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The method of lines of force as expounded by Faraday and promulgated by Maxwell is here well exposited. That these lines may be straight or curved is explicitly stated.
Now by 1854 the work of Hamilton(1832 and 1843) was notorious among researchers . In fact the Mathematical societies were up in arms regarding his mathesis of the imaginaries! Lewis Caroll lampooned him in Alice in Wonderland and Kelvin and others took against him. In the meantime in 1844 Hermann Grassmann independently was rewriting mechanics in terms of his idea of a lineal Algebra. He went way beyond Hamilton in generality. Thus the concpt of lines of force or mechanics, clearly exposited in Newtons work for forces was a current if misunderstood conception .
Hamilton worked to clarify the notion of a vector he had envisaged, especially in regard to pencils of light, but also more generally . Meanwhile Grassmann worked to obtain a professorial position by expounding a method that was the key to understanding the mechanics of his time . His aim was to give this key to the Prussian school children to enable them to compete on the world stage as self actualising innovative people no longer overshadowed by the French elite , or hindered by German incompetence.
The lines of force therefore have a pedigree, but to use them to illustrate force, power and energy of a medium in this way was clearly "non geometrical!" However it is topological and thus deeper than Geometry, having to do with the way or pattern of thought we employ when thinking about space and a medium.
When lines are used in this way to exposit a field of force we conceptualise an invisible action at each point in space, in this regard we establish a lineal frame , that refers activity and motion to a defined object , so in addition to the orthogonal reference frame for position we may superpose a lineal reference frame ( straight or trochoidal) to give force and direction at every position.
The 2 together form the concept of a: field in both electric and magnetic descriptions, a pressure gradient in hydrostatic and hydrodynamic descriptions and so a means of representing in space or in ny medium a pattern of forced behaviours.
It is salutary to think that before this concept was well grounded, mathematicians and theoreticians had no means of applying their ideas to real physical phenomena. Rather they described generally abstract principles.
Now the use of polarity lines in Magnetim as lines of force is clearly misleading! These field lines for magnetism do Not depict lines of force but rather lines of polarity orientation .
We know fom experiment that the forced behaviour is attractive and rotational. It appears repulsive but in fact that repulsion always accompanies an attempt to rotate into an attraction position.
The behaviour of ion filings while appearing to be forced to link up do so by rotating into position, not by being dragged to or pushed away from the poles long these lines.
What would true lines of force look like for magnetism?
The magnetic polarity orientation surfaces around a wire when wrapped into a solenoid became the lines of the H field inside the solenoid and the B field outside the solenoid where the intensity varied the farther away from the solenoid the test dipole was moved.
The solenoid produced iron filing patterns similar to a bar magnet giving rise to the motion hat electric current caused magnetic behaviour.
However, the B field is on the theory of maxwell and Faraday caused by summing the surfaces of Equipotential . Thus the B field is a depiction of the sum of Equipotential electric charge so called. Equipotential charge by definition creates no current flow of charge . This is because charge force is equal in this surface.
This means that the B field lines or surfaces , the commonly depicted magnetic polarity lines are posited to be orthogonal to the lines of force. The lines of force are therefore orthogonal to the curvature of the B file lines giving. A pattern of acceleration that is greater at the poles and weaker in the centre where the so called Bloch Wall is.
These lines of force are usually calculated using a dipole source according to Biot and Savot, and the magnetic moment is adduced from these calculations . But the calculation is based on an assumption that the force behaviour is the same.
Although the " correct" idea is" by analogy " it works both ways: by analogy the calculated force is analogous to the Equipotential surface of a solenoid magnetic field, that is the polarity orientation surface of a bar magnet .
The polarity orientation surface is alo the surface of minimum magnetic moment. The magnetic moment demonstrates the 2 opposing forces that exude from a magnet orthogonal to the curvature of the polarity orientation surface.
While the B field is customarily shown as a Uni directional vector bundle it is physically 2 opposing "Faraday lines of force at varying intensity, and swings between+& - intensity.
This is thoroughly confusing since the observed rotation of the polarity orientation surfaces are used to deign motor operation.
The patterns do not alters axially because they are caused by a constant rotational force on the plasma on the screen .
Meta is a preposition that usually means "external to", or the bit before a defined something starts or after it ends. So it is always relative to something.
Some argue that the prime mover is ontological, and therefore God ultimately. But this is one interpretation among many.
Few realise that Newton, and Galileo took this concept to mean that space is at every conceivable point potent! This potency is what engenders motion . The motion is not defined but it is observable within seemingly non corporeal( no corpuscular bodied) space as well as within corporea( bodies within mon corporeal space).
This ultimately is the origin or basis of the field notion, and the potential field concept described as an algebraic formula of ratioed quantities.
For simplicity I would say let us presume that the prime mover is essentially a reference frame. In so saying I lay before you a particular interpretation of the prime mover concept., not excluding any others nor indeed implying mutual exclusivity! Super positioning is the modern term for this approach!
Now a reference frame is a pure abstract motion that is entirely subjective, but we can agree subjectively with others on an objective reference frame providing that frame is dynamically stable!
