set up by those two conflicting forces to see which combinations of atomic number Z, and electron orbital quantization n, can allow tolerable levels of internal mechanical strain. The task is quite straightforward provided we do not confuse the problem by looking for a short cut route in our analysis. It is tempting to calculate the magnetic energy density and compare this with the strain energy density, taking that comparison to be decisive. Here, however, energy is something which is pooled amongst the vast number of interactions that arise within the ferromagnetic crystal, whereas the force components which are decisive in determining mechanical strain are individual to the charges that they act upon. The positions or states of motion of those charges, as electrons, is determined by the specific values of those force components and not by some statistical average.
Another pitfall which must be avoided is that of thinking that ferromagnetism arises from something termed 'electron spin'. Remember that ferromagnetism, as the property of the lodestone, and gravitation as a universal force affecting all matter, are phenomena that have mystified mankind throughout the ages. Also, the challenge of unifying the theories governing electromagnetism and gravitation have eluded physicists right through the period of the development of atomic theory. Once the atom began to yield its secrets, they studied that atom in isolation, as an ionized particle, which emitted a radiation spectrum when duly excited. They were then looking at properties of the atom which had no real bearing upon the way those atoms interact when locked together in a crystal. Furthermore, they were looking at the atom in an era when science had turned its back on the idea that there was something of an aethereal nature filling space devoid of matter. So when they saw effects in those atoms that might betray a reaction property involving energy exchange and interaction with that aethereal 19th century medium, they had to hold faith with their new 20th century beliefs and this required that the inner workings of the atom were self-contained. If the numbers governing their quantization conditions then had to imply that electrons had special characteristics, a 'spin' that was not the kind of spin that engineers contemplate, then, so be it. 'Spin' became the magic word. It compounded the problem of understanding ferromagnetism.
The consequence of this was that those physicists who turned their minds to ferromagnetism became convinced that ferromagnetism arises from 'electron spin', but yet they still cannot explain in terms, meaningful to the discerning student, how it is that iron is ferromagnetic, whereas copper is not ferromagnetic. Nor can they begin to explain gravitation, which is, in a sense, a property analogous to ferromagnetism. It is an attractive influence which is seated in the synchronous motion of electric charge, but which involves extrapolation of ferromagnetism, as a property of crystalline matter, to the realm of a 'crystalline' medium permeating all space.
THE NATURE OF FERROMAGNETISM
This was the title of Chapter 3 in my book Physics without Einstein, which was published in 1969 (See Books and Reports section of these Web pages). I shall here be extending this account of ferromagnetism well beyond what was covered in the book, but, even though there is a little repetition of what has been said in the above Introduction, it is appropriate to reproduce, in full, the text of that chapter. My object is to show that I did put my findings on record at that time and, as the substance of what I had discovered is very relevant in understanding how we can apply ferromagnetism to tap energy from the orbital motion of the quantum underworld of our environment, I want to assure the reader that my thoughts on the matter have had time to mature. Indeed, as will be seen, there is much progress to report.
Do not be misled by the title of that book 'Physics without Einstein'. The title means precisely what it says, but it does not mean that I was ignorant of Einstein's theory or had not understood it. No, it means simply that we can progress further to reach new horizons in the field of energy technology, if we follow a route alternative to that taken by Albert Einstein. It needs physics of the kind meaningful to the engineer who can apply the underlying scientific principles to technological advantage. The pathway forward was a track through the jungle of ferromagnetism, a subject, the principles of which are not well understood by the physicist, but which is at the very heart of virtually all electrical machines that generate the power on which we are so dependent.
The text copied from my book now follows. Bear in mind that the book was published in 1969. It gave an insight into the nature of ferromagnetism that you will not find elsewhere, even though the research reported on ferromagnetic properties generally is vast in its extent. Yet what I disclose here is only an 'insight' as there is very great scope for academic research projects aimed at performing the computer analysis that can take forward what I have outlined in this brief account.
