D O C U M E N T 3 0 J A N U A R Y 1 9 2 2 5 5 Dear Einstein, Well, now—you are such a devil of a fellow that you will naturally be correct in the end. But I would still like to grasp clearly, with much greater certainty than before, if the classical theory really does demand a bending of the image. I am now full of suspicion about every step of the proof. In any case, I would like to draw your attention to a very short note by Gibbs [Scientific Papers, vol. II, page 253 = Nature (vol. 33, p. 582, April 1886)].[3] It refers to the measurement of the velocity of light in a dispersive medium with the aid of the rotating mirror method. There light waves, set in fanlike opposition to one another, are also sent back by the rotating mirror and Lord Rayleigh drew attention to it[4] [Nature, vol. 25 (1881), page 52.—He incidentally retracted the result he indicated there in favor of Gibbs’s better result.], because these waves rotate as they traverse the dispersive medium (as you, of course, said). Now Gibbs observes a “group” of such fanned waves and recalls primarily that one must distinguish between the propagation velocity of the waves V(λ) and the propagation velocity of the wave “group” U(λ). Then he shows: Each individual wave plane does indeed rotate (just as each spoke on a wagon wheel of a moving wagon does) but if one “runs along with the group,” i.e., at the velocity U(λ), and thus fixes on a “point in the middle of the group,” then one sees the following: the consecutive wave planes of the wave fan go through this (run- ning) point, one after another (as their veloc. V(λ) U(λ)) yet the orientation of the wave normal for all these consecutive wave planes is always the same (just like an observer traveling along on the wagon, who is constantly watching the upper rim of the wheel, sees the consecutive spokes passing by in vertical positions). Why am I telling you all this?– Not because I clearly see that these remarks prove anything against your claim that according to the classical theory your exper- iment has to come out positive, but only because it shows how many things one might perhaps have forgotten in these considerations.– I don’t know whether one should fuss at all with group velocities in any way in your derivation (an argument for yes immediately crops up)—but assuming yes, then Gibbs’s result perhaps is important, after all: in that by running along with the group from the beginning to the end of the bisulf.-of-carb. tube, you can’t speak of an “increasing inclination of the wave planes” at all anymore. For, look at what happens: The canal-ray particle, as it passes through the slit (or during an even shorter time—but at most during 10−8sec),[5] emits a “fanned wave-group.” This group
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