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

principle of correlation is expressed and various applications given, but the
"energy" terms of the equations are expressed in units of heat and not work.
The Erhaltung is the full expression of Helmholtz's ideas on theoretical
physics and on energy. Its "Einleitung" is the clear and conscious indication of
the methodological control Helmholtz had achieved on his own researches.
Helmholtz outlined a four levels structure. Two basic physical hypotheses
(impossibility of perpetual motion and central Newtonian forces) were placed at
the first level, "the" principle of conservation at the second, empirical laws at the
third and natural phenomena at the fourth. Moreover the two basic hypotheses,
echoing various elements of Kantian philosophy, were not presented as self
evident but as the result of a philosophical 'explanation'..
In my view the need that Helmholtz felt to justify his own version of the
conservation principle on higher grounds (on two physical hypotheses in turn
justified on philosophical grounds) is a clear indication of Helmholtz's
consciousness of the possibility of alternative formulations of the principle itself.
Helmholtz not only wanted to express a principle, but also to establish the
framework and the rules following which principles could be formulated and
used. This is what makes Helmholtz's approach mark a major step in the
emergence of theoretical physics, and shows that his version of the principle was
not only the application of a (meta)physical assumption, but the application of a
sophisticated methodology. The two physical assumptions (first level) are meant
to bring together, not without problems, two different but well known traditions
in physics 17, and thus to offer secure grounding for the whole enterprise.
Helmholtz believed that this was not enough and decided to justify the first level
on more abstract grounds: he connected the principle of impossibility of perpetual
motion with the principle of sufficient reason, a transcendental condition for the
intelligibility of nature, and gave a conceptual explanation of the model of central
forces in the Kantian style. Finally he hinted at an "empirical" principle of a cause
effect relationship to be embedded in the formulation of the principle of
conservation (second level). This principle, in turn, had to be compared with
existing empirical laws (third level) and to predict new ones, to eventually
achieve the intelligibility of natural phenomena (fourth level).
17 In this context I think that Elkana's suggestion of Helmholtz unifying Newtonian
and analytic mechanics can be accepted: Elkana The Discovery ; but for a better
characterization of trends in mechanics see: Grattan-Guinness, Ivor. "The varieties of
mechanics by 1800", paper for the Hegel and Science Conference, typescript, 1989.