A Caveat
8.1.1.
In this chapter our aim is to view some selected areas of physics in the light of the theory of physical fundamentals we have just outlined. But, first, a caveat. The conception of the Cosmos we are advancing is an attempted synthesis of rational cosmology (metaphysics) and empirical cosmology (science). Now, the science of physics accounts for that large and basic part of our empirical knowledge wrought out of the observations of physicists. And the greater and most important part of these observations consists of the readings of precisely calibrated registering instruments in experimental set-ups - pointer readings, in short. But the physicists' world-view does not consist of these measurements, but of what, within a framework of certain fundamental physical notions which they regard as either self-evidently true, or at least as possessing a solid foundation in common sense, they have inferred from them. But, as I hope I have shown in earlier chapters, because physicists, unable as a species to rise above naive realism, persist in falsely predicating of the objective world attributes which belong only to the subjects perceiving this world, their inferences as to the nature of physical fundamentals remain, for the most part, radically false.

8.1.2.
Now, although in the comparatively crude classical era many philosophers pointed out this basic source of error, physicists themselves found their experimental observations sufficiently consistent with their naively realistic (i.e. mechanistic) physical conceptions as to believe these to be substantially true. But in our post-classical era, when laboratory physics has attained to a precision, subtlety and penetration enabling it to investigate the details of sub-microscopic processes, even the phyicists have realised that their mechanistic conceptions, derived from the behaviour of macroscopic bodies, are powerless to cope at a fundamental level. C.E.M. Joad well expressed the situation in 1933 - since when it has changed only for the radically worse: "Unable to carry the analysis of matter further without raising philosophical problems, physicists show a tendency to do their philosophising for themselves. Inadvisably, as one cannot but feel, for the philosophising of the physicists is noticeably inferior to their physics, and eminent men are at the moment engaged in making all the mistakes which the philosophers made for themselves some three hundred years ago and have been engaged in detecting and correcting ever since." (Guide to Modern Thought, Faber and Faber 1933).

8.1.3.
However, since the laboratory physicist works primarily with measure-number algebra, not physical theory, post-classical theoretical physics has been able to achieve considerable success in organising its instrumental readings at a mathematical level; but not, as classically, to give an even superficially satisfactory physical interpretation of these laboratory formulae. Thus, commenting on Maxwell's electromagnetic theory, the immediate precursor of our post-classical era, Herbert Dingle has this to say: "Nothing could more clearly express the change that had come over physics. Experiments more and more confirmed the deductions that were made from the theory when the symbols in the equations were given certain physical meanings, while the justification for giving the symbols those meanings continued to elude everyone." (Science at the Crossroads, Martin Brian and O'Keeffe, 1972, p132). Unable to transcend his mechanistic naivities, the contemporary physicist is perforce reduced to a kind of mechanism run mad - a kind of self-contradictory mechanism larded with arbitrary 'quantum' rules; though he has enough insight into the nature of these pseudo-conceptions (at least, in his more mature moments) to regard them as mere 'models' serving a heuristic purpose, rather than as conceptions mirroring objective reality. Moreover, again and again, particularly in the more popular publications, one finds offered as experimentally established fact, what are, in reality, no more than inferences and calculations from experimental data on the assumption of the truth of radically false theories. On the assumption that the motion of heavenly bodies must be both regular and circular, Ptolemaeus, by adding epicycle to epicycle could account for the observed motions of the planets; but this did not alter the fact that both this assumption and the epicyclic theory grounded on it, were false. It would be as well if the reader kept this general epistemological situation steadily in mind throughout this chapter.

Beyond the Classical
8.1.4.
With the Fatal Trap built into its theoretical foundations, Newtonian physics was never going to provide an even remotely rational account of the physical world. Its undeniable successes in elucidating the nature of physical processes, despite this in-built interdiction, may be ascribed to two major factors. Firstly, its incorporation of reductionism, even if in the only, radically false, conception of it open to the fatally trapped intellect; secondly, the mathematically oriented methodology that made possible - if only on a descriptive level - coherently interconnected systems of precisely defined concepts. As one would expect, its explanatory successes were radically restricted to
(i) discovering the mathematically expressible, if inexplicable, laws governing the interactions between physical bodies, and
(ii) showing that the more local laws were no other than the more comprehensive operating under specific sets of conditions. Newtonian physics had nothing intelligible to offer as to the nature of such fundamental concepts as matter, space, time, charge and force - to say nothing of why animate, sentient beings should emerge and evolve within a physical universe thus conceived.

8.1.5.
The direction of physical discovery proceeds essentially from the macroscopic to the microscopic. But nature itself proceeds in the precisely opposite direction, since macroscopic entities have arisen eventually as syntheses of microscopic. We might say that science moves in the direction of analysis, nature, in that of synthesis. Now, in attempting to explain the unknown, the scientist inevitably draws upon conceptual models formed on the known. But, in this case, the known (macroscopic) requires, eventually, to be explained in terms of what gave rise to it - the microscopic, which is unknown. Clearly, scientific explanation of the microscopic can only be a very tentative undertaking guided by all manner of assumptions, which, drawn from knowledge confined to the macroscopic, will almost certainly be untrue. Newton worked on the assumption that the fact that the microscopic world has given rise to the macroscopic is sufficient guarantee of their both being governed by the same basic laws. One cannot say that this assumption is false, but it takes insufficiently into account the possibility that the operation of the one set of laws might produce very different kinds of effect at the two levels. One cannot just scale down from situations involving zillions of electrons and vast distances to hypothetically analogous situations involving only a handful of electrons and minute distances, and assume that essentially the same situation obtains. But, of course, the natural tendency is to make just such false comparisons, a paradigmatic case being the Bohr atom, the so-called planetary model of the atom, where the electrons were envisaged as revolving around the atomic nucleus like so many planets around the sun, even if with the addition of some ad hoc, empirically demanded, constraints.

8.1.6.
With the steady elaboration and refinement of its instruments and methods, it was inevitable that Newtonian physics must sooner or later be capable of achieving accurate measurements of natural processes on a level sufficiently fundamental for the radical limitations of its fundamental notions to be indisputably revealed. This time arrived at the end of the nineteenth century, and initiated an era when even the most philosophically opaque scientist has been forced to accept that the Newtonian account of the world is radically inadequate. Processes were discovered that did not conform to Newtonian laws: more exactly, that the formalisms based on Newtonian conceptions no longer gave correct answers when experimentally obtained values were inserted into them. At first it was thought that the physical world might be governed by two sets of laws - one at the micro- (or quantum) level, and one at the macro- (or classical) level. But a much simpler and more rational solution, now universally accepted, soon presented itself. Just as Newton had contended (8.1.5.), only one set of laws did indeed operate throughout. But this consisted precisely of the laws operating between individual 'particles' - of whose inner structure Newton knew nothing. So that the general epistemological situation was that, hitherto, physics had been able to operate only with 'particles' in such vast numbers that the individuality of all the subtle quantum effects manifested by individual, or small groups of particles had been effectively erased - buried within statistically quantified ensembles.. It was these last that the laws of Newtonian - now referred to as classical - physics described. This already told physicists something about this mysterious sub-microscopic behaviour: that the classical laws governing the behaviour of 'statistical ensembles' defined a limit which the quantum laws must approach as the numbers of particles increased indefinitely. But this Correspondence Theory, as it is called, although true enough, offered the essentially Newtonian, or classical, physicist no clue as to what the natures of the entities events and situations might be, which, at this fundamental level, were producing all these very un-classical effects. How was the 'fatally trapped' Newtonian physicist to proceed?

Insurmountable Handicaps
8.1.7.
Thus handicapped, then, the only way the Newtonian physicist could cope theoretically with this influx of classically anomalous results was to propose essentially Newtonian models and then modify these in all manner of arbitrary ways to accommodate the pointer readings. But as, inevitably, such a blatantly ad hoc method grounded on a false ontology produced only physical conceptions of deepening incoherence, the credibility of these steadily declined until it was apparent to all that they had to be accorded an essentially new and inferior ontological status. Although they could no longer be taken seriously as descriptions of physical reality, nonetheless they served a useful epistemological purpose in providing some kind of quasi-physical framework to which to attach, however unsatisfactorily, the mathematically coherent, and experimentally vindicated systems of measure-number equations that the 'theoretical physicists' were busily creating. No insurmountable, or even major, difficulties were encountered here, it being a comparatively easy matter for the mathematicians to modify, combine, and elaborate the classical equations in such ways as gave satisfactory results when pointer readings were inserted into them. After all, even in the classical era, it was strictly the measure-number equations, not the physical conceptions of which these were seen as the quantitative description, whose validity the experimental physicists were testing. For the great majority of physicists - much less concerned with understanding the physical world as part of a rational universe, than with being able to manipulate it in the interests of applied science - this constituted a perfectly acceptable state of affairs.

Hidden Variables
8.1.8.
However, there exists a small minority who have never accepted this radical downgrading of their subject, but who still conceive physics in the old sense of natural philosophy: as that part of the general aspiration to understand the universe as a coherently interconnected system of entities, which concerns itself with physical nature. These are generally known as 'hidden variable' theorists, since they believe that the conceptual chaos of quantum theory implies that there must exist an ontological level more fundamental than any so far revealed by physics, in terms of which all the lacunae and conflicts of current theory could be coherently resolved. One might sum up their achievements to date by conceding that they have afforded some tantalising glimpses into physical processes at these ultimate levels, but that, in default of a systematic understanding of the Fatal Trap, they have not been in a position to do more.

8.1.9.
Now, of course, such a profound understanding of physical fundamentals is precisely what we claim to have acquired through our ultimate experiential analysis. We claim to have shown that matter is not a stuff but a periodic process whose ultimate constituents are instant events; that time and space, far from being independently existing particulars, are, as temporal relations and spatial relations respectively, abstracted general attributes of this process. And within this fundamental schema, we have proceeded to identify, in precise quantitative terms, such basic physical parameters as duration, distance, motion, mass, charge and force. In this chapter, then, the principal objective is to account for quantum phenomena in terms of these ultimate physical concepts as so defined. Now, as we saw earlier (6.5.), there are two fundamental modes by which ultimate events become associated, which I name the proximate and the sympathic. It is proximate association which is the dominant organising mode in the physical world; but sympathic association is also present, out of which presence, in this context of proximate association, there arise and evolve the whole vital, mental, and spiritual dimensions of existence. Now, just what part we conceive that sympathic association may play in what orthodoxy rates as non-living processes, we must perforce defer to our next chapter: in which - devoted as it is to the emergence of the biological world - sympathic association, and its precise relation to proximate association, form our principal concern. However, there is one straightforward implication of our fundamental physical parameters as so far described, which we have not yet touched on, in which proximate association is alone involved, and which possesses immense implications for the understanding of quantum processes. This is the effect of phase on the causal relations between physical sequences. We therefore first deal, in a general way, with the fundamental structural and, hence, causal parameters of phase relations. Then, with our set of basic physical parameters complete, we shall attempt by their means to bring some measure of rational coherence to the principal conceptions of quantum physics.

PHASE RELATIONS

Systemic properties of distance qua distance
8.2.1.
If two periodic processes are interacting regularly, one factor strongly affecting the nature of these interactions will be the relative displacement of their periods in time. Such displacements and their effects are known as phase relations. Phase relations play a major role in phenomenal physics simply because so many natural phenomena which appear uniform, disclose themselves on more searching investigation to be rapidly periodic. This is especially the case with 'radiation' where two 'waves' may add to, or subtract from, one another's effects purely as a consequence of their phase relations. Inevitably, in our noumenal theory, where the ultimate 'particles of matter' themselves are conceived as periodic processes, phase relations assume even greater importance. In such a synoptic work as this we can do little more than introduce such an immense topic - which means, in effect, that we shall confine our investigations almost wholly to phase relations between equiperiodic sequences.

8.2.2.
What do we mean when we say that two equiperiodic sequences (that is, electrons) are "in phase"? Since (as against the sympathic mode) there are no instantaneously produced effects in that proximate mode of togetherness overwhelmingly operative at the physical level, it would be inapposite to base phase relations on synchronicity. Instead, we shall say that equiperiodic sequences A and B are in phase if the effect instants on one sequence occupy the same periodic positions as their causal instants on the other. As distances between sequences change, so will their phase relations. Since either one of two sequences can be regarded as the causal sequence, and, since - because of the different orientation of their common direction of absolute motion relative to the line joining them - the phase relations of B with respect to A, will not be the same as those of A with respect to B, it is always necessary to specify in any instance which sequence is being regarded as the causal sequence. The distance, λcm = Nρ points, we call the wavelength of the sequence. And because T/τ seconds = N instants, and λ/ρ cm = N points, wavelength may be regarded as the distance analogue of period.

8.2.3.
For two sequences, each of period N instants, and if all movement of the sequences is ignored in the interests of a basic exposition, there will obviously be N possible phase relations of the effect sequence in relation to the causal, yielding a total of N² cause/effect instant pairs. Assuming further, for the sake of simplicity, that N equals 3n, where n is the period root, then it is a simple matter to calculate that for all pairs of like sequences of equal period, the ratio of repulsions (R) to attractions (A) will be:
[(2n x 2n) + (n x n)]/[(2n x n) + (n x 2n)] = [4n² + n²]/[2n² + 2n²] = 5n²/4n² = 5/4.
So that of the (3n)² = 9n² instant pairs, 5n² will be repulsions and 4n² will be attractions. This 5:4 ratio over all phases holds true for any pair of like sequences however different their periods: exactly, for sequences where N is a multiple of 3, and closely approaching 5:4 - asymptotically, as the period root increases - when N = 3n±1.

8.2.4.
What does differ profoundly with difference in phase between two equiperiodic like electrons is the variation from this constant overall (that is, over all phases) 5:4 attraction/repulsion ratio. For around half the phases the ratio may vary as greatly as 2:1 against. We call phases where two like electrons attract, or two unlike electrons repel, contrary phases; and phases where two like electrons repel and two unlike electrons attract, congruent phases. As a simple example, consider one period of two negatrons each of period 3 instants. Then,according to their distance apart, one of essentially three possible cause/effect situations is possible:

Congruent Phase	Contrary Phase	Contrary Phase
N1.......N2	N1........N2	N1........N2
0..........0 = Repulsion	0...........X = Attraction	0...........0 = Repulsion
0..........0 = Repulsion	0...........0 = Repulsion	0...........X = Attraction
X.........X = Repulsion	X..........0 = Attraction	X...........0 = Attraction
Overall....... R ..(3 - 0)	Overall........A..(2 - 1)	Overall.........A..(2 - 1)

Total Overall Repulsion.......(5 - 4)

A similar table, but with attractions and repulsions interchanged, can be constructed for one positron and one negatron. So that, in general:

Further exploration of the relation between repulsion and attraction for two like equiperiodic sequences, reveals that the number of phases where attraction is dominant, and those where repulsion is dominant, are about equal, and together account for the great majority of the phases, the remaining phases being those where numbers of instant attractions and repulsions are equal. Moreover, all the attractive phases are consecutive, and positioned symmetrically about the maximum phase shift. Once again, if N = 3n±1, the above is closely - asymptotically, as the period root increases - approximated to. There are further constancies also, but all this is more appropriately expressed in diagrammatic form. Finally, to state the obvious: the content of this whole section applies equally to two unlike equiperiodic sequences if "attraction" and "repulsion" are interchanged. We illustrate all this in the four following diagrams:

VARIATION WITH PHASE SHIFT OF REPULSION/ATTRACTION PREDOMINANCE BETWEEN TWO LIKE EQUIPERIODIC SEQUENCES

Effect sequence relative to causal sequence:

ONE PERIOD (X - Y) OF FIGURE 1

Effect sequence relative to causal sequence:

AN EXAMPLE. Two like electrons: N = 18 instants. (Velocity = c/18).

Effect sequence relative to causal sequence:

In Figure 4 below we show all 12² = 144 instant attractions or repulsions of a negatron by a positron, both of period 12 instants, over one phase cycle. And in Figure 5 we show the alternations of attraction and repulsion over three phase cycles of a negatron by a positron, with particular attention to those attraction/repulsion interfaces where repulsion is in the direction of the positron.


ONE 12 INSTANT PHASE CYCLE

The Correspondence Principle
8.2.5.
It is this deviation of instant forces from an overall mean of 5:4 congruent to as much as 2:1 contrary - in phase blocks constituting up to half the total when periods (and that implies speeds) are equal - that is exploited by, and in effect creates the quantum world. In the typical situation investigated by classical physics, containing a vast number of interacting electrons at comparatively great distances from one another, components, perhaps of many types of atom and molecule, individual deviations from the mean tend to average out, so that the 5:4 congruent ratio everywhere prevails. In essence, this constitutes the “correspondence principle” of quantum theory. But in those intra-atomic, or, at most, intra-molecular, situations forming the quantum domain, characterised by attractions and repulsions between comparatively few electrons at short distances from one another, matters are far otherwise. Here, individual deviations stand out sufficiently to provide the basis of a system of physical interactions comprising a level of order altogether more subtle, varied, and complex than that investigated by classical mechanics.

WAVES AND VIBRATIONS

8.3.1.
One of the few genuine advances in understanding achieved by 'the new physics' is the realisation that substance and change are much more intimately interconnected than was ever suspected in the classical era. And, indeed, to the ontologically alert mind, what the advance of experimental physics has been revealing ever more plainly is that physical substance is not a stuff but a process of some kind. But owing to the 'fatally trapped' mechanistic mind-set of the physicist, all the abundant evidence for the periodic nature of the spatially elementary 'particles' of matter has simply been misconstrued either as unintelligible waves (of what?)¹ or the spatial oscillations of intrinsically unchanging particles.² In our theory, the ultimate simple elements of the physical world are organised into a process through those kinds of interrelationship we term temporal and spatial. As one of the most eminent advocates of 'hidden variable' theory succinctly, if somewhat loosely, put it:
"I say the actual process which takes place is fundamental and space and time are the means of describing the order in this process."³
Owing, however, to the practical man's naively obsessive bodies-in-space conception that we are calling the Fatal Trap - and of which the orthodox scientific world-view is the systematically elaborated consummation - these two kinds of interrelationship have been abstracted and reified as the independently existing absolutes, time and space, thereby degrading the substantial elements of the process to featureless, unintelligible bits of 'matter'. It is therefore hardly surprising that, as we pointed out earlier (4.4.13), these three altogether fictitious disjecta membra that is, matter, time, and space resulting from so crude a dismemberment of the physical process, have defied all attempts to bring them into intelligible relation: not only with each other, but also with the life and mind that empirical science has indisputably shown to have emerged from them. So that - to repeat - all the abundant evidence pointing to 'matter' as a periodic process of some kind, has been misinterpreted by the attempt to assimilate it to the classical study of waves and vibrations in fluids, strings, and membranes, not forgetting the aether of space, that all-pervasive jelly in which every material particle was supposed to be embedded, and which served (among other things) as the 'substantial' medium for electromagnetic radiation. We now briefly consider five topics basic to quantum physics - the de Broglie Wave, Planck's Constant, the Schrõdinger Equation, the Photon, and Heisenberg's Uncertainty Principle - in the light of our fundamental physical conceptions - but with these wise words constantly in mind:
"As long as we are not told what matter waves are waves of, the wave theory is not a physical theory."⁴ and "When we have two theories of interaction that contradict one another: the wave theory and the photon theory, and yet both have to be used, it raises the suspicion that we may be totally wrong in the approach which has been made up till this time."⁵

