Introduction to World Magnet Model (WMM)
We have recently been made aware that 2025 is the year of the world magnetic model (WMM). As we have discussed earlier, magnetism underlies almost all fundamental experiments. Moreover the year 2025 will also introduce the Artemis II, III lunar space missions. Eyes on the skies. So there is opportunity to engage with the WMM problem now. It’s becoming understood that magnetic fields at the poles are dangerously misunderstood.
The recent translation (Assis and Chaib 2015) has been crucial in our understanding of Ampere’s masterpiece and his interactions with the leading scientists of his time. Ampere had no formal education, yet became a professor of mathematics at l’Ecole Polytechnique in Lyons and then Paris. We are specifically interested in Ampere’s hypothesis of electrical molecular currents. A revealing comment included in a footnote quoting from William’s 1981 brief biography on Andre-Marie Ampere:
[begin quote]“There was no doubt that Ampere took his electrodynamic molecule [that is, the hypothesis of currents of electricity around each molecule] seriously and expected others to do so too. In an answer to a letter from the Dutch physicist van Beck, published in the Journal de Physique in 1821, Ampere argued eloquently for his model, insisting that it could be used to explain not only magnetism but also chemical combination and elective affinity [sic]. In short, it was to be considered the foundation of a new theory of matter. This was one of the reasons why Ampere’s theory of electrodynamics was not immediately and universally accepted. To accept it meant to accept as well a theory of the ultimate structure of matter itself.” [end quote] (Assis and Chaib 2015, footnotes pp.24)
We have no qualms about Ampere’s electrodynamic molecules and their applications to “ultimate theories of matter”. In fact we are persuaded by Ampere’s argument for homogeneous electrodynamic theories. Magnetism (in Ampere’s conception) is always to be found in environmental electrical currents (i.e. charged matter in motion). Ampere seeks the source of the earth’s magnetism in electrical currents at both the microscopic level in atomic structures, and global macroscopic currents in and through the earth. We cannot be certain whether Ampere ever looked beyond the earth under his feet to the Sun as a source of geomagnetism.
So what about the year 2025 being the year of the world magnetic model?
The most difficult aspect of the WMM is that earth’s magnetic field is always changing. We understand magnetic forces as dynamic by definition and susceptible to change. But can we really be confident in our maps being accurate one, two, four years later? Obviously cartographers assume the earth’s land masses are not perceptibly moving. Actually WMM is aware of this variability problem. Hence WMM is revised every five years. We quote from the report “State of the Geomagnetic Field: December 2023”: [begin quote] “The main geomagnetic field is constantly changing due to convective flow of and waves in the Earth’s liquid outer core. As the system is essentially chaotic on longer timescales, this change cannot be entirely predicted, and so the accuracy of the WMM slowly decreases over time, necessitating that it be regularly updated (typically every five years).” [end quote]
Here we notice the reference to fluid analogies, like the convective flow of waves in earth’s supposed “liquid outer core”. What is the convective flow? Wikipedia would suggest that convection arises from some lower heat layer, and then radiates upwards towards the surface. It’s strange really. Also observe the expression “essentially chaotic on longer timescales.” This is another assumption of the fluid model assumptions. Observe also the reference to the necessity(!) of regular updates which are typically every five years. We do not necessarily share in these standard fluid assumptions. Again referring to Ampere, we insist on homogeneous descriptions, as far as possible. So we do not commit to arbitrary fluid hypotheses at this stage.
It is typically presumed that an object is magnetic depending on it’s internal atomic structure. But what is the role of the environment in magnetic effects? For example if a rock on the moon has certain magnetic orientation, and this rock is transported to the earth, will the rock again be magnetic?, and how can we relate the magnetic forces between the two points? Is it possible for a rock to be magnetic when it leaves the moon, and arrives to earth non magnetic, or vice versa? Could it be possible that we take a rock from earth, bring it to the moon, and then return to the earth in the same location, and observe that the magnetic orientation of the rock has changed?
These are questions, but we must insist that there is an environmental contribution, depending on an object’s interaction with its environment. This is inherent to Ampere’s electrodynamic explanation of magnetism: the interacting current is external, or internal to the object, but it’s part of the environment. By contrast, the magnetic field \(B\) as defined by the Maxwellian classical approach is supposed to be a local object: at the point \(x\) one wants to obtain \(B=B(x)\) directly. But is this possible? These are admittedly fundamental questions, hence we repeat them.
