Conservation and Innovation : Helmholtz's Struggle with Energy ...
Conservation and Innovation : Helmholtz's Struggle with Energy ...
Conservation and Innovation : Helmholtz's Struggle with Energy ...
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the simple passage from one to the other" 137. This was "another step forward<br />
towards simplifying the underst<strong>and</strong>ing of all natural phenomena" 138.<br />
It is indeed surprising that such a great innovation is seen as a failure by modern<br />
commentators 139 <strong>and</strong> discarded; I believe instead that an analysis of its origin<br />
outlines some specific features of a theoretical <strong>and</strong> a mathematical approach to<br />
physics. This can be shown relating <strong>Helmholtz's</strong> approach <strong>with</strong> Leibniz's one <strong>and</strong><br />
comparing it <strong>with</strong> Clausius's one.<br />
In my opinion, to achieve his result, Helmholtz made use of a Leibnizian<br />
inheritance 140. First the duality lebendig Kraft-Spannkraft strongly resembles the<br />
older one between vis viva-vis mortua; the terms themselves are very similar:<br />
while the vis viva has almost the same expression, the meaning of Spannkraft is<br />
very close to the older Leibnizian counterpart:<br />
"the ..... vis viva, produced by an infinite number of applications of vis<br />
mortua " 141<br />
But between <strong>Helmholtz's</strong> <strong>and</strong> Leibniz's ideas of positional "energy" there<br />
are two main differences that explain the success of the more recent formulation:<br />
a) Helmholtz provided a formal quantitative expression; b) the Newtonian forces<br />
are part of it.<br />
Helmholtz, making proper use of the Newtonian concept of force, <strong>and</strong><br />
accepting the full inheritance of Newtonian mechanics, provided a formal<br />
expression for the second term of the duality that was missing in Leibniz.<br />
But other Leibnizian elements can be outlined: the equality of the two<br />
terms in the mathematical expression is no longer the indication of an analytical<br />
identity. Being two independent physical concepts, now the equality has the<br />
meaning of a causal relation: the variation of one member implies the variation of<br />
the other. The equality holds at every instant during a process. This is a<br />
Leibnizian concept of conservation:<br />
137 Planck Princp P.37<br />
138 See Planck Princip P.37<br />
139 Kuhn thinks that Helmholtz "fails to recognize" the integral as "Arbeit", see above<br />
n.19; Lindsay too is surprised for the lack of the term "Arbeit" <strong>and</strong> stresses the mistake of<br />
considering an integral as the sum of lines. Lindasy Applic. of <strong>Energy</strong> P. 16.<br />
140 A Leibnizian influence on Mayer has been often remarked, on Helmholtz it has<br />
been only briefly pointed out by Planck Princip P.35, Koenigsberger H v H P.49; Elkana<br />
Disc Chapt 1 n.31.<br />
141 Leibniz : Specimen Dynamicum (1695) quoted in Lindsay Hist P.122.