The de Broglie Wave
8.3.2.
As we saw in our last chapter (7.1.14.), distance between physical simples is given by c x time lapse between selecting (causal) simple at instant t₁ and selected (effect) simple at instant t₂: that is, by c x (t₂-t₁). Also, (7.2.4.) we spoke of every physical simple always being at some abstract location; so that any location, at any instant, may be occupied or not occupied by a physical simple. Hence, by 'effect location' of a causal simple (A), we mean the location that a second simple (B) would have to occupy in order to be subject to an instant effect originating in A. That is, the distance AB = c x (t₂-t₁). Now, consider one period, T=Nτ (7.1.15.), of any physical sequence at location A: after some time lapse t (t >T), if the effect location of the first causal simple of a period is at a distance r₁=ct points from the location of that period, then the effect location of the second causal simple in the same direction, will be at a location r₂=(ct-1) points distant and so on, the distance away, in the same direction, of the effect location of the last causal simple of the period, being r_N = (ct-N) points. Hence, at any instant, the number of effect locations of this period in any direction will be r₁ - r_N = ct - (ct - N) = N points. That is, at any instant, the possible effect of a period (Nτ) of a sequence, in any direction from that sequential period, will have a linear spread of Nρ. This linear spread, Nρ, we call the wavelength, λ, of one period, (T=Nτ) of a sequence. Wavelength (λ) is thus, as it were, the distance analogue of the period (T), with λ:ρ :: T:τ . Since λ = Nρ, and N = T/τ, it follows that λ = ρ/τ x T, or λ =cT. Now, we are claiming that our ultimate sequences are what phenomenal science calls positive and negative electrons. At any time the sequence has a certain period (T) which is an intrinsic attribute of the electron at that time. And although the wavelength (λ) is not itself an intrinsic attribute of the electron, its value is always that of this intrinsic attribute, T, multiplied by c, the universal constant of spatio-temporal interaction. But why do we speak of a wavelength when there is no wave? Only because periodic action at a distance is the closest analogue in reality to the electromagnetic waves of mechanistic orthodoxy.

8.3.3.
Nearly eighty years ago it was discovered that when a parallel beam of electrons is shot either onto or through a crystalline substance, such as metal foil, it is scattered in such a way as to produce diffraction rings, closely similar to those which a beam of X-rays of definite wavelength would produce. Here, then, was clear evidence for orthodoxy that electrons were associated with waves. The theory that matter possessed wave-like properties was made more acceptable by the fact that numerous experiments made over previous decades had seemed to reveal that radiation possessed particle-like properties. And, indeed, on the strength of this latter, Louis de Broglie (1892-1987) anticipated the above experimental finding by more than three years by producing a prima facie acceptable measure-number equation: λ_dB=h/mv , where λ_dB is the de Broglie wavelength of the electron wave, m and v the mass and velocity respectively of the electron, and h, Max Planck's universal quantum of action (action = energy x time). Since λ_dB and v are the only variables, it follows that this equation implies that the wavelength of the electron wave is always inversely proportional to the velocity of the electron.

8.3.4.
What is the relation between the de Broglie wavelength (λ_dB) of an electron, and our sequence (=electron) wavelength (which we will henceforth refer to as λ_s)? Now, λ_dB = h/m_ev, and it is easily shown that h = 2πm_er_ec/α where r_e is the classical electron radius, and α (=1/137.0) a dimensionless constant known as the fine structure constant. Hence, λ_dB = 2πm_er_ec/m_ev = 2π/a x r_ec/v. But λ _s = cT = cNτ. And since v = c/N, or N = c/v (7.1.15.), and cτ = ρ = r_e (7.1.14) it follows that λ_s = cNτ = ρc/v = r_ec/v. But this would make λ_dB = 2π/α x λ _s only if 'v' in the equations for λ_s and λ_dB meant the same thing. Unfortunately, it does not. In the λ_s equation, v is the absolute velocity of the electron. But what is it in the de Broglie relationship?

8.3.5.
By definition, a de Broglie wavelength is associated with an electron. A precise value is accorded this wavelength: it is inversely proportional to the velocity of the electron, the constant of proportion being h/m_e. Obviously, this can only even begin to make sense if the electron has a certain definite velocity. Now, this immediately rules out relative velocities, because, at any time, the electron possesses a relative velocity to every body in the universe. It must, and can, therefore, refer only to the electron's absolute velocity. But according to relativity theory - proven false (5. Notes:1), though the great majority of quantum physicists accepts it - there is no such thing as absolute velocity. How is this seeming impasse to be overcome? The velocity actually used in calculating the de Broglie wavelength is that of the incident electron's velocity relative to the crystal surface it is shortly to impact. But, unless the electron is possessed of some kind of foreknowledge, how can the body it is moving towards play any role in determining its internal structure? Moreover, the electronic constituents of the crystal are in constant and varied motion. Which precise state of which electron or electrons of the crystal is each incident electron’s velocity relative to? One has only to ask such questions to realise the absurdity of an intrinsic property of the incident electron being determined by the crystal surface it is moving towards.⁶ So that unless the investigator is content either to settle for obvious nonsense, or simply to evade the problem, he has no choice but to accept that if an electron is associated with a wavelength inversely proportional to its velocity, this velocity must be absolute. But, as I say, the velocity which is found to be inversely proportional to the experimentally determined wavelength is that of the incident electron relative to the crystal. So that λ_s = r_ec/v_a and λ_dB = 2π/α x r_ec/v_r where v_a and v_r stand respectively for absolute velocity and relative velocity - relative, in this case, to the crystal surface, and hence to the laboratory.

8.3.6.
But, this absurdity of the de Broglie wavelength's being in some way intrinsic to the electron and, at the same time, inversely proportional to its velocity relative to the crystal surface, is by no means the only objection to it. Its length is far too great for it to be associated with an electron. And this cannot be evaded by viewng it as the wavelength of an electron beam, since orthodoxy is agreed that the group velocity of this beam must be taken as equal to that of the individual electrons of which it is composed; and it is from this common velocity that the value of λ_dB for an individual electron is calculated. To what, then, must we ascribe this mismatch? λ_dB = h/m_ev. But the value of h, as we have seen, is 2m_er_ec/; and neither α nor 2π can conceivably be intrinsic to a free electron. α is an essentially atomic dimension, being equal to √(r_e/a₀), where a₀ is the Bohr radius. Now Planck arrived at h, supposedly the ultimate quantum of action, through his work on harmonic oscillators, of period 2π/ω. But why should the magnitude of all the myriad interactions of nuclear physics, between electrons, quarks, muons, pions, neutrons etc. be constrained by an action quantum derived from work on ambient electrons when little or nothing was known about the behaviour of sub-atomic particles in the nucleus and elsewhere? It would seem clear, then, that h, through its inclusion of α and 2π cannot be in any way intrinsic to a free electron. In further support of this, it will be recalled that de Broglie was influenced in his choice of electron wavelength by the fact that h/m_ev = 2πa₀: the circumference of the electron’s orbit as, on Bohr's theory, it circled the hydrogen nucleus with an orbital velocity of αc.⁷ He thus thought of the electron's associated wave as constituting a standing wave around the atomic nucleus.

8.3.7.
But if 2π and α are not built into the electron wavelength, how is it that the value of the de Broglie wavelength agrees with the value of the wavelength as calculated from the width of the diffraction rings? This calculation is, of course, based on the assumption that the electron wave is a wave resembling an electromagnetic wave. Now, because all interaction is force-at-a-distance (∝ 1/distance²), and retarded by a time = distance/c) there certainly exists a basic similarity between the interactions with the crystal of electromagnetic radiation (which, of course, has a material source) and of electrons, which never actually collide with those of the crystal. But, of course, the situation in the two cases is very different. Yet not so different but that the electrons produce diffraction rings. Now, obviously there must be radiation of some wavelength which would produce similar rings; but this does not mean that the very different process of electronic reflection has any structural connection with this particular wavelength. Both nature and human life abound with instances of similar effects being produced from widely differing causes. This would account for h - and hence α and 2π - entering the de Broglie formula; clearly, the atomic electrons of the crystal are involved in the dimensions of the diffraction rings when these are produced by electrons, in a way in which they are not when these are produced by electromagnetic radiation. There is a further circumstance which tends to confirm that this is a correct reading of the situation. As we saw earlier (8.3.3.) what first drew attention to a possible similarity between a beam of electrons and electromagnetic radiation was the similarity of their effects when interacting with a crystal. And when a beam of X-rays passes through a crystal it is found that some of them have increased in wavelength such that Δλ = λ₀(1 - cosθ) where θ is the scattering angle, and λ₀ equals h/m_ec = 2πm_er_ec/αm_ec = 2π/α x r_e = 2π/α (=861 points).

