| To citizen-scientist Franklin flying a kite in an 'electric' storm was reputed the first reversal-of-charges, by century-subsequent physicists upon discovering the electron, But the further discovery of magnetism, in an increasing capacitive-field where, there is no charge-flow but displacement, required returning to the original designation... And, ultimately, aside sci-fi and Maxwellian formulæ characterizations, there was not even requirement, for calling, magnetism, a primary force... (nor electrons negative)... |
[See also THE FARADAY-MAXWELL TEASE (ppt-video trailer)]
* (The titular "harmonic magnetism" implicates the mathematical Complex derivative "harmonic" where df(z)/dz ≡ ∂f(z)/∂x ≡ ∂f(z)/∂(iy) : z ≡ x + iy ; considered because charge can stand-alone like 'real' electrons but magnetism cannot--like 'real-zeroed-out' companion-field only...)
CLASSICAL BACKGROUND:
It has come to my attention that contemporary college course discussions of magnetism, still, have an "anomaly" regarding the magnetism of charged particles: I shall resolve that here, then resume my discussion...
The anomaly as it appears, as it is called out as such in Chap. 27 of a recent prominent university textbook (ver. 12), is depicted as follows:
Two charged particles approach at velocities, v, -v, and the magnetic field of one by moving, deflects the moving other, additionally to their electrostatic fields, But, if considered in the frame of one, where itself is not-moving and has no magnetic field therefore, or, is not-moving in the magnetic field of the other moving-alone and is therefore unaffected (as their equation is for charged particles moving in magnetic fields, not, field-field-interactions per sé)... this they declare 'an anomaly' and leave it no further resolved as such--consigning it to the past-eventuality of Special Relativity--another problem to repair...
But, their missing calculation tells us their mathematics is anomalous: needing not merely adjustment for lightspeed relativity, but for frame relativity of the 'plain ordinary' sort--cf 'Newtonian' energy ½mv² holds fully two digits of significance at 10% lightspeed and we should expect magnetic formulæ to be so workable and accurate up to 10% lightspeed...
We begin with a simple construction, a wire carrying a current, the wire having a charge-carrier electron density at drift velocity vdrift (so-called because the systematic movement of electrons in simple cases is far-slower than their thermal, velocities)... the result is called, a magnetic field around the wire, and its field density presses-apart to expand... (Note that electrons are negative-charges and we use the Lefthand rule where we thumb the electron direction of motion and finger-curl the magnetic field curl-direction; the Righthand Rule, is for positive, charges.)
Now suppose we move the wire, in the opposite direction with velocity v = -vdrift, Since the charge-carrier electrons are at zero-drift velocity, in our frame, they're not producing a magnetic field, in our frame, so, Where, is the magnetic field to be accounted-of--?
Notice, that the wire was neutral, (charge carriers are not additional, charges, as we handle later, but those free to move through the wire), and the positive charges in total equal the negative, except, that, for those specified as not-moving-with the wire but stopped in our-frame, the total charge moving includes the positive charges as in excess (total in excess) by the same amount but in the opposite direction--and whence an opposite magnetic field, in the opposite direction--which equals, our original, field, in our original direction...
This holds for all, wires, protons p, electrons e, and all velocities v unto lightspeed-relativistic, because
the total charge-current moving in one direction is:
pwire * vwire - (ewire - edrift) *
vwire - edrift * (vwire - vdrift)
= edrift * vdrift the wire-relative-electron-drift current...
in all cases... and where pwire = ewire for neutral wire...
THINKABOUT: If the wire were vibrating mechanically lengthwise, then, atomic nuclei being more massive than electrons, the proton-positive charges should lag in oscillation phase behind the electron-negative, phase, resulting in broadside E-M radiation that would ultimately still (or 'cool') the wire...
