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Mathematics at TCD 1592-1992

400
years of
MATHEMATICS
by T. D. Spearman

THE AETHER

The grand concept of the world aether, an all pervasive medium which penetrated matter and extended throughout the universe, was of fundamental importance in nineteenth century scientific thought. It was believed that wave phenomena of any kind required such a medium within which to happen and to propagate. The existence of light, generally recognized by 1840 as a wave phenomenon, and its propagation throughout the universe demanded the existence of the aether as a mechanical medium subject to dynamical laws.
Many attempts were made to construct a dynamical theory of the aether which was consistent with the observed features of light propagation: none was entirely satisfactory, but McCullagh's model, although it was not a complete dynamical theory, did reliably reproduce the observed phenomena. Even more remarkably some forty years later, after it had been shown that light was just one aspect of the wider phenomenon of electro-magnetic radiation, G.F. Fitzgerald showed that Mac Cullagh's aether was a suitable medium for the propagation not just of light but also of radiant heat and of electromagnetic radiation in general. Another Irishman, Sir Joseph Larmor, who became Lucasian Professor of Mathematics in Cambridge in 1903, also worked at Mac Cullagh's aether. He incorporated particles, positively and negatively charged electrons, postulating that matter was composed exclusively of these two types of particle, and developed his so-called electronic theory of matter, based on Mac Cullagh's model.

MAC CULLAGH
as controversialist.

Mac Cullagh on several occasions found himself in contention with regard to priority in obtaining new results. On 30th November 1838 a letter from M. Neumann of Königsberg, was read out at an Academy meeting. This had been addressed to Hamilton, as President, and claimed priority over MacCullagh in establishing the laws of crystalline reflexion and refraction. These claims were trenchantly refuted by MacCullagh. An opposing theory of the aether formulated by the French mathematician Cauchy, whose conclusion had achieved a widespread acceptance, was rather brusquely rejected; `from these simple considerations it is evident that the theory of M. Cauchy is unsound; but a closer examination will show that it is entirely without foundation, and that it ts directly opposed to the very pheomena which it professes to explain.' MacCullagh was not lacking in self assurance when at the age of 24 he claimed to have anticipated Hamilton's discovery of conical refraction. He wrote as follows to the Philosphical Magazine `when professor Hamilton announced his discovery of Conical Refraction he did not seem to have been aware that it is an obvious and immediate consequence of the theorems published by me, three years ago...'. Whereas this may have been true the fact was that MacCullagh had not proceeded to draw the relevant conclusions from his results and his implied criticism of Hamilton was not justified. Hamilton was understandably put out and MacCullagh had to be prevailed upon by Lloyd to at least partially recant. In the following issue of the Philosophical Magazine he wrote, `The introductory part of my note which appeared in your last issue was written in haste, and I have reason to think it may not be rightly understood'.

Since Einstein, the existence of the aether has ceased to be a necessary or relevant hypothesis. Yet a modern world view demands the existence of a complex fluctuating energy-rich vacuum: an image which closely parallels that of the classical aether. There is a certain irony in that what relativity took away the quantum revolution in some sense restored. Of course classical aether models, such as Mac Cullagh's, have little relevance for the rich, teeming, all-pervasive vacuum as it is now understood, which can only be described in the language of quantum field theory, nevertheless there is a continuity in concept and vision which causes the idea of the aether to retain a certain fascination even today.


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