# Part II: Magnetism

Growing fields of study specialize, ideally leading to ever deeper understanding. Since, over time, each new field develops its own culture, this fragmentation can lead to isolated groups with incommensurate views.

In principle, physics is immune from balkanization because we follow a strict scientific method of experimental hypothesis testing. Theorists compete to explain each new experimental result, and experimentalists design new experiments to distinguish among these competing explanations. Eventually one theory passes every experimental test and everyone moves on. What used to be cutting edge is now accepted knowledge.

The great philosopher of science Thomas Kuhn called the most entrenched theories paradigms.[1] Franklin’s law of the conservation of charge, for example, became a paradigm during the eighteenth century. It has been continuously applied ever since, so there is no reason for a physicist to actually test it.[2]

Sometimes, however, scientists come to consensus too quickly, and the wrong theory becomes a paradigm. The more entrenched the paradigm, the more likely that a physical misconception will be propagated to the next generation of scientists. Over time, experimentalists ignore clearer and clearer evidence, and theorists come up with odder and odder theories, all to preserve the existing paradigm. Finally someone presents an alternative theory that elegantly explains the existing observations. At this point, the field is forced to go through a paradigm shift, after which a great burst of productivity usually follows.

The old paradigm can, however, linger—often for good reasons. For example, Galileo’s observations of the phases of Venus debunked the geocentric model of the solar system,[3] throwing the field of astronomy into turmoil. By this time, however, systems of time keeping and celestial coordinates were already well established, so astronomers still use the geocentric representation for those applications—even though nobody today actually believes that the sun revolves around the earth. Like the geocentric model of the universe, the pole model of magnetism lasted for centuries before being debunked.

Coulomb not only developed his law of electrostatics, but also a parallel law for magnetism. Coulomb’s pole model posited an inverse square law between magnetic poles, exactly analogous to electrostatics and gravity. Magnetization, therefore, was due to the separation of northness from southness, in exactly the same way that separation of positive from negative charge causes electrical phenomena.

Luckily, André-Marie Ampère developed a competing model of magnetization, involving microscopic current loops rather than the separation of northness from southness. Since current loops are the classical analog to quantized angular momentum, we credit Ampère with finding the correct paradigm.

However, Ampère’s classical picture completely failed to predict why magnets stick to steel. Without quantum mechanics, it actually predicted a repulsive force, just as we now observe in superconductors. Thus, for very good scientific reasons, Ampère failed to convince most scientists, especially those working with permanent magnets.

James Clerk Maxwell avoided the controversy by making his field equations work with both representations. He did this by introducing two electric fields, D and E, and two magnetic fields,  H and B, Physicists pretty much agreed that E was the fundamental electric field, which could be measured in situ. Which magnetic field one considered more fundamental, however, depended on one’s favored model of magnetic matter.

Under the pole model interpretation, H was called the magnetic field and considered more fundamental, while B was the magnetic induction. Under Ampère’s current loop paradigm, however, B is considered the true magnetic field, while H has little intrinsic meaning. Since both interpretations predict the same macroscopic phenomena, it made little difference which model one chose to apply. Thus, scientists and engineers would use whichever paradigm simplified their particular analysis or worked better at explaining their own experiments.

The beauty of the pole model is that the same intricate mathematics of Newtonian gravity and electrostatics can be recycled into solving magnetostatics problems. The heroes of electrostatics, including Gauss and Poisson, defined a magnetic pole density ${{\rho }_{\text{M}}}$, analogous to the electric charge density. Next they applied a pseudo-Gauss’s law, $\vec{\nabla }\cdot \vec{H}={{\rho }_{\text{M}}}$, and introduced a corresponding magnetostatic scalar potential ${{\phi }_{M}}$ that satisfies $\vec{\nabla }{{\phi }_{M}}=\vec{H}$.  Using these laws of magnetostatics, they successfully characterized the measured magnetic field surrounding any permanent magnet.

The only catch is that magnetic monopoles do not exist. Moveable magnetic “poles” are simply convenient fictions, which have no real physical meaning.  However, the definitive experiments debunking the pole model did not take place until 1915.

Like timekeeping after Galileo, some fields of magnetics that matured in the nineteenth century continue their existing practices to this day. This is primarily true of geomagnetism, because the magnetic scalar potential does an excellent job of empirically modeling the magnetic field surrounding the earth. Just as no modern timekeeper believes that the sun orbits the earth, no modern geophysicist actually believes that poles move around inside of magnets. However, there is a significant cost to changing existing practice, with no additional benefit in geological predictive power.

There are additional costs, however, of continuing to use unphysical legacy models, which are borne by you, the student. You must not only learn how the natural world works to the best of our twenty-first century knowledge, but you must also learn the history of your own field of study. Only through historical context can you distinguish practices based on current physics from those based on past physics.

[1] Kuhn, Thomas S., The Structure of Scientific Revolutions, (Chicago: The University of Chicago Press 1962).

[2] The astute reader will protest. Charge conservation has been tested more accurately than any other law of nature (p. 49). Yes, but the purpose of that experiment was to observe neutrinos from space. Confirmation of charge conservation was simply a fun byproduct of an existing experiment. Why spend resources to confirm something we already know?

[3] Aristarchus of Samos proposed the heliocentric model of the solar system in the third century BC. However, critics pointed out that it predicted very fast prevailing winds and annual variations in the brightness and location of stars, none of which were observed.