THE PHYSICS OF CREATION: LECTURE NO. 2
Gravitation: An Introduction: Continuation
Gravitational Energy Flow: 1979-1980
This Lecture No. 2 continues, now under a heading which is updated to the 1979-1980 period, that of this author’s contribution to the subject.
Having shown that the energy E of the interaction between two bodies has the distribution illustrated below:
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we can see that in both cases any increase or decrease in E occurs exclusively at the range x from either body.
Energy shed by the reference body (kinetic energy, for example) and fed to the interaction has, in the Coulomb case, to traverse, on average, a distance x to reach the locality of its deployment and, in the gravitational case, the distance is, on average, 2x/3.
Now, ignoring the Coulomb interaction for the moment, we will concentrate our attentions upon the gravitational interaction, having the Gerber theme in mind. Recall Fig. 1:
and ask yourself how energy shed by the sun and by the planet travels into the intervening space and then finds the equilibrium which depends upon the changed distance from sun to planet. It would be foolish to think that it travels along a pencil thin line drawn between sun and planet. We cannot assume that the interaction energy is all deployed into two core regions, one in the sun and one in the planet, because our derivation of the energy distribution pattern tells us otherwise. It must lie at points spread throughout space, where x is a range in all directions centred on either body.
This invites the suggestion, therefore, that there has to be energy transfer as between sun and planet and via a route that takes the longer journey in space. A small perturbation may deploy some energy from the kinetic energy of the sun, which energy package makes that journey of mean length 2x/3. Its initial destination is not the planet, but rather a multitude of staging points in surrounding space, there being energy then drawn into the planet from those staging points, but having to travel a further mean distance of 2x/3.
This means that we face the problem of allowing for each energy package to make its journey over a wide range of path lengths, taking different periods of time. We can say that any energy in transit at any instant will not be effective in asserting forces as between sun and planet. This is why we need to know how much energy is actually on the move at any instant, being neither kinetic energy or effective as interaction energy.
Now there is a formula in Newtonian theory which says that mass falling in a gravitational field travels a distance that is proportional to the square of its time of fall t. If we had to say how long it would take, on average, for a number of such masses to travel with the same acceleration but from different heights, then we would declare that we must take the root mean square of t as it applies to that mass system. We can expect, therefore, that, assuming those energy packages travel at the same speed, which Paul Gerber took as the speed of light, we are interested in the root mean square of the distance energy has to travel in making that double journey over the average range of 2x/3.
The fact that the gravitational interaction energy is represented by a linear relationship proportional to x means that we need to integrate x2 over that linear range and divide the result by 2x/3 to obtain a relationship:
where T is the root mean square value of the time retardation involved in energy transfer in the overall two-part journey between sun and planet.
Given this value of T it is then a very easy task to deduce how this affects Newton’s Law of Gravitation.
As shown in the U.K. Institute of Physics paper in which this theory is recorded, the energy deficit, meaning the amount of energy in transit between sun and planet at any instant is then:
where G is the constant of gravitation, M is the mass of the sun and m is the mass of the planet. The centrifugal acceleration f of the planet is v2/x, where v is the orbital velocity in a circular orbit of radius x. This acceleration acting for the retardation period T gives the measure of the displacement under the central gravitational force corresponding to the deficit energy quantity given by equation (9).
From equations (8) and (9) that energy deficit becomes:
Now the quantity -GMm/x is the gravitational potential energy of the system. Therefore the effect of retardation, if we assume that gravitation involves a law of force conforming with the energy distribution of the magnetic interaction, is to increase G as it applies in Newton’s Law of Gravitation effectively be the factor:
Note that this is a very simple conclusion from a simple proposition as based on really determining the form of the interaction energy distribution in the space enveloping sun and planet. We have not had to wander through a complicated maze of four-space equations and infer that the mass of the sun distorts space itself. All we are saying is that, if the energy which moderates the motion of the planet about the sun takes time in transit to adjust to the elliptical orbital motion, then that energy cannot also be part of the kinetic energy of the planet. In short, the radial oscillations of the orbit will be slower than the period of revolutionary period of the orbit.
To translate energy into a force expression we need to remember that the conservation of planetary angular momentum renders v inversely proportional to x, making the v-dependent energy expression in (10), inversely proportional to x3. This means that, upon differentiation of the energy term to get a force term, we find that the factor in (11) converts to:
Thus in a force equation the value of G needs to be increased by this factor in order to account for retardation effect. This modifies Newton’s Law of gravitation:
to:
these being laws of motion expressed in polar coordinates (u,r), where u is 1/x and h is vx.
