For over 150 years, since Faraday and Maxwell made quantitative study possible, magnetism has been studied exhaustively and used in endless ways to enhance our lives. However, despite its inestimable value, and despite all the millions of man-hours it has been studied, no one has discovered what magnetism is!
What can IPP contribute toward explicating this mystery? Here are a few IPP concepts that may be germane:
Now, let's see if we can use these concepts to discover the structures of magnetic fields, and their mode of interaction with moving charges.
Since a magnetic field is a very complex phenomenon, we will do well to approach the total concept in stages. As a first step, let's attempt to find the de Broglie wavelength of electrons flowing in a typical metallic conductor used in a magnet coil:
We know that the current impulse travels through the wire at nearly the speed of light (let's choose 0.9c), but we also know that conduction electrons in the bulk of the copper wire travel much more slowly. Let's compute the electron drift velocity for 1A of current in a 1-mm.-diameter wire (#18 AWG). Here are some useful facts:
Copper has 29 protons and electrons, and an atomic weight of 63.55. Copper metal has a density of 8.92 g./cc. Its atoms form a cubic lattice. The following calculation gives the number of copper atoms/centimeter in cardinal directions of the copper cubic lattice:
Cu atoms/cc = (8.92/63.55) x 6.022 x 10e23 = 8.45e22
No. of Cu atoms/cm = (8.45e22)1/3 = 4.39e7
What we shall assume, to determine the de Broglie wavelength, is that the electric current passing through the wire is rather like an incompressible fluid passing through a large diameter pipe, which feeds a very restricted nozzle at its end. You will see that the nature of the incompressible fluid defines the impulse propagation time, while the amount of fluid feeding the pipe determines the amount leaving, as well as its velocity. It is easy to see that the emerging velocity of the electrons can be many orders of magnitude higher than the electron velocity through the "pipe". Our interest will be in determining the "pipe" electron velocity, and the de Broglie wavelength of the "pipe" electrons, whose motions produce the magnetic field. Here is a sequence of calculations leading to our goal:
A current of 1 A. conveys a charge of 1 coulomb/second, which is equivalent to 1/1.602e-19 = 6.24e18 electrons/second.
The number of conduction electrons (@ one/atom) available in each cm. of #18 AWG copper wire (1 mm. in diameter):
0.25p x (4.39e6)² x 4.39e7 = 6.64e20 electrons
The instantaneous number of translating electrons present in each cm. of wire at 0.9c propagation velocity:
6.24e18/(0.9 x 3e10) = 2.31e11 electrons
The translational velocity, ve, of the "pipe" electrons:
ve = 2.7e10 x 2.31e11/6.64e20 = 9.39 cm./sec.
The de Broglie wavelength of the magnet-coil ("pipe") electrons, assuming that all of the available conduction electrons participate in the coil current, and ve is their average drift velocity:
de Broglie wavelength = h/meve = 6.63e-27/(9.11e-28 x 9.39) = 7.75e-1 cm.
Thus, the de Broglie (drift) wavelength = 0.78 cm.*
* You may have been wondering, as I did, what is happening to the other 28 electrons orbiting around each copper nucleus, as the current propagates through the wire. My perception is that all these electrons participate in passing the current impulse by subtle shifts of their orbits relative to the nucleus, but, being bound, can't contribute to the "pipe" current, and, thus, these bound electrons don't affect, or contribute to, the de Broglie wavelength.
Obviously, the above de Broglie wavelength must be viewed as some component of momentum, common to all the "pipe" electrons, which adds to all the other diverse components of momentum that each conduction-band electron possesses, such as orbital motion, thermal noise, changes in coil directions, or drift of the whole system through space.
Since the de Broglie wavelength is seven times larger than the wire diameter, all the conduction-band electrons in a cross-section of the wire are within the first node of each other's matter waves. Thus, these electrons are constrained to drift at identical speeds, because their proximity causes hemispherical shrinkage components to interchange among all "pipe" electrons, until all have acquired precisely equal integrated drift momentum relative to the wire axis. Thus, their "drift" matter waves will become synchronized, and, hence, create large-scale phenomena.
