The main difficulty is to account for the observed principle that "opposites attract while the same repels".
Right there, as an author I experience a linguistic difficulty. While opposites in some sense is relatively defined within any context, the choice of word fir "the same" is not.
The question is immediately begged, the same what?. It should be begged at opposites, but that phrase has an alternative use of its own which makes it less questionable, that is less provoking of the begging question.
The initial idea was to list materials with these electric tension properties in triboelectric lists. Earlier, magnetic rocks had regions identified as directionally dynamic, and these exhibited attraction and repulsion in a tribomagnetic list. Here the tribulation was not merely friction, but also heating, quenching and hammering!
The behaviours of these material thus did not exhibit this strong behavioural statement!
We now fully recognise dia magnetism, paramagnetism, ferro magnetism, anti ferro magnetism. Similarly we recognise dielectric , insulators, conductors, plasmas in the Tribology electric lists.
Opposites attract is a first approximation which is a misleading rule of thumb in theoretical or philosophical considerations. Similarly likes repel is also misleading. By introducing these simplistic rules into our education of young physicists we actually obscure the dynamics of what is being studied. It came as a shock to me, that such rules did not hold sway in the early pioneering work of the early experimenters, and it took brush with Ed Leedskalnins elegant works to realise just how tainted our modern views of everyday observables actually is!
Thus I have distinguished the vorticular structure into its core and shell, defining an inward spiralling shell and core as a neutron and an outward spiralling core and shell as an anti neutron. It is how ome may be turned into or generate the other that I propose to explore here.
I really have to give a big shout out to the reticent Laz Plath.
For me his suite of now free apps on trochoids have been crucial. They now represent the model of the boundary or shell dynamics aroound a vortex core, especially an inward vortex core.
As yet he has not responded to my request to communicate so that he can modify his apps to include a outwardly spiralling dynamic core fully.
Laz shows here what I mean by a twistor. It is an" arc vector", and in this case is particular to a circle. Twistors in general are trochoids. Thus twistors add and scale, but they combine by the same parallelogram law as lineal vectors. However curvature also has to be factored in. The combined result is therefore more complex than lineal vectors.
The vide shows how twistors can structure themselves so that multiple twistors are bound together.
Considering the points as test particles one would normally expect lineal trajectories on collision, but in fact the collision trajectories indicate a rotational motive has or is being transmitted to the points. .
Newton does not know how this is achieved. He posits an impulsive force, which coaxes the motion, or an attractive force that acts continually, or a repulsive force that acts continually or some combination of all 3. Hence the fluid dynamic situation is more complex to model by proportions. . It is therefore amazing that the exponential vector variable can use simple proportions to control the trochoids.
Their are 2 major points to make here.
The first is almost universally newtons centrifugal force has been downgraded as a real force by theorists. The second is that Sir roger Cotes was on the brink of discussing the logarithmic proportion of force acting radially with Newton. Thus, what I am calling a twistor, and explaining in terms of trochoids was the next big thing in the topic of orbits in space. Newton's gravitational law would have been remarkably generalised.
I will allow the reader to meditate on that last point, while I discuss an equally important failing in the first point.
Because centrifugal force has come to be so denigrated, the general power of Newtonian mechanics has been muted. It seems that theoreticians cannot conceive of an equal and opposite force that acts centrifugally in " reality". Or rather, they do not want to consider a gravitational or mechanical force that acts centrifugally.
Therefore gravity is. A non physical force because it does not obey the rules of Phusis, that is there should be 2 of everything opposing each other. The reason for this seems to be the tangential line. Of all the lines to pick as a" real " force line, the tangent is the most impossible! Thus the mysterious tangent takes the place of real curvature!
We are so schooled in it, that we even question curvature of motion! What is our supposed justification? Newton's first law of motion, made grand as the law of inertia!
The " good" or " right" line in the inertial law is the first unnatural constructed line in the Greek mechanical system. When we refer to Euclid, we see that it is in fact the second ideal magnitude in the system following the seemeia on and it is constructed, it is a gramme! Thus Newton used a well understood elementary, introductory notion of a constructed ummatural line to lead the reader to the main considerations of his principles.
By this I mean to emphatically state that Newton did not posit that straight line actions are real. The system of forces in an inertial equilibrium are so complex that a straight line always requires as much manipulation as any other trajectory, and clearly most trajectories are curved lines when drawn . The straight line in his first law of motion is the tangential line to the actual motion. By describing it in this principled way, he unites ancient and modern philosophical observation with empirical mechanics. The tendency in motion that is the motive for motion is a reactive acceleration in line with the contact pressure, if the body did not act in line ith the applied force, there would be no measure tht could be established mechanically, because no proportion would make sense, nor old any force truly act on a body consistently because the body would move in such an awkward manner!
