The reply to the second Catt Question, given by Josephson was not followed by any great response until then. In fact as shown by this lecture the situation is not well understood.
Prof Lewin can be heard to remark, " the charge build up could be solved using dsQ but I do not know a method to do so". He then justifies Maxwells displacement current as a brilliant solution to a very " messy" problem. This solution actually avoids detailed analysis! That is, any dynamic structures synthesised from the model elements are ignored by assumption.
Both replies rely on the Spaciometry of Electromagnetic Theory and it is as well to consider Spaciometric methods and what they encode.
I have in earlier blogposts explored the spaciometry of the sphere, and drawn attention to the Newtonian Reference Frame that underpins it. Indeed thei reference frame can be traced back to ancient times, But Newton gives it its Quintessential expression.
It is well to observe that Newton deliberately designed his philosophy to acomadate anything in generality. That is in analogy, which is derived from the Eudoxian form of "reasoning" called Logos Analogos.This itself was the fundamental reasoning of the Pythagorean Scholars at the level of Mathematikos, and itself is found in the reasoning of Vedic and Sanskrit scholars of Astrology, in fact in the reasonings of all adept Astrologers. You will shortly reads Newtons opinion on absolute measure. But let me clarify his intent: absolute measure is defined by changes in dynamic spherical,motions. These are the only self contained infinite magnitudes that enwrp the infinite fractal structure he eloquently describes. The sphere is so special a philosophical tool of measure that it passes all analysis, and underpins all absolute synthesis.
The Newtonian Spaciometry is an adjunct to Newtonian Fluid Motive Philosophy, or what i have previously called Shunya Field Theory. My prior theory i have to update in terms of the empirical findings that underpin Catt Theory c. This i will do as i progress.
Modern mathematics has attempted to encode or model spatial measures algebraically. The divergence and grad are 2 related models of source and sink and steepness of flow or motion from one position to another. The curl is an algebraic process that attempts to measure Local differences in a velocity " field" and to highlight potential rotation of a free moving boundary.. It is called the vorticity.
Despite its name it does not measure vortices! It's measure is the difference in the velocity in a combinatorial order across a velocity field. It is very much akin to the divergence except that it is a vector not a scalar, and the process of arriving at it is through a cross product.
This short introductory series gives a clear description of the different modelling tools.
We can see that we have to physically measure a vector field. We also have to physically measure a scalar field. What are these empirical measures? A bit of flotsam or jettison moving about in the flow.. We can actually do this measurement for a electrodynamic field and a magneto dynamic field with suitable test objects.
We have to recognise what Newton said in devising his reference frame.
As the order of the parts of time is immutable, so also is the order of the parts of space. Suppose those parts to be moved out of their places, and they will be moved (if the expression may be allowed) out of themselves. For times and spaces are, as it were, the places as well of themselves as of all other things. All things are placed in time as to order of succession; and in space as to order of situation. It is from their essence or nature that they are places; and that the primary places of things should be moveable, is absurd. These are therefore the absolute places; and translations out of those places, are the only absolute motions. But because the parts of space cannot be seen, or distinguished from one another by our senses, therefore in their stead we use sensible measures of them. For from the positions and distances of things from any body considered as immovable, we define all places; and then with respect to such places, we estimate all motions, considering bodies as transferred from some of those places into others. And so, instead of absolute places and motions, we use relative ones; and that without any inconvenience in common affairs; but in philosophical disquisitions, we ought to abstract from our senses, and consider things themselves, distinct from what are only sensible measures of them. For it may be that there is no body really at rest, to which the places and motions of others may be referred. But we may distinguish rest and motion, absolute and relative, one from the other by their properties, causes and effects. It is a property of rest, that bodies really at rest do rest in respect to one another. And therefore as it is possible, that in the remote regions of the fixed stars, or perhaps far beyond them, there may be some body absolutely at rest; but impossible to know, from the position of bodies to one another in our regions whether any of these do keep the same position to that remote body; it follows that absolute rest cannot be determined from the position of bodies in our regions. It is a property of motion, that the parts, which retain given positions to their wholes, do partake of the motions of those wholes. For all the parts of revolving bodies endeavour to recede from the axis of motion; and the impetus of bodies moving forward, arises from the joint impetus of all the parts. Therefore, if surrounding bodies are moved, those that are relatively at rest within them, will partake of their motion. Upon which account, the true and absolute motion of a body cannot be determined by the translation of it from those which only seem to rest; for the external bodies ought not only to appear at rest, but to be really at rest. For otherwise, all included bodies, beside their translation from near the surrounding ones, partake likewise of their true motions; and though that translation were not made they would not be really at rest, but only seem to be so. For the surrounding bodies stand