3.4.8 Maxwell's Methods and Views

The Profound Meaning Behind His Math.

May 22, 2024

An administrative note… I am on an extended vacation. I probably won’t be responding to comments in a timely fashion. However, I have posts already lined up for the next several weeks, so you won’t have to miss a single installment of Fields & Energy.

Maxwell placed heavy reliance on physical analogies. He developed several mechanical models of the æther, the supposed medium which transmits electric and magnetic influences. He constructed these models to correspond to known behavior, and then studied them to see what additional behavior they predicted. In this fashion, Maxwell made his crucial discovery of the displacement current that makes the connection between a changing electric field and a magnetic field.

Maxwell recognized these analogies as conceptual tools, ways by which the physically real relationship was to be understood or illustrated. For instance, in his classic paper “A Dynamical Theory of the Electromagnetic Field,” Maxwell made this clear:

I have on a former occasion attempted to describe a particular kind of motion and a particular kind of strain, so arranged as to account for the phenomena. In the present paper I avoid any hypothesis of this kind; and in using such words as electric momentum and electric elasticity in reference to the known phenomena of the induction of currents and the polarization of dielectrics, I wish merely to direct the mind of the reader to mechanical phenomena which will assist him in understanding the electrical ones. All such phrases in the present paper are to be considered as illustrative, not as explanatory [[i]].

Although Maxwell worked on a more abstract, mathematical level than did Faraday, he kept his ideas closely linked to Faraday’s physical conceptions. Maxwell took to heart Faraday’s physical views on electromagnetism and developed the mathematical abstractions whereby Faraday's ideas could be rigorously described. Despite working on this abstract level, Maxwell did not lose his tie to reality. He understood that his theoretical models were tools to be used in understanding natural phenomena and did not launch into flights of fancy based on potentially spurious similarities between his models and reality.

From the prevalent action-at-a-distance perspective, electromagnetic energy was associated with charges. Energy vanished from charges over here and appeared at charges over there as electromagnetic systems interacted with each other. What, if anything, might happen in between was idle philosophic speculation, not a matter for consideration by the action-at-a-distance theory. “Shut up and calculate,” was the prevailing wisdom. Maxwell took a different view.

Extending on work done by his friend [[ii]], William Thomson (1824-1907) (later Lord Kelvin), Maxwell adopted the idea that the energy was distributed throughout space, associated not with the charge, but with Faraday's fields:

In speaking of the Energy of the field, however, I wish to be understood literally. All energy is the same as mechanical energy, whether it exists in the form of motion or in that of elasticity, or in any other form. The energy in electro-magnetic phenomena is mechanical energy. The only question is, Where does it reside? On the old theories it resides in the electrified bodies, conducting circuits, and magnets, in the form of an unknown quantity called potential energy, or the power of producing certain effects at a distance. On our theory it resides in the electro-magnetic field, in the space surrounding the electrified and magnetic bodies, as well as in those bodies themselves.... [[iii]].

Maxwell regarded this as one of the central ideas of his theory of electromagnetism, delivering an insightful and memorable paper on the history of action-at-a-distance, contrasting that view against his and Faraday’s [[iv]].

Although Maxwell is best known for his pioneering work on electricity and magnetism, he also contributed to the kinetic theory of gases – deriving the laws governing the behavior of gases from the idea that gases consist of atoms.

Ironically, the foundations of Maxwell’s kinetic theory were first discovered by other investigators. In 1820, John Herapath (1790–1868), proposed a paper introducing a kinetic theory of gases to the Royal Society of London who rejected his largely correct treatment.

In 1845, another young scientist, John James Waterston (1811–1883) introduced a more rigorous paper on the kinetic theory of gases. The Royal Society rejected it, too. Figure 3.34 shows these often-forgotten scientific pioneers.

Figure 3.34: John Herapath (1790–1868), left, and John James Waterston (1811–1883) [**[v]**], right.

These papers “failed peer review,” according to Wikipedia, as if that excuses the incompetence of the scientific establishment [[vi]]. It would be more honest to say that peer review failed these papers and their authors. Clifford Truesdell (1919–2000), noted mathematician, natural philosopher, and historian of science, had this to say about the shameful incident:

We have seen the Royal Society twice in thirty years with maximally pompous humbuggery and humbugging pomposity stifle the truth in favor of the wrong, twice bury a great man in contempt while exalting tame, bustling boobies whose whole lives add nothing to the science passed on to our day.… the Society’s position in those two years was so strong as to stop dead two careers in mathematical physics which at their short beginnings gave promise second to few in the century… [[vii]].

