'SUBTLE is THE LORD' 129longer one. The content of his articles is partly kinematic, partly dynamic. Here
I shall discuss only their kinematic part, leaving the remainder until the next
chapter.
The June paper begins with the remark that neither the aberration of light and
related phenomena nor the work of Michelson reveals any evidence for an absolute
motion of the earth. 'It seems that this impossibility of demonstrating absolute
motion is a general law of nature.' Next Poincare refers to the contraction hypoth-
esis and to Lorentz's paper of 1904 [L20] in which—as he has it—Lorentz had
succeeded in modifying the hypothesis 'in such a way as to bring it in accordance
with the complete impossibility of determining absolute motion.' This statement
is not quite correct, since (as was mentioned earlier) Lorentz had not succeeded
in proving the covariance of the inhomogeneous Maxwell-Lorentz equations.
Poincare was to return to this point in July. However, in June he already had the
correct transformation properties of the velocities, the point Lorentz had missed.
'I have been led to modify and complete [Lorentz's analysis] in certain points of
detail.'
Poincare then turns to the transformations (Eqs. 6.14-6.16), 'which I shall
name after Lorentz,' and continues, 'The ensemble of all these transformations,
together with the ensemble of all spatial rotations must form a group; but in order
for this to be so it is necessary that* e = 1; one is thus led to assume that « = 1,
a result which Lorentz had obtained in another way.'
The final topic discussed in this paper concerns gravitation. Following
Lorentz's dynamic picture, Poincare reasons in a more general and abstract way
that all forces should transform in the same way under Lorentz transformations.
He concludes that therefore Newton's laws need modification and that there
should exist gravitational waves which propagate with the velocity of light!
Finally, he points out that the resulting corrections to Newton's law must be
O(v^2 /c^2 ) and that the precision of astronomical data does not seem to rule out
effects of this order.
The July paper of Poincare gives many more details. Its Section 1, entitled
'Lorentz Transformation,' contains the complete proof of covariance of electrody-
namics. 'It is here that I must point out for the first time a difference with Lorentz'
[PI6]. Section 4 contains a discussion of 'a continuous group which we shall call
the Lorentz group.' Poincare explains his argument for € = 1: starting from Eqs.
6.14-6.16, consider the inverse of these transformations, that is, replace v by —v.
Clearly,
Moreover, from a rotation of 180° around the y axis it follows that
*I use the notation of Eqs. 6.14-6.16; Poincare used the symbol / instead of e.