HEISENBERG'S THEORY
Heisenberg's theory of ferromagnetism attributes the ferromagnetic state to an alignment of electron spins in atoms due to exchange forces. In wave-mechanical terms, the probability that an electron in one atom will change places with an electron in an adjacent atom is given by an exchange integral which is positive or negative according to the ratio of the radius of the relevant electron shell r and the atomic spacing d. In general, this integral is negative since the attractions between the atomic nuclei and the electrons are greater than the repulsions between the nuclei and between the electrons. It is positive when there exists a certain ratio d/r of the distance between the adjacent atoms of the crystal and the radius of the electron shells containing the uncompensated electron spin. Slater (Physical Review, v. 36, p. 57, 1930) presents the data:
Metal Fe Co Ni Cr Mn Gd d/r 3.26 3.64 3.94 2.60 2.94 3.10The conclusion drawn from this is the empirical presumption that, for ferromagnetism to exist, d/r must be greater than 3.0 but not much greater. [It is noted that the symbols r and d are used here to denote the dimensions in an atomic lattice are the same as used by the author in his theory pertaining to the quantized orbits and lattice dimensions of structured form of the vacuum medium. The coincidental feature that the ratio d/r is slightly more than 3 in the lattice of the vacuum medium is deemed to be fortuitous.]
As Bates (Modern Magnetism, 3rd Edn. Cambridge University Press, p. 327, 1951) points out, in Heisenberg's theory the exchange forces depend upon the alignment of the electron spins but the forces between the spins themselves are not responsible for the ferromagnetic state. Ferromagnetism is presumed to be due to interaction forces between the atoms because these forces apparently have a common feature if the ratio d/r has an approximately common value, evidently greater than 3.0 but not much greater. However, is this a sufficient explanation of the ferromagnetic state? Also, accepting that the exchange forces do have values coming within certain limits which are conducive to the ferromagnetic state in the ferromagnetic substances, what really is the link between these forces and the intrinsic magnetism? How do the electron spins get aligned and why is it that so few electrons in each atom have their spins set by action of the exchange forces? Why is Heisenberg's theory so vague in its quantitative account of the ferromagnetic state? Also, since in Chapter 2 it has been argued that ferromagnetism is not primarily associated with electron spin, as is popularly believed, but is in fact due to the orbital motion of electrons, how is this to be related to Heisenberg's theory?
THE CAUSE OF FERROMAGNETISM
In considering the nature of ferromagnetism, the idea that magnetic energy is a negative quantity, presented in the previous chapter, has immediate significance. Magnetism may have a tendency to become the preferred state and ferromagnetism will result if the other forms of energy which go with this magnetic state can be fully sustained by the source of magnetic energy itself. This is simple physics without recourse to exchange integrals defining probabilities of electron interchanges between atoms.
On this point of negative magnetic energy, it is appropriate to note that it is included as a negative term in magnetic domain theory where the equilibrium states of magnetic domain formation are evaluated (see Kittel, Rev. Mod. Phys., v. 21, p. 9, 1949). "The minus sign merely indicates that we have to supply heat in order to destroy the intrinsic magnetization."
To say that energy has to be supplied to destroy intrinsic magnetism is to say that energy is needed to restore the undisturbed state of the field medium (the aether) since the disturbance, which is magnetism, has yielded energy and needs it back to be restored to normal. If ferromagnetism, meaning an alignment of the magnetic moments of adjacent atoms in a crystal, needs other energy to sustain it, such as strain energy, this other form of energy can participate in the return to the demagnetized state. But the question of whether a substance is or is not ferromagnetic must depend upon the ratio of the available energy from the magnetic source and the sustaining energy needed, as by the strain. If this ratio is greater than unity, there is ferromagnetism. Otherwise there is no ferromagnetism.