C.F. Gauss and Erdmagnetismus
[Missing references. Will be corrected in future post. -JHM]
The World Magnet Model is still based principally on Carl Friedrich Gauss’ (1777–1855) fundamental research in the earth’s magnetic field and his memoirs on the subject, e.g. Gauss’ memoir “General Theory of Terrestrial Magnetism”. Gauss is credited with “demonstrating” that the dominant geomagnetic field is generated from the earth’s interior. This is treated in the above memoir. Gauss’ argument claims to be independant of hypotheses as to the origin and cause of earth’s magnetism. We are amazed how Gauss openly discusses Ampere’s molecular current hypothesis, although Gauss himself adopts Poisson’s magnetic fluid approach. It’s surprising to discover that Gauss was so perceptive of Ampere’s brilliance, and ready to admit them insofar as consistent with experiment.
Gauss’ argument is deduced from his assuming a Coulomb-Poisson type force law between the supposed magnet \(NS\) dipoles. Gauss assumes that the magnetic potential is integrated by a Coulomb type expression \(V=\int d\mu/r\) where \(\mu\) is assumed to be the distribution of “free magnetism”. This is a naive concept by today’s standards. Thus Gauss defines the magnetic force as the gradient of a harmonic potential.
Here we remark that Gauss is correct in reasoning that Coloumb’s formula is consistent with AMCH. Thus Gauss seems to be aware of Ampere’s 1824 results which demonstrated the equivalence of Poisson’s 1823 magnetic force law. But here we think there is a deficiency in both Poisson’s and Ampere’s treatment of the dipole force. Regarding Poisson, we think the molecular magnetic fluid cannot reasonably sustain a dipole surface without an external force. Likewise we criticize Ampere’s electrodynamic solenoid (Assis and Chaib 2015, ch.9–10) as insufficient, since there is by necessity an external force necessary to balance the repulsive force of the parallel closed currents. In both cases we claim they do not satisfactorily address the need for external power supply. Our own interpretation is that Ampere was motivated to demonstrate the equivalence of his force law between currents and the molecular current hypothesis with Poisson’s 1823 results. In otherwords, Ampere’s 1824 papers [Ibid] were reactionary, in a sense, and not conclusive.
Remark. Gauss considers the “magnetic fluid” as consisting of north and south molecules. But it’s known that there are no material carriers of magnetism, and there are no isolated magnetic poles. Therefore the fundamental premise of the Coulomb-Poisson force seems flawed. Moreover Gauss applies an electrostatic principle of Poisson to represent the distribution of “free magnetic fluid” as supported on the boundary surface of the sphere. This leads to Gauss’ spherical harmonic model of the earth’s magnetic field, and his assumption that the magnetic potential \(B=\nabla \phi\) is the gradient of a harmonic potential (!)on the surface of the earth and exterior according to Coulomb-Poisson’s proposed magnetic force law.
Thus Gauss presumes that the source of geomagnetism, i.e. the source of the north and south poles, lies in the interior of the earth. We do not necessarily agree with the esteemed Gauss’ analysis. Yet this analysis remains the dominant model today, the coefficients of the potential are fit according to Gauss’ method of least squares.
However Gauss himself reasons beyond his own model, reasoning in Article 36 of his memoir: [begin quote] “Another part of our theory on which there may exist a doubt is, the supposition that the agents of the terrestrial magnetic force are situated exclusively in the interior of the earth. If we seek for their immediate causes, partly or wholly, without the earth, and confine ourselves to known scientific grounds, we can only think of galvanic currents. But the atmosphere is no conductor of such currents, neither is vacant space; thus, in seeking in the upper regions for a vehicle of galvanic currents we go beyond our knowledge. ·But our ignorance gives us no right absolutely to deny the possibility of such currents; we are forbidden to do so by the enigmatical phenomena of the Aurora Borealis, in which there is every appearance that electricity in motion performs a principal part. It will therefore still be interesting to examine what form magnetic action arising from such currents would assume on the surface of the earth.” [end quote].
Thus we are led to further consider the electrodynamic cylinders and the dipole surfaces, and our earlier critique that both models require an external force to maintain the assumed separations. There is an idea here that the earth’s magnetic fields are secondary electric effects caused by the primary Birkeland polar circuits. This is the external force necessary to maintain the charge separations in Ampere’s dynamic solenoid, and likewise would be the force providing the energy required for the dipole magnetic separation assumed in Poisson’s explanation.
For us, the key is that Ampere’s idea of perfectly parallel electrical currents defining the cylinder are not physically realistic. Parallel currents repel. Therefore any parallel currents, as we understand them, would require an external power source to maintain the separation. Apparently this idea is rather common in plasma physics, where it’s understood that double layers only exist in nontrivial currents.
So the conclusion? That we need to look to the aurora and correct the error common to both Ampere and Poisson in the electrodynamic cylinder and the magnetic dipole layers, respectively.
[To be continued –JHM]