Equation (14) is the law of gravitation which emerges from Einstein’s General Theory of Relativity, albeit after a very convoluted passage through mathematics which few scientists can understand, and it is therefore very instructive to see that we can derive the same equation on a more logical basis and so have an explanation that is consistent with the astronomical observations that are relied upon to support Einstein’s explanation of the planetary perihelion phenomenon.
Discussion
Having now overtaken Einstein’s contribution to the theory of gravity by showing how we can derive the law of gravitation which does have the refined features pertaining to anomalous planetary perihelion motion, but by an argument which develops the link with electromagnetic theory, we reach the threshold of an major onward advance, one which Einstein could not begin to contemplate.
Remember that we have exploited the fact that the mutual repulsion of two like electric charges by virtue of their Coulomb interaction is associated with a field energy deployment that tries to get as remote as possible from either charge. In contrast the two in-line like polarity electric charges moving in the same direction indicated an attraction coupled with the magnetic field energy seeking to get as close as possible to either charge. By ‘possible’ here is meant ‘consistent with the overall energy potential complying with the empirical measure of the force action between the two charges’. Note that I was mindful of the need to find a way of linking gravitational attraction and magnetic attraction. That reference to ’empirical measure’ was applicable only to the Coulomb interaction. As to the magnetic interaction I was, at first, indulging in a little wishful thinking. I knew that no one had ever measured the actual forces effective between two isolated charges owing to their electromagnetic interaction. Everything concerning that, as discussed thoroughly in Clerk-Maxwell’s famous work ‘A Treatise on Electricity and Magnetism‘, 1891, had involved hypothesis and assumption coupled with empirical data derived from actions involving a closed current circuit.
However, long before explaining gravity was on my agenda, I had discovered a method of deriving from first principles the law of electrodynamic force as between two discrete electric charges in general motion. That generic law did tell me how electrodynamic forces of mutual attraction are set up as between two like-polarity electric charges, and, indeed, this was found to be a special case where those charges move in directions that are mutually parallel.
Eventually my discovery was accepted for publication by a peer reviewed scientific journal. I refer to my 1969 paper ‘The Law of Electrodynamics’ [4]. Here I was treading a pathway in a direction contrary to orthodox teaching, but I knew I was on firm ground. That ground became all the firmer when Dr. Eagles, after seeing my calculations of field energy distribution for the Coulomb interaction, and for the electrodynamic case for the in-line moving charge interaction, then computed the magnetic field energy deployment for the general case [3]. His findings made it clear that what I was saying about interaction energy trying to move as far from the charges as possible, if there was to be mutual attraction, was correct.
A study of the spatial magnetic field energy distribution in the electromagnetic interaction of two moving charges reveals a horrible pattern which changes illogically as the charges move in different directions. More than this, however, as Dr. Eagles concluded, the orthodox assumption based on the thought that retardation of electric field action accounts for electromagnetic force interaction is erroneous. In his words, put less bluntly as can be seen from the abstract of the paper, reference [3], that assumption “appears to be misleading”.
The problem with all this, one which beset Einstein’s efforts without him even suspecting that it was a problem, was simply the fact that the Lorentz force law is invalid as applied to the fundamental problem of charge interaction as between discrete charges. With it the orthodox theory of the magnetic field collapses as well, because the field energy can only be correctly determined if the fields considered are set up by electrical charges which are part of a closed circuital flow of current.
The story I have to tell on this is lengthy and will occupy several later Lectures in these web pages, so I will close this account by a brief further mention of the efforts of Paul Gerber. Look at the reference data below. Gerber’s paper was published in Germany in 1898, one hundred years ago and some 17 or so years before Einstein announced to the world that he had a new law of gravitation which gave explanation for the anomalous perihelion advance of planet Mercury [5].
Read its title! The English translation is ‘The space and time propagation of gravitation’. Take note that Gerber, arguing speed of light propagation of the gravitational action, derived a result which formulated the term expressing the 43 second of arc of anomalous advance per century. Take further note, if you ever care to compare that formulation with the one presented by Einstein in his seminal paper on the subject, that not only the formula but the algebraic symbols in the formula are identical to those used by Gerber. Yet Einstein did not acknowledge Gerber’s prior contribution!