Why is iron ferromagnetic to the exclusion of so many other elements? The answer to this question is that it so happens that in the atomic scale iron is positioned to have properties for low interaction forces between atoms, with a significant alignment of certain electron states. In addition, iron is strong enough to withstand the effects of these forces, which are many tons per square inch and do approach the normal breaking stresses of metallic crystals. Further, iron, as well as nickel and cobalt, does happen to have a rather high modulus of elasticity so that the energy needed to sustain the strain is relatively low.
Why does the ferromagnetic property disappear as temperature is increased through the Curie point? There are the conventional explanations for this in the standard works on magnetism, such as that of Smart, (Effective Field Theories of Ferromagnetism, W.B. Saunder & Co., 1966). A simple alternative answer which appeals to the writer is that, since the modulus of elasticity does decrease rather rapidly with increase in temperature, by the right amount, the strain energy needed to sustain magnetism increases to cross the threshold set by the ratio mentioned above. This threshold is at the Curie point.
If ferromagnetism is so closely related with internal strain, and if this internal strain is high, and if at high strain the modulus of elasticity becomes non-linear, all of which are logical, then, at least in some ferromagnetic substances, there should be significant changes in the modulus of elasticity at the Curie point. This is found to be the case. The phenomenon has been discussed by Doring (Ann Phys. Leipzig, v. 62, p. 465, 1938).
It is shown below how the elements of a theory of ferromagnetism can be based on the above argument. The analysis is simplified by the expedient of regarding the Bohr theory of the atom as applicable. This merely serves to allow easy calculation of the stresses mentioned.
STRESS ENERGY ANALYSIS DUE TO ORBIT-ORBIT INTERACTIONS IN A FERROMAGNETIC CRYSTAL LATTICE
In view of the different account of the gyromagnetic ratio given above (i.e. in Chapter 2 of 'Physics without Einstein at pp. 32-36), the ferromagnetic state can be regarded as due to electrons in orbital motion, rather than a mixture of spin and orbit actions. The electron in orbit traversing a circular loop at a steady speed will be taken seriously, notwithstanding the wave-mechanical aspects and the accepted improbability of such steady motion in an atom. The purpose of this is to facilitate the approximate calculations presented here. Offset against this also, one can argue that the Principle of Uncertainty, as used in wave mechanics, may well only have meaning when viewing events in atoms on a statistical basis. This principle is no warranty that, in some atoms, those of certain size, arranged in certain crystal configurations and under certain energy conditions, just one electron could not defy the principle, as viewed by an electron in an adjacent atom, and actually be in a harmonious state of motion with such electrons in adjacent atoms. The motion of electrons in atoms is not random. Statistically, wave mechanics helps us to understand the systematic behaviour of atomic electrons, but they are a mere mathematical tool used for this purpose and not a set of laws which a particular electron has to obey. If, energetically, it suits the electron to move steadily in an orderly orbit, it will do so. Such is the premise on which the model to be studied is based, and with it the Bohr theory of the atom will be used.
Imagine two adjacent atoms arranged in a crystal lattice with their electron orbits aligned along the crystal direction linking the particles. This is illustrated in Fig. 3.1. Only one electron per atom is taken to be in this state.
The atoms are spaced apart by a distance d. Each atom has a nuclear charge Ze, an electron system depicted as a cloud, shown shaded, of charge e -Ze, and a single electron of charge -e describing a circular orbit of radius r and velocity v. In effect, it is assumed that one electron in each atom has adopted a motion in strict accordance with Bohr's theory, whereas the other electrons form, statistically, a charge centred on the nucleus, but not screening the orbital charge from the electric field set up by the nucleus.
The orbital electrons are taken to move in synchronism in view of their mutual repulsion. Then the following components of interaction force between the two atoms may be evaluated in terms of the radius r of the electron orbits and the velocity v of the electrons.
