This is a continuation of Lecture No. 2

It is the continued text of the 1986 paper on 'The Mystery of Mercury's Perihelion'.

[.....It was as if the formula for the 43 arc seconds per century advance was not already known from the prior work of others, which Einstein presumably chose not to acknowledge.]

In this regard, it should be understood that, before Einstein appeared on the scene, the physics of the 19th century had offered explanations for the precise advance of Mercury's perihelion. The speed parameter c had appeared in electrodynamic equations and efforts were made to formulate analogous gravitational equations. These led to advance of perihelion. Suppose gravitation propagates at a finite speed c. This means that the radial perturbations of the planetary orbit will be retarded in relation to the orbital period. In each successive orbit it will take a little longer for the planet to come to perihelion and this means that the orbit will advance progressively. The only question was that of determining the rate of advance numerically. Physically, the advance was inevitable within the accepted framework of 19th century physics. The 19th century analysis of this proceeded on the assumption that gravitation propagates at the speed of light and culminated in a paper by Paul Gerber published in a leading German journal in 1898 [Zeitschrift Math. Phys., v. 43, p. 93 (1898)]. It was entitled: 'The Space and Time Propagation of Gravitation' and, by analysis using retarded potential theory, Gerber arrived at the identical formula for the rate of advance of Mercury's perihelion that later was used in Einstein's 1916 paper on general relativity, which appeared in Annalen der Physik. (Note: If Einstein did not know Gerber's 1898 paper, is it not curious that he presented the formula for the rate of perihelion advance in an identical form, even in the use of the same upper and lower case forms of the same typographical symbols?)

As we read Whittaker's historical account [E.T. Whittaker, 'A History of Theories of Aether and Electricity: The Classical Theories)', Nelson, London, p. 208 (1951)], Weber's earlier ideas on electrodynamics led Tisserand in 1872 to work out that, if gravitation propagated at the speed of light, the perihelion of Mercury would advance 14 arc seconds per century. At that time the estimated anomaly was 38 arc seconds per century, but by 1898 Gerber's analysis gave a value three times that of Tisserand, namely 43 arc seconds, in full accord with the value adopted by Einstein in 1916.

It was only when Einstein's paper appeared that a revised and updated version of the Gerber paper was sent to Annalen der Physik [P. Gerber, Ann. Phys., Lpz., v. 52, p. 415 (1917)]. It was published in January 1917. Gerber was deceased at the time his paper appeared in print and so he could not defend it against Seelinger's attack [H. Seelinger, Ann. Phys., Lpz., v. 53, p. 31 (1917)]. It was claimed that Gerber's analysis was flawed. However, Oppenheim [S. Oppenheim, Ann. Phys., Lpz., v. 53, p. 163 (1917)] took up the challenge, stressing that the issue of finite propagation speed of gravitation was still open as a basis for explaining the perihelion anomaly. This led Seelinger into a response holding firm to his position [Ann. Phys., Lpz., v.54, p. 38 (1917)]. Thus it was that Gerber's work was committed to oblivion. However, it was mentioned in the 1921 review of the literature by Pauli and emerged in translated form in the 1958 book by Pauli entitled 'Theory of Relativity'. The following text appears on p. 169:

'Recently, an earlier attempt by P. Gerber has been discussed which tries to explain the perihelion advance of Mercury with the help of the finite velocity of propagation of gravitation, but which must be considered completely unsuccessful from a theoretical point of view. For while it leads admittedly to the correct formula - though on the basis of false deduction - it must be stressed that, even so, only the numerical factor was new.'

The footnote acknowledges Gerber's 1898 paper and states that the 1917 paper appearing in Annalen der Physik was a reprint of a paper appearing in a rather obscure journal dated 1902. It may well, therefore, have been submitted to Annalen der Physik after his decease and by a colleague (Gerber was a school teacher) seeking to relate what Gerber had proposed long before with the new result claimed by Einstein.

Gerber had obtained the correct formula 18 years before Einstein, but by a 'false' method. So, can it also be that Einstein has obtained the correct formula as well, but also by the wrong method? In saying this it is well to remember the preface note attributed to Heaviside in 1893 and quoted at the front of Brillouin's book (as referenced above):

'To form any notion at all of the flux of gravitational energy, we must first localize the energy'.

