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 real starting point for the 86 paper was the search for an<br />
expression of the kinetic potential in Maxwell's theory. The old restrictive<br />
hypothesis according to which velocity is solely part of the vis viva, as a<br />
homogeneous quadratic function, has to be dropped. Helmholtz, at the very<br />
moment when the contiguous action theory was receiving its own non<br />
mechanistic local principle of conservation, gives up <strong>with</strong> the requirement so<br />
strongly defended for almost forty years: he recognizes that energy can be any<br />
function whatever of the coordinates <strong>and</strong> velocities. The retreat from the 1847<br />
positions is now almost complete: a lasting element is that the new interpretation<br />
of energy is still in the mechanical framework.<br />
But Helmholtz, now sixty-four <strong>and</strong> at the height of an extraordinary<br />
career, is again ready to start working towards new unifying horizons. The new<br />
regulative principle, PLA, should not be confined to mechanics <strong>and</strong> optics;<br />
Helmholtz applied it to electrodynamics <strong>and</strong> attempted to extend its range to<br />
thermodynamics:<br />
"From these facts we may even now draw the conclusion that the<br />
domain of validity of the principle of Least Action has reached far beyond the<br />
boundaries of the mechanics of ponderable bodies. Maupertuis’ high hopes for<br />
the absolute general validity of his principle appear to be approaching their<br />
fulfilment, however slender the mechanical proofs <strong>and</strong> however contradictory the<br />
metaphysical speculations which the author himself could at the time adduce in<br />
support of his new principle. Even at this stage, it can be considered as highly<br />
probable that it is the universal law pertaining to all processes in nature ..... In<br />
any case, the general validity of the Principle of Least Action seems to me<br />
assured, since it may claim a higher place as a heuristic <strong>and</strong> guiding principle in<br />
our endeavour to formulate the laws governing new classes of phenomena." 406<br />
These statements are part of the 1886 paper on PLA. A second paper<br />
was to appear in 1887. C. Neumann analysing Helmholtz’s work in a long<br />
treatise of 1898, remarks that <strong>Helmholtz's</strong> electrical investigations can be divided<br />
into two groups: the first (1870-75) has its roots in the general conceptions of<br />
Newton’s gravitational theory, i.e. in the principle of direct actionat-a-distance.<br />
406 Helmholtz, Hermann. "Ueber die physikalische Bedeutung des Princips der<br />
kleinsten Wirkung." In Crelle's Jour 100 (1886): 137-66 <strong>and</strong> 213-22. Repr. in WA 3. Pp.203-<br />
. Quot. from; Yourgrau <strong>and</strong> M<strong>and</strong>elstam. Variational Principles in Dynamics <strong>and</strong> Quantum<br />
Theory. 2nd ed. London: Pitman, 1960. P.143.