These force components are, simply, the electrostatic and electrodynamic interaction forces between the two electrical systems defined. If the last term is expanded, then, neglecting high order terms in r/d, since r is less than d for all cases and very much less for most, it becomes:
On Bohr theory:
It follows that, as Z increases, the attractive force component diminishes and the repulsive force component increases. The zero force state occurs when:
The above calculation is merely to demonstrate that the approach being pursued may prove profitable.
To develop the theory on more realistic, though still approximate, terms, the transverse forces have to be taken into account in stress energy considerations. The force in the lateral sense between two atoms in the crystal lattice will be effectively all electrodynamic. The electrostatic action of the orbital electron of one atom will, on average, tend to act from a point close to the nucleus when its action on the other atomic nucleus is considered. It follows from the law of electrodynamics developed in Chapter 2, that the force (ev/c)2/d2 will act in the lateral sense. This will create components of stress energy precluding the total stress energy from passing through zero as Z increases. This will make the ferromagnetic state less likely to occur and very much will depend upon the value of the related magnetic field energy and stress energy.
To proceed, the stress in the substance will be taken to be of the order of 1/d2 times the elemental force just deduced. This is taking into account only forces between adjacent atoms in a cubic lattice. The actual force will be greater than this, perhaps by a factor of two or three. Although there are many atoms interacting, when the spacing doubles the forces are reduced in inverse square proportion. Further, the harmonious nature of the electron motions may not be seen as such for interactions over large distances. In travelling a distance d of 2x10-8 cm at velocity c of 3x10-10 cm/see, the electrodynamic action, for example, involves a transmission time of 0.67x10-18 seconds. In this time, for Z=23 and n=2, equation (3.1) shows that the electron may move 1.7x10-9 cm. This is slightly more than one quarter of a revolution. This really means that this approach to explaining ferromagnetism requires a redefinition of the synchronous state assumed in Fig. 3.1. In fact, since energy considerations are involved, the mutual repulsion forces between the electrons in orbit urge maximum separation, subject to the propagation velocity. This velocity may be different from c, but this does not matter. We take it that synchronism exists as viewed by each individual atom. This means that electrons in adjacent atoms are out-of-phase in their motion as viewed from remote positions. It also means that atoms not adjacent to the one under study will be seen by that atom to have orbital electrons also out-of-phase. There is an exception for successive atoms along the magnetization direction and transverse to it along the crystal axis, because the effective value of d increases in integral steps. From considerations such as this, it may be shown that the prime term is the energy due to interaction with atoms adjacent in the crystal lattice directions. The energy will be greater than this only provided the surrounding atoms are seen to be in synchronism and make a significant contribution to the energy required. If these atoms are out of synchronism, they may add to, or subtract from, the energy, but, overall, should have little effect.
Along the direction of magnetization, there will be a stress Fx,
given by:
In terms of Young's Modulus Y and Poisson's Ratio s, the strain energy density is:
The pattern of the high susceptibility atoms has a grouping matching the minima of the strain energy curves. This encourages the strain analysis approach to explaining ferromagnetism. The minima of the strain energy curves corresponds to the increased likelihood of ferromagnetism, though this latter state can only occur if the magnetic energy (being negative) exceeds in magnitude the strain energy. Of importance here is the fact that the strain energy density and the magnetic energy density are of the same order of magnitude, thus making select states of ferromagnetism feasible in some materials but not in others. The strain energies of the order of 107 ergs per cc, correspond to stresses of tens of tons per square inch. This means that selectivity for the ferromagnetic state may also depend on the rupture strengths of the materials; ferromagnetism clearly being more likely in strong materials of high Young's Modulus.
The understanding of ferromagnetism by its relation to stress properties may prove of interest in that it may be that under the very high pressures prevailing inside the earth, even materials which are not ferromagnetic at the surface may become ferromagnetic. Young's Modulus may then be of no importance and a compression modulus may be the factor which is deciding the state of balance between stress energy and magnetic energy.