Now let's consider a point charge in space, a negative electron, resting or moving by itself, distant from any electrostatically, magnetically, compensating, positive proton charges, (in fact it could be affixed on a strand of insulator without a conductor)... As there are no locally compensating charges, the electron stands-out in neutral space, Nevertheless when the electron moves there is effectively an equivalent positive-space-charge backflow-through (accelerating-decelerating like half a swing of a pendulum), and-around, local to the electron, escaping its oncoming, negative charge field, and refilling its ongoing: Mathematically it's equivalent: a structured charge flowing one way, a space-filling-difference-charge flowing oppositely to make up the difference point-for-point at the former positions, leaving the structure standing intact but translated...
And both together, charge and backflow, in equivalence like as it was for the neutral wire but here the point charge rides in excess, generate the magnetic field observed for a moving, particle--the point charge by one,-hand rule, the space-charge-flow oppositely by the other,-hand rule: equaling the same in total... (We're setting-up this relation because, in the next step, we're going to separate the two by that clever capacitor--that can distinguish, particles...)
Notice that this-kind of space is distinguishable as positve-space charge -and- negative-space charge coexisting-at-or-in the same point place--a little like 'indistinguishably close virtual pairs'... a little like 'differentiable fields'... a little like 'neutralized zones'... a little like 'red and green paints mixing to black'... (We discuss the nature and structure of electrons and charge-as-helicity in another article not related to this textbook 'anomaly')...
THINKABOUT: Compensating-space-charge-opposition-backflow is analogous to a semiconductor 'hole' equaling successive electrons moving in the opposite-direction except, 'holes' are discrete missing-electron possibilities in atomic bonding structures and this analogy is thus coarse and thus-far...
So now when a point charge is moving relative to our cosmic-space-frame that is not, its electric field moves with it and its opposite-space-charge moves oppositely, but ever with it, and, both-together-in-total generate a magnetic field that also, moves with it, (this was not discussed in the book): Magnetic fields of moving particles are in effect continually-repositioning, magnetic fields, not, moving, magnetic fields: for, the faster the particle goes, only the more backflow passes-through: the backflow has its own limiting speed (finite) while its central point-of-identity advances equally with the point charge... And, both-together-in-total generate the total, magnetic field -that is- the same in-total as for electrons moving in a wire where the wire, is not, moving...
This is where point charges and electric and magnetic fields diverge in theory: the speed of backflow has a separable speed coefficient not-related to the particle motion, though it limits it, right down to zero-velocity of the particle and zero-backflow of the field, and zero-crossover: This gives us a clue as to what the charged particle is, and, why the magnetic field is proportional to the speed of each alone--a locally stable compacted energy 'bubble' pressing-out against the opposite-space-charge-field...
But this must also hold for the particle frame wherein the cosmos is moving but the particle is not, and, it must have equivalent magnetic equations in effect for the oncoming particle moving at -2v relatively (it always was, in the statement of the anomaly)... which means the 'framed-standing' particle must be generating a magnetic field without its own frame-local motion but the motion of the cosmos in the opposite direction drawing out its opposite-space-charge backflow--generating the field, or some-portion thereof, half, or all...
THINKABOUT: We have now defined a magnetic field produced in a standing spot, and we must rewrite the equations to represent this...
THINKABOUT: This also means that a charged particle can determine whether its inertial frame is moving relative to the cosmos, e.g. by Hall-effect devices surrounding it on all axes, (something purportedly impossible for the ultimate Special Theory of Relativity), but this may not be an easy task inside a space-laboratory, for the walls of the experiment take part: every atomic mass unit 0.9 GeV, 6 ·1023 per gram, and tonnes, megagrams per spaceship, dragging the cosmic æther, (cf like bubbles rising in a column of water drag the water to flow up too a little because it takes a little bubble-push to get the water to flow-around each), overwhelming a puny experiment:--the charge might have to be tested outside in the open cosmic flow, or, tested inside a moving tube of neutral mass... (In essence we have moved the anomaly from the seeming inability to book any calculation whatsoever, to making meaningful calculations holding up to lightspeed relativistic but cannot yet necessarily explain why experiments do not detect freestanding magnetic fields... but, on the otherhand we do have good expectations for that: such as the difference between rolling waves, that pass through each other mostly unaffected, vs. surge waves, that mutually carry each other along; and such as the electron by its standout charge slows approaching electrons and speeds-up their balance of protons thus inducing a compensating standing magnetic field inside a neutral shell--a nano-transformer-wave 'outside' the experiment and its detectors...)