There are2 sorts of dynamic stability: so called static equilibrium, and the other is dynamic equilibrium. These are ancient ideas found within the Yi Ching for example or in Jain teachings etc. Aristotle merely expressed these motions in his native Greek language, but of course so systematically that I now believe he was an Asbergers sufferer, a high functioning Autistic Spectrum Disorder sufferer.
So our reference frame as a prime mover is fixed only by consensus! Personally my reference frame is fixed relative to me, and I won't here address the psychological requirements. For the notions of identity.
Suffice it to say that my personal reference frame is dynamic bis a bis the consensus reference frame, thus to ascribe potency to the consensus reference frame seems at odds because it is my subjective frame that is moving!
So the puzzle was, how can an inanimate body move and further continue to move after being disturbed from a state of rest?
The favoured answer was due to non corporeal entities( invisible) yet able to I tract with corporeal bodies. The more general philosophical answer was Life itself was inherent in moving bodies and still bodies were dead. So when Newton exposited both rest and uniform motion as being equivalent in some sense he cut through the limitations of presuming life and death as sources of motion. In fact he was developing Galileos idea that we are unable to distinguish absolute motion from relative motion if that motion is unifor, and produces no sense of acceleration or velocity variation.
The Dialogo sets out a Fractal notion of the known universe in which the prime mover is a reference frame that provides potency at every point. Thus Jupiter and its moons are an absolute( independent) system because that region of the reference frame provides the potency for the Jovian system! But superpositional ly the sun proves that a larger potency may be applied to all these fractal sub regions. .
This is a curious idea that no one centre dominates every action, but that all centres contribute to a combined or resultant action, but we see this promoted in Huygens theory of light propagation based on Grimaldis theories of light! Grimaldi was Galileos Nemesis, appointed by the pope to disprove Galileo.
So the reference frame provides potency in an of itself at each point independently( absolutely) of any neighbouring point.
The issue was ignored by Descartes who posited corporeal collisions as the level of exposition for potency, and this was a good starting point.
However, in these quantum Theiretical days this simply won't do! The problem I say arises because the straight line was given primacy for describing action.
The line segment is an old symbol for encoding topological information, but it was never necessarily straight. It was called in the Greek a good line or a true line. In many instances this is straight, but in general it is curved or specifically trochoidal. .
The principles of Mechanics are based or depicted on 2 lines, both good for the observed situation. The prime one is the conical curved line, and within the conical curves a special line called a straight one is uniquely identifiable.
Newton in establishing his laws of motions and axioms includes both. In fact he leads the reader from the immediate local experience of a good line( which is in fact a tangential one) through observations regarding a toy spinning top, to the celestial good line which being beyond our direct senses turns out to be by Kepler an Ellipse!
In general these are members of the conic sectional lines.
This appreciation was so rare in Newtons time that Bernoulli was forced to enquire of Newton how he determined the shape of orbits by his methods, and why he was so certain! Newton replied mysteriously, but in fact from his note we see he thoroughly explored Apollonius conic theory from the works Barrow brought back to England after enduring great perils.
In short, I mean to say that the issue of fractal potency disappears when you place arc lines or citcular locii as the prime motion at every point in space!
The prime mover or prime reference frame engenders circular motions of all mplitudes, frequencies and phases. It is the supepositioning of these circular motions that combine to give all other motions including straight line motions.
Of course I mean spherical motions when I write circular , but the point is clear, trochoidal surfaces are the prime theoretical topology for motions in space . The Plenum, as DesCartes supposed is probably naturally " Wavelike" and vortices or Archimedian screws are a better foundational particle for any atomists!
However, I am not an atomist. I am a fractalists.
Imagine walking on a swimming pool! Reactively viscous materials make this possible .
Reactive viscosity provides all necessary ingredients for an action at a distance effect . The physical properties exhibit in the local region of action while everywhere else they are not observably present. That is very much what a Dirac delta function attempts to depict in measurement schemes.
Newton states that he does not exclude impulse forces from his dynamics! That is to say he accepts explanations that describe the behaviour observed by any rational means. Famously Feynman rejects explanations that use elaborate impulse schemes like Le Sage even though Newton himself was very interested in Le Sages work.
There are reasons to not precisely follow Le Sage but no reason to reject out of hand a scheme based on push/ collision Mechanics if it includes rotational structures like vortices as fundamentals.
Since these patterns are on the surface of a region it is instructive to imagine that the fourier analysis suggests internal rotations are occurring within the regions body.
The Fourier transform itself depicts the fixed boundary of a form, that is a reactive viscous form at the boundary.
The upshot is that rotationalnconstuctiveband destructive forces in a medium can produce locl force conditions like action at a distance fails to describe! Rotationl or that is magnetic pressures could produce standing wave patterns that interact to impulse centipetal or centrifugal attraction or alternatively axial repulsion.
