1 4 0 D O C U M E N T 1 4 9 A P R I L 1 9 2 2
149. From Paul Ehrenfest
[Leyden,] 17 April 1922
Dear Einstein,
You’ll understand why I opened the letter.[1] That I read it afterwards as well,
you’ll pardon.
Perhaps in answering the letter the following may be useful to you:
1.° Because my attention as a student in Göttingen was drawn by Klein to Ham-
ilton’s original papers, I learned to admire them exceedingly and always regretted
(just like Klein!) that there is no published collection available particularly of his
papers on optical mechanics.[2]
2.° I don’t know about his quaternion papers, but those on optical mechanics are
very grand. Their genesis is this: As an astronomer, H. was naturally interested in
geometrical optics (like Gauss, Kepler, etc.). The computations were always gov-
erned by the concept: “path of lightrays ,” so the question arises with him: What
can be gained if, in the sense of the wave theory of light (but neglecting the terms
representing diffraction), the rays are interpreted as the normal trajectories of wave
surfaces and hence characterizes an optical instrument as an apparatus for trans-
forming wave surfaces (always excluding diffraction)?– It is only in a discussion
of homogeneous media that he pursues the thought further: Instead of the regular
differential eq. governing the course of the light rays—comes the partial differen-
tial eq. of 1st order (neglecting diffraction), which governs the propagation of the
wave surfaces. If it is integrated, there follows by differentiation the path of the
(orthogonal) rays of light.
(By imagining the integrals of the wave surface as arranged in series expansions,
he obtains a complete “theory of the errors” of an instrument: spher[ical] aberration
and the like).
Now, however, he also notices this: If one regards optics as emanative, therefore
minim[um] per Fermat “action integral”
On the other hand, is constant for all light rays that lead from one point
of light to one and the same light-wave surface. So he sees:
refractive index n
in glass
in vacuum
---------------------------------- =
nds n-----dt
--- - v2dt. = =
n ds
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