Saturday, March 19, 2011

A Tiny Bit Of Heaviside

I spoke too soon. The last two of the parts for the prototype were in fact mailed by P. (Vielen Danke, P.! Das ist ein wunderbares geschenk und Ich war total ueberrascht mit deine freundliche hilfe!) but they hadn't arrived at my place. In the meantime, I've prepared by disassembling the old prototype to refit the new parts. They're finally here. Assembly clock starts now.

I'm currently reading a biography by Paul Nahin titled Heaviside: A Sage in Solitude. I recommend this book to all amateur physicists as a great introduction to the drama of 19th century science becoming the modern physics that we know now. Heaviside knew, corresponded, argued and propounded theories with a good number of those whose names now fill the textbooks of electromagnetism - Wheatstone, Maxwell, Poynting, Helmholtz, Faraday, Kirchhof, Boltzmann, J.J.Thomson, Searle, Tesla, Wiener etc etc.

Heaviside himself in his last days attempted to draw an analogy between gravity and electromagnetism (source: Nahin, Paul; Oliver Heaviside: A sage in solitude, pg 307, 1987 IEEE Press) "with the key link being the localization of energy in a field." Einstein had better luck than Heaviside in finding a formulation for gravity within 12 years of Heavisides own attempts, nonetheless, it is instructive to see what Heaviside made of the link between electromagnetism and gravitation.

Begin Quote "If one brings two charges together, energy is required to overcome the repulsion, and it is this energy that goes "into the field" (giving a positive field energy density in space). Two masses, on the other hand, attract each other and it takes energy to keep them apart, leading to the (strange) result of a negative field energy density for space in the case of gravitational models. This result, implying the presence of less than no energy in space, so bothered maxwell he gave gravity up as beyond 19th century physics. Heaviside too reached the same conclusion:" must be confessed that [negative energy density] is a very unintelligible and mysterious matter."

Heaviside based his analogy on an ether ("It is as incredible now as it was in Newton's time that gravitative influence can be extended without a medium..."), and reached the conclusion that gravity effects most likely propagate "immensely fast," probably much faster than the speed of light. This is all anti-relativistic, but of course Heaviside was writing this 12 years before Einstein published his Special Theory of Relativity. "

End Quote

One might wonder what less than no energy in a spatial region might be -perhaps, to have less than no energy in space might for example be energy that moves and carries mass away from the region of space, altering the local gravitational potential of the space itself.

Perhaps gravity's negative energy field is an acknowledgement that the energy is trapped in an 'inductive' field configuration and is therefore a reacting-entity that operates upon processes causing energy exchange in the local region of the inductive field.

We know that we can classify capacitances as positive impedances and inductors as negative impedances already. To associate positive and negative field energy correspondingly to the two kind of elements is only natural then. And we would see that a gravitational field is an energy field holding a spinning, inductively suspended earth as the central motor of the sun gyroscopically attempts to spin the earth out of the solar plane (in which our planet executes its orbits around the sun) and reaps the gyroscopic result that the input and output channels are orthogonalized - the spins the earth out the soalr plane and the earth responds by executing an orbit in the solar plane. Maybe we have difficulty comprehending gravity with our electricalized physics models because we have not used the concept of inductively suspended angular momentum as the equivalent of the electrical coil. Just a thought.

Another counterintuitive fact about electricity that Heaviside reasoned out regarding electromagnetism concerns a topic researched by Poynting first and slightly later, completely independently by Heaviside - the direction of flow of energy in a wire carrying an electric current. Like in the case of a gyroscope (my earlier prototype, whose results you have seen, most prominently in the Inductive Effect video) or in the case of an inductively suspended spinning wheel(as in my new prototype I will be testing soon), the direction of the energy's expressed movement and the direction of the wire (if it is assumed to be straight for the purpose of the analysis)are orthogonal to each other.

Heaviside and Poynting's research on this topic created a revolution in the field of eletromagnetism by changing the way physicists would model electromagnetism forever. Here is a passage regarding this important singular research with a suggestion of gyroscopic overtones of great importance to us as seekers of flying machines, from the book "Oliver Heaviside: A Sage in Solitude" by Paul J Nahin.

