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As ed explains simply, " modern theory neglects half the magnetic current!" the rotating magnetic field of Örsted is not described by the right or left hand rule! There are 2 gyres that twist against and through each other. Thus Arago's disc rotates in one direction and a compass needle points. Directly at the rotating edge. Thus in " pole magnetic" terms the poles hunt and follow the " opposite" pole and the compass rotates with the rotating disc. In tribomagnetic/ electric terms, the friction between disc and air ' charges" the disc which then induces a charge in the compass . The compass is attracted and repelled which torques the needle , but the rotation transmits a twist in the torque that rotates the needle in the direction of the rotating disc.
These 2 models both naturally explain the rotation coupling in their fundamental terms, which involve both fundamentals. However the rule that wires with current flowing in the same direction attract each other seems to be a mistake.
The two gyres move against each other . Thus ABC moves against ACB , they also pass through each other . Opposing gyres give a net 0 gyre , but we see that coupling " causes" twisting. In the compass. Ed shows that the gyres are not closed loops but expanding gyres. The north pole expands on one side of the wire( wire aligned East West) and the south pole on the other. These are captured by his inducting fish wire " needles". You can see some of this structure in Dinu's video.
Thus the wires carrying around it the same gyrating space will attract by magnetic pole models .
By gyre interaction , if the viscosity is great enough the rotation would result in a twisted wire that will repel at certain points of contact and not repel at other points of contact.
In free space we see that this results in rotationl displacement followed by attraction.
When I look at the behaviour of plama on the sun the rotational repulsion attraction " cycle" is evident. The simple charge or pole models are uitable for local or very small behaviours in ths cycle, but the gyre models give a better intuition.
Einstein took great pains to conceal the aether basis to all his ideas, for war reasons. At that time espionage rules were simple. The word or concept of aether was taken to mean you were a Nazi sympathiser! Later after the atomic bomb he made an impassioned plea for the restitution of the aether concept into physics.
In my elements you will note the presence of gear chains. This and filamentation is my mechanism for spatial interaction in viscous media. The complex rotations of the 3 gyres are certainly capable of setting up such complex gear chain and coupled transmissions.
Newtons work applies to the rotational situation because he applied it successfully to such situations, which is how he came to posit centripetal and centrifugal force, however this is not to say Newton was inerrant. He clearly dd not understand the rotational behaviour of fluids, but he was careful to not jump to conclusions without empirical basis. His work in book 2 was a personal "fail", and yet it advanced fluid dynamics in so many fruitful ways.
The point mass Newton used was, is and can only be a physical abstraction in this case Newton was careful to ensure it was identified with the centre of force action, that is the Barycentric centre of a corpuscular object. In this case it is " sensible" to merely ignore rotation of the centre, but that is not the same as denying the rotation of this Barycentric point!
Contemporary science operates in the language of kinetic/potential dualism of energy, all other types - electric, magnetic, chemical, atomic, nuclear, heat, etc. - being all but a manifestation of one or the other type. However, at the next level of introspection, potential energy is probably nothing but the energy associated with a hidden motion of invisible substance so minute that it should be relegated to an altogether different scale in the hierarchical structure of the universe. Indeed, it seems meaningless to speak of energy in the state of utter stillness. If so, energy duality should be perceived as duality of energy associated with two modes of motion irreducible to each other - translational and rotational.
Anyhow, that is the mode of thinking, which, in my view, has the potential of making progress in understanding the nature of potential energy. Concentrating attention exclusively on the "how" potential energy works, leaving aside the "why" it works the way it works (in other words, refusing even to contemplate the "mechanism" of potential energy) is a sure way to block the advancement of scientific knowledge.
When current carrying wires are placed next to each other, rather than attract or repel, they oscillate.mthat is they attract and repel sequentially . Eventually the settle into a state of dynamic equilibrium.
The Biot Savnt law and amperes law are derived from current carrying loops!
What the difference is is the difference between translation and rotation! It is a huge dynamical difference!
I shall continue to search, but like electros tic induction the reasonableness of the explanations are mechanically suspect, relying on a charge model . It is equally explainble in terms of a rotational medium model, that is a spaciometric vortex model.
For example: why have such a complicated process for summing the triangles? Secondly some ratios seem odd or misapplied. I do not think the demonstration gives the whole story!
The issue of metrication is very implement and pragmatic. You find a Metron that fits and you count that! The issue comes only when you wish to use a standard Metron that does not fit. But then why would you do that? Usually the answer is " we'll we only know the measurement in these units!". I am still smashed by how many people still want temperature measurements in Fahrenheit!
Certain traditions build p around certain numerals, but in this case Archimedes would have had no problem applying a summation method of this sort, especially using the most appropriate formula for a general solution!
However, using geometrical relationships to establish mpirically laws is fraught with difficulties, procedurally and philosophically. Newton, in establishing his philosophical grounds was careful to replace experiential conception with defined measure, even if he used the same name for the concept and the measure!
I have found it instructive to read hs actual introduction to the Principia, as he explains much that others choose to leave out.
The fundamental concept is Newtons derived concept of Motive. This is intimately related to his understnding and interpretation of Aristotles Metaphysics. This ancient work on motion and movement is the prime argument for the existence of a universal being, beyond our Ken, which motivates everything causally while itself bring causless! However, rather than introduce that philosophical debate ino physics Newton argues for the fundamental general notion of causative motive as axiomatic. Then this cause transforms corporeal matter in measurable ways, by which measurable behaviours we might have some limited sense of the divine awesome powers in which we live and move and breath and have our very being!