To estimate the strength of the magnetic field, in the moving-particle case, and decide how much is due to the charged particle itself and how much to its displacement current backflow, we return to the wire experiment this time moving with-the-cosmos, in a four-way comparison... In, the cosmos-frame, the electron flow, as before but now totaled with its displacement current backflow, provides the magnetic field, But, in the moving-electron-frame, the same magnetic field is provided by the combined, electron displacement current, but, not the electron standing still, plus, the moving wire protons, but, not their-displacement current as there is none within the co-moving cosmos... But, in the third-way, if we remove the wire from the cosmos-frame, the electron and displacement current backflow produce the same magnetic field, and yet, in the fourth-way, in the electron-frame, there is no wire and, no protons, for the same, magnetic field... implying, the displacement-current-backflow produces all, the magnetic field... electrons are, like energy-dimples in a pool of space, standing-out because the utter vastness, of this pool, is yet immeasurable--except by those very electrons, et al...
Note. The term, displacement, may seem appropriate suggesting like a boat displacing its weight in water when the boat moves one-way there is a small wake and displacement current going around the boat the other-way... However, water is a different realm: its displacement current is the flow of neutral mass, whereas for the electric field the flow is non-neutral, charge--which yields a plane of contention halfway, that, between the parallel plates of a capacitor the charge field is neutral like local space, zero charge equidistant from the positive and negative and there is no charge current there, and, neutral flow produces no magnetic field... but the magnetic field still exists: because it is still differentiated... so--we do not call it, a 'displacement current', but prefer the term, 'differentiation current', in that the magnetic field exists when in any one spot the opposite charges are flowing in opposite directions... albeit the enthusiast may compromise to call it, 'differentiation-displacement current', to capture both, senses...
BUT BEFORE WE CONTINUE ON MATHEMATICAL CERTAINTY ALONE-- (classical physics is experimental)
Our result is, thus far, mathematically, proven, but, whereas the 'outerspace' experiment has not-yet-been done that measures a magnetic field about a point charge in open space moving with no local compensating mass dragging the aether-field, Let's retrace the discussion back to reconsider from halfway and take a new route forward... The neutral wire moving at any-speed short of lightspeed-relative generates the same magnetic field, and, a moving charged particle, passing-by at any-speed relative to the wire, sees the same magnetic field and its deflective force (acceleration), And, therefor if we advance to consider it in its own frame, wherein it the particle is not,-moving yet its deflection due to the wire's magnetic field must be calculably the same, we must reconsider, either the particle is being deflected by its wire-relative velocity -but which we already know is not possible since the wire's magnetic field is the same irrespective of the wire's velocity relative to any-frame, or,--therefor--the particle is being deflected on its cosmos-relative velocity--as nothing else but the 'unseen' æther exists to answer for the consistency of all results... We have thus returned to our mathematically proven result, and have its simple formulæ, and proven the existence of the æther (not saying it's solid--it's probably liquid at cosmic pressure anyway but may be calculated on a 'solid'-number-metric in a mathematically-existential sense)...
NEXT:
We must decide the backflow equations, but which will not be easy because the assumption of sphericity of the point charge and its field, though tending so, is not entirely valid, and, the backflow velocity is either constant speed (directionally variable only, cf constant photon speed irrespective of the electric-field polarization potential unless the photon is actually churning internally), or whether it has some speed-acceleration: TO WIT--
THINKABOUT: Though the book and generally physicists depict the electric field about a charged particle as radially symmetric about its 'centerpoint' and, angularly uniform, If, the electric and magnetic fields correlate in motion, by one or the other, then the field can-not-be, uniform, because by the Brouwer Fixed Point Theorem 'combing hair on a sphere' there must be at-least one 'cowlick' where the movement stops, ergo the other field is zero... and, in the real-particle-case we expect it'll be a pole pair, symmetric and graded... The remainder of this possibility, that the 'cowlick' may precess at greater than the speed-of-light (the 'scissors effect'), is beyond present scope...