Pages 115-119

Begin Quote

Energy And Its Flux

By 1884 the principle of the conservation of energy was well established, but it hadn't been many years before when the idea of just energy, alone, was a new and strange one. The concept of force was the prominent one as late as the 1850s, for example, and it seemed to be intuitively the 'thing' that should be the hinge pin of dynamics, whether the system under consideration be mechanical or electromagnetic. The development of thermodynamics in the early and mid parts of the 19th century, however, began the process of elevating energy and changes in energy to the level of importance we attach to them today. Writing in 1887 Heaviside expressed this as, "There are only two things going, Matter and Energy. Nothing else is a thing at all; all the rest are Moonshine, considered as Things."

The ability to store what seemed to be astonishing amounts of energy in the newly perfected (1881) lead acid battery (by Camille Faure) led to a special flurry of interest in the matter, among even the general public. There was something about storing and transporting electrical energy (although a battery is really a box of chemicals) that was special, and particularly appealing to the Victorian mind. Coal was just a dirty rock out of the ground, while electricity was modern!

So, with all this interest in electrical energy, it is not surprising that people were also paying attention to its more abstract properties such as its conservation and even how it moves about. There is more to the conservation of energy, however than may be apparant at first glance. As Heaviside put it in 1891,

The principle of the continuity of energy is a special form of that of its conservation. In the ordinary understanding of the conservation principle it is the integral [total] amount of energy that is conserved, and nothing is said about its distribution or its motion. This involves continuity of existence in time, but not necessarily in space also. But if we can localize energy definitely in space [my emphasis- this is a most important idea, one we'll pursue with interest], then we are bound to ask how energy gets from place to place. If it possessed continuity in time only, it might go out of existence at one place and come into existence simultaneously at another. This is sufficient for its conservation. This view, however, does not recommend itself. The alternative is to assert continuity of existence in space also, and to enunciate the principle thus: When energy goes from place to place, it traverses the intermediate space.

And then a little later in the same passage, writing of the mathematical result that precisely specifies just how electromagnetic energy "traverses the intermediate space", he said,

This remarkable formula was first discovered and interpreted by Prof. Poynting, and independently by myself a little later. It was this discovery that brought the principle of continuity of energy into prominence.

Heaviside was referring, of course, to John Henry Poynting (1852-1914). Professor of physics at the University of Birmingham, Poynting combined his considerable ability in physics with that f a skilled mathematician and this double edge to his powers led to the writing of many papers which Oliver Lodge called "sledge-hammer communications". This certainly was the right way to describe the impact of Poynting's powerful paper "On the transfer of energy in the electromagnetic field," published by the Royal Society in its Philosophical Transactions in 1884. Starting with the Maxwellian idea of localized field energy Poynting was able to derive the elegantly simple vector expression E x H, now called the Poynting vector, for the flow of electromagnetic energy through space.

Poynting's paper, as well as some of the odd implications of the result, attracted a good deal of attention. Oliver Lodge, in particular, was tremendously impressed by it and wrote a curious paper (with a very long title!) in response. Lodge was particularly fascinated by the idea of being able to track a individual "bit of energy", writing ".. the route of the [bit of] energy maybe discussed with the same certainty that its existence [is] continuous as would be felt in discussing the route of some lost luggage which turned up at a distant station in however battered and transformed a condition." This semi-metaphysical paper seems not to have had much impact, but its opening words, describing Poynting's paper were prophetic, calling it "a paper which cannot but exert a distinct influence on all future writings treating of electric currents."

One of its most profound influences was the complete overthrowing of how people think of energy flowing in a wire carrying an electric current. In fact according to ExH the electromagnetic energy doesn't flow through the wire but into it, sideways from the fields surrounding the wire! This seemingly "crazy" conclusion was not greeted with Lodge's excitement by many of the "old-time" electricians. In 1891, for example, Silvanus Thompson and John Sprague became embroiled in a dispute over the nature of energy flow in electric circuits. Sprague held tot he old view of energy transfer through a wire, while Thompson argued for the revolutionary new viewpoint. The debate appeared over an extended period of time in the Correspondence sectin of The Electrician, and finally the journal felt it necessary to terminate the issue with an editorial: ..although we undoubtedly side with Prof. Thomson's views, there is no doubt much which appears, at first sight, highly artificial in the elaborate structure of lines of electric and magnetic force and induction, complicated still further, as it is, by the more recently discovered lines of energy-flow .. the idea that energy is located at all, and that, when it changes it position, it must move along a definite path, is quite a new one. The law of the conservation of energy implies that energy cannot disappear from one place without appearing in equal quantity somewhere else; but although this fact has long been accepted, it is only within the last few years that the idea of transference of energy has been developed, or that anyone has attempted to trace out an actual path along which energy flows when it moves from place to place. The idea of an energy current is of more recent date than the electro-magnetic theory, and is not to be found explicitly stated anywhere in Maxwell's work. I believe that the first time it was applied to electrical theory was in the pages of The Electrician, by Mr. Oliver Heaviside, to whom so much of the extension of Maxwell's theory is due. The idea as also independently developed and brought to the notice of the Royal Society in a Paper by Prof. Poynting.