in the like relation to the surrounded as the exterior part of a whole does to the interior, or as the shell does to the kernel; but, if the shell moves, the kernel will also move, as being part of the whole, without any removal from near the shell. A property, near akin to the preceding, is this, that if a place is moved, whatever is placed therein moves along with it; and therefore a body, which is moved from a place in motion, partakes also of the motion of its place. Upon which account, all motions, from places in motion, are no other than parts of entire and absolute motions; and every entire motion is composed of the motion of the body out of its first place, and the motion of this place out of its place; and so on, until we come to some immovable place, as in the before-mentioned example of the sailor. Wherefore, entire and absolute motions can be no otherwise determined than by immovable places; and for that reason I did before refer those absolute motions to immovable places, but relative ones to movable places. Now no other places are immovable but those that, from infinity to infinity, do all retain the same given position one to another; and upon this account must ever remain unmoved; and do thereby constitute immovable space. The causes by which true and relative motions are distinguished, one from the other, are the forces impressed upon bodies to generate motion. True motion is neither generated nor altered, but by some force impressed upon the body moved; but relative motion may be generated or altered without any force impressed upon the body. For it is sufficient only to impress some force on other bodies with which the former is compared, that by their giving way, that relation may be changed, in which the relative rest or motion of this other body did consist. Again, true motion suffers always some change from any force impressed upon the moving body; but relative motion does not necessarily undergo any change by such forces. For if the same forces are likewise impressed on those other bodies, with which the comparison is made, that the relative position may be preserved, then that condition will be preserved in which the relative motion consists. And therefore any relative motion may be changed when the true motion remains unaltered, and the relative may be preserved when the true suffers some change. Upon which accounts, true motion does by no means consist in such relations. The effects which distinguish absolute from relative motion are, the forces of receding from the axis of circular motion. For there are no such forces in a circular motion purely relative, but in a true and absolute circular motion, they are greater or less, according to the quantity of the motion. If a vessel, hung by a long cord, is so often turned about that the cord is strongly twisted, then filled with water, and held at rest together with the water; after, by the sudden action of another force, it is whirled about the contrary way, and while the cord is untwisting itself, the vessel continues for some time in this motion; the surface of the water will at first be plain, as before the vessel began to move: but the vessel, by gradually communicating its motion to the water, will make it begin sensibly to revolve, and recede by little and little from the middle, and ascend to the sides of the vessel, forming itself into a concave figure (as I have experienced), and the swifter the motion becomes, the higher will the water rise, till at last, performing its revolutions in the same times with the vessel, it becomes relatively at rest in it. This ascent of the water shows its endeavour to recede from the axis of its motion; and the true and absolute circular motion of the water, which is here directly contrary to the relative, discovers itself, and may be measured by this endeavour. At first, when the relative motion of the water in the vessel was greatest, it produced no endeavour to recede from the axis; the water showed no tendency to the circumference, nor any ascent towards the sides of the vessel, but remained of a plain surface, and therefore its true circular motion had not yet begun. But afterwards, when the relative motion of the water had decreased, the ascent thereof towards the sides of the vessel proved its endeavour to recede from the axis; and this endeavour showed the real circular motion of the water perpetually increasing, till it had acquired its greatest quantity, when the water rested relatively in the vessel. And therefore this endeavour does not depend upon any translation of the water in respect of the ambient bodies, nor can true circular motion be defined by such translation. There is only one real circular motion of any one revolving body, corresponding to only one power of endeavouring to recede from its axis of motion, as its proper and adequate effect; but relative motions, in one and the same body, are innumerable, according to the various relations it bears to external bodies, and like other relations, are altogether destitute of any real effect, any otherwise than they may perhaps partake of that one only true motion. And therefore in their system who suppose that our heavens, revolving below the sphere of the fixed stars, carry the planets along with them; the several parts of those heavens, and the planets, which are indeed relatively at rest in their heavens, do yet really move. For they change their position one to another (which never happens to bodies truly at rest), and being carried together with their heavens, partake of their motions, and as parts of revolving wholes, endeavour to recede from the axis of their motions. Wherefore relative quantities are not the quantities themselves, whose names they bear, but those sensible measures of them (either accurate or inaccurate), which are commonly used instead of the measured quantities themselves. And if the meaning of words is to be determined by their use, then by the names time, space, place and motion, their measures are properly to be understood; and the expression will be unusual, and purely mathematical, if the measured quantities themselves are meant. Upon which account, they