Part I: Sneaking Up On Einstein

As far as the laws of mathematics refer to reality, they are not certain,

and as far as they are certain, they do not refer to reality.

– Albert Einstein (1879–1955)

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Section 1 Section 2 Section 3 Section 4 Section 5 Section 6

Chapter 4

Section 2: Faraday, Thomson, and Maxwell

Clerk Maxwell (pronounced “Clark”) graduated in 1854 from Trinity College, Cambridge, with a Bachelor of Arts degree in mathematics. His close relationships with previous Cambridge graduates included William Thomson (1824-1907) (later Lord Kelvin), Professor of Natural Philosophy at the University of Glasgow, and George G. Stokes (1819-1903), Lucasian Professor of Mathematics at Cambridge. Thomson and Stokes were among the top, if not the top mathematical theoreticians in mid-19th century England. In a letter dated February 20, 1854, Maxwell asked Thomson for advice in studying the new science of electricity:

If [one] wished to read Ampère Faraday &c how should they be arranged, and at what stage & in what order might he read your articles in the Cambridge Journal?

If you have in your mind any answer to the above questions, three of us here would be content to look upon an embodiment of it in writing as advice.8

William Thomson’s education and career had been enhanced and facilitated by his father, James Thomson, who was appointed to the Chair of Mathematics at the University of Glasgow in 1832. Thomson graduated from Cambridge in 1845 at age 21, then traveled to Paris and studied French scientific and mathematical methods. In Paris, Joseph Liouville (1809-1882) encouraged Thomson’s professional interest in Michael Faraday, whom Thomson knew and interacted with in London, by suggesting that the reconciliation of Faraday’s electrostatic experimental results and the views of the French mathematicians, Ampère, Coulomb, Poisson, etc., could be a fertile field of mathematical endeavor.

Intrigued by Liouville’s suggestion Thomson wrote several papers over the next few years based on Faraday’s experimental results, including:

On a Mechanical Representation of Electric, Magnetic and Galvanic Forces (1847).

On the Mathematical Theory of Electricity (1848).

On the Mathematical Theory of Magnetism (1851).

After receiving Maxwell’s request for guidance, Thomson shared with him the challenge presented by interpreting Faraday’s written experimental results using mathematical formalism. Faraday’s work on electricity and magnetism intrigued Maxwell and he began his research by reading Thomson’s papers on the subject.

Maxwell’s first published paper based on Faraday’s work attempted “to shew how, by a strict application of the ideas and methods of Faraday, the connexion of the very different orders of phenomena which he has discovered may be clearly placed before the mathematical mind.”9 The resulting paper, On Faraday’s Lines of Force, was read in two parts to the Royal Society, London, on December 10, 1855, and February 11, 1856.10 The paper, based on fanciful ad hoc analogies rather than Faraday’s experimental results, can be seen as the logical extension of Thomson’s earlier work.

Six years later Maxwell published a second paper, On Physical Lines of Force, in which he again employed Thomson’s method of creating fanciful ad hoc analogies while seeking a mechanical rationale for magnetic lines of force, was published in 1861-1862. He wrote:11

I propose now to examine magnetic phenomena from a mechanical point of view, and to determine what tensions in, or motions of, a medium are capable of producing the mechanical phenomena observed. If, by the same hypothesis, we can connect the phenomena of magnetic attraction with electromagnetic phenomena and with those of induced currents, we shall have found a theory which, if not true, can only be proved to be erroneous by experiments which will greatly enlarge our knowledge of this part of physics.12

Maxwell’s definitive paper on electricity and magnetism, A Dynamical Theory of the Electromagnetic Field, was published in 1864.13 His work had progressed to the point of proposing a bona fide physical theory which focused on developing the mathematical formalism of Faraday’s physically real experimental results as opposed to the fanciful ad hoc analogies and particles acting at a distance employed in the first two papers. In the introductory paragraphs he explained:

The theory I propose may therefore be called a theory of the Electromagnetic Field, because it has to do with the space in the neighbourhood of the electric or magnetic bodies, and it may be called a Dynamical Theory, because it assumes that in that space there is matter in motion, by which the observed electromagnetic phenomena are produced. (Maxwell’s emphasis)14

In the 1864 paper Maxwell also acknowledges Faraday’s priority with regard to the transverse propagation of electric and magnetic fields:

The conception of the propagation of transverse magnetic disturbances to the exclusion of normal ones is distinctly set forth by Professor Faraday * in his “Thoughts on Ray Vibrations.” The electromagnetic theory of light, as proposed by him, is the same in substance as that which I have begun to develope in this paper, except that in 1846 there were no data to calculate the velocity of propagation.

* Philosophical Magazine, May 1846, or Experimental Researches, III, p. 447.15

Far removed from the actual, historical events as we enter the 21st century CE, it is of some interest to note that Faraday’s paper, Thoughts on Ray Vibrations, was published 18 years before Maxwell published his Dynamical Theory of the Electromagnetic Field.

Continued in Section 3: Faraday, Maxwell, and Einstein

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Reference Notes (Click on the Note number to return to the text):

8 Larmor, Sir Joseph, editor. Origins of Clerk Maxwell’s Electric Ideas, p. 3. Cambridge University Press, 1937.

9 Maxwell, James Clerk. The Scientific Papers of James Clerk Maxwell [1890], vol. 1, pp. 157-158. W. D. Niven, editor. Two volumes bound as one, Dover Publications, New York (no date).

10 Ref. 9, vol. 1, pp. 155-229.

11 Ref. 9, vol. 1, pp. 451-513.

12 Ref. 9, vol. 1, p. 452.

13 Ref. 9, vol. 1, pp. 526-597.

14 Ref. 9, vol. 1, p. 527.

15 Ref. 9, vol. 1, pp. 535-536.

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Back to Chapter 4, Section 1: The Great Mystery

Index: Consciousness, Physics, and the Holographic Paradigm

Last Edit: August 13, 2010.

Comments and suggestions welcome.

This paper is a work in progress.

Please check for the latest update before quoting in other venues the concepts and hypotheses presented here.

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Copyright © 2004-2010 by Alan T. Williams. All rights reserved.