where '0' refers to the rest frame. Since T^ is traceless and since the rest frame
is spatially isotropic, these transformation relations at once yield Eqs. 7.31 and
7.32.
Dynamic rather than kinematic arguments had led to the concept of electro-
magnetic mass. Dynamic rather than kinematic arguments led Poincare to modify
Lorentz's model. In his brief paper published in June 1905, Poincare announced,
'One obtains ... a possible explanation of the contraction of the electron by assum-
ing that the deformable and compressible electron is subject to a sort of constant
external pressure the action of which is proportional to the volume variation'
[PI4]. In his July 1905 memoir he added, 'This pressure is proportional to the
fourth power of the experimental mass of the electron' [P15]. In Chapter 6, I
discussed the kinematic part of these two papers. More important to Poincare was
the dynamic part, the 'explanation of the contraction of the electron.' It is not for
nothing that both papers are entitled 'Sur la Dynamique de 1'Electron.'
In modern language, Poincare's dynamic problem can be put as follows. Can
one derive the equations for a Lorentz electron and its self-field from a relativis-
tically invariant action principle and prove that this electron, a sphere at rest,
becomes an ellipsoid when in uniform motion in the way Lorentz had assumed
it did? Poincare first showed that this was impossible. But he had a way out. 'If
one wishes to retain [the Lorentz theory] and avoid intolerable contradictions, one
must assume a special force which explains both the contraction [in the direction
of motion] and the constancy of the two [other] axes' [PI5].
Poincare's lengthy arguments can be reduced to a few lines with the help of
Ty,. Write Eq. 7.31 in the form
158 RELATIVITY, THE SPECIAL THEORY
where V = 4va^/3y is the (contracted) volume of the electron and P = 3/uc^2 /
16ira^3 is a scalar pressure. Add a term pPS^, the 'Poincare stress,' to 7^, where
p = 1 inside the electron and zero outside. This term cancels the — PV term in
£dm for all velocities, it does not contribute to Pelm, and it serves to obtain the
desired contraction. Assume further—as Poincare did—that the mass of the elec-
tron is purely electromagnetic. Then n ~ e^2 /a and P ~ M/«^3 ~ M^4 , his result
mentioned earlier. Again in modern language, the added stress makes the finite
electron into a closed system. Poincare did not realize how highly desirable are the
relations
which follow from his model! (See [M7] for a detailed discussion of the way Poin-
care proceeded.)