Editing Augustin-Jean Fresnel (section)

==== Breakthrough: Pure transverse waves (1821) ====

[[File:Andre-marie-ampere2.jpg|thumb|<div style="text-align: center;">André-Marie Ampère (1775–1836)</div>]]

In the draft memoir of 30 August 1816, Fresnel mentioned two hypotheses—one of which he attributed to Ampère—by which the non-interference of orthogonally-polarized beams could be explained if polarized light waves were ''partly'' [[transverse wave|transverse]]. But Fresnel could not develop either of these ideas into a comprehensive theory. As early as September 1816, according to his later account,<ref>Fresnel, 1821a, §10.</ref> he realized that the non-interference of orthogonally-polarized beams, together with the phase-inversion rule in chromatic polarization, would be most easily explained if the waves were ''purely'' transverse, and Ampère "had the same thought" on the phase-inversion rule. But that would raise a new difficulty: as natural light seemed to be ''un''polarized and its waves were therefore presumed to be longitudinal, one would need to explain how the longitudinal component of vibration disappeared on polarization, and why it did not reappear when polarized light was reflected or refracted obliquely by a glass plate.<ref>Fresnel, 1866–70, vol.&nbsp;1, p.&nbsp;394n; Fresnel, 1821a, §10; Silliman, 1967, pp.&nbsp;209–210; Buchwald, 1989, pp.&nbsp;205–206,{{tsp}}208,{{tsp}}212,{{tsp}}218–219.</ref>

Independently, on 12 January 1817, Young wrote to Arago (in&nbsp;English) noting that a transverse vibration would constitute a polarization, and that if two longitudinal waves crossed at a significant angle, they could not cancel without leaving a residual transverse vibration.<ref>Young, 1855, p.&nbsp;383.</ref> Young repeated this idea in an article published in a supplement to the ''Encyclopædia Britannica'' in February 1818, in which he added that Malus's law would be explained if polarization consisted in a transverse motion.{{r|young-1818|p=333–335}}

Thus Fresnel, by his own testimony, may not have been the first person to suspect that light waves could have a transverse ''component'', or that ''polarized'' waves were exclusively transverse. And it was Young, not Fresnel, who first ''published'' the idea that polarization depends on the orientation of a transverse vibration. But these incomplete theories had not reconciled the nature of polarization with the apparent existence of ''unpolarized'' light; that achievement was to be Fresnel's alone.

In a note that Buchwald dates in the summer of 1818, Fresnel entertained the idea that unpolarized waves could have vibrations of the same energy and obliquity, with their orientations distributed uniformly about the wave-normal, and that the degree of polarization was the degree of ''non''-uniformity in the distribution. Two pages later he noted, apparently for the first time in writing, that his phase-inversion rule and the non-interference of orthogonally-polarized beams would be easily explained if the vibrations of fully polarized waves were "perpendicular to the normal to the wave"—that is, purely transverse.<ref>Buchwald, 1989, pp.&nbsp;225–226; Fresnel, 1866–70, vol.&nbsp;1, pp.&nbsp;526–527,{{tsp}}529.</ref>

But if he could account for ''lack'' of polarization by averaging out the transverse component, he did not also need to assume a longitudinal component. It was enough to suppose that light waves are ''purely'' transverse, hence ''always'' polarized in the sense of having a particular transverse orientation, and that the "unpolarized" state of natural or "direct" light is due to rapid and random variations in that orientation, in which case two ''coherent'' portions of "unpolarized" light will still interfere because their orientations will be synchronized.

