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

Planck asserts that the reduction of all the forms of energy to two main ones is a
great merit, a simplification and a great heuristic tool, but that nevertheless this is
insufficient to deal with in complicated situations, like electromagnetism, still
partly unknown. This means that the principle 'per se', without the contribution of
experimental results, cannot give definite answers.
To apply Helmholtz's's principle to a process that takes place in a system of
bodies it is necessary to add together all the different kinds of variations of vis
viva on one side, the sum of tension forces on the other side and equate the two
groups. The sum of all the identified terms representing the vis viva and the
tension forces at a given instant is the "force" (energy) of the system, constant if
the system is isolated. Of course all the identified different terms of the sum have
to be numerically expressed on the basis of a common unity of measurement,
usually mechanical work; thus their mechanical equivalent has to be found. But in
this process of identification of the different terms contributing to the energy of
the system we find a methodological difficulty:
"there is not a general rule with which we can calculate a priori the value of the
equivalent (i.e. the expression of the different terms), independently of the
principle itself" 413
Often in the past wrong identifications of the equivalents led to wrong
conclusions (Planck quotes Descartes and Carnot 414).
Helmholtz's principle with its reduction of all the energy terms to two main forms,
kinetic and positional, is without doubt a great heuristic tool to find out the
different energy terms, but does not solve all the problems. That is, there is
always an indetermination and then an arbitrariness in the identification and
expression of the energy terms.
There is in fact a complicated interplay between the general framework of the
principle and the empirical laws.
From an existing and accepted empirical law the expressions of the tension
forces and of the vis viva have to be identified (and the law rededuced). Instead
for a realm of phenomena not yet described by laws or with laws not sufficiently
corroborated, if we assume the principle to hold true some useful guide-lines for
the formulations of empirical laws can be produced. Sometimes the principle
leads to discover new laws, in other cases the discovery of new experimental
laws will add new energy terms to the principle. Again new experimental data
413 Planck Prinzip p.38
414 Planck Prinzip Pp.7-9 e 13-17