Planck's Constant
8.3.8.
When h was first proposed as an ultimate quantum of action, little or nothing was known about interactions between sub-atomic particles. As we have seen, h has α[= √(r_e/a₀)], an essentially atomic dimension, built into it; as well as 2π, deriving from the circumstance that Planck arrived at h via his work on harmonic oscillators, of period 2π/ω. Why should the magnitude of all the myriad interactions of nuclear physics, between electrons, quarks, muons, pions, neutrons etc. be limited to an unsurpassably small action quantum incorporating α and 2π instated at a time when little or nothing was known about them? Merely to ask this question is to realise that h cannot possibly be an ultimate quantum of action.

8.3.9.
The de Broglie wavelength (λ_dB) equals h/m_ev_r. And we have shown (8.3.5.) that our sequence wavelength (λ_s) equals r_ec/v_a = m_er_ec/m_ev_a. That is, what corresponds to h in our 'absolute' equation is m_er_ec. We propose that this is the ultimate quantum of action, and denote it by H. Now, action = energy x time, and our ultimate quantum of time is τ. But r_e = ρ(our ultimate quantum of distance) = cτ. Hence, H, which equals m_er_ec = m_e x cτ x c, or H = m_ec² x τ. So that the energy component of our ultimate quantum of action is m_ec². Orthodoxy calls this the potential energy of the 'rest mass' of the electron. But that is merely a concession to current conceptions. I would suggest that the reason why m_ec² plays so basic a part in physics is because it is the energy component of the truly ultimate quantum of action. It is also worthy of note in this context that m_ec² = e²/r_e, where e is electron charge.

Schrödinger's Wave Equation
8.3.10.
As David Bohm states: "Practically the entire quantum theory is contained in the wave equation ..." and "... the wave equation may be regarded as playing the same fundamental role in quantum theory as Newton's laws of motion do in classical theory".⁸ Sir Arthur Eddington referred to it as, "A dodge, and a very good dodge too".⁹ Wavelengths imply waves, and basically, the Schrödinger [= wave] equation is no more than a well-known classical equation relating a harmonic wave function to its wavelength, with this wavelength given the de Broglie value, h/m_ev.
Thus, when Ψ is a harmonic wave function d²Ψ/dx² + (2π/λ)²Ψ = 0. General solutions of this classical wave equation are: Ψ = Asin(2π/λ)(x-vt) for a progressive wave, and Ψ = 2Asin(2πx/λ)cos(2πvt/λ) for a stationary wave, where A is the amplitude of the progressive wave. When we make the substitution λ= h/m_ev, this wave equation becomes the Schrödinger equation: d²Ψ/dx² + (2πm_ev/h)²Ψ = 0, and the corresponding values of Ψ, the wave function, can be obtained by substituting h/m_ev for λ in the above general solutions. All these equations are easily generalised to 3 dimensions. What gives this simple dodge such importance? Its principal field of application is wherever electrons are moving in orderly ways as parts of orderly systems, and this, preeminently, is in atoms and molecules. Now, here, the velocity of the electron is, we suspect, constantly changing, so that its de Broglie wavelength is also constantly changing; but if this wavelength pertains to a harmonic wave then, whatever the electron's velocity, the relationship d²Ψ/dx² + (2π/λ)²Ψ = 0 holds true throughout. Now, since λ= h/m_ev, where h and m_e are constants, it is clear that if we know λ we know v, from which it follows that we also know momentum (= mv) and kinetic energy (= 1/₂mv²) of the electron or the beam. Moreover, through knowing that the kinetic energy [= total energy (W) - potential energy (V)] is 1/₂mv², the wave equation can easily be put into the more useful form: d²Ψ/dx² + (2π/h)²x 2m_e(W-V)Ψ = 0. In addition it can be shown that it is reasonable to assume that the value of Ψ², for any value of x, gives the probability of a single electron, or the proportion of electrons in a beam, being within a volume element at this distance. Now, all this would be of little help if the physicist knew nothing about the physical systems he is investigating, but usually this is not the case. He often knows something, or may make reasonable assumptions, about the energy conditions of the system, more especially about conditions obtaining at the system’s boundaries. And by putting such values either into the Schrödinger equation or directly into the wave function Ψ, he can often obtain further, if probabilistic, information about the positions and speeds of the electrons in the system, and their variation with time.

8.3.11.
Water waves or sound waves are transmissions through a material medium of local oscillations of the material particles composing that medium. Whatever reality the wave referred to by the Schrödinger equation may possess can only be grounded on the repetitive activities of electrons - themselves spatially elementary periodic sequences of qualified simples.
"It is rather surprising that the frequency of these electron waves should also contain an arbitrary constant; it suggests that, although the equations of wave mechanics are correct in their description of how matter actually behaves, these waves have not the same sort of reality as sound or electromagnetic waves."¹⁰
Passing over the question of the reality of electromagnetic waves - the arbitrary constant referred to by Professor Mott is that taken as defining the zero of potential energy; but he might just as well have taken the relative velocity giving the value of the kinetic energy (1/₂mv²). We are here up against essentially the same fatal objection that we encountered (8.3.5.) with the de Broglie wavelength: confusing the unique value possessed by some structural component of an entity and the myriad values this possesses relative to similar such components in a myriad similar entities. The only "reality" such a wave possesses is purely heuristic; that of a computational procedure auxiliary to the conceptual fictions of the fatally trapped theoretical physicist... and much the same might be said of the whole quantum theory based upon it:
"All that is clear about the quantum theory is that it contains an algorithm for computing the probabilities of experimental results. But it gives no physical account of individual quantum processes. Indeed, without the measuring instruments in which the predicted results appear, the equations of the quantum theory would be just pure mathematics that would have no physical meaning at all. And thus quantum theory merely gives us (generally statistical) knowledge of how our instruments will function."¹¹

8.3.12.
But if the Schrödinger wave possesses no existence outside the minds of physicists, how has its equation attained even the limited success which it undeniably has? Obviously, because it must contain somewhere within it, in no matter how fantastic and distorted a form, some correspondence with physical reality. There are, in fact, three main reasons for this qualified success.
(i) The most basic is that which we have already noted (8.3.2-5.): the correspondence between the de Broglie wavelength (λ_dB= 2πr_ec/αv_r) on which it is based, and the 'wavelength' (λ_s = r_ec/v_a) of a qualification sequence. Combining these two equations, we have λ_dB = 2π/α x v_a/v_r x λ_s. Now, v_r is the velocity of the electron relative to the crystal surface, whose absolute velocity as a whole we may take as the absolute velocity of the Earth (v_E), variations in which will be comparatively small. Hence, v_a = v_r + v_E , so that λ_dB = 2π/α x (v_r + v_E)/v_r x λ_s or λ_dB = 2π/α x(1 + v_E/v_r) x λ_s. Clearly, therefore, the smaller the value of v_E/v_r - that is, the greater the value of v_r - the closer will λ_dB approach 2π/α x λ_s.
(ii) Another reason is that the wave function (Ψ) from which the Schrödinger equation derives is a sinusoid. Now, while most, perhaps all, of the basic periodicities of nature are not sinusoidal, nevertheless, so far as theoretical physics is concerned, Fourier analysis renders it possible, by means of a superposition of sinusoids, to approximate any periodic activity to any requisite degree of accuracy.
(iii) A third reason is that, as a sinusoid, the wave function (Ψ) provides naturally a series of values of x , differing by π, where the wave function (Ψ) is zero. These are regions where there will be no electrons, and half-way between them will be regions where the probability of an electron existing is a maximum. Now, as we shall shortly see, as a consequence of the dependence of attraction and repulsion between electrons on their phase relations, ontological reality provides a by no means dissimilar state of affairs.

The Photon
8.3.13.
It was, above all, the Compton Effect that alerted orthodoxy to the fact that radiation exhibited particle in addition to wave properties. And just as waves of radiation are simplistic, 'fatally trapped' extrapolations from waves in physical media, so photons are similarly naive extrapolations from physical particles. Not only are these two conceptions internally incoherent, they are equally incoherent in relation to each other. All this incoherence arises from the total failure of orthodoxy to grasp the true situation, which is that particles are qualification sequences, and that every such sequence exerts a selective effect on every other. As between any two physical sequences, the magnitude of such a selective effect is inversely proportional to the square of their distance (r) apart, and retarded by a time given by this distance divided by c ('the velocity of light'). Quantum effects due to radiation are ascribed by orthodoxy to the individual photons, each supposedly being possessed of an energy equal to hv, where v is the frequency of the photon. But, as Burniston Brown states "... any 'quantum' effects are due to the individual structure of the particles, and not to any 'quantisation of radiation'.¹²
Now, our particles are qualification sequences, each with a period of N instants. And the absolute speed (v) of each sequence is c/N. Hence, the minimum possible increase in absolute speed Δv = c/(N-1) - c/N = c/N(N-1) cm s^-1 = 1/N(N-1) points instant ^-1.But this increase in absolute speed occurs over one period; so that minimum acceleration, a = 1/N(N-1)pt inst^-1 pd^-1. Similarly, minimum retardation = 1/N(N+1)pt inst^-1 pd^-1. But, as we established earlier (7.1.14.), a = Σ_N[Σ_M-1(1/n²)] pt inst ^-1 pd^-1, where n = distance in points, M = number of qualification sequences in the physical world, N = number of instants in the one period, and Σ denotes vector summation. So that this value must be quantised for acceleration, both positive and negative. We must believe that the ideal acceleration as given by a =Σ_N[Σ_M-1(1/n²)] pt inst ^-1 pd^-1 is cumulative, actual acceleration occurring as it builds up to 1/N(N±1)pt inst^-1 pd^-1, with any residue contributing to the next real acceleration. The reader will have noticed the similarity between this situation and that earlier (7.5.) posited for ideal and real distances. Another point, obvious enough, but perhaps worth stressing, is that minimum acceleration increases as N decreases. So that the faster a sequence moves, the greater its accelerations, but, ceteris paribus, the longer the interval of time between them. Thus, the faster a "particle" moves, the greater the force that is required to effect any change in its absolute speed. All this applies only to speed; the directional component of acceleration will be quantised according to the accommodation of ideal to real direction noted earlier (7.5.3.).¹³