This was five years before Gerber published his first paper. The message is clear. How can one think of calculating the delay effects of finite propagation of gravitation unless we know the route travelled by the energy and the seat of the source? Gerber and his predecessors assumed that it would travel along a straight line from Sun to planet, a very direct line of transit. In fact, the energy is likely to be spread over the field enveloping the Sun and planet. It must travel along numerous lines of flux all of which will imply a longer route than was used by Gerber. So if he did get it wrong and underestimate the rate of advance, may not a correct analysis put things right? This has been the author's own challenge! The computations have been performed and, in fact, Gerber's original formula can be sustained by heeding Heaviside's advice, supported by Brillouin, and really coming to grips with the calculation.

The author's paper was published in 1980 by the Institute of Physics in U.K. [H. Aspden, Jour. Phys., A: Math. Gen., v. 13, p. 3649 (1980)]. Predictably, however, it has aroused no interest, because relativity remains sacrosanct; its doctrines cannot be supplanted. The author has also developed the same theory and its extensions in his book 'Physics Unified' published in the same year 1980.

The perihelion of the planet Mercury has become synonymous with the name of Einstein, but, quoting again and finally some words of Heaviside which were used to open Chapter 11 of this author's book 'Modern Aether Science':

'The Einstein enthusiasts are very patronizing about the 'classical electromagnetics and its ether', which they have abolished. But they will come back to it by and by. Though it leaves gravity out in the cold, as I remarked about 1901 (I think), gravity may be brought in by changes in the circuital laws, of practically no significance save in some very minute effects of doubtful interpretation (so far). But you must work fairly with the Ether and Forces and Momentum, etc. They are realities, without Einstein's distorted nothingness.'
................(Unpublished notes of Heaviside, March 1920)

Apart from the commentary on Mercury's perihelion, much of what has been said above will be reminiscent of views expressed by N. Rudakov in the beginning of his book 'Fiction Stranger than Truth' [Rudakov, P.O. Box 723, Geelong, Victoria 3220, Australia (1981)]. This excellent study of the metaphysical labyrinth of relativity was the first revelation to this author that his (my) non-mathematical book 'Modern Aether Science' was, in 1973, branded by a reviewer as the work of a crackpot. The work did receive two critical reviews, one in Nature, and both naming the same reviewer, a strong and now well placed member of the relativistic aristocracy. This reviewer was no crank in the eyes of the Establishment; he had just had a book of his own published showing how relativity was consistent with the universe erupting from a pin point, expanding and then, as time reversed, contracting back into its initial singularity! Such is the arena in the modern struggle between we Davids and the relativistic Goliaths.

This paper in The Toth-Maatian Review ended with a footnote which the Editor, Harold Milnes, had added as an 'Editorial Comment':

'We, too, have been very favourably impressed by Rudakov's excellent work. His criticisms of the relativity theory aredefinitive; after them, there is nothing left to that theory that may be seriously considered further by intelligent men of science. It is a pity that this person (Rudakov) seems to have departed from the scene of action, intimidated, we are given to understand, by a fear of controversy and the usual muck raking by the third line relativists.'



The above paper dates from July 1986 but my own story concerning the perihelion of Mercury dates back more than 25 years before that. I had been developing my own account of energy storage in the vacuum by electromagnetic induction and my research was based on experimental anomalies that I encountered in my academic research. I came to believe that the aether was the essential foundation and was told that I was living in the past and should study Einstein's theory.

Well I had studied Einstein's theory already, at least to the point where I understood its scope and how its mathematics evolved the result formulating the perihelion advance of a planet in orbit around the Sun. Faced with my own interpretation of the role the aether plays in the process of electromagnetic induction and Einstein's theory, which offered no solution to the induction problem, I went my own way and I was rewarded almost immediately.

