Conservation and Innovation : Helmholtz's Struggle with Energy ...

principe. L’expèrience nous montre que l’ènergie d’un champ èlectromagnètique
se dècompose en deux parties, l’ènergie èlectrostatique et l’ènergie
èlectrodynamique. Maxwell a reconnu (que si l’on regarde) la premiére come
reprèsentant l’ènergie potentielle U, la seconde comme reprèsentant l’ènergie
cinètique T." 433
Maxwell thus solves the problem, allowing in addition a Lagrangian derivation of
the equations and so fulfills the possibility of a mechanical explanation of
electromagnetism. The grounds of acceptance of Maxwell’s theory in Poincarè’s
analysis are clearly the ones referring to energy. Maxwell’s (and not Poynting’s)
approach is preferred in view of its links with the mechanical expression of both
PCE and PLA. This judgment is explicit already in 1890 and was to be reasserted
in 1902 434. Hertz’s experiments, instead, up to 1894 were considered doubtful
and in 1902 were considered to lend only indirect support. The
desubstantialisation of ether theory was to weaken the experimental difference
between contiguous action and delayed action-at-a-distance theories, but was to
strengthen the theoretical difference between the PCE’s of the latter theories and
a local PCE expressed by the contiguous action theory. Poincarè’s choice of
Maxwell from 1890 to 1902 is not referred to Poynting’s development (second
step of localisation) but to Maxwell’s substantialisation (first step). This is due to
the relevance he attributed to the asserted possibility of a mechanical
explanation 435. Poincarè’s approach is very different from Hertz’s axiomatic
assumption of Maxwell’s equations and his rejection of both a mechanical
explanation and of a Lagrangian derivation. But still PCE, and specifically
Helmholtz's PCE, was the principal reason for Poincarè’s choice of Maxwell.
In the important process of the emergence of theoretical physics
discussions on the meaning and the role of Helmholtz's approach to energy
conservation were basic. Acceptance or denial of the mechanical world view, of
the sharp distinction between kinetic and potential energy and of the privileged
status of the central forces depending only on the distance were among the key
issues, while others, non strictly mechanical interpretations of the principle of
conservation, started to become mere and more important. At the end of the
century in every research programme (mechanical, electromagnetic, energetic,
thermodynamic) a specific version of the principle was put forward, and new
433 Poincarè La Science p. 223.
434 Poincarè La Science pp.216-25.
435 Poincarè La Science pp.216-25.