Paul Gerber was a schoolmaster, deceased by the time Einstein’s paper appeared, but, well, I will not enlarge on this, save to say that when all this came to light in 1917, within a year or so of the appearance of Einstein’s paper, there was sequel. It is worthy of the attentions of those who write about the history of science. Begin by looking up the contributions by Oppenheim [6] and Seelinger [7, 8] in the same journal that published Einstein’s paper. Yes, you will find that Gerber did make a mistake in his mathematical analysis, but he obtained the correct formula by applying the idea that gravitation transferred between sun and planet at the speed of light. His error, one repeated in electrical analysis by so many of our orthodox physicists, was in imagining that there is a retarded action rather an actual transfer of energy and not then seeing that that energy could not all travel along a pencil-thin line drawn between sun and planet. His critics jumped on an error in his analysis and ignored the substance of his argument. That error should have been corrected in the 1916-1920 period, before Einstein’s theory got the hold it has today. I have shown how it may be corrected, thanks also to encouragement from the words of Oliver Heaviside and Leon Brillouin.
I could, as I did in the last few words of my Institute of Physics paper [1], point to the related concerns of Moon and Spencer [9]:
“.. who have contended that relativistic electrodynamics leads us away from accepted magnetic field theory in treating this problem (that is the doubt concerning of our knowledge of the law for interaction between two isolated charges in motion).”
I concluded that 1980 Institute of Physics paper, which has formed the basis of this Lecture, by referring readers to the discussion chapter of my book ‘Physics Unified’ [10]. It was published in that same year, 1980, and indeed it was written essentially to update my early writings by bringing the substance of that Institute of Physics paper into book form. The book includes the onward analysis of gravitational theory leading to the derivation of G, the constant of gravitation, in terms of the charge/mass ratio of the electron.
I ask, if you, the reader, are a scientist interested in gravitation. If so, what has been your opinion on my contribution? If you have had no opinion because you have not heard of my work, then why is that? Does publication of a paper such that discussed above not warrant rejection if it is deemed wrong? Scientists of the 1916 Einstein era jumped on their chance to attack Gerber’s paper, which anticipated Einstein’s result, given that they had seen an error in his analysis. Why are they not jumping on my efforts? Or rather, why are they not jumping for glee at my having discovered the route to knowledge concerning G that Einstein missed?
If you are a student setting out on a career in physics, then try writing an essay explaining and justifying the differences between my explanation of the anomalous perihelion motion of the planet Mercury and that delivered by Einstein. See if that helps you to convince yourself which is right!
Remember that the key to the unification problem is the major step of abandoning field theory as such and working with energy proper, even though field theory works well for the Coulomb electrostatic interaction. The simple fact is that field theory, whatever its roots and its success, in the teachings of Clerk Maxwell, fails us when we address the problem of how two discrete charge elements interact electromagnetically.
References
[1] H Aspden, ‘The inverse square law of force and its spatial energy distribution’, J. Phys. A: Math. Gen, v. 13, pp. 3649-3655 (1980).
[2] H Aspden, ‘The spatial energy distribution for Coulomb interaction.’, Lett. Nuovo Cimento, v. 25, p. 456 (1979).
[3] D M Eagles and H Aspden, ‘The spatial distribution of the interaction contribution to the magnetic-field energy associated with two moving charges’, Acta Physica Polonica, v. A57, p. 473 (1980).
[4] H Aspden, ‘The law of electrodynamics’, Journal of the Franklin Institute, v. 287, p. 179 (1969).
[5] P Gerber, Z. Math. Phys., v. 43, p. 93 (1898).
[6] S Oppenheim, Ann. Phys., Lpz., v. 53, p. 163 (1917).
[7] H Seelinger, Ann. Phys., Lpz., v. 53, p. 31 (1917).
[8] H Seelinger, Ann. Phys., Lpz., v. 54, p. 38 (1917).
[9] P Moon and D E Spencer, Journal of the Franklin Institute, v 257, p. 305 (1954)
[10] H. Aspden, ‘Physics Unified’, Sabberton Publications, P.O. Box 35, Southampton, England.
At this stage it is recommended that the reader should procure one of the remaining copies of my book Physics Unified, which is still in print or borrow the book from a university library or public library which has it in stock. The book is a stock item at the Stanford University Bookstore in California, USA and can be purchased from the author (see related web page Aspden Publications) or by using an on-line book ordering facility such as is provided by accessing www.waterstones.co.uk or www.bookpages.co.uk and entering the name of the author: Harold Aspden, or the relevant ISBN No. 0 85056 0098 or ISBN 0 85056 0101, for hardback or softback, respectively, as your search query. Note that the softback version will be out-of-print in the very near future.
Students are recommended to work through the sequence of 10 Tutorial Lessons before moving on to the next Lecture.