do strain the sacred writings, who there interpret those words for the measured quantities. Nor do those less defile the purity of mathematical and philosophical truths, who confound real quantities themselves with their relations and vulgar measures. It is indeed a matter of great difficulty to discover, and effectually to distinguish, the true motions of particular bodies from the apparent; because the parts of that immovable space, in which those motions are performed, do by no means come under the observation of our senses. Yet the thing is not altogether desperate: for we have some arguments to guide us, partly from the apparent motions, which are the differences of the true motions; partly from the forces, which are the causes and effects of the true motions. For instance, if two globes, kept at a given distance one from the other by means of a cord that connects them, were revolved about their common centre of gravity, we might, from the tension of the cord, discover the endeavour of the globes to recede from the axis of their motion, and from thence we might compute the quantity of their circular motions. And then if any equal forces should be impressed at once on the alternate faces of the globes to augment or diminish their circular motions, from the increase or decrease of the tension of the cord, we might infer the increment or decrement of their motions; and thence would be found on what faces those forces ought to be impressed, that the motions of the globes might be most augmented; that is, we might discover their hindermost faces, or those which, in the circular motion, do follow. But the faces which follow being known, and consequently the opposite ones that precede, we should likewise know the determination of their motions. And thus we might find both the quantity and the determination of this circular motion, even in an immense vacuum, where there was nothing external or sensible with which the globes could be compared. But now, if in that space some remote bodies were placed that kept always a given position one to another, as the fixed stars do in our regions, we could not indeed determine from the relative translation of the globes among those bodies, whether the motion did belong to the globes or to the bodies. But if we observed the cord, and found that its tension was that very tension which the motions of the globes required, we might conclude the motion to be in the globes, and the bodies to be at rest; and then, lastly, from the translation of the globes among the bodies, we should find the determination of their motions. But how we are to collect the true motions from their causes, effects, and apparent differences; and, vice versa, how from the motions, either true or apparent, we may come to the knowledge of their causes and effects, shall be explained more at large in the following tract. For to this end it was that I composed it.
We do often confuse the measure with the phenomenon, and this is to be avoided at all costs.
What we see and what we measure, and by measuring represent may differ substantially.. I hope to donsetrate that the spherical vortices and trochoidal flow patterning we see or experience may be represented by fractal generator sculptures to a certain extent, enough to give insight into the larger dynamic.
Heaviide, in emphasising Gauss law in Maxwell's system, introduced a spaciometric measure for Charge, devised by Gauss. Without defining charge, the method assigns a boundary to capture it. Charge is gained or lost relative to that boundary. Thus Gauss law is the definition of Divergence.
The gaining or loss of this undefined charge has an associated " vector" field. That is we can measure this charge being gained or lost across this boundary. How can we measure what is undefined?
The grad measure is used to guide the definition of the measure of charge flow or displacement.
Finally , still undefined but now conceived as a fluid charge is investigated by its vector field description to see if it has local variations in the vectors. This flow of charge is variously assumed to be a diffusion flow or a light speed flow. The "particles " characteristics change from an electron to a photon accordingly! The curl is used to model this, and this is where it gets it's name. By curling the fingers around the supposed charge carrying wire in the direction of the magnetic field twistors/ vectors we supposedly get the electric field vectors, or the electric current / charge vectors describing their flow field..
I hope it is clear that these models actually fudge the empirical data subtly. It is not the convoluted nature of them or the tautological definitions. It is the careless application of a differential calculus algorithm to the empirical data, which is either ill defined or defined to suit.
Here prof Lewin defines a charge as an alpha source. From his he defines a through current. Because we cannot utilise alpha particles as charge sources we use beta particles, or electrons. However when we try to calculate the speed of the electric current through a wire , the beta particles do not approach light speed..so what does this speed or vector actually mean?
The propagation of a strain wave in an electric fluid is precisely what Maxwell meant. But his contemporaries continued to misunderstand him because wave theory was not accepted until youngs double split experiments, and a medium, the aether was not empirically verifiable. It was not until Einstins 1905 papers that particle physics accepted the strange wave particle duality as a compromise., to heal a divided science of physics.
Tesla, Heaviside,Poynting were on the outside of the consensus. They neither accepted the electron or the photon or the wave particle duality.. They recognised Relativity as a fudge to cleverly retain the aether without calling it that. It was called a Hamiltonian or a Lagrangian instead.
We can see from prof Lewins presentation that an impressive structure is in place, due mostly to Heaviside., but he does not tackle the empirical problems of the battery and the signal in his introductory course, he glances through it at the end of his course.