Newtons principle avoids ll these real problems by using the tangent to the actual locus in space of the motion to define the applied force. This he kinaesthetically and intuitively describes as the " right" line of uniform motion.
Now many have noted that this uniform motion only exists in the absence of forces or pressures. But sincebforcesvandnpressurescare ubiquitous, it is fatuous to say that such a motion exists anywhere but ubjectively in the mind of the observer. It is the mind of the reader that is being conducted by Newtons presentation to the principles, spiritual or intellectual laws that can be apprehended only by fully engaging the senses. These sensations are then transmuted into Ideas andvasnideas can be treated by the principle book on Platonic theory of Ideas, the Euclidenn Soikeioon/ .
Of course, if you have never read Proculus,Pappus, Apollonius and even Euclid, you would not apprehend these literary and classical references in Newton's structured writings. Newton published in Latin, not to obscure his ideas but to refer them to the attention ofvScholarsbwho would be familiar with their classical allusions.
The upshot of this is that from a geometrical mechanical perspective, circular motion nd centripetal nd centrifugal motion were the models of real motions. The tangential motion was a model of an impulsive motion!
Now we also have to account or the Newtonian use of proportionality. The use of a line cut into segments to define proportionality is as old as Euclid. We may go back to Sumerian clay tablets to see its use even then. But it isbHermann Grassman who in discussing his 's mathematical system for teaching geometry and all mathematics in Stetin, who describes he line segment as a symbol as surely as any letter or curious mark in Algebra may be taken as a symbol! This insight thus expressed is immediately evident in all Newtons work, and explains what he meant by proportion.
However, it also draws attention to the dumbing don of Scholars, or their general ignorance to the fact that the ancients habitually thought in these ways . That is that a line was a mere symbol or analogy for some other magnitude. In particular those magnitudes of the other senses that could not be directly drawn such as taste, touch, smell and hearing, could be represented directly and proportionally by a line of some sorts.
Grassmanns lineal algebra is precisely what he describes it as, anmalgebranwhich uses points ( dots or marks) and line segments between points as symbols. Having conceived the idea from his fathers strict conventions in geometry, often called a formalism, and also an axiom, he then proceeds to use the printers block, the Buchtafeln of typefaces to distinguish these line segments and points. He reserves the numerals to represent something a line segment also does and that is count. But numerals represent our considered reflexive description of all magnitudes when counting. Over millennia we have used lines and marks to aid in counting as well as objects nd magnitudes of all sorts. The Arabic Indian numerals have finally been universally adopted as an international standard notation for all counting!
Measurement is not to be confused with counting, but in fact measurement requires the counting of magnitudes. I have dealt with this topic in the blogs on number.
So Newton is using the line as an analogy, a symbol of other magnitudes which are proportional to the line segment. He chooses to use the line segment for displacement, or velocity and or acceleration and finally for motive. Not all lines are Equal! I set out a series of blogs precisely on this topic.
Now using the line for motive means that immediately he can apprehend a metaphysical description of sink and source in terms of the geometry ofbMechanics, and Hereford also in the ideas of Euclid's Stoikeioon! We are in a different world when this is done! In fact, following the influential work of the Grassmanns as it littered through central European (Lebsch and his svhool) and Italian mathematical physics by Peano, Einstein draws directly from Levii and Ricci this incredible aspect on physics, which I claim was in Newton's mind when he wrote His Principia.
So now returning to the lineal representation of motive, it is clear that rotational motive was clearly considered by Newton, but not fully apprehended. As orbGrassmann he expresses an intention to consider the circular line as a symbol. This it seems he was not able to get to before his death.
Rotational motive is the most general notion, but it's proportion is not based on the straight line segment. The proportion of circular motive is based on 2 lines. The straight line segment called the radial, and the curved line segment called an arc.
Thus we come back again to the Eudoxian notion of proportions being encoded not only in line segments, but also in planar forms! The planar forms have proportions that are dependent on 2 connected lines that rotate around a point in which they meet.
This is the higher proportioning of the Greek system of Spaciometry. On this bilineal proportioning based on a common point of rotation, Newton constructed his Principia.
This so called Quadratic Proportional thinking, is so distinctively Greek , that we fail to comprehend it . It is in fact well laid out in Book 2 of Euclids Stoikeioon, and further developed in books 5 to 7 as proportion, similarity and ratio.. In fact it is based on the real surfaces of a form distinctively laid out in a fractalised pattern called a mosaic.
I have blogs that explain this in more detail.
The one thing that a mosaic cannot do very well is vary! Yet all Greek proportioning isvDynamic including translation and rotational dynamics as well as scaling and reflection!. The very cornerstone to this dynamism is what is called Pythagoras theorem for the plane. Euclids proof of this theorem fundamentally unites rotation, parallel lines, arcs and conservation of magnitude, along with congruency, similarity nd proportionality..
I am writing a paper on this point as I speak.