It is not known exactly when Fresnel made this last step, because there is no relevant documentation from 1820 or early 1821{{hsp}}<ref>Buchwald, 1989, p.&nbsp;226.</ref> (perhaps because he was too busy working on lighthouse-lens prototypes; see [[#Lighthouses and the Fresnel lens|below]]). But he first ''published'' the idea in a paper on "''Calcul des teintes…''" ("calculation of the tints…"), serialized in Arago's ''Annales'' for May, June, and July 1821.<ref>Fresnel, 1821a.</ref> In the first installment, Fresnel described "direct" (unpolarized) light as "the rapid succession of systems of waves polarized in all directions",<ref>Buchwald, 1989, p.&nbsp;227; Fresnel, 1821a, §1.</ref> and gave what is essentially the modern explanation of chromatic polarization, albeit in terms of the analogy between polarization and the resolution of forces in a plane, mentioning transverse waves only in a footnote. The introduction of transverse waves into the main argument was delayed to the second installment, in which he revealed the suspicion that he and Ampère had harbored since 1816, and the difficulty it raised.<ref>Buchwald, 1989, p.&nbsp;212; Fresnel, 1821a, §10.</ref> He continued:
{{blockquote|It has only been for a few months that in meditating more attentively on this subject, I have realized that it was very probable that the oscillatory movements of light waves were executed solely along the plane of these waves, ''for direct light as well as for polarized light''.<ref>Fresnel, 1821a, §10; emphasis added.</ref><ref group=Note>In the same installment, Fresnel acknowledged a letter from Young to Arago, dated 29 April 1818 (and lost before 1866), in which Young suggested that light waves could be analogous to waves on stretched strings. But Fresnel was dissatisfied with the analogy because it suggested both transverse and longitudinal modes of propagation and was hard to reconcile with a fluid medium (Silliman, 1967, pp.&nbsp;214–215; Fresnel, 1821a, §13).</ref>}}
According to this new view, he wrote, "the act of polarization consists not in creating these transverse movements, but in decomposing them into two fixed perpendicular directions and in separating the two components".<ref>Fresnel, 1821a, §13;{{tsp}} cf.&nbsp;Buchwald, 1989, p.&nbsp;228.</ref>

While selectionists could insist on interpreting Fresnel's diffraction integrals in terms of discrete, countable rays, they could not do the same with his theory of polarization. For a selectionist, the state of polarization of a beam concerned the distribution of orientations over the ''population'' of rays, and that distribution was presumed to be static. For Fresnel, the state of polarization of a beam concerned the variation of a displacement over ''time''. That displacement might be constrained but was ''not'' static, and rays were geometric constructions, ''not'' countable objects. The conceptual gap between the wave theory and selectionism had become unbridgeable.<ref>Cf. Buchwald, 1989, p.&nbsp;230.</ref>

The other difficulty posed by pure transverse waves, of course, was the apparent implication that the aether was an elastic ''solid'', except that, unlike other elastic solids, it was incapable of transmitting longitudinal waves.<ref group=Note>Fresnel, in an effort to show that transverse waves were not absurd, suggested that the aether was a fluid comprising a lattice of molecules, adjacent layers of which would resist a sliding displacement up to a certain point, beyond which they would gravitate towards a new equilibrium. Such a medium, he thought, would behave as a solid for sufficiently small deformations, but as a perfect liquid for larger deformations. Concerning the lack of longitudinal waves, he further suggested that the layers offered incomparably greater resistance to a change of spacing than to a sliding motion (Silliman, 1967, pp.&nbsp;216–218; Fresnel, 1821a, §§&nbsp;11–12; cf.&nbsp;Fresnel, 1827, tr.&nbsp;Hobson, pp.&nbsp;258–262).</ref> The wave theory was cheap on assumptions, but its latest assumption was expensive on credulity.<ref>"This hypothesis of Mr.{{nnbsp}}Fresnel is at least very ingenious, and may lead us to some satisfactory computations: but it is attended by one circumstance which is perfectly ''appalling'' in its consequences. The substances on which Mr.{{nnbsp}}Savart made his experiments were ''solids'' only; and it is only to solids that such a ''lateral'' resistance has ever been attributed: so that if we adopted the distinctions laid down by the reviver of the undulatory system himself, in his ''Lectures'', it might be inferred that the luminiferous ether, pervading all space, and penetrating almost all substances, is not only highly elastic, but absolutely solid!!!" — Thomas&nbsp;Young (written January 1823), Sect.{{nnbsp}}{{serif|XIII}} in "Refraction, double, and polarisation of light", ''Supplement to the Fourth, Fifth, and Sixth Editions of the Encyclopædia Britannica'', vol.{{nnbsp}}6 (1824), at p.{{nnbsp}}862, reprinted in Young, 1855, at p.{{nnbsp}}415 (italics and exclamation marks in the original). The "Lectures" that Young quotes next are his own (Young, 1807, vol.{{nnbsp}}1, p.{{nnbsp}}627).</ref> If that assumption was to be widely entertained, its explanatory power would need to be impressive.