126 RELATIVITY, THE SPECIAL THEORY
sequence of Lorentz transformations* is a product of the nineteenth century.
Lorentz referred to tf defined by Eq. 6.16 as a modified local time. Concerning
the scale factor e, he remarked that it had to have a well-defined value which one
can determine only 'by a deeper knowledge of the phenomena.' Note that it is, of
course, not necessary for the interpretation of the Michelson-Morley experiment
to know what e is. (As for all optical phenomena in free space, one may allow not
only for Lorentz invariance but also for scale invariance, in fact, for conformal
invariance.) In 1899 Lorentz did not examine whether his theorem of correspond-
ing states could be adapted to the transformations represented by Eqs. 6.14-6.16.
- Lorentz finally writes down the transformations (Eqs. 6.3-6.4) [L20].
He fixes e to be equal to unity from a discussion of the transformation properties
of the equation of motion of an electron in an external field. This time he attempts
to prove a theorem of corresponding states (that is, Lorentz covariance) for the
inhomogeneous Maxwell-Lorentz equations. He makes an error in the transfor-
mation equations for velocities ([L20], Eq. 8). As a result, he does not obtain the
covariance beyond the first order in v/c (compare Eqs. 2 and 9 in [L20]).
I shall return to this 1904 paper in the next chapter. However, as far as the
history of relativistic kinematics is concerned, the story of Lorentz as precursor to
Einstein is herewith complete.
- Larmor. Larmor's prize-winning essay Aether and Matter [L10] was
completed in 1898 and came out in 1900. It contains not only the exact transfor-
mations (Eqs. 6.3 and 6.4) but also the proof that one arrives at the FitzGerald-
Lorentz contraction with the help of these transformations [L21]. Larmor was
aware of Lorentz's paper of 1895 and quoted it at length, but he could not have
known the 1899 paper.
It is true that Larmor's reasonings are often obscured by his speculations (of no
interest here) about dynamic interrelations between aether and matter. However,
there is no doubt that he gave the Lorentz transformations and the resulting con-
traction argument before Lorentz independently did the same. It is a curious fact
that neither in the correspondence between Larmor and Lorentz** nor in
Lorentz's papers is there any mention of this contribution by Larmor.
The first time I became aware of Larmor's work was in the early 1950s, when
Adriaan Fokker told me that it was known in Leiden that Larmor had the Lorentz
transformations before Lorentz. Alas, I never asked Fokker (an ex-student of
Lorentz's) what Lorentz himself had to say on that subject.
- Poincare. In 1898 there appeared an utterly remarkable article by Poin-
care entitled 'La Mesure du Temps' [P5].+ In this paper, the author notes that
'we have no direct intuition about the equality of two time intervals. People who
*For the simple mathematics of this reduction, see standard textbooks, e.g., [P4j.
**This correspondence is deposited in the Ryksarchief in the Hague. I am grateful to A. Kox for
information related to this correspondence.
fThis essay is available in English as Chapter 2 in The Value of Science [P6].