We should not interpret this to mean that all the matter-wave oscillators will have drift components of identical phase, but merely that each drift component will be locked to the phase which the composite signal of the group has in its vicinity. In other words, viewed from a distant point along the line of the group's velocity, all the individual energy components of the drift matter-wave system will be additive - although, of course, they will be attenuated as the inverse square of the group's distance, and, because the components differ in phase and direction over the length of the wire, they will add vectorily.
Since the integrated spin vector of each drifting hovering electron invariably points either in the direction of motion, or directly opposite to this motion (as I demonstrated graphically in Fig. 1-6 of the online book), we can infer that the alternating fields of the "pipe" electrons' hovering oscillators will all be normal to the direction of drift (in an integrated sense). Of course, the wavelengths of these hovering oscillators are much too small (c/f = 3e10/1e23 = 3e-13 cm.) compared to the average separation of "pipe" electrons (1/4.39e7 = 2.3e-8 cm.) to effect synchronization of the hovering frequencies of adjacent "pipe" electrons directly. Thus, it is reasonable to conclude that the hovering oscillators will have all directions of polarization, and both spin directions, such that their alternating charge fields completely cancel, yielding no group effect, whatsoever.
So, to discover the nature of magnetic fields, we must seek our understanding of them in the synchronized de Broglie matter-wave components of these hovering oscillators. What characteristics will these waves have? Here are some plausible deductions:
Now comes the tricky part of this analysis! Let's ask this question: Do the "pipe" electrons, seeing a succession of gradients layer by layer, continue to accelerate as they move through the wire, or do they reach a steady-state velocity in moving through just one layer, which velocity they maintain throughout their progression down the wire? The answer becomes obvious when we reflect on the nature of the matter-waves generated by this gradient:
Here is how to perceive this phenomenon:
Since the splitting of spherical shrinkage contributes equal momentum to the two separating particles, their oppositely directed drift will manifest identical de Broglie wavelengths, even though the Cu ion, being about 110,000 times heavier, will be drifting 110,000 times slower*. The two de Broglie wavelengths will also have the same phase. This is easily understood, since they must sum to a spherical shrinkage LD oscillator of twice each de Broglie oscillator's mass-energy. Also, the charge fields of the de Broglie waves of the two particles will also be additive, such that they wax & wane together at every point in the surrounding space, and have an integrated value equivalent to the inverse-square-diminished value of their central static charge-displacement field. The magnitude of this central field is, of course, equal to the voltage applied to the two ends of the wire divided by the linear number of Cu atoms in the wire.
* This tendency of the copper atoms to move when current passes through a wire is well known to makers of electromagnets, and they make certain that the magnet coil is mechanically constrained. Thus, the momentum opposite to the group of conduction electrons may ultimately be required to move the magnet coil, the magnet's core, and even the laboratory, depending upon how firmly all are bound together. You should see that our analysis is not affected by these variables.
Thus, the static field across each copper atom transmogrifies in the process of drift-generation, to become a field component of the oppositely-directed matter-waves of each atom in the wire. Here, then, is the answer to our beginning question: The "pipe" electrons will drift with a velocity equivalent to the acceleration of one lattice layer! Notice, however, that, as the conduction electrons drift away from their host ions, they penetrate another layer of the copper lattice, and thereby neutralize the ions in that layer during their transit, although both are drifting in opposite directions. We see, then, that the voltage gradient in the wire is no longer generated by displacement of the orbitals relative to the nucleus, but is, rather, created by a multiplicity of de Broglie matter waves.
Now, adding together the various gestalts we have accumulated in the above discussions, we finally are able to describe -
Placing an electromotive force between the two ends of a conducting wire causes each atom in the wire to become a point of origin of two oppositely-directed de Broglie matter-waves, each wave so constituted as to produce an inverse-square charge field everywhere parallel to the wire axis at the matter-wave's point of origin. These oppositely-moving de Broglie waveforms, which exist in the form of infinitely expanding & drifting lattice-density oscillations, have the same frequency & phase, and sum together to form a composite charge field whose gradient & direction is determined by the vector contributions from all the hovering oscillator drift components of every atom in the magnet coil wire.
