3.5 Summary and Conclusions

Maxwell's Theory, and the Importance of a Thoroughly Conscious Ignorance

Early investigators cast electromagnetism in a Newtonian mold, accepting the point-mass, action-at-a-distance interpretation as a starting point. In this view, objects over here influenced objects over there with no intermediary mechanism. By meticulous experimentation, Coulomb, Ampère, Gauss, Faraday, and others uncovered the details of how electricity and magnetism work. Even some who made the most significant theoretical leaps were themselves also experimentalists. Pioneering geophysicist and experimentalist, Carl Friedrich Gauss, devised and employed sophisticated techniques to measure geomagnetic fields in addition to devising the mathematical relation that came to be known as Gauss’s Law. Gauss was reputed to possess a certain mathematical talent as well. Maxwell repeated many of Cavendish’s early experiments, acquainting himself with the experimental basis behind electromagnetic theory.

And what was that theory?

Electric field lines originate on positive charge and terminate on negative charge. In the absence of charge, electric fields form closed loops. The direction of the lines indicates the direction of the electric force per charge; the density or concentration of the lines is proportional to the intensity of the force. Magnetic field lines show the direction of the torque that would align a small compass needle. Fields of both kinds tend to spread out to fill the available space. Electric field lines are perpendicular to conductors. Current – moving charge – is the source of a magnetic field, and the magnetic field curls around a current in a closed loop in the orientation determined by the right-hand rule. There’s a component of the magnetic field that depends on the current and another component that depends on how quickly the current is changing. A changing current – accelerating or decelerating charge – gives rise to an expanding ring of magnetic field that ripples out in a manner first envisioned by Faraday in 1832.

Maxwell consolidated the work of Ampère, Ohm, Faraday, Gauss, and others to compile his laws of electromagnetism. Adding the concept of displacement current, he made the critical connection between electromagnetism and optics. He proved that electromagnetic disturbances propagate at the speed of light, and he worked out the mathematical theory of electromagnetic waves.

What were the key features of Maxwell’s approach?

Maxwell studied the overlooked experimental research of Cavendish and constructed elaborate conceptual models to try to understand how electromagnetism functions. “If we are ever to discover the laws of nature,” Maxwell explained, “we must do so by obtaining the most accurate acquaintance with the facts of nature and not by dressing up in philosophical language the loose opinions of men who had no knowledge of the facts which throw most light on these laws” [[i]]. He avoided making unnecessary hypotheses, and he made clear that he regarded these models as merely conceptual tools. Nevertheless, he was convinced that somehow energy exists stored in the space around charges and currents.

Meanwhile, Ohm, Kirchhoff, and others were developing the theoretical basis of electronics, and telegraphy was emerging as a leading-edge application of electromagnetic science.

The mathematical details involved in applying the complicated equations are best left to a formal course in electromagnetism. However, Faraday’s field approach allows for an intuition of what they mean and how they work that doesn’t rely on a rigorous mathematical understanding.

Acceptance of these revolutionary ideas took time. Faraday’s simple picture did not appeal to professionals steeped in the mathematics of potential theory who considered the counter-intuitive action-at-a-distance model validated by the success of their formulas at predicting the results of experiments. And novel ideas are almost always accepted with reluctance. One historian had this to say about André Marie Ampère’s discoveries:

It might be thought that these discoveries of Ampère would be welcomed with great enthusiasm. As a matter of fact, however, new discoveries that are really novel always have, as almost their surest index, the fact that contemporaries refuse to accept them. The more versed a man is in the science in which the discovery comes, the more likely is he to delay his acceptance of the novelty. This is not so surprising, since, as a rule, new discoveries are nearly always very simple expressions of great truths that seem obvious once they are accepted yet have never been thought of. They mean, therefore, that men who consider themselves distinguished in a particular science have missed some easily discoverable phenomenon or its full significance, and so, to accept a new discovery in their department of learning, men must confess their own lack of foresight [[ii]].

Ampère’s difficulties securing acceptance for his ideas paled in comparison to those of successful innovators, like Ohm, let alone those whose promising careers were completely crushed, like those of Herapath and Waterston. As Maxwell noted, “…thoroughly conscious ignorance … is the prelude to every real advance in knowledge” [[iii]]. The ability to set aside preconceptions and give a fair hearing to revolutionary new ideas is almost as rare as revolutionary new ideas, themselves. Skilled practitioners, confident and arrogant in their competency, regularly turn a blind eye to the advances in theory or practice that could take their art to the next level of understanding.

Maxwell died at age 48 in 1879 leaving behind him a legacy of electromagnetic pessimism. FitzGerald and others wrestling with Maxwell’s theory to try to make sense of it would have to carry on without the help of their master. We can only speculate how Maxwell might have matured his theory if he’d lived another couple of decades. FitzGerald and Maxwell’s other successors however, a band of intrepid, independent-thinking disciples that historian Bruce J. Hunt called, The Maxwellians, would follow and extend the path Maxwell blazed and come close to bringing electromagnetism to fruition [[iv]]. Through real-world exposure to the applied electromagnetic science of telegraphy, they would learn how to make FitzGerald’s possibility of electromagnetic waves into a reality.

Next time, 4.0 Electromagnetism Comes of Age: Possibility Becomes Reality

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References

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[i] James Clerk Maxwell, "On Action at a Distance," Proceedings of the Royal Institution of Great Britain, Vol. VII, reprinted in  The Scientific Papers of James Clerk Maxwell  (W.D. Niven, ed.), (New York:  Dover, 1953?) pp. 318.  Originally published, 1890.

[ii] O’Reilly, Michael Francis (writing as Brother Potamian), and James Joseph Walsh, Makers of Electricity, New York: Fordham University Press, 1909, p. 251.

[iii] Maxwell, James Clerk, “The Kinetic Theory of Gases,” Nature, July 26, 1877, p. 245.

[iv] Hunt, Bruce J., The Maxwellians, Ithaca: Cornell University Press, 1991