SPECIAL DISCUSSIONS:
We can estimate common magnetism from the electrodynamics, summarizing here--
PARALLEL WIRES: consider the flow of electrons in two parallel wires: each passing electron impinges on the extended fields of each individual nucleon-proton and electron in the adjacent wire - and deflects. Where there is no systematic flow in the second wire, the electrons in the first wire impinge balancedly: the electron-proton impingements attract, and the electron-electron impingements repel, cumulatively equally: and there is no net force: no systematic deflection. [Impingements also equalize Fermi-temperatures] Where there is systematic opposition flow, the electron-electron impingements are faster, more frequent: and repulsion cumulatively exceeds electron-proton attraction - there is systematic deflection, and the wires repel. Where the currents flow in systematic conjunction, the electron-electron impingements are slower, less frequent: and repulsion is cumulatively exceeded by electron-proton attraction - there is systematic deflection [mutually toward], and the wires attract.
TRANSFORMER WIRES: consider the application of an electric potential to the primary of a transformer (coil) wire: an opposite charge develops in the adjacent secondary wire - then the flow of electrons in the primary increases the Fermi-temperature in the secondary proportionably to the excess - and a restoration current flows: back-out the secondary.
SELF-INDUCTION WIRES: similar, but a current must flow.
[However, there is a -secondary- direct magnetic force-line similarly qualified in sub-leptonic quantum-helicity charge-winding flow]
[2014/11/05] COMPARE GRAVITO-MAGNETIC INDUCTION:
A parallel discussion/insight on electromagnetism is found in answering the question of how much mass-energy is in the potential-energy field around a gravitational mass: Briefly, the question arises in ascertaining that 'potential energy' is, mass-energy: it is where an in-falling 'test particle' gets its kinetic energy by immediate-direct conversion of potential energy (and mostly-not from its own mass; see gravity); The point is then made how-much, and while the potential force may be large and constant holding objects in orbits, as soon as something starts to 'fall in' and convert the local-field mass-energy potential to kinetic, the near-field becomes diminished, its force reduced, and near-field objects follow partially-released paths 'backward', appearing as 'like magnetic induction' to the simple-observer...we are more familiar with electromagnetic, induction, because its effect is 1042.6 more-noticeable, but, deep inside electric charges, the effect should be significant, producing additional convections, and 'stronger' forces and energies (see electron)...
In this way 'there-is-no-point-mass-or-charge' because it's distributed in its potential field: the equational balance is in the 'static' force vs. 'extractable' energy of a potential-energy field and the local density of objects: A particular-given potential-field source can only provide up to its own total mass-energy, and that's distributed 4π around and by inverse distance uniformly, to the first-order Galilean-Newtonian approximation, and accessible at the speed of light (or gravity), and charges moving with the potential gradient, even in atomic orbit, upset their own near-field...it's an equation to be resolved...
[2015/07/13] THE FARADAY-MAXWELL TEASE: (See ppt-video trailer)
Faraday Law insights, timing-explanations and realism-anomalies, lead to a simpler plainer 5th-grader elemental 'gedanken' analysis which discovers a 'transformer paradox' where adjacent drive-wires exhibit counter-B-fields... Furthermore the insights include Maxwell's missing explanation of B-field expansion-to-infinity where university-level studies do retarded-field calculations as 1/R2 potential already nicely settled-out instead of pre-infinitely-settled--which may also lead to an answer on power-limited potential-fields both electromagnetic and, gravitational...
