Monday, October 5, 2009

BYOJL #2: Maxwell's Treatise on Electricity and Magnetism

No I was not on vacation - some days I have other things which must be done, and as yet I have no grad students (or even undergrad students) to assist. Perhaps it is as well you had some time to catch up - we all have plenty of reading to do, plenty of thinking, plenty of putting what we read and think into action - and - what is even more important - plenty of praying. If we do not start our work with prayer, be it technical or literary, practical or abstract - we will get nowhere, no matter how hard we work.

Today I present the second article in our new series, "Building Your Own Jaki Library" - that is, books which Father Jaki refers to, and which are important for our work in science, in philosophy, and in history - and what is more delightful, books which are presently available in print!

James Clerk Maxwell's A Treatise on Electricity and Magnetism, is available as a two-volume set from Dover: volume one and volume two.

For the classical physicist understanding a phenomenon meant simply reducing it to the Newtonian laws. It was therefore a source of deep satisfaction for them to learn that the mathematical interpretation of a physical process in which gravitation played no part might show a striking resemblance to the law of gravitation. Maxwell was particularly eager to point this out in connection with the law of the conduction of heat in uniform media. Newton's laws were also the ideal Ampere had emulated in his work with such success that Maxwell was prompted to say: "The whole theory and experiment seems as if it had leaped, full-grown, full-armed, from the brain of the Newton of electricity."
[SLJ The Relevance of Physics 73 quoting JCM ToEM II:175]

Another experimental method of verifying the inverse square law in electrostatics was first pointed out by J. Priestley and brought to a very high order of accuracy in later times. Characteristically enough, the argument rested on analogy with the absence of gravitational force inside a spherical shell. To Priestley such analogy suggested that a law of attraction obeying the inverse square law should be the reason why pithballs placed inside an electrified metal cup would experience no force on themselves. As could be easily seen, even the slightest departure from the inverse square law would result in observable effects, and this Cavendish tried to ascertain. His result was negative, and from the sensitivity of his apparatus, he concluded that the exponent in the force law was between 2.02 and 1.98. This was one of Cavendish's many important experiments that lay unpublished until edited by Maxwell in 1879. Maxwell himself repeated the experiment with a much greater accuracy and gave 2.00005 and 1.99995 as the limits for the variation of the value of the exponent permissible by the experimental error. This was a thousandfold improvement on Cavendish, but was by no means the last word on the subject. In 1936 S. J. Plimpton and W. E. Lawton improved the accuracy of the experiment by another factor of ten thousand, setting the limits of variation as 2.000,000,002 and 1.999,999,998.
[SLJ ibid 251 referencing JCM ToEM I:81-83]

... in his [Maxwell's] article on Faraday in the Encyclopaedia Britannica, he even poked fun at those mathematicians "who have rejected Faraday's method of stating his law as unworthy of the precision of their science." For all their mathematics, Maxwell noted, they "have never succeeded in devising any essentially different formula which shall fully express the phenomena without introducing hypotheses about the mutual actions of things which have no physical existence, such as elements of currents which flow out of nothing, then along a wire, and finally sink into nothing again." By contrast, Faraday, with no recourse to mathematics, came up with one of the most seminal laws in physics. For Maxwell this was not without the deepest significance, because Faraday's original statement was a model of perfection. It remains to this day, wrote Maxwell, "the only one which asserts no more than can be verified by experiment, and the only one by which the theory of phenomena can be expressed in a manner which is exactly and numerically accurate, and at the same time within the range of elementary methods of explanation." There is indeed much food for thought in the fact that Maxwell deemed it very fortunate for physics that Faraday was not a "professed mathematician" and was thus left at leisure to "coordinate his ideas with his facts and to express them in natural, untechnical language."
[SLJ ibid 354; the final quote is from JCM ToEM II:176]

Culture is the art of finding the true proportion in things, situations, and human affairs. Consequently, any ingredient in culture must take its place in the whole according to its own proportion of truth, uncertainty, and error. By ignoring history, it is easy to forget that errors, blind alleys, wrong assumptions, and illusions in physics far outnumbered the successful efforts. Faraday, for one, found that even in the most successful instances not a tenth of his preliminary ideas and conclusions could be carried to satisfactory completion. In his diaries failures were recorded as faithfully as successes, in the conviction that an awareness of failures was indispensable for progress. No one upheld this view more resolutely than Maxwell, whose electromagnetic theory was deeply rooted in the study of Faraday's notes. Comparing the methods of Ampère and Faraday, Maxwell warned his students that it was necessary to study both in order to get a view in depth of a scientific theory. Ampère, said Maxwell, does not show the steps by which he arrived at his perfect demonstration: "He removed all traces of the scaffolding by which he had raised it." Faraday, on the other hand, made known both his successful and his unsuccessful experiments, both his crude and his developed ideas. Therefore, if Ampère's research should be read, to hear Maxwell state it, as a "splendid example of scientific research," Faraday's writings should be studied "for the cultivation of a scientific spirit."
[SLJ ibid 519-20 quoting JCM ToEM II:175, 176]

There is one other reference which is wonderful as it gives us a bit of Pierre Duhem's thoughts on this important book, as well as an insight into Duhem's own work:
The same volume of the Bulletin contained a precious insight into the horizons within which Pierre saw the accomplishment of the task of perfecting physics. In a review of the French translation of Maxwell's Treatise on Electricity and Magnetism, he wrote: "Maxwell's Treatise faithfully represents what the science of electricity is in the country of Green and Faraday. The fundamental ideas and the manner of presentation notably differ from the doctrine and mode of exposition adopted in the country of Coulomb and Ampere as well as in the country of Gauss." From this it would have been most tempting to draw a conclusion savoring of chauvinism at a time when French science eagerly sought to recover its erstwhile leadership. But Pierre was committed to the fullness of truth regardless of national provenance. "Perhaps the [French] reader of Maxwell's work will regret the absence there of the clarity of French physicists and of the rigor of German geometers; yet, the methods of the English mathematician will help him in the discovery of new consequences by forcing him to retrace the principal theories of electricity in an order different from, and sometimes inverse to, that to which he is accustomed." These lines were so many anticipations, in a nutshell, of a famed analysis to be given by Pierre two decades later of the colouring of the physicist's reasoning and discourse according to his national origin. In this connection too, Pierre, still in his mid-twenties, had a keen consciousness of ideas that were to distinguish his work for the rest of his life.
[SLJ Uneasy Genius: The Life and Work of Pierre Duhem 67]

No comments: