The Fruitful Collaboration of André-Marie Ampère and Augustin-Jean Fresnel

In my post, Two Productive Research Programs in the Early 19th Century, the first of a three-part series on the replacement of Continental science by the British in the 19th century, I stated that in the beginning of that century, there were two productive research programs: 1) the luminiferous ether, and 2) action-at-a-distance. In France, in the École Polytechnique, the two individuals whom I associated with these two programs were, respectively, 1) Augustin-Jean Fresnel (1788-1827), and 2) André-Marie Ampère (1775-1836).

Augustin-Jean Fresnel and André-Marie Ampère

Little did I know that each of Ampère and Fresnel influenced the other in the latter’s pursuit of his ideas. I was astonished to learn something of this in Ampère’s Electrodynamics, in which André Assis and João Chaib gathered and translated the writings of Ampère, first in Portuguese¹, then in English². I introduced the latter in my post English Translations of Coulomb, Ampère and Weber.

For years, Fresnel even lived in Ampère’s home in Paris:

Fresnel began to study at the École Polytechnique in 1804, the same year in which Ampère began to teach at this institution. They began to have close contact around 1814 when Fresnel began his interests in optics. In order to improve his financial situation, Ampère used to rent a room in his Parisian home to some friends. Fresnel lived there from 1822 until his early death in 1827, when he was 39 years old. [Assis and Chaib, p.103]

Today, we remember Fresnel’s main contribution as being the proposal that light propagates through transversal, not longitudinal waves. It turns out that this idea was in fact proposed to Fresnel by Ampère. Here are Fresnel’s actual words, dated to August 1816³:

Two systems of undulations in which the progressive movement of the molecules of the fluid is modified by a transverse to-and-fro movement, which is perpendicular to it and equal in intensity, could exert no action on each other, when the progressive movement is matched by the discordance of the transverse movements, or vice versa, because then the resultants of these two forces in each system would have rectangular directions. There is yet another hypothesis that could explain the absence of fringes in circumstances that are moreover favourable to their production: it would be that of transverse vibrations that present both condensed and dilated nodes on the same spherical surface, resulting in points of agreement and discordance so close together that the eye, unable to distinguish them, would have the sensation of a continuous light. We often see waves on the surface of water that undulate in this way in the direction of their length; but so far I have tried in vain to explain the phenomena using these hypotheses, the first of which was indicated to me by M. Ampère. This would not be sufficient, moreover, and it would still be necessary to explain how light is thus modified by reflection or double refraction.⁴ [my emphasis]

Here is how Assis and Chaib summarized the situation:

Ampère initially accepted the corpuscular theory of light, which he also called the “system of emission”. Fresnel, on the other hand, defended the wave theory of light. Ampère changed his mind in 1816 due to Fresnel’s influence. Fresnel initially believed that the luminous waves were due to longitudinal vibrations in the ether, in analogy with sound waves in air. Ampère suggested to Fresnel to consider luminous transverse waves instead of longitudinal ones, in order to explain satisfactorily several phenomena, including light polarization. Fresnel himself acknowledged that this fundamental idea of transverse vibrations orthogonal to the direction of propagation of the luminous wave was due to Ampère. [Assis and Chaib, p.103]

As for Ampère, his explanation of magnetism was that it was the result of microscopic electric currents in magnetized bodies. And it turns out that this idea originated with Fresnel! Here are Ampère’s actual words wrote, dated to 1821⁵:

This hypothesis (the hypothesis of currents around particles) was communicated to me by M. Fresnel, who found several advantages in considering the electric currents of the magnet in this way. I would be straying too far from my subject if I were to set out the reasons that can support it, those that seem to me to make more probable the way in which I first conceived the electric currents of the magnet, as I have admitted it in the course of this Memoir, and especially if I were to examine a third way of conceiving them, which, completely preserving the analogy of the curves closed in planes perpendicular to the axis of a magnet, and of the lines that go from the positive end of a conducting wire to the negative end, parallel to its length, an analogy proved by so many facts that it has, for the most part, indicated to me in advance, presented, for the calculation of the mutual action of two currents, the same facility as Fresnel's hypothesis, and tended, moreover, to reduce to a single principle the ordinary electrical attractions and repulsions, and those which I have recognised between two electrical currents, by accounting for all the differences which seem to establish, between the one and the other, a dissimilarity or even a complete opposition.

This third hypothesis, which I deduced from certain facts that I have since recognised can be explained equally well in the one I am presenting here, is moreover too far removed from the way in which all physicists have considered the cause of electrical phenomena for us to dwell on it. Whatever the opinion one adopts on such subjects, the facts and the laws to which these facts are subject remain the same, as do the means by which man can arrive at a knowledge of these laws.⁶ [my emphasis]

Once again, here are Assis and Chaib:

As regards the electrodynamic conception of magnetism, it was Fresnel who supplied a fundamental contribution to Ampère’s thinking. Initially Ampère believed in macroscopic electric currents flowing inside magnets and in the Earth in order to explain their magnetic properties. Fresnel suggested to him the conception of microscopic currents flowing around the iron or steel particles of a magnet, instead of macroscopic currents flowing around the axis of the magnet. Fresnel presented a comparison between these two electrodynamic conceptions of magnetism in two papers. [Assis and Chaib, p.103]

So it turns out that both Fresnel and Ampère contributed to each of the two productive research programs of the beginning of the 19th century, despite the fact that the two programs presupposed different paradigms. It should perhaps not be surprising, then, to find out that Ampère, despite writing in favour of Newton’s Third Law, and despite his own law respecting Newtonian principles, actually believed there to be some kind of fluid through which the interactions between electric currents manifested themselves, as he wrote in 1824⁷:

As for myself, I hardly doubt that the attractions and repulsions of electric currents are, like [Newtonian] attraction, a result of the movements of the fluid that fills all space…. But, as the dynamics of fluids and the particular properties of the fluid which fills space are far from being sufficiently well known for us to be able to calculate the effects of these movements, I persist in believing that we must conclude the formulae which express the forces of observations reduced to general empirical laws, just as Newton deduced the formula for action from the laws of Kepler, just as I deduced mine from laws similar to those of Kepler, the action of the impossibility of imparting to a moving conductor whose two ends are in the axis of rotation a continuous movement around this axis, etc....⁸

From the above, it seems that it will be of great utility to study in detail the development of both optics and electrodynamics in the heady days of the early École Polytechnique, and to read in detail not just the papers, but also the correspondence of those two great physicists, Fresnel and Ampère, and their respective colleagues.

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1. André Koch Torres Assis e João Paulo Martins de Castro Chaib. Eletrodinâmica de Ampère. Análise do significado e da evolucão da força de Ampère, juntamente com a tradução comentada de sua principal obra sobre eletrodinâmica. Campinas, Brasil: Editora Unicamp, 2011.

2. André Koch Torres Assis and João Paulo Martins de Castro Chaib. Ampère’s Electrodynamics. Analysis of the Meaning and Evolution of Ampère’s Force between Current Elements, together with a Complete Translation of his Masterpiece: Theory of Electrodynamic Phenomena, Uniquely Deduced from Experience. Montreal: Apeiron, 2015.

3. Augustin Fresnel. Nº XV (A). Mémoire sur l'influence de la polarisation dans l'action que les rayons lumineux exercent les uns sur les autres. In Henri de Senarmont, Émile Verdet et Léonor Fresnel. Œuvres complètes d'Augustin Fresnel. Tome Premier. Paris: Imprimerie Impériale, 1866.

4. Deux systèmes d’ondulations dans lesquelles le mouvement progressif des molécules du fluide serait modifié par un mouvement transversal de va-et-vient, qui lui serait perpendiculaire et égal en intensité, pourraient n’exercer aucune action l’un sur l’autre, lorsqu’à raccord du mouvement progressif répondrait la discordance des mouvements transversaux, ou réciproquement, parce qu’alors les résultantes de ces deux forces dans chaque système auraient des directions rectangulaires. Il y a encore une autre hypothèse qui pourrait expliquer l'absence des franges dans les circonstances favorables d'ailleurs à leur production : ce serait celle de vibrations transversales qui présenteraient à la fois des nœuds condensés et dilatés sur la même surface sphérique, d’où résulteraient des points d’accord et de discordance si rapprochés que l’œil, ne pouvant les distinguer, en aurait la sensation d'une lumière continue. On voit souvent à la surface de l’eau des ondes ainsi ondulées dans le sens de leur longueur; Mais j’ai essayé inutilement jusqu’à présent de rendre raison des phénomènes avec ces hypothèses, dont la première m’a été indiquée par M. Ampère. Cela ne subirait pas d'ailleurs, et il faudrait encore expliquer comment la lumière se trouve ainsi modifiée par la réflexion ou la double réfraction. [p.394]

5. M.-A. Ampère. VIII. Analyse des mémoires lus à l'Académie les 11 et 26 décembre 1820 et les 8 et 15 janvier 1821. In La Société française de physique. Collection de mémoires relatifs à la physique. Tome II. Mémoires sur l'Électrodynamique. Première partie. Paris: Gauthier-Villars, 1885.

6. « Cette hypothèse (l’hypothèse des courants autour des particules) m’a été communiquée par M. Fresnel, qui trouvait plusieurs avantages à considérer de cette manière les courants électriques de l’aimant. Je m’écarterais trop de mon sujet si je voulais exposer les raisons qui peuvent l’appuyer, celles qui me paraissent rendre plus probable la manière dont j’ai d’abord conçu les courants électriques de l’aimant, telle que je l’ai admise dans le cours de ce Mémoire, et surtout si je voulais examiner une troisième manière de les concevoir, qui, conservant complètement l’analogie des courbes fermées dans des plans perpendiculaires à l’axe d’un aimant, et des lignes qui vont de l'extrémité positive d’un fil conducteur à l’extrémité négative, parallèlement à sa longueur, analogie prouvée par un si grand nombre de faits qu’elle m’a, pour la plupart, indiqués d'avance, présentait, pour le calcul de l’action mutuelle de deux courants, la même facilité que l’hypothèse de M. Fresnel, et tendait, en outre, à ramener à un principe unique les attractions et répulsions électriques ordinaires, et celles que j’ai reconnues entre deux courants électriques, en rendant compte de toutes les différences qui semblent établir, entre les uns et les autres, une dissemblance ou même une opposition complète.

« Cette troisième hypothèse, que j’avais déduite de quelques faits que j’ai reconnus depuis s’expliquer également bien dans celle que j’expose ici, est d’ailleurs trop éloignée de la manière dont tous les physiciens ont considéré la cause des phénomènes électriques pour qu’on puisse s’y arrêter. Quelle que soit l’opinion qu’on adopte sur de pareils sujets, les faits et les lois auxquelles ces faits sont soumis restent les mêmes, ainsi que les moyens par lesquels il est donné à l’homme d’arriver à la connaissance de ces lois. » [pp.139-140]

7. 392. Ampère à M. Auguste de La Rive, professeur de Physique à l'Académie de Genève. Paris, 2 juillet 1824. In L. De Launay. Correspondance du Grand Ampère. Volume II. Paris: Gauthier-Villars, 1936, pp.658-659.

8. C’est sur cet extrait que j’en ai fait un sans calcul que j’ai envoyé à M. Pictet pour qu’il l’insère, si cela lui convient, dans la Bibliothèque universelle. Je ne crois pas que cet excellent ouvrage périodique puisse rester étranger à un travail qui, en complétant la théorie de l’électricité dynamique, donne toutes les lois de cette sorte d'action : lois qui resteront toujours, quelles que soient les hypothèses qu’on adopte pour la cause de ces phénomènes. Quant à moi, je ne doute guère que les attractions et répulsions des courants électriques ne soient, comme l’attraction [newtonienne], un résultat des mouvements du fluide qui remplit tout l'espace. J’ai suffisamment exprimé ma pensée sur ce sujet aux pages 205 et 214 de mon recueil. Mais, comme la dynamique des fluides et les propriétés particulières de celui qui remplit l’espace sont bien loin d'être assez bien connues pour qu’on puisse calculer les effets de ces mouvements, je persiste à croire qu’on doit conclure les formules qui expriment les forces des observations réduites à des lois générales empiriques, comme Newton a déduit la formule de l'action des lois Képler, comme j’ai déduit la mienne de lois semblables à celles de Képler, l’action du conducteur [sinuée ?] l’impossibilité d’imprimer à un conducteur mobile dont les deux extrémités sont dans l’axe de rotation un mouvement continu autour de cet axe, etc. [p.658]