Heisenberg's Uncertainty Principle
8.3.14.
The Uncertainty (or Indeterminacy) Principle, first enunciated by Werner Heisenberg is, like so much else in 'the new physics', an amalgam of classical and quantum ideas, deriving, in this case, from a naive welding of the mathematically precise but physically absurd conception of the electron as a 'wave packet', to the classical conception of group waves in a material medium. It follows, as a necessary consequence of making this connection, that simultaneous precise measurements of an electron's momentum and its position are mutually exclusive. This has the inescapable implication that to seek for a more detailed, precisely determined theory of physical processes is futile, since the notion of a precise electron trajectory (in terms of both position and momentum) is now meaningless. Now, as in reality, the electron is no 'wave packet', but a precise sequence of instant events at a precise spatial location; and radiation is force-at-a-distance between instant events, all at precise spatial locations, this conception of Heisenberg's is radically false, and hence has no relevance for the nature of physical reality. However, it does raise two interesting points, both concerned with the relation between noumena and phenomena. All that the phenomenally restricted physicist can ever directly register are the effects of his measuring instruments upon his senses. Hence he is doubly removed from those physical processes which are affecting his measuring instruments. Moreover, in many cases the barrier between the observer and the physical world is intensified by the circumstance that in order to measure some specific part of it, he is first obliged to interfere with it in some imprecise way. From all this, then, it is obvious that if the physicist aspires to say anything about the nature of the objectively existing world at all, he is obliged to make inferences from his observational data as to the nature of the noumena - the entities of the physical world - that are the objects of his study. In short, as we explained in Chapter 2, science no less than metaphysics, is obliged to make use of rational evidence. So that in so far as Heisenberg's Principle is asserting that the physicist can never directly experience what is happening in the physical world, and is hence obliged to make inferences if he wishes to understand what is, it is merely stating what should be obvious to any rational person.

8.3.15.
However, many would claim that the Principle is asserting far more than this: namely, that indeterminacy is an inherent characteristic of physical reality itself - more particularly, that an electron does not have a precise position when it has a precise momentum, and vice versa. This is the ontological as against the merely epistemological interpretation of the Principle. Now, there is an insuperable objection to the truth of this interpretation. As finally established by Kant, 'existence' is not a predicate. To say, 'X exists' is to say something of a different order from 'X is large' or 'X perceives'. It tells us nothing about the particular nature of X but only that the universe contains something (the ontological object), that we call X, defined by the possession of a certain set of attributes. As for what these collectively are, we mean simply something that to a conventionally accepted degree of closeness, resembles a subjective state (the epistemological object), purporting to refer to X. Now, as a particular part of the universe, an electron, by definition, has a particular nature: any indefiniteness attaching to it therefore applies only to the nature of the phenomenon, the electron-as-conceived, not to the noumenon - the electron-in-itself. So that, to sum up: indeterminacy is an attribute that can legitimately be applied only to our knowledge of an object with reference to that object, never to the object of knowledge itself.

8.3.16.
Ever since it was first advanced, the acceptance or otherwise of this posited limitation of our physical knowledge has divided the physics community; the majority, including Bohr, settling for it, but a not inconsiderable minority, among them de Broglie, Schrödinger, and Einstein, and later, Bohm, rejecting it. These have seen the manifold confusions, contradictions, and lacunae of modern physics as pointing unequivocally to the existence of a more fundamental level of activity, which no in-built interdict prevents our investigating - certainly theoretically, and perhaps (who knows?) practically. They claim, therefore, that there exists an underlying realm of 'hidden' variables whose proper understanding can alone bring ontological coherence to physics. And, indeed, Bohm¹⁴ was able to prove, without even needing to stray beyond the confines of quantum theory, that nothing so far established by that theory was incompatible with the existence of hidden variables. And nothing has happened since to invalidate this conclusion.

THE ATOM
THE ATOMTHE ATOM

8.4.1.
For present purposes, the modern theory of the atom can be viewed as falling into three distinct periods, the three key dates being: (i) 1897: J.J. Thomson’s discovery of the electron; (ii) 1911: Rutherford's discovery of the minute but massive positively charged atomic nucleus; (iii)1925: the inception of the wave mechanics of de Broglie, Schrödinger, and Born. The first period was dominated by the 'plum pudding' model of Kelvin and J.J. Thomson. In this model, positive charge was conceived as constituting a uniform background throughout the spherical atom, with the equal and opposite negative charge as contributed by a number of minute equally charged particles - the electrons - positioned throughout in the atom in some geometrically regular arrangement. Then, under the influence of an external field, each electron was shifted relative to the background positive charge by an amount dependent on both the strength and direction of the field, and its own location within the atom. But there would always be a general tendency for the electrons to regain their basic positions: those they occupy when the atom is not subject to the distortions of an external field. Owing to inertia they will tend, in so regaining them, to oscillate about these mean positions with a definite frequency dependent upon their position in the atom, but with diminishing amplitude as restoring forces steadily assert themselves. Such simple harmonic oscillations are what we detect as electromagnetic radiation, the different frequencies depending, as I say, on the electrons' different positions in the sphere of positive charge. But although this was an attractive theory, making general sense according to the knowledge of the time, little success was achieved in matching theoretically calculated values with values obtained by calculations from experimental data. In this, conception, then, the atom was viewed essentially as some kind of sharply tuned harmonic (sinusoidal) oscillator.

8.4.2.
It was abandoned virtually overnight with Rutherford's production of undeniable evidence that the background cloud of positive charge was a complete fiction; that, instead, the equal positive charge was concentrated in a single massive but minute region at the centre of the atom. "In 1911 Rutherford introduced the greatest change in our idea of matter since the time of Democritus".¹⁵
The overriding question, now, was: How are the electrons related in terms of motions and positions to this central nucleus? And to answer this question satisfactorily entails resolving an obvious problem. The electrons are negative, the nucleus is positive, opposite charges attract, the positive nucleus is massive in comparison with an individual electron: why, then, do the electrons not fall into the positive nucleus, instead of remaining at some distance from it? What is it that prevents the electrons so falling? Henceforward, acceptance of any new model of the atom centred on its answering this question satisfactorily.

8.4.3.
The most widely accepted model was proposed by Niels Bohr. This constitutes the paradigmatic example of the fatally trapped physicist attempting to adapt mechanism to cope with the quantum realm. It is sometimes known as the planetary model, since it is little more than a scaled down version of the solar system, with a few arbitrary ad hoc rules slapped on to cope with the special quantum conditions. Here, for different kinds of chemical element, anything up to 90+ individual electrons were thought of as circling a central nucleus. This was composed of the same number of protons, each of equal and opposite charge to an electron, but some 1837 times more massive. There were also many neutrons (roughly the same as the number of protons) in the nucleus, each about the same mass as a proton but carrying no charge. The electrons, it was thought, did not fall into the nucleus under its inverse square electrical attraction for much the same reason that the moon did not fall to earth, or the earth into the sun, despite being attracted to it - in this planetary case by gravitation: because its 'centrifugal force' just counteracted this centripetal attraction, and so maintained the electron in its circular or, more probably, elliptical orbit. This electron velocity turned out to be very great: c/137 in the case of the single hydrogen electron in its ground state. But one feature of this 'planetary' conception which had no counterpart in the actual solar system was that only certain orbits were allowed: those whose angular momenta were nh/2π, where n is an integer, and h, Max Planck's quantum of action. Notice that, in striking contrast to its predecessor, this model, far from being an oscillatory conception, contained no oscillators at all! Instead, there were only electrons at discrete energy levels orbiting a massive nucleus. The electrons were supposed to revolve without radiating, which, of course, brought with it the ambivalent consequence that they could never be 'directly' observed! Any discrepancies in angular momentum between calculations from the model and calculations from observational data could always be accounted for by the hypothesis of electron spin. 'Observed' frequencies were thought to arise from the fall of an electron from an energetically higher orbit to a lower. This was regarded as instantaneous despite the evidence that at each 'transition' radiation persisted for as long as 10^-8s. These frequencies, were obtained by dividing the energy difference, ΔE = E_n - E_m between the two levels, by h. But they could not be related in any meaningful way to the frequencies of revolution of the electrons involved. Meanwhile, evidence continued to accumulate that atomic electrons were oscillating. In recent years this has received the strongest possible confirmation from laser technology: " ... the basic concepts of maser action are actually relatively simple and can be understood almost entirely from a classical viewpoint, with only limited appeals to quantum terms and concepts."¹⁶ Also: "We have a great wealth of evidence that atoms behave like sharply tuned oscillators in the processes of emitting and absorbing light... If the emitted light is analysed with an interferometer, it is found to consist of wave trains of finite length. The length of the wave trains, divided by c, defines a time τ which corresponds to the mean life of the radiating atoms in their excited state, and the surplus energy of a collection of excited atoms decays exponentially as e^-t/τ as the energy is radiated away."¹⁷