My aether could not have linear momentum, but it could have angular momentum. When I pictured body Earth in orbit around the Sun as enveloped in a coextensive sphere of aether rotating with it about its axis, I knew I was looking at what was effectively a pendulum bob in motion about a distant axis. By this I mean that I was looking at two components, one being the normal picture we see of a rotating sphere of matter describing an orbit around a remote axis and the other being an aether component. The latter itself has two parts. One is a spherical hole, which I thought would be coextensive with the space occupied by the planet. The other was the aether displaced by the motion of that hole with the planet around the Sun. Now, I knew that the electric particles which give the aether its mass property move at a high speed associated with their quantum jitter (Zitterbewegung). Therefore, I did not assume that I was dealing with a fluid medium displaced by matter, which would mean that the fluid pushed ahead of the planet by translational forward motion of its substance would simply flow backwards around the planet. Instead, I took the view that, once those particles came free from their organized motion sharing that quantum jitter, they would simply deploy their existing kinetic energy to travel at their full speed and rectilinearly across the region of space within that 'hole'. Here was the point of mentioning that 'pendulum bob'. The angular momentum of the aether hole plus its content of aether particles in reverse flow would not be zero. It would be that of a sphere of the aether's mass density rotating at the angular velocity of the planet's motion around the Sun.

This may need a little thought, based on the reader's familiarity with Newtonian mechanics, but here, to be sure, was a feature that could bring in the aether's angular momentum properties into the discussion of solar system dynamics. Believe it or not, the aether does have a mass density and it is of the order predicted from classical studies of electromagnetic wave properties. 19th century physicists deemed it to be of the order of 100 gm/cc. There is also need for rigidity to sustain the lateral vibrations as they propagate at the speed of light, but it is a quasi-rigidity governed by those aether particles (or sub-electrons, to use the terminology of one of these lecture topics) forming a structure which can dissolve at its boundaries.

So far as Mercury's anomalous perihelion motion is concerned, you, the reader, can now work out the rate of advance of perihelion yourself. You need simply to know, firstly, the effective mass density of the aether in its spin condition. There is a zero momentum, or rather a cancelling momentum, for rectilinear motion. Then you need to know that aether mass density and the radius of the 'hole', which should be a little larger than that of planet. By factoring the variation of aether angular momentum into your equation of motion for the planet about the Sun, the resulting anomalous progression of perihelion is derived.

This was how I first tackled the problem of the perihelion anomaly in the 1950s, having already calculated that aether mass density in deriving the value of Planck's quantum of action from basic theoretical analysis. For the record I mention that in the book I wrote towards the end of 1959, which I published myself early in 1960 under the title 'The Theory of Gravitation', the chapter on perihelion motion showed that the above method gave the following data:

* For Earth: Observed value: 4.6 arc sec/century
* For Earth: Relativity value: 3.83 arc sec/century
* For Earth: Aether value: 5.2 arc sec/century
* For Mercury: Observed value: 42.56 arc sec/century
* For Mercury: Relativity value: 43.03 arc sec/century
* For Mercury: Aether value: 44.3 arc sec/century

Now, in doing my theoretical research, I had not set out to enter any contest with Einstein's theory. I simply wanted to get my point across about the nature of magnetic induction and how the aether stores energy in a way that allows its recovery in our electrical machines. To be told I was wrong because there was no aether was extremely frustrating and it was that made me alert to the need to look for what Einstein had missed. Already, in developing my theory from day one, I had been lucky enough to be led from my study of ferromagnetism to see how electrodynamic force interactions can give a force that is needed for unification with gravitation. My target therefore was not the problems which concerned Einstein, but rather deducing G, the constant of gravitation, in terms of e/m, the charge/mass ratio of the electron.

My pre-1960 efforts on that, as summarized in Chapter 4 of that book, show that I was on track. Indeed, equation (24) in that work gave the formula for G in terms of e/m, m/M and the dimensionless fine structure constant (1/137). Here, M was a mass also derived theoretically, but of value virtually equal to that of the neutron, that is very slightly larger than the mass of the proton. G was evaluated as within one part per thousand accord with its observed value.

I therefore knew that aether theory of this kind could bear fruit, but these were early days, and my story here concerns that perihelion motion of the planets.