SUMMARY
In this chapter, it has been shown how the nature of ferromagnetism can be explained without recourse to wave mechanics, The law of electrodynamics developed in Chapter 2 and the principles of negative magnetic energy are applied successfully in the analysis. In the next chapter we will explain how the theory is reconciled with wave-mechanics. It will be shown that an electron can spend some time in a Bohr orbit and some time in its wave mechanical state. Thus, a factor has to be applied to lower the magnetic energy curves in Fig. 3.2, so limiting the elements in the ferromagnetic state still further.
The text of Chapter 4 in 'Physics without Einstein' ended here, but I shall now update the discussion.
ONWARD DISCUSSION
The main contribution I had made in developing the above theory of ferromagnetism is summarized in Fig. 3.2. The threshold condition for ferromagnetism was determined by internal mechanical stress and the ferromagnetism was quite definitely seated in the orbital motion of electrons and not in that notion of 'electron spin'.
I was gratified that the theory seemed to work for a single orbital electron in the 3d state, which had that orbital component matching the n=2 quantum level of the Bohr atom theory. The measured quantization in Bohr magnetons per atom in iron was 2.221, which seemed close enough. However, that small difference worried me. It needed explanation. Note also that I had to reconcile in my mind the reasons why the mutually attractive electrodynamic forces between atoms in an extended structure were not over-dominant. I wanted the synchronous orbital motion of electric charge, as a quantized state, to play a role in gravitation, which seems unbounded in its range of action, but yet there had to be something limiting the range of action of those corresponding electron interactions in the ferromagnet. Otherwise the iron crystal would surely crush itself to the point where ferromagnetism collapses.
Looking back, I expect that is why I laboured with the problems of propagation delay in determining phase shifts in the synchrony of the electron motion in adjacent atoms. I saw, however, that that meant there was inconsistency between my account of ferromagnetism and the account I gave in that book for gravitation, even though I had shown how to calculate the precise value of G, the constant of gravitation, from first principles.
My hope, however, in publishing my theory was to stimulate interest which could lead others to contribute improvement and clarification, but, some 30 years on, that was obviously mere wishful thinking as I have seen no such response. I attribute it to the fact that physicists in general were satisfied with Einstein's doctrines and had less interest in understanding ferromagnetism in spite of its direct association with the machine technology which powers the world. Even nuclear power, which many see as arising somehow from the work of Einstein, depends upon electrical machines, which all depend upon ferromagnetism. Then there is the technology of the aerospace industry which depends upon striving to conquer gravitation, which many see as a subject also vindicating Einstein's theory, even though Einstein never did discover the Holy Grail which hid the unifying link between electromagnetism and gravitation.
[I cannot resist here noting that the caption on the cover of my book immediately below the title 'Physics without Einstein' reads 'A confrontation with the anomalies of electromagnetism which reveals a unified explanation for the physical phenomena of the universe'].
In the years which followed publication of that book I did solve that problem of reconciling 2.221 and 2 as the atomic quantization of iron atoms in their ferromagnetic saturation state. The secret, as will be fully explained, comes, in the first instance, from the realization that there might be two electrons in each atom contributing to set up that 2.221 Bohr magneton state. Basing this on electrons in orbital motion corresponding to two Bohr magnetons, to reach the 2.221 figure, all one has to do is to say that the magnetic field produced by charge in motion is really twice as strong as we think it is but that there is a reaction in the enveloping space medium which halves its average effect. If the field were produced by current in a solenoid then twice what is expected, halved, is what is expected, but what is involved in this game of 'action and reaction' is a thermodynamic activity of motion charge in the reacting field and energy transfer by thermodynamic processes can involve time delays which are hidden by the retardation inherent in magnetic inductance.