8.4.4.
This Bohr model, despite its great and obvious defects, was nonetheless the last physical model advanced by physicists. No other physical cause (overlapping of wave-fields not falling into this category) could be found for keeping the negative electrons from falling into the positive nucleus. But this seemingly unavoidable 'planetary' conception, brought so many drawbacks in its train, and accounted for so few of the experimental facts, that it could not be viewed as other than radically unsatisfactory. Wave mechanics¹⁸ - "a dodge and a very good dodge too" (8.3.10.) - was therefore welcomed as an ingenious way out of this impasse. This transfer of allegiance from the Bohr atom to the wave-mechanics of Schrödinger marked a return to an oscillatory conception, but with the great difference from the Kelvin-Thomson model that this latter version side-stepped any precise physical conceptions; instead, confining any precision to equations in which quantitative descriptions of classical sinusoidal oscillations played a central part.¹⁹ At the same time, many features of the Bohr atom were retained: a massive central nucleus composed of protons and neutrons; discrete, if only probabilistic, allowed energy levels for the ambient electrons; their sudden transferences from one such level to another; and the conversion of such changes in energy into frequencies by dividing them by h. So that, as the basis for a physical theory of the atom, wave mechanics was little more than a vague, confused compromise between the classical oscillator model and the Bohr planetary model. I say "little more" because it did incorporate the genuinely new element of the de Broglie wavelength. True, it no longer put forward any physically intelligible causal conception of the atom, but by this time physicists were becoming resigned to the circumstance that the physical world was beyond their understanding, while, at the same time, still susceptible of precise quantitative investigation. And, as we noted earlier (8.1.7.) this was henceforth seen as the way forward. In fact, doing their best to make a virtue of necessity, some hailed it not as a mere pis aller, but as the latest and most sophisticated manifestation of the only coherent method - the mathematical - of conceptually organising the physical world that had ever been a realistic option for the human investigator.

8.4.5.
We, however, having successfully dismantled the Fatal Trap, find ourselves in a very different cognitive position. In possession of a fully rational theory of the nature of, and relations between, matter, space, and time, we are in a position to do somewhat better than mechanistic orthodoxy in formulating a coherent physical theory of atomic structure. We have already dealt with the real, intrinsic structure of positive and negative electrons - the fundamental physical 'particles' - and have noted (8.1.9.) that the key to atomic structure must lie in their ever-varying phase relations and hence complexly changing attraction/repulsion situations.

A NEW CONCEPTION OF THE ATOM

8.5.1.
As we have just seen, the main reason for the effective abandonment of the Bohr model as an acceptable conception of the atom lay in its postulate that the electrons must revolve at high speeds around the central nucleus as the only way to prevent their falling into it. Not only is there no experimental evidence that they do so, but the abundant evidence that there is much oscillatory activity within the atom is left unexplained. Moreover, just how chemical bonding occurs between atoms composed of such rapidly revolving components was - to put it no more strongly - difficult to conceive. Our conception of physical fundamentals, on the other hand, provides a natural reason why ambient negatrons are not necessarily attracted towards the positive nucleus; and from this same cause, not only is much oscillatory activity implied, but a simple and natural mode of chemical bonding provided.

8.5.2.
This new conception of the atom centres on the 'hidden' variable of like electrons attracting and unlike repelling in some of their phases: 'contrary' behaviour attaining a maximum - of half the possible phases - when the two electrons are equiperiodic (8.2.4.). As a consequence, when distances, periods, and phase relations assume the right values, pair bonding of electrons, both like and unlike, inter- as well as intra-atomic, occurs as a natural and ubiquitous feature of atomic - and molecular - structure. In the Bohr atom the planetary negatrons were, of necessity, required to orbit the nucleus at high velocities in order to generate a 'centrifugal force' (really, of course, inertia) sufficiently strong to counteract the centripetal force of the attracting nucleus. But if a proton repels an electron in up to half its phases, no such high speed revolutions - conceivably no revolutions at all - are required to keep the electron away from the nucleus. In The Nature of the Chemical Bond (p.35), Linus Pauling writes, " ... it has been found by experiment that the normal hydrogen atom does not have any angular momentum". Although orthodoxy has always accounted for this in terms of the cancelling out of oppositely directed angular momenta, the true explanation, according to the present theory, is that nothing is revolving or rotating.

8.5.3.

EQUILIBRIUM POSITIONS OF ATOMIC NEGATRONS

FIGURE 6

The reader is referred back to Figure 4 (8.2.4.). In Figure 6 (a reproduction of Figure 5, which derives from Figure 4) we may take the + charge as the hydrogen nucleus, and the - charge as its associated negatron. In which case α, β, γ are equilibrium positions of the negatron, since if it moves from any of these either towards, or away from the positive nucleus, the force from this will counteract its motion. These repulsion/attraction (R/A) interfaces will occur naturally at a distance λ apart, and at a distance of nλ±p points from the nucleus, where n is an integer, λ the electron wavelength, and p a number (< λ/2) that depends on the phase relation between the negatron and the nucleus.
Since λ= cT, and T = ρ/v, it follows that λ= ρc/v. Because ρc is a constant, λ must be inversely proportional to the absolute velocity of the atom. The principal component of the absolute velocity of atoms on planet Earth, is, of course, that of the Solar System. Many attempts have been made to determine the absolute velocity of the Solar System - e.g. those of Sagnac and of Marinov. Though the results differ considerably, the majority yield a value of around 300 km.s^-1, or c/1000. For earthly atoms this implies a value of λ of around ρc x 1000/c = 1000ρ (1000 points),²⁰ with an annual variation of the order of ±60ρ, and a corresponding variation of 60nρ of all the R/A interfaces, moving towards or away from the nucleus as velocity increases or decreases.

8.5.4.
A complete oscillation of a negatron about an interface is obviously divided into four sections. And basically determining its motion in each of these is the inverse square force exerted on it by the atomic nucleus. This conforms to the equation v²=2k(1/x-1/a), where v is the velocity of the negatron relative to the nucleus, k is a constant (= e²/m_e = c²ρ, where e is electron charge), a is the initial distance, and x the final distance of the electron from the nucleus, with x and a interchanging their values for each of the four sections of the oscillation. Now, I say "basically" advisedly, since there are many modifying parameters in operation.

8.5.5.
Both the attractive and the repulsive forces exerted by the nucleus are restoring forces. Clearly, if they alone were acting, and the nucleus stayed unchanged, then the negatron, once settled at the interface, would remain there. But the negatron oscillates to a greater or lesser degree about the interface since the forces acting on it will be constantly varying. Among these forces will be those from the other negatrons as they change their positions. Also, forces from neighbouring atoms and beyond, will be in a state of constant flux. Every one of these will impel the negatron either away from or towards the nucleus; and every such force will be opposed by the nuclear force, thus tending to maintain stability. Moreover, the nucleus itself must be far from static. Its components will doubtless be oscillating, if only with small amplitudes. Then again it may lose or gain neutrons. Finally, its absolute velocity (and hence the periods of all its constituent electrons) will be constantly changing; to look no further - both diurnally and annually for earthly atoms. All these nuclear changes must insure that its forces on any ambient negatron are constantly changing. But, even more importantly, these nuclear changes must entail that the distance of the R/A interface from the nucleus is also constantly changing, since, as we have seen (8.5.3.), 'wavelength' is inversely proportional to absolute velocity (λ = ρc/v). Inertia will ensure that there will be constant oscillation of this variously acted upon negatron about this changing interface. Such oscillations will not, of course, be sinusoidal, since neither the forces causing them nor the restoring forces are simple harmonic. But, as we pointed out earlier (8.3.12.), any oscillation, however complex, can be expressed as a sum of Fourier components, and hence approximated to a sinusoid to any requisite degree of accuracy.

8.5.6.
Now, since v = c/N, where N is the number of instants in one period (i.e. N = T/τ), all these changes of velocity of the negatron, whether caused by disturbing or restoring forces, require that its period is changing in inverse ratio. And since contrary phases are at a maximum when the velocities, and hence the periods - in this case of nuclear proton (effectively) and ambient negatron - are equal, this tends further to weaken nuclear repulsion - already, of course, the weaker response by an overall ratio of 4:5 - and strengthen attraction. However, at these distances from the hydrogen nucleus (remember, that a₀ is around 18.75λ), the negatron velocity, over a maximum distance of λ/2, varies from c/1000, by something of the order of 10 units of denominator at most. Moreover, there are certain compensating factors operating. Firstly, since the negatron is being attracted at the side of the interface further from the nucleus, its velocity as it passes through the interface will be at a maximum, and consequently, its range of repulsive phases at a minimum. But as soon as the repulsive sector begins, this velocity will fall towards c/1000, where the repulsive phase range is a maximum. Secondly, since the repulsive side is closer to the nucleus than the attractive, it will be by that much the stronger force. Thirdly, although, in this conception, revolutions of the electrons do not play anything like the fundamental role they do in the Bohr atom, they are not necessarily absent, and any such motion will add a 'centrifugal force' opposing any centripetal attraction.