Writing in the introduction to Waterston’s collected works, J.B.S. Haldane (1892–1964) argued:

It is probable that in the long and honourable history of the Royal Society no mistake more disastrous in its actual consequences for the progress of science and the reputation of British science than the rejection of Waterston’s papers was ever made .... There is every reason for believing that had the papers been published physical chemistry and thermodynamics would have developed mainly in this country and along much simpler, more correct, and more intelligible lines than those of their actual development [[viii]].

The great value of history lies in the lessons it teaches us for guiding our conduct today. The sanitized version of scientific history in which science is a linear progression of truth building upon truth ignores the reality that scientists are not immune to all the petty jealousies, laziness, monetary incentives, and rivalries that characterize most every human institution.

Figure 3.30: George Francis FitzGerald (1851–1901) [**[xi]**].

Sadly, Maxwell did not live long enough to see his pioneering electromagnetic work come to fruition. Maxwell’s untimely death at age 48 in 1879 left his successors with some keen physical insights and a collection of ingenious (if awkwardly expressed) equations. Just a couple of weeks after Maxwell’s death, George FitzGerald (1851–1901) prepared and presented a short paper, “On the Impossibility of Originating Wave Disturbances in the Ether by Means of Electric Forces” to the Royal Dublin Society in 1879. FitzGerald was only barely persuaded to change the title from “Impossibility” to “Possibility” at the last minute:

…we may assert a very general theorem concerning the displacement currents which Professor Maxwell assumes… that however these may be produced by any system… they will never be so distributed as to originate wave disturbances propagated through space outside the system [[ix]].

FitzGerald’s pessimistic interpretations discouraged Oliver Lodge (1851–1940) and others [[x]] from pursuing Maxwell’s ideas.

Next time: 3.5 Summary & Conclusion.

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References

[i] James Clerk Maxwell, A Dynamical Theory of the Electromagnetic Field, §73 (Edinburgh: Scottish Academic Press, 1982), p. 70. Originally published as "A Dynamical Theory of the Electromagnetic Field", Philosophical Transactions of the Royal Society of London CLV (1865).

[ii] See Whittaker, Op.Cit., p. 222.

[iii] James Clerk Maxwell, A Dynamical Theory of the Electromagnetic Field, §74 (Edinburgh: Scottish Academic Press, 1982), p. 70. Originally published as "A Dynamical Theory of the Electromagnetic Field", Philosophical Transactions of the Royal Society of London CLV (1865).

[iv] James Clerk Maxwell, "Action at a Distance," Proceedings of the Royal Instituion of Great Britain, Vol. 7, 1873-5, London, p. 49. As quoted in The Scientific Papers of James Clerk Maxwell (W.D. Niven, ed.), (New York: Dover, 1953?) pp. 317. Originally published, 1890.

[v] See: https://www.wikidata.org/wiki/Q1700613#/media/File:Waterston.jpg

[vi] “John Herapath later independently formulated a kinetic theory in 1820, but mistakenly associated temperature with momentum rather than vis viva or kinetic energy. His work ultimately failed peer review and was neglected. John James Waterston in 1843 provided a largely accurate account, again independently, but his work received the same reception, failing peer review even from someone as well-disposed to the kinetic principle as Davy.” See https://en.wikipedia.org/wiki/History_of_thermodynamics, accessed 19 March, 2018. In addition, Davy was involved in reviewing Herapath’s work, not Waterston’s.

[vii] Truesdell, Clifford, “Establishment Stifles Genius: Herapath and Waterston,” collected in An Idiot’s Fugitive Essays on Science, New York: Springer-Verlag, 1984, pp. 397-398.

[viii] J. B. S. Haldane, The Collected Scientific Papers of John James Waterston, London: Oliver & Boyd, 1928,. p. lxv.

[ix] FitzGerald, George, “On the Possibility of Originating Wave Disturbances in the Ether by Means of Electric Forces,” From the Scientific Transactions of the Royal Dublin Society, read November 17, 1879. See Collected Works, p. 92.

[x] Hunt, Bruce J., The Maxwellians, Ithaca: Cornell University Press, 1991, p. 33.

[xi] FitzGerald, Geroge Francis, The Collected Works of George Francis Fitzgerald, London: Longmans, Green, & Co., 1902. See front piece.

John Plaice

Aug 29

The key is to control the narrative, and to continue to rewrite it as necessary. Whether the narrative happens to be close to the truth or far from it is of little importance.

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