Two electrons in an atom, each quantized in 2 Bohr units, will develop a field action that is, not 2 Bohr magnetons in strength, but 8 Bohr magnetons. However, the ferromagnetic state could flip sequentially between the three mutually orthogonal x, y, z axes of the body-centred cubic iron crystal to spend equal times in each of the directions +y, -y, +z, -z, +x, +x, where x is the direction of polarization. This means that the primary effect of the Bohr magneton quantization is 8/3 or 2.667, but this is offset by half of this amount being effective for equal times in those same six directions. The offset in the x direction is then one sixth of 2.667, which is 0.444, so that the overal quantization observed is 2.222, less a very small amount to allow for the time of transition in the reorientation process. So, 2.221, as measured, fits quite well and we have here the clue we need to advance the theory.
I was, of course, not just seeking to explain a number. That numerical factor was a clue but there had to be more support for the physics involved. This support came from the consideration of strain anisotropy and anomalies connected with volume magnetostriction effects, notably in the transition between ferromagnetic and non-ferromagnetic states.
However, I then ran into a problem. I had to picture how two electrons in orbit in the same atom can contribute to magnetic polarization in the same direction, whilst retaining much the same result for the mechanical stress analysis. If those electrons were moving in juxtaposition about the atomic nucleus their interaction, electrostatically and electrodynamically with counterpart electrons in other atoms has a compensating effect which substantially reduces the stress levels already estimated. Yet I knew that there was clear evidence of the existence of very high mechanical stress in iron and nickel, attributable to the ferromagnetic condition.
It took a while, but I eventually came to a choice between two alternative explanations. I have presented one of these in the latter part Essay No. 6, where I contemplated a statistical migration of electrons in orbits that were mutually orthogonal, the two electrons jumping from position to position in their respective orbits but, in the main, not making those jumps at the same time. However, keeping that possibility in mind, I will not be satisfied on this matter until I have made a thorough analysis of the following alternative possibility. I would welcome initiatives by any reader who leads the way on the analysis involved, because I shall not get around to that for quite a while.
The alternative is this. I see the electrodynamic interaction forces between the contributing electrons in each atom as arising from their mutually parallel motion. These forces are attractive, sufficiently so as to offset the repulsive electrostatic forces set up by the synchrony of these electrons and keep the overall mechanical stress within the stress limits of the crystals forming the ferromagnet. Now, this electrodynamic effect implies a negative energy potential condition which could make it easier for the two electrons of a given atom to adopt positions in their common orbits that are not those giving the dynamic balance. You see, in the normal dynamic balance condition, they always move in opposite directions and that means that, in setting up interactions with their counterparts in adjacent atoms, they will have an attraction force as between those that are nearest and a repulsion force between those that are more separated. The question then is whether the energy potentials involved would favour a relative phase shift of the electrons in their orbits, albeit thereby affecting the dynamic balance (a state applicable anyway to an atom of odd Z). By this is meant one which has the two electrons chasing one another around in orbit with a 90 degree phase shift so that their electrodynamic current vectors are at right-angles to each other. This would eliminate the repulsive electrodynamic action as between the electrons in adjacent atoms. It should, therefore, be a state of minimal potential energy.
On such an assumption those two electrons in common orbit at any instant in an atom would satisfy the analysis above leading to that 2.222 Bohr magneton quantization.
It is doubtful, however, that the condition just described could ever be detected by experiment, since the electrons are too close to the atomic nucleus in the ferromagnet crystal. However, there is scope for rigorous calculation of states of stress and strain and the study of the effects of stress on magnetic properties might indicate ceertain threshold levels which affect such measurements.
Although I now suspect that the ferromagnetic condition in iron really stems from two orbital electrons in the n=2 shell, it has sufficed to accept the traditional picture and regard two 3d electrons as contributing in each atom and dividing their contributions to magnetism along one of the x, y, z axes, in the following way, the 2 symbolizing that there are two electrons contributing to that state of magnetism in each of the following alternative states:
period x y z (a) +2 0 0 (b) 0 +2 0 (c) 0 0 +2 (d) +2 0 0 (e) 0 -2 0 (f) 0 0 -2occurring for equal times, not necessarily in the order listed.