Of course, we must perceive these charge-field-containing oscillations as merely a component of a much more complex de Broglie waveform containing many more components of hemispherical shrinkage. The mix of hemispherical shrinkage components will undoubtedly differ among all the individual particles comprising the copper wire. These components fall into four basic categories:
The last two components of momentum, being random in amplitude and direction among the individual conduction electrons comprising the coil current, can produce no group effects. We can also ignore in our analysis the momentum components due to the laboratory's velocity relative to absolute space, since these normally remain unchanged over the course of an experiment.
Thus, we can confine our analysis of magnetic fields to the field-induced momentum components of the oppositely drifting conduction electrons & copper ions in the magnet coil.
A magnetic field is simply an implicit charge field developed by the summation of field-containing de Broglie matter-wave components from the totality of oppositely drifting conduction electrons & ions in a conductor. The gradient & direction of this implicit charge field will be found to vary continuously, because the sources of the de Broglie waves are uniformly distributed along the breadth and length of the conductor, and take their individual gradient directions from the direction of current flow at each point in the conductor. Thus, the geometry of the magnetic field external to a current-carrying conductor depends upon four things:
There is no need to elaborate on the first three points, since all of you physicists are expert at the integrations needed to calculate the electric field gradient at any point in this external implicit charge-field pattern. What you should notice, however, is that IPP's notion of a magnetic field allows us to purge physics of all the complicated rules of the directions of magnetic lines of force relative to direction of the initiating current flow, and the direction of the magnetic force relative to the direction of movement of a charged particle. All one needs to keep in mind is the way in which the voltage gradient applied to a magnet coil is manifest in the multiplicity of de Broglie waves forming this charge-field pattern. Then, knowing the direction and gradient of this field at each point, we can easily determining the direction of deflection of a charged particle moving through this point - it just becomes a problem in electrodynamics.
The charge-field-containing de Broglie matter-wave concept of magnetic fields is a good start, but we obviously need to understand point #4, above, to fully understand magnetism. We need to know how the nature of the medium surrounding the source of these de Broglie waves affects the implicit charge-field generating process.
To illustrate, suppose that a portion of the external medium is a conductor. Won't the charge-gradients developed by the de Broglie waves in this conductor cause separation & opposite drift of the conduction electrons and ions in this conductor? And won't these drifting electrons and ions in the external conductor create charge-containing de Broglie waves which rob energy from the magnetic field, tending to lower its de Broglie frequency, which interacts back upon the coil current to increase the flow of "pipe" electrons sufficient to maintain the same EMF per layer of the copper lattice? So IPP shows us why the net result of placing an external conductor in a magnetic field is to increase the coil current - but many complications accompanying this insight remain to be explained.
For example, there is the problem of understanding ferromagnetism, diamagnetism, and permanent magnets from the IPP perspective. These problems obviously relate to the ease or difficulty of establishing temporary, or permanent, circulating currents in various materials immersed in magnetic fields. And the key to understanding the mechanisms of these currents lies in discovering how adjacent atoms in a conductive matrix can adjust their electron orbitals so that they intermesh, and thereby continually pass electrons from one to another as part of a group electron orbital process. If the conductive atomic matrix has properties that permit continuous loops of these orbitally, connected adjacent atoms, then electron current can flow in these loops forever with no energy loss.
I suspect that IPP will eventually show us why these conductive loops exist only in conductors made from a limited number of elements from the periodic table. And this understanding will derive from IPP's insight that the configuration of an atom's electron orbitals is determined by the shape of its nucleus, and, thus, from IPP's ability to discern (ultimately) the actual geometric configurations assumed by the nucleons that comprise each isotope of each element, and the way the surface charges of these nucleons vary during the synchronized charge-exchange cycles of adjacent nucleons. Achieving these insights to elements throughout the whole periodic table will be a tremendously challenging task, and I am content to pass this on to younger minds.