In the end Newton seeks only to glorify his god not to comprehend him/ it.
In short, the motion of vis and vis viva is not defined beyond common sense. Thus the common sense notion of pressing and pressure , stress or tension are good mouth concepts but they require related but different measures. The most general measure is that of pressure.mthese measures are derived by calculation, and defined by a process of companion. Newton uses what can be metronised! Hydrostatics establishes density, rulers establish geometric forms that can be called Arithmoi and thus counting and factorisation rules can be applied. Corporeal bodies can be measured, their positions defined and displacements measured. The final element required was a constructed notion called absolute time, by which he combined duration and astronomical position ( or rather astrological position) . Such a concept really only became possible with the invention of accurate timepieces. Huygens and others were instrumental in that development, but it really was a social as well as scientific movement towards greater efficiency in travel and communication and commerce.by sea.
So pressure as a measure reminds us we need a medium , a motion and a surface of contact.action at a distance is thus anathema to these measures.
While continuous media seem to be unphysical, it is really atomic corpuscles in a vacuum which are a unphysical construct. All we can " sensibly" say is that density variation is ubiquitous and fractal, and any apparent distance between dense regions has never proved to be empty of everything!
Is amperes law correct with regard to current direction?
These ideas provide a welcome challenge to the gyre or vorticular pressure model for magnetism I am advancing here.
Here is a quote from Ether and the Theory of Relativity by Albert Einstein illustrating how badly a logical deduction can go wrong when one misses on the fractality of nature: This quote suggests that it does not even occur to Einstein that the distribution of matter in the universe might have a fractal nature (which is implicit in the principle of scale invariance, by the way). Indeed, if the distribution of matter is essentially fractal then any logical conclusion that is hinged upon the possible values of the mean density of matter is meaningless for the simple reason that mean density of matter cannot be defined: the value of mean density you get will depend on how you do the averaging - anywhere from zero to infinity. There is no meaningful way of defining the notion of mean density for the entire universe where the substance distribution is essentially fractal.
Think again about the cylinder area paradox - mathematically it is in the same league. By that I mean that the value of the cylinder area you get will depend on how you choose the limit process. In other words, the result you get will depend on the degree of wrinkleness so to speak (in Mandelbrot's parlance - fractal dimension) of the approximating surface made up of triangles which are decreasing infinitely in size with each step of the chosen approximation process.
By applying the qualifier corresponding to the word aether I want to emphasize that the aether, which is responsible for the phenomenon of gravitation, probably is not the same aether that is the seat of electromagnetic phenomena.
If the invisible substance of the universe turns out to be fractal in accord with the principle of scale invariance (aether1, comprised of aether2, comprised of aether3, ... ad infinitum) then the search for the unified field theory à la Einstein is, inexorably, a futile exercise.
http://www.ampere.cnrs.fr/parcourspedagogique/zoom/courant/formule/index-en.php
In this theory moving fluid or charge gave rise to magnetic force. In particular the charge moved in a loop pattern.
As far as I can find out Ampere experijmented on looped conductors and derived his law from looped conductors. It appears to be Biot and Savart who first idealised the magnetic force along an infinite wire. Biot , like Newton imagined an infinite cylinder to describe the behaviour of the " fluid" round it. You will find this in Book 2 of the Principia. However, this was a mistake Newton made in attempting to understand the behaviour of fluids around a rotating stressor!
The difference between a closed loop and an infinite wire could not be more marked! A rectilinear helical propagation in fluids causes repulsion not attraction between parallel propagations in the same direction. . However a circular helical propagation creates by necessity a bipartisan flux phenomenon through the central disc. Thus while at the edges of the discs a pair of wires will repel each other within the central region a common flux will flow. The nature of this flux is vorticular and filamental . In a similar or analogous manner to Betnoullis fluid pressure law the venturri effect of the flux leads to a lower internal pressure. This pressure is low enough for the external pressure to force the wire loops together , overwhelming their natural repulsion.
Thus Ampere measured the attractive resultant force of the circular loop, and ignored the empirical repulsion between the wires which is a smaller effect. It was apparently due to Biot that the mistake was made, asserting attraction between parallel wires of infinite length. The only experimental data I have found refutes that assertion. In practice, amperes law is based on measurements of loops of wire, that is on the magnet analogue , not the electric prototype or primitive assumed by Ampere.
The rotational nature of so called magnetism means that an " individual" pole magnet will not be found. The polarisation of magnetic phenomenon arises out of rotational behaviour.
The assumption of a primitive charge naturally took Ampere to the microscopic level, a scaled assumption based on the behaviour of conducting loops. However, the loop itself as a contiguous ( continuous but discrete) phenomenon is sufficient if it is dynamic. The material loop in motion requires no primitive to explain its behaviours beyond an assumed "first cause " logical system. However that is not even necessary if one can accept human limitation to knowing and the evident fractal structure of natural phenomenon.
Their belief system has to change if the magnetic base of our understanding is yo be realised. We see that already they are attempting to move from a standard magnet at 4° kelvin to some fancy electronic circuitry supposedly controlling single electrons. The ld standard is based on a magnet and electromagnetic photon voltage generation. Then a formula is used to calculate a current of the required standard. It des not even matter if the wires attract or repel, because that is not used to actually measure a defined unit!
This video shows that any circuit behaves like a solenoid. Thus ampere was not able to experimentally isolate a line segment to correspond to the infinite wire pair used in the classical definition of the ampere.nwhat is observed therefore is not the attraction of 2 wires but the attraction of two wire loops or circuits.