8.5.7.
A further complicating factor is that all the accelerations resulting from these nuclear and atomic forces are superimposed upon a basic velocity: the absolute velocity of the Earth, which we are taking to be around c/1000. And, of course, this itself is continually varying as a consequence of the Earth's annual and diurnal cycles. And the fact that sequence period is inversely proportional to absolute speed implies that the periods, and hence the phase relations, of electrons must vary with the orientation of any localised motion with respect to the absolute motion of the Earth. One would suppose that there would be a general tendency for all oscillations to occur, as far as possible, on a plane at right angles to the Earth's motion, since then symmetry of motion between the two opposing directions of the oscillation would be preserved. In which case, other things being equal, there would be a tendency in free atoms for their ambient negatrons to settle on that great circle of the spherical interface oriented at right angles to the motion of the Earth.

8.5.8.
In general, then, as non-nuclear forces displace a negatron from a R/A interface, nuclear forces will act so as to restore it. But these disturbing forces will sometimes be sufficiently strong to so increase the oscillations of some negatron as finally to give it a velocity too high for the nuclear force either in the repulsive or the attractive half of the band to bring it back to the interface. Such a contingency will be more frequent the greater the distance of the negatron from the nucleus, since, other things being equal, nuclear forces fall away with the square of the distance. The negatron is thus forced into a neighbouring R/A band either closer to or further from the nucleus. When this happens, the negatron will tend to be captured by this neighbouring band, oscillating about its central interface. As it will reach this new band already moving, and at a distance of λ/2 from its interface, its oscillations about this new interface will initially be of a high amplitude. They tend to die away exponentially through the action of damping forces, their rate of decay differing with different energy levels, but may still be of sufficient magnitude to be detectable after a lapse of 10^-8s. Whether a negatron is displaced towards or away from the nucleus will depend on the direction of the impinging forces. Moreover, there will presumably be a fairly stringent limit to the number of negatrons that can be accommodated within any one band, so that a vacancy must be available in order for a negatron to settle at a new R/A interface. So that an ousted negatron may not be captured by a neighbouring zone, but by one more remote, or even leave the atom altogether. The general picture at any time, over an atomic ensemble, is for numbers of negatrons to be moving in both directions with respect to the nucleus.

8.5.9.
By far the main source, direct and indirect, of such disruption for atoms at the Earth's surface is, of course, the sun. Now, it will be recalled that where distances, and hence phase relations, between electron pairs are random, the effect over all phases is for like electrons to repel and unlike to attract with a R/A ratio of 5/4. It is only where distances apart, and hence phase differences, are limited to certain values that these ratios are radically departed from. But the heat and light from the sun is essentially random both in phase and frequency. So that it cannot be its direct action on the ambient negatrons that gives rise to light. Most substances consist of chemically bonded atoms (v.i. 8.6.), and it is the coordinated oscillatory response of these elastic bonds in numerically vast systems of bonded atoms that gives rise to regular motions and hence regular changes in period and phase of their electronic constituents. It would be reasonable to assume that these atomic oscillations include oscillations of the atomic nuclei. In which case, since v = ρ/T, the periods of their electronic constituents must change accordingly. The effective wavelength, λ(=cT), of any nuclear proton must therefore increase and decrease by the same number of points as the period changes in instants. And so, in consequence, must the distance (nλ +p) from the nucleus of every R/A interface, and any ambient negatron which happens to be occupying it. As we noted above (8.4.3.), an 'observed' frequency (ν) in the Bohr atom was found by dividing the difference in energy levels by h, since dividing an energy by an action gives a frequency: (E_j - E_i)/h = E_j /h - E_i /h = ν_j - ν_i = ν - that is, one frequency minus another. However, in the Bohr atom no such frequencies as ν_j and ν_i existed. But in this model they do, which would suggest that 'observed' frequencies are, in fact, 'beat' frequencies between oscillating electrons at different energy levels.

8.5.10.
In the Bohr atom the positive charge on the nucleus ranging from one unit (for hydrogen) to 92 units (for uranium) attracts each ambient negatron. Certainly, such varying parameters as distance from nucleus, angular velocity, and repulsive forces from other negatrons can go some way to accounting for the stability of each negatron despite these wide differences in attractive force, but to believe that they account for it satisfactorily is to put a great strain on our credulity. Our model escapes this difficulty altogether, since any strengthening of the nuclear forces on a negatron at an interface will affect attractive and repulsive phases equally. Increase of nuclear charge also implies the possibility of negatron stability at greater distances from the nucleus, thereby increasing the effective diameter of the atom. However, a problem does arise respecting the increase of distance from the nucleus of the innermost interface. We will return to this point later ( 8.5.15.).

8.5.11.
An obvious question that arises is: Why is n no smaller than 18 for the ground state of the hydrogen atom? The answer must lie along the following lines. We have seen that the number of contrary phases attains a maximum - of N/2 - when the two electrons are equiperiodic, although the preponderance ratio, over all phases, of attractions to repulsions remains constant at 5:4 whatever the two periods. Now, as we have seen, there is often significant oscillation of a negatron about its equilibrium position. This means that, except at the extremes, its absolute velocity will be greater than that of the nuclear positron, and at a maximum when it is passing through the interface. Hence, except at the oscillation's extremes, negatron and positron are not equiperiodic, and the less equiperiodic they are, the more, broadly speaking, will congruent (attractive) phases preponderate over contrary (repulsive). And the closer the negatron is to the nucleus, the greater its velocity as it passes from the strengthened attractive band into the comparatively weakened repulsive. There must therefore exist a distance from the nucleus when this repulsive band is too weak in comparison with the attractive to bring the accelerated negatron to rest relatively to the nucleus. So that the negatron continues on to the next interface, reaching it with an even higher velocity, and so on. And, on empirical grounds, we are postulating that, under normal conditions, this breakdown of stability, due to the growing imbalance between attractive and repulsive forces in the hydrogen atom, occurs when the negatron is less than a distance of a₀ from the nucleus - that is (if λ= 1000ρ) when n < 18.

8.5.12.
As for the other extreme position of the hydrogen negatron - that is, the distance of the furthest stable A/R interface from the nucleus - this will clearly depend upon the magnitude of the nuclear charge. For the uranium atom this is 92 times stronger than that of the hydrogen atom. Orthodoxy assigns a diameter of the order of 10^-10 m for the atom. When λ=1000 points (1 point = 2.818 x 10^-15 m), this implies that there are some 35 A/R interfaces to an average atom. But since, as we have just seen, the first 18 of these are unstable, that leaves 17 possible A/R interfaces for a negatron to settle; beyond this the nuclear force is presumably too weak to provide any significant stability. It might be thought that, at separations of only 1000ρ, these interfaces are too close for the frequencies of any negatrons oscillating about them to be distinguishable. But, as has long been known, the atom is very sharply tuned. Indeed, the width of its average tuning band is only 0.04% (1/2500) of the frequency, which is far smaller than the difference between the frequencies of oscillating negatrons in adjacent zones, which, by my calculations (admittedly somewhat suppositious) - is of the order of 4% (1/25) of the frequencies concerned.

8.5.13.
When we attempt to describe the atom on a more detailed level, we are faced with so many possibilities for each parameter - each of which effects all the others - that the best we can do at present is to review a few of the more rationally and empirically attractive options. To begin with much the most structurally important feature of the atom - its nucleus: this is composed of protons and neutrons, the latter in somewhat greater numbers; the neutron/proton ratio increasing fairly steadily from 1 to around 1.6 with increasing number of protons from hydrogen (1) to uranium (92). Neutrons are composed of equal numbers of positrons and negatrons: 920 of each. A proton is simply a neutron that has lost two negatrons and a positron, the clamped negatron-positron pair vacating the scene altogether, but leaving the remaining negatron to hover around the nucleus at one of its more distant repulsion/attraction interfaces. The first question to ask is: How are the neutrons and protons arranged in the nucleus?

8.5.14.
The chaotic 'liquid drop' model is an absurdity not even worth cursory consideration. Of course the nucleus is structured no less than the atom. In fact, since the distances between the R/A interfaces are equal to, the wavelength of the proton's surplus positron, which depends upon its sequence period (λ = cT) which, in turn depends upon the positron's absolute motion (T = ρ/v), it follows that the distances of the R/A interfaces, about which the negatrons oscillate, depend fundamentally on the absolute velocity of the surplus positron within each of the nuclear protons. The adherence of a proton to a neutron will be by induction. A neutron is made up of an equal number of positrons and negatrons. The excess positron in the proton will, on the whole, repel the positrons in the neutron and attract the negatrons Since these are now closer to the protonic positron, the attractive force will outweigh the repulsive and there will be a marked tendency for the neutron to adhere to the positive region of the proton. There is much evidence that the alpha-particle, consisting of two protons and two neutrons, is exceptionally stable. We conceive it thus:

_-⁺N⁺_-
P        P
^-₊N₊^-

AN ALPHA-PARTICLE

 

 

Moreover, alpha particles are a common decay product of radioactive transformations. These two facts suggest that atomic nuclei may well be alpha-structured.

