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

different from the one joining the active material points "force" could be gained
or lost ad infinitum; c) if forces were different from central, a system of bodies at
rest could be set in motion by the effect of its own internal forces 133. The
hypothesis of central forces depending only on distances is thus basic to
Helmholtz's view, but these three results are not without problems as seen in the
previous subsection.
In my view Helmholtz's summary of his second chapter does not do
justice to the results he had obtained. A real shift in meaning occurred in fact: the
well-known old equation written at the beginning of the chapter had acquired a
new interpretation; we already knew that the stress could be with the tradition of
analytical mechanics on the first term (the duck : conservation of vis viva), with
mechanical engineering on the second term (the rabbit: transmission of work);
now with Helmholtz the stress was on the equivalence between the two.
The introduction of the term Spannkraft reveals a real meaning shift: with
the tension force we are very far from the concept of work and very close to the
idea of potential energy. It is not in fact work done but work that can be done,
capacity to do work. Work acquires now the role of a unit of measurement for a
new theoretical concept. Planck outlined the great importance of the step
undertaken:
"However insignificant this interpretation might seem at first glance, the
perspective that it opens on all fields of physics is nevertheless extraordinarily
wide, because now the generalisation to every natural phenomenon is evident." 134
In 1887, with prophetic insight, Planck declared 135 also that with
Helmholtz's formulation the principle of conservation of "force" became similar
to the one of conservation of matter: "force" as matter cannot be increased or
diminished, but can appear in different forms. The two basic forms of "force", vis
viva and tension force, can appear in many ways: vis viva as motion, light, heat;
tension force as elevation of a weight, elastic or electric potential, chemical
difference 136, and so on.
"But the sum of all these reserves of force (so to say accumulated in
different stores) is invariably the same and all natural processes only consist in
133 Helmholtz Erhaltung Pp.19-20
134 Planck Princip P.37.
135 Planck Princip P.37
136Probably in the sense of different energy levels connected with chemical bonds.