Briefly, The Faraday-Maxwell approach (clarified by Lenz, later reformulated by Heaviside) assumed magnetic fields should exist as standalone features of the vacuum, though they did-not have but proposed a magnetic monopole particle, as the E-field has electrons, in particular the B-field-change curled the E-field (D-field), But Faraday's original explanation, which Maxwell shrunk to calculus, was based on the notion of a calculatory-façade loop and computing sin(angle)... the result worked for Faraday but it hid the 'realism' of physics in mathematical virtuality--it assumed that B-field reaches out from the current-drive wire to the E-field space which by interaction reaches back to the electrons...a pushy-feely notion that fell out of the sin() calculation whether or not Faraday or Lenz or Maxwell or even Heaviside understood or even noticed the implications such as exorbitant-delay and, while pushy-feely may yet prove to be the case, it is expectably strongest locally to the pushy-source and feely-destination...
The 5th-grader insight, basically a 1940's college textbook on Electricity and Magnetism, was that the magnetic and electric fields interact most-directly (partially-delayed by 1/Rn coefficients tbd) so-as-to exhibit the central-values for smeared timings over multiple loops at low frequencies where the speed of conduction (ca 60% lightspeed) was not distinctly measurable or detectable (it was not a transmission-line transformer)... the immediate consequence was entirely consistent with Faraday's area-rule but more-real-like as the 5th-grader's drive-B-field had the same-EMF-vector-direction effect on all, wires, near, far, the arithmetic difference being their cumulative curl, and so the half-flipped of Faraday-Maxwell's rule which in curling the E-field had put back-EMF on the near wires and by circuitry-argument looped-back,-EMF on the far wires... purely a calculatory-method difference: Faraday-Maxwell integrated the EMF curl over the area enclosed within, the loop, while the 5th-grader insight allowed that the farther-wire had weaker circuit-looped-fore,-EMF and so seemed to contribute back-EMF: The total EMF is the same but the 5th-grader used an equivalence to get the area as the-amount-in,-minus-the-amount-out (the area-near-and-far minus the area-far) taking advantage of its realistic speed-of-light-driving-the-distant-buildup in lieu of Faraday's virtual-arithmetic-equivalence simplification... However, despite its similarity the 5th-grader's equivalence exposes a 'transformer paradox' which must yet be answered--
The 'transformer paradox' is simply that in the 5th-grader insight it’s as-if countering-B-fields
between drive-wires are not-canceling, but ‘squeezing’ electrons... not-unreasonable, allowing that
countering-EMF bucks,-rather-than-pass, (and which quantum mechanics might not even think-of in
its first-place: it'd be a sub-phase-distortion possibly nonlinearly incalculable)...
SOME THINKABOUTS:
ADDITIONAL:
We must now recognize what is causing the magnetic field--that it is the displace-current-backflow, not the broadside motion of the electric field... for example at the midway of the moving charged particle its field is strongest because of the fore-displacement-current-passing-back, not the strength of the electric field at the midway: Though these two line up -if the field is symmetric,- the equation must call out one not the other...
DEVELOPMENT NOTES: Total field passed through, Time spent in the field...
To frame this, Let's designate the point charge as a virtual submarine boat moving through neutral space, amid its wake and backflow of spot-local opposite-field flowing around it... Now, In the frame where the point charge is stopped, the localized backflow of opposite-charge space, extracted from the neutral cosmos moving oppositely, generates the same-as-our-original magnetic field, (It doesn't need a proton-heavy-wire to generate the total-charge-current equation as for wires: It differentiates space itself: its differential-displacement current suffices to do the work of magnetic-field-generation...)
The oncoming particle, then, moving relatively -2v, (but it always was, relatively), is passing through the magnetic field that is proportional to the velocity of cosmic-space... but the equation for magnetic fields and their attractions and repulsions were never relative to each other, but correlative to the cosmos: the field forces multiply one-times-other...
This article was done initially in development of a project SesQuaTercet movie-story.