5 4 D O C U M E N T 3 0 J A N U A R Y 1 9 2 2
The ray thus moves in a circle. As [emerges] from our earlier considerations
The radiation emitted at time therefore propagates in a bent line, to be pre
cise, on a circular path. The wavelength normal that according to one of our earlier
results has the direction of the radius vector drawn to the starting point hence
undergoes a deflection in the sense of a growing x of magnitude
. . . . (14)
This result is equivalent to our equation (3). To see this, one only has to take into
account that the beam’s rotational velocity is outside of the dispersive dielectric;
inside it, therefore, it is equal to , which term is set equal to . Furthermore,
for one has to set length l of the dispersive layer and introduce for V the refrac
tive index n, for the frequency ν.
Thus rigorous proof is provided that equation (3), which is not confirmed by
experience, is in fact a consequence of the undulatory theory.
30. From Paul Ehrenfest
[Leyden,] 19 January 1922
Dear Einstein,
To facilitate reading this letter:
Borrowing a remark by Gibbs (1886), I believe I can show: even if one grants
you the rotation of the wave planes as proportional to the length of the bisulf[ide]
ofcarb[on]tube, there follows (on a purely classical basis) a negative result for
your experiment on a classical foundation.– The point is: group of
waves![1]
Sheets A, B, C reiterate more clearly what pages 1, 2 present somewhat messily.
Forgive me if I am mistaken. Please reply to me, if only briefly and provision
ally.
Don’t forget, either, to indicate the address of the Spanish professor, about
whom I wrote yesterday on my
postcard.[2]
Don’t be angry with me if I am wrong; don’t be angry with me if I am right.
With warm regards, yours,
P. Ehrenfest
t 0=
r0
r0ndω
1
 
dn
 γ⋅
q
Δ

q
Δn
  γ
V
ω

r0
dω ω