For many years following this early work, I was struggling with the problem that, in regarding the advance of perihelion as a function of a planet's aether radius, I had introduced a variable that I could not check with observation. I knew that, for body Earth, the upper ionosphere was the appropriate radius to put in the equation. For Mercury, the orbit of which has a high eccentricity, my equation had to allow for the aether radius being staged in having an inner and outer spherical boundary, as a function of that eccentricity. I was, therefore, more satisfied with the result for the Earth than for Mercury. I also recall that Venus could pose a problem, depending upon the true value of the observed advance of perihelion. This was certainly not known, with anything like the certainty that applied to Mercury. I noted that the radius of the aether might need to be less that the radius of the planet in some cases.

It was for this reason that I concentrated my onward efforts on developing the theory as it applied to interpreting the basis of the dimensionless physical constants, because these are known to very high precision. This led me more towards particle physics and the underlying quantum features rather than cosmology, whereas Einstein's theory had been seized upon by those who champion cosmological topics.

It was therefore not until 1976 that I really began to look for other ways of addressing the perihelion problem. Then, starting from scratch, as it were, I made the bold step of seeing if I could begin with Kepler's third law of planetary motion and simply allow for the retardation of energy transfer in a radial perturbation. I adopted the following hypothesis: If a particle of relatively small mass m is acted upon by a particle of relatively large mass M so as to be accelerated towards M at a rate f, then the force which M exerts on m is that applicable when m is a distance s further away from M, s being the distance ft2/2 corresponding to acceleration f in the time t, where t is the time taken for energy to travel from m to M and back to m.

When I allowed for the differential effect of this upon the radial and orbital periods of cyclic oscillation in the formulation of Kepler's law, what emerged immediately in a few lines of school-level mathematics was the formula for perihelion advance derived by Paul Gerber and later adopted by Einstein.

I needed a little time to weigh what this meant to my aether theory, but I thought I had to at least try to get this derivation published. It was in no way dependent upon an argument which required mention of the aether. I was having very great difficulty getting my papers accepted by scientific journals at that time and I even wondered if I might succeed in this quest if by using an alias. That I did, as a test of the journal referee system, and, to my great surprise, the very short two-page paper I then wrote on this Kepler-based derivation of the perihelion formula was accepted. The alias I used was J. N. Kidman, using the maiden surname of my mother-in-law, thinking this was apt name for use as an alias in this instance.

Teachers of Newtonian mechanics who wish to introduce anomalous planetary perihelion motion in their teaching syllabus will find it of interest to look up that paper. Its title is 'Quantum Gravitation and the Perihelion Anomaly' [Lettere al Nuovo Cimento, v. 18, pp. 181-182 (1977)]. No longer published, this was, at the time, an English-text scientific periodical offering rapid publication, the publishers and referee structure being the Italian Institute of Physics. As a side comment, it is interesting to note that Einstein turned to this journal for publication of his later papers when he too found it difficult to satisfy U.S. journal referees.

From then on, dating from that 1977 period, I was on the look out for ways in which to give a more formal basis to this method of solving the perihelion problem and by 1980 I had discovered the correct way forward. However, the fact remains that I wondered how I had been misled by the earlier pre-1960 analysis of Mercury's perihelion anomaly based on aether theory. It is only now (1997) that I am ready to commit to a position on this dual theory proposition. I have come to believe that the energy retardation theory explains the actual perihelion motion, but that what I have said above about compliance with aether angular momentum applies as well. What this means is that the unknown variable, the radius of the aether sphere rotating with the planet, is not determined necessarily by the physical extent of the planetary body. Instead, in order for the aether angular momentum to adjust in compliance with the planet's orbital motion, so as not to interfere with the motion of the matter system, that variable parameter must adopt the right value. In short, the aether spin radius of the planet is determined as a secondary consequence of the Newtonian dynamics of the solar system, as adjusted to bring in the energy retardation in radial Sun-planet orbital perturbations.

For those who are interested in technological issues but have read this far, there is much that I will have to say on the vacuum spin theme as it applies to laboratory tests on a new kind of electrical machine. However, at this point, I bring this particular lecture to an end, but note again that there will be a Part II discourse to follow on 'Why Einstein was Wrong', where I address the subject from a different perspective.