144 RELATIVITY, THE SPECIAL THEORYinertial frame as one single Lorentz transformation with the velocity v, + v 2
[Kl]. (It took Pauli a few weeks before he grasped Thomas's point.*)
- Applications. In his June paper, Einstein put his postulates to use in ways
which are now standard textbook material. No derivations will therefore be given
in what follows next. (For Einstein's own derivations, see [SI].)
a) From the postulates to the Lorentz transformations, as already discussed.
b) From the Lorentz transformations to the FitzGerald-Lorentz contraction of
rods and the dilation of time:
e) The transformation law for light frequencies:
*See the correspondence between Pauli, Bohr, and Kramers between February 26 and March 12,
1926 [P4].
**See Section 6a for the meaning of the various symbols. For comments by Einstein on the drag in
dispersive media, see [E5a].where / 0 and t 0 are, respectively, a length and a duration in the rest frame.
The kinematic origins of these relations were not at once generally understood.
In 1911 Einstein still had to explain: 'The question whether the Lorentz con-
traction does or does not exist is confusing. It does not "really" exist in so far
as it does not exist for an observer who moves [with the rod]; it "really" exists,
however, in the sense that it can as a matter of principle be demonstrated by
a resting observer' [E4].c) The addition of velocities, already mentioned.
d) The relativistic expression of the aberration from the zenith:
where <t> is the angle between a monochromatic light ray with frequency v and
the x direction. Thus Einstein is the discoverer of the transverse Doppler effect:
i/ differs from v even if the motion of the light source is perpendicular to the
direction of observation. In 1907 he published a brief note about the experi-
mental detectability of the transverse effect [E5].f) Not found in the June paper is a derivation of the Fresnel formula**