In fact, The Electrician was perfectly correct in this proud claim for the priority of Heaviside. Poynting's paper certainly did not appear in print until sometime after June 19, 1884 and yet, in the June 21, 1884 issue of The Electrician Heaviside wrote (in a passage entitled "Transmission of Energy into a Conducting Core"):

The direction of maximum transference [of energy] is therefore perpendicular to the plane containing the magnetic force and the current directions, and its amount per second proportional to the product of their strengths and to the sine of the angle between their directions.

These words are not remembered today, and it wasn't until Jan 10, 1885 that Heaviside published the same result as is found in Poynting's paper (which is why historians today always write of Heaviside's discovery as dating from "the year after" Poynting's). Heaviside took a somewhat different view of history, however, and while he never disputed Poynting's credit, he also took care to remind his readers of the June 21 date, as when he wrote (in March 1885):

The transfer of energy in a conductor (isotropic) takes place not with the wire, but perpendicular thereto, as I showed in The Electrician for June 21, 1884, thus being delivered into a wire from the dielectric outside.

It is not clear when Heaviside first learned of Poynting's paper, but there is an interesting note on one of his copies of Nature (dated March 26, 1885) which was prompted by a report on a mechanical model (made of wheels and rubber bands) invented by FitzGerald, "illustrating some properties of ether." In particular, this model showed how "the energy of the medium was conveyed into" was a wire and "not along its length according with that Prof. Poynting has recently shown to be the case in all electric curents." Heaviside's note shows he was by them most familiar with Poynting's work, and thought his own more comprehensive:

But it is only true for conduction current, not for all currents. Not true in the dielectric [where the displacement current cannot be ignored]. The general formula for energy current ...[was] proved by me for conductors in the summer of 1884, and in January 1885 extended to all media non-homogenous as regards capacity, conductivity and permeability.

While Poynting may have beatenHeaviside into recognized print, and while Poynting's mathematics was impeccable, it is curious to note that his physics has a flaw which seems to have fone unnoticed, or at least uncommented upon, for the last one hundred years, except for Heaviside's own comments about it. Even with impeccable mathematics, however, many found Poynting's (and Heaviside's) ideas on energy transfer hard to believe, and not all of the skeptics were "old timers" like John Sprague. As Professor J.J. Thomson wrote two years after Poynting's paper,

This interpretation [the Poynting vector] of the expression for the variation in the energy seems open to question. In the first place it would seem impossible a priori to determine the way in which energy flows from one part of the field to another by merely differentiating a general expression for the energy in any region with respect to time, without having any knowledge of the mechanism which produces the phenomena which occur in the electromagnetic field...

These words show Professor Thomson, the bright young academic star of English physics at the time, was still committed to the Maxwellian goal of mechanical model building. But eventually even Thomson came around and in 1893 he called Poynting's result "a very important theorem" and "of great value." There was no mention of Heaviside's contributions to the energy flux theorem by Thomson, and I find this particularly ironic because this slighting by Thomson was to be his fate too, with another equally important result. And to make it doubly ironic, Heaviside was also involved in this (Heaviside's role is again forgotten,, along with Thomson's).

End Quote

Asa parting thought, let me remind you that as J. J. Thomson pointed out in 1893, the Poynting Vector product equation does indeed require a priori knowledge of the mechanism which produces the phenomena rather than being a general energy expression and such is also the fate of gyroscopic and inductively suspended angular momenta

This tells us that the true understanding of the phenomena rests on a higher level model that incorporates this a priori knowledge.