You can then see that, on average, the primary polarization effect in the x direction is 1/3 times the contribution of the two electrons, whereas there is no net polarization along the y and z axes. However, in mechanical stress terms, given that stress, whether compressive or tensile, is proportional to the square of force, we see that each axis has an equal share of the stress state. The action overall produces isotropic strain, which fits well with what is observed having regard to the known levels of high strain locked into the ferromagnetic condition.
We can now proceed with our analysis on the basis that two 3d electrons in the n=2 orbital condition will contribute 4g Bohr magnetons, where g is the gyromagnetic ratio which scales up the effective magnetic moment by a factor of 2. This gives 8 Bohr magnetons for each atom or 8/3 per atom effective along the x axis of magnetic polarization.
Note that the reaction field which operates, instant by instant, to halve this primary polarization will be directed against the instantaneous polarization vector, each of unit strength. This means that the 4/3 reaction will be asserted against the 8/3 amount for only one third of the time, giving 2.666 minus 0.444 or 2.222 Bohr magnetons as the theoretical net polarization per atom, not allowing for retardation in the transitional activity.
The task of reconciling the observed Bohr magneton polarization in iron at saturation is therefore accomplished and we have preserved the basis of the mechanical stress calculation as developed by the author in 'Physics without Einstein'.
On the strength of this we can revisit the formulation quoted in Part I of this Essay from 'Physics without Einstein':
This applied if d were set at 2x10-8 cm. Now that we can take n=2 as the definitive value, we can advance the analysis using the more representative value of 2.8x10-8 cm for d applicable in iron. This alters that 4,000 figure to 2,000 and, with n=2, results in Z having the effective value of 19. However, we have altered the geometry of the relative positions of the electrons and so the basic calculations need to be reworked. Also one needs to perform the calculations by computer and extend the range of computation over many atoms.
The analysis has value, apart from testing the interest in ferromagnetism, because it should allow the verification of a proposition used elsewhere in developing aether theory. The synchrony of electrons in orbit should imply electrodynamic interaction forces to be calculated without concern for retardation effects. This is based on the assumption that if energy is not changing then the forces cannot be retarded. I well know that, in the 1969 Chapter 3 text of my book 'Physics withour Einstein, I was following convention when I referred to the restrictive effect of retardation effects on the analysis, but I am now holding to my no-retardation position, given no energy change. Somewhat similar, and indeed even stronger considerations, apply to the electrostatic force interaction, but that is a subject I do not wish to develop here. See [1988a]. Suffice it to say that one needs to perform the rigorous computer calculation needed to explore the overall value of that 4,000 approximation factor. The interaction calculations should be extended to cover a whole section of the atomic lattice of the body-centred cubic structure, making due allowance also for the fact that such a structure intermeshes two simple cubic atomic lattice arrays.
I have not hitherto performed such calculations, but I may do that eventually and, in that case, will extend this Essay to present the findings. Meanwhile, I will be attentive to feedback should any reader undertake this task. I end this Essay by drawing attention to the case I have put elsewhere in a published paper referenced in these Web pages for the 'half-field reaction' theory as applied also to nickel and cobalt. See [1987c]
As to the conflict in what I have just described and what I wrote in the latter part of the Essay on the Exclusion Principle which introduced this ferromagnetic topic. I have argued two separate reasons for the 2.221 Bohr quantization. One is a kind of quantum-electrodynamic effect and the other is a more classical kind of electrodynamic interaction. Both give the same result, but I would prefer to know which interpretation is correct. That issue is something that will, I trust, be resolved by performing those computations I have just mentioned.
Priority attention has, however, to be given to the experimental projects which aim to exploit this knowledge of the quantum-orbital state of ferromagnetism as powered by reaction involving the vacuum medium which I call the 'aether'.
Readers may find it interesting, therefore, to move on from here to Lecture No. 7 which discusses the 'free energy' technology demonstrated by Hans Coler.