While this is a strobe lighting effect it illustrates how what we see is not always what is physically happening! Our neural networks average actual events to provide us with an experience sufficient for survival . However when the strobe is at the frequency of the drips the drips appear round and rotating . But then the drops appear to float upwards . Kinaesthetics reveals that the water system fills a cup , so one needs to use experimentalmresultsbinnall modalities.
However the second is reactive viscosity exhibiting action at a distance. Ignore the sine wave idea, it is actually rotation that is involved.
The video explains haptic force patterns in a continuos medium
Tangible media demonstrates how reactive viscosity can cause action at a distance behaviours
Illustrating attractive behaviour
The Fourier transform sums rotations as coupled entities with independent but motile centres . A gear chain must be a connected set of rotations whose centres are in a fixed topology to one another, and thus the sum of the rotations is not a trochoid resultant, but a topologically consistent set of rotations that physically transmit rotation around and or along the topological form .
The independent centres in a rigid or flexible chain are constrained by actions on the centres which may follow a static or dynamic path of stability or fail, in which case the gear chain is no longer a sound topological form, or a stable one.
It may fail in many ways including explosively into smaller intact trochoidal topologies of gear chains or a trochoidal firm
This paper deals in detail with planetary gear TRAINS which is the better term for some of what I need to u der stand. In particulate vorticular gear trains , by pulleys or rubber contact gears as distinct from toothed gears also need to be included in the Investigation .
These rigid gear systems will further need to be adapted to cover vortices whose shapes and internal/ external pressures will vary over time . The vortices may expand or contract during these times causing dynàmic changes in the whole system of the gear train( planetary)
For example an explosive event in a medium may be initially modelled by a citcular expanding sun gear . While the traditional thinking is to use rays emanating from a point to initially depict this, it is probably more accurate to use arcs expanding atound the point, providing both radial and tangential body pressures which would naturally generate, rotating regions in the surrounding medium
How these vorticular regions ride the expanding shock wave and organise into filaments is of interest , particularly in eositing the transmission of so called electromagnetic radiation .
We know that a broadcast signal dr erases in power with radial distance but we rarely think about how we can detect a signal from Voysger after all these years if the signal is indeed disappearing spherically! Vortices hold there power over remarkable distances and after reflrction( ie vortex rings) despite the fact that they do decay over time.
These are questions to be determined by further research"
The planetary gear train model is the best for fluid dynamics
Carefully observing these animations or videos of coloured ink flow one begins to realise that nowhere is there a central point from which pressure is emanating As in the traditional representation of a region of pressure!
Instead regions of density represent where one expects low and high pressure to be. That is to say that low pressure and thickness of a region coincide with fluid motion in that region. The streams of motion are stretched out and therefore compressed both topologically to maintain total" mass" of the region , but simultaneously for the external region to remain in contiguous contact with the inner coloured region. By these constraints we see a mass stretched into thin streams but the streams themselves bound regions which become stretched as well.
The colour does not diffuse because the motion is highly directional, indicating that both the coloured and the dark regions have directionally relative stretch or flows sometimes opposite relative to each other, but the total may move as one system of opposing flows.
The density/ pressure in those flows may be dynamically stable, making the whole system subject to an external density/ pressure system.
At the central region the flow direction changes into or out of the screen and there proximity mixing is seen. This may be simply finer and finer stretched contiguos regions( Wada lines) rather than chaotic mixing..
Centrally the region appears more dynamically stable in terms of how wide it is indicating a stable density / pressure region. The inner core is also stable but not necessarily at the same measurable pressure! Given the dynamic rotation of the ' wall' region the measured pressure would be greater as a "stopping pressure" reading than that in a core which may be rotating at a much lower circular velocity.
Why does the system not collapse to a point? Because point pressure sources are a representational artefact. We may have cavity or nuclear ion regions of very high or relatively higher density/ pressure but it is the circular velocity around these that determine the overall behaviour. If the circular velocities combine they may in fact stretch around a greater region resulting in a reduction of overal pressure/ density. But if the circular velocities combine to increase around the same or a smaller region, the measured pressure/ density will also increase. . What controls this outcome appears to be the central core activity. If it is fast enough in the direction orthogonal to the combining circular velocities the diameter of the resultants circulation may be maintained or lessened!
When steam bubbles initiate around a nuclear ion point the surface velocity of the bubble increases until the bubble breaks away . The expanding surface arises because the surface is moving faster than the I ternal core can move to accommodate the increase in surface velocity,
This is just one aspect of a complex surface interaction which results in the bubble rising to the surface of the liquid where the surfaces combine releasing the core as steam.
Eventually the bubbles become so large and the surfaces do intermingled that the pot boils in a so called turbulent manner.
Evaporation on the other hand occurs without turbulence because the surface nucleation sites are small enough to be indistinguishable from Brownian motion of the surface which may be driven at least in part by the phase change mechanism.
Changes in phase are not discussed here, requiring further research and thought . The particle explanation indicates that contiguity of rotational regions is the changed factor, with standing rotational formations becoming erratic and" un systematic or unpredictable or chaotic" in effect, and stretched over a larger region by arc extension.
Modern techniques used to perform a groundbreaking experiment almost 200 years old!