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
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
[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
The canal-ray particle, as it passes through the slit (or during an even shorter
time—but at most during
emits a “fanned wave-group.” This group
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