8.5.15
Although, as we stated earlier (8.5.10.), our model resolves the problem of how single negatrons can remain part of a stable atom despite the wide range of attractive nuclear forces to which they are subjected, this wide range does pose a problem of a different kind. We have already claimed (8.5.11.) that the first seventeen zones around the hydrogen nucleus are too unstable for negatrons because of the strength of the forces involved. But, of course, with a multiplicity of protons in the nucleus, the nuclear forces at the R/A interfaces are rendered proportionately stronger. So that, as the number of nuclear protons increases, the innermost negatrons move progressively further and further from the nucleus. So that the distance from the nucleus of uranium’s innermost stable interface should be some nine or ten times (that is, √92) times greater than that of the hydrogen atom. But the empirical evidence would seem definitely to negate uranium atoms of a size of this order. However, there is at least one other major factor to be taken into account.. The number, however large, of protons in the nucleus, implies an equal number of extra-nuclear negatrons. And despite their far greater mass, n protons + n-plus associated neutrons carries only the same charge as n negatrons. Now, it is obvious that, assuming an overall 5:4 repulsion preponderance between any two negatrons, however many negatrons there are at an interface, they must all repel each other away from the nucleus. And with the right spatial arrangements (doubtless rich in symmetries) between them this mutual repulsion may well be greater, even up to the maximum of every instant per period. Of course, with more than one occupied interface the situation becomes much more complex. It could well be that for each atom there exists more than one stable arrangement of its negatrons. In which case, disruption of any such arrangement will tend to bring about a collective readjustment and final resettlement into some other. So that it does not seem impossible that with the right spacing between them, 92 extra-nuclear negatrons may be accommodated in an atom whose overall size is not that much greater than a hydrogen atom’s. Finally, as we shall see (8.6.) negatrons tend to pair bond, and this must surely have some effect - iif only to lessen the number of interfaces they need occupy.

THE COVALENT BOND

8.6.1.
Finally, we will consider the negatron-negatron bond. Such bonds are both inter- and intra- atomic. Interatomically, they constitute the principal chemical bond - the covalent. Were it not for the existence of contrary phases, when like particles attract, such bonding would be a pure absurdity. But with these accounting for up to half the possible phases, a simple natural and ubiquitous mode of atomic linkage is provided. Within the atom, negatrons occur principally in the form of bonded pairs, with each unpaired electron at an outer interface constituting a valency unit - a potential partner in a covalent bond. Where this bond differs intrinsically from the positron-negatron bond, as incorporated in the atom, is that both sequences are fundamentally free to move. They are thus equal partners. Also, of course, it is repulsion, not attraction, that is preponderant here. Since both sequences are free to move, we have to consider forces in both directions. Always, for stability, the force must be opposed to the direction of motion; so that at an equilibrium position each sequence must be repelled by the other when it moves towards it, and attracted when it moves away from it. In short, the repulsion zone of an interface must always be in the direction of the other sequence. Since both partners in the bond are free to oscillate about their respective equilibrium positions, equality of period, and hence stability, are more easily maintained than in the case of the nuclearproton-negatron bond. No particular restrictions are thus placed upon velocity; but since repulsion preponderates, there is little likelihood of the two sequences ever coming together.

8.6.2.
Reference to Figures 1 and 6 shows that a stable situation results when sequence A leads like equiperiodic sequence B (sequence B lags sequence A) by nN/2 instants, and the two sequences are nλ/2 points apart, with n an odd integer. We illustrate this in the accompanying figure.

Figure 7

 

For convenience we take the equilibrium position of negatron X as fixed. Y₁, Y₂, and Y₃ are then three possible equilibrium positions for another negatron to take up with respect to X, at distances apart of λ/2, 3λ/2, 5λ/2 ...points respectively. With λ taken as 1000ρ (= 2.818 x 10^-12m), these will be at a distance of 500ρ, 1500ρ, 2500ρ ... (= 1.409, 4.227, 7.045... x 10^-12 m). (For comparison, the Bohr Radius, a₀ = 18,779ρ (= 52.92 x 10^-12 m.). Clearly, the smaller the value of n, the greater the energy locked into the bond. Just which value n takes in any bond-forming situation must depend on the conditions obtaining at that time. But since - in the interatomic case, at least - each negatron is already a multi-bonded constituent of an atom, it is the structures of these atoms which must be principally responsible for this value. If the negatrons belong to planet Earth, this negatron-negatron, or covalent bond will tend, for reasons of equiperiodicity, to take up an orientation in a plane at right angles to the motion of the Earth²¹.

NOTES

1 "As long as we are not told what matter waves are waves of, the wave theory is not a physical theory." G. Burniston Brown, Retarded Action-at-a-Distance, (Cortney Publications, Luton, 1982, p.141).
2 In speculating on the nature of the relationship existing between the wave aspects and the particle aspects of an electron, Louis de Broglie writes "... if the particle is considered ... at rest ... it could be compared to a small clock..." and "I thus easily demonstrated that, during the motion of the particle in the wave, the internal vibration of the particle was constantly in phase with that of the wave ... " The Reinterpretation of Wave Mechanics, Foundations of Physics, (Vol. 1, No. 1, 1970, p.6).
3 David Bohm, in a discussion on Quantum Physics, The BBC Third Programme, (1962).
4 See Note 1 above.
5. Guy Burniston Brown, ibid p.72.
6 "In fact, quantum theory requires us to give up the idea that the electron, or any other object has, by itself, any intrinsic properties at all. Instead, each object should be regarded as something containing only incompletely defined potentialities that are developed when the object interacts with an appropriate system". (David Bohm, Quantum Theory, Prentice-Hall,1951; republished Dover, 1989, p.139). To be fair to Bohm, he wrote this book (just) before he became a leading advocate of 'hidden variable' theory. The notion that an exquisitely precise, immeasurably complex physical universe could arise as a consequence of relations between intrinsically ill-defined entities is a particularly choice example of the pseudo-profound nonsense in which the fatally trapped physicist is forced to take refuge in his attempt to avoid contradiction. But if you are seeking to give a rational account of the detailed processes of the world within a radically irrational theoretical framework, contradictions are inescapable, no matter how ingenious the contortions and evasions you resort to in order to avoid them.
7 λ_DB =h/m_ev =2πm_er_ec/αm_ev =2πr_ec/α²c =2πr_e/α² =2πr_e/(r_e/a₀) =2πa₀.
8 (Quantum Theory, 1951. Repub. Dover 1989, p.79 and p.219).
9 Quoted, Guy Burniston Brown, ibid. p.73.
10 N.F.Mott. Elements of Wave Mechanics, 1952. Cambridge University Press, p.45.
11 (The Undivided Universe An Ontological Interpretation of Quantum Theory by David Bohm and Basil Hiley, 1991 Ch. 1, pp. 1-2).
12 Guy Burniston Brown, ibid. p. 73.
13 In view of the prominence of β = (1/√(1 - v²/c²) in non-Newtonian mechanics, the following considerations may perhaps be of relevance.
Consider any velocity, v = c/n. Then the immediately lesser velocity will be c/(n+1), and the immediately greater, c/(n-1). The arithmetic mean (A.M.) of these two adjacent velocities will clearly not be v. Instead: A.M. = [c /(n+1) + c/(n -1)]/2 = (nc - c +nc + c)/2(n² -1) = nc/(n² -1) = (c/n)/(1 -1/n²) = v/(1 - v²/c²) = β²v.
Also, for the corresponding geometric mean (G.M.): G.M. = √[(c/n+1) x (c/n -1)] = √[c²/(n² -1)] = √[(c²/n²)/(1 -1/n²)] = √[v²/(1- v²/c²)] = v/√(1-v²/c²) = βv. {Notice that β = Arithmetic Mean/Geometric Mean}.
14 (Physical Review vol.85, no.2, Jan.1952 pp. 166-193)
15 E. N. da C. Andrade. An Approach to Modern Physics, 1956. London. G.Bell and Sons Ltd., p.139.
16 A.E.Siegman, An Introduction to Lasers and Masers, McGraw Hill, 1971, p.viii.
17 A.P.French, Vibrations and Waves, Chapman & Hall, 1971, pp. 105-6.
18 "Wave mechanics is a system of equations which determines the behaviour of the fundamental particles of physics, the electron, the proton, and the neutron, and their interaction with radiation." (N.F.Mott ibid. p.21)
19 "It is well-known that in the days of the mathematical theory of wave-mechanics, developed with the aid of analogy, an attempt was made to give the wave-function y a physical meaning, and that this has failed, many writers falling back on what is merely a verbal subterfuge by saying that matter has a 'dual character'." Guy Burniston Brown, ibid. p.137.
20 On the assumption that the absolute velocity of the Earth is around c/1000, the following consideration may be relevant. The value of a₀, the radius of the hydrogen atom, is given as 5.292 x 10^-11 m. Hence, a₀ = 5.292 x 10^-11/2.818 x 10^-15 = 1878 points. If, for some reason, the negatron is in phase with the nuclear positron at a distance apart of nλ, then p [see 8.5.3.] = -λ/4. In which case, 19λ-λ/4 = 18·75λ = 1878, or λ= 1002ρ; whence v = c/1002.
21 It is conceivable that this tendency for electrons to oscillate in a plane at right angles to the Earth's motion (see also 8.5.7.) might go some way to accounting for the null result of the Michelson-Morley experiment, since its cumulative effect must be to lengthen the transverse and shorten the longitudinal arm of the apparatus.

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