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

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With reference to these four levels Helmholtz could draw an explicit distinction between theoretical physics (dealing with deductions from level two to three, that is with the applications of the principle to empirical laws) and experimental physics (dealing with the inductions from level four to three, that is from natural phenomena to empirical laws). It is in my view important to remark that the dividing element between theoretical and experimental physics is not meant to be the use of mathematics. Thus theoretical physics was not at all identified with mathematical physics. In my opinion, with this Introduction, Helmholtz marks explicitly the emergence of theoretical physics, as a discipline distinct not only from experimental physics but also from mathematical physics. The most striking characteristic is Helmholtz's consciousness of the role of the four levels of the hierarchy, a consciousness that allowed him later to modify some specific elements of his scheme, leaving the methodological structure unchanged. The great and successful novelty is the stress on the interplay of the second and third level : since 1847 physical laws (level three) had to satisfy more and more not only experiments and natural phenomena (level four), but also theoretical principles (level two). These principles were also to be seen as heuristic tools to "discover" empirical laws: a complete new field of inquiry is open, theoretical physics, which is not primarily based on an extended use of mathematics. A basic characteristic of the principles is to be general, that is, to unify the different branches of physical knowledge. Helmholtz's methodological worries show also that he was obviously aware of the difficulties of his gigantic plan to unify natural sciences under one regulative principle. As I try to show below the Erhaltung is in fact "only" a plan that requires corroboration. If a discovery was made by Helmholtz in 1847, it was not that (of a specific formulation) of energy conservation, still a theoretical proposal lacking new experimental data and a secure mathematical grounding 18, but that of theoretical physics. In the Erhaltung an effort at showing the equivalence between the two main hypotheses (level one) is made in the first chapter, while the deduction from these hypotheses of Helmholtz's version of the principle of conservation (level two) is the object of the second chapter. The following four chapters deal with the interactions between levels two and three, that is with the application of the 18 See below the difficulties with the geometrical interpretation of the integral, in section 3 of the Erhaltung, and with the definition of selfpotential, in section 6.
principle to the existing empirical laws and with the attempt at deriving new empirical laws on theoretical grounds. In the Erhaltung no new experimental data (level four) are offered and the few regarding the mechanical equivalent of heat available at the time are criticised, also on the basis of a mistake on the conversions of the units of measurement, and disregarded. What Helmholtz really did in his Erhaltung was to lay the foundations of theoretical physics, through the conscious interplay of conceptual models, regulative principles, mathematical techniques and experimental results. His formulation of the energy principle was a specific application of this wideranging methodology and thus was meant to have the greatest number of possible applications. But Helmholtz's foundations of theoretical physics while being connected are not coextensive with his approach to energy conservation and will survive the latter. Helmholtz's methodology was in fact extraordinarily successful. Energy theory, that is theoretical physics applied to energy problems, changed the shape of physics : after 1847 physical laws no longer had only to face the challenge of experimental results, but also had to be judged on more theoretical grounds, in their relation with the conservation principle. But in turn the principle had, from the beginning, different formulations. From the point of view of Helmholtz's methodology, the other formulations of the principle of energy conservation can be seen as less methodologically sophisticated, but not less physically interesting. From 1847 on in physics the traditional theoryexperiment interplay was united with and often overcome by theory-principle interplay. Poggendorff's refusal of the paper for publication in the Annalen is an indication of the difficulty for experimental physicists to accept the new ideas, but it did not last long. An English version of the Erhaltung appeared in 1853 and the third paper of the energy section of Helmholtz's collected works mentioned above reveals that, just a few years after Poggendorff's refusal, the controversy with Clausius (1852-54), which revealed the first deep differences between a theoretical and a more mathematical approach, was entirely published in the Annalen . Moreover in six reports (1855-59), written for the Fortschritte der Physik and dealing with the "Theorie der Wärme", Helmholtz discussed and compared his own approach with an already wide literature: this might be considered the first history of energy conservation. Between 1862 and 1865, in the Philosophical Magazine , an international controversy on the "priority" of the "discovery" showed that the topic had become basic in scientific research.
Page 1 and 2: Fabio Bevilacqua Conservation and I
Page 3 and 4: different formulations 4 and priori
Page 5 and 6: and interesting results, despite th
Page 7: principle of correlation is express
Page 11 and 12: the origin and meaning of the princ
Page 13 and 14: Whether physiological research, apa
Page 15 and 16: In a discussion on the origins of a
Page 17 and 18: his "Wärme" that one of the differ
Page 19 and 20: generate a determined equivalent of
Page 21 and 22: "Bericht", despite the application
Page 23 and 24: experiments in the most disparate b
Page 25 and 26: The premise reveals that the struct
Page 27 and 28: intelligible if it can be referred
Page 29 and 30: elevant consequence of the deductio
Page 31 and 32: Needless to say the plan was to be
Page 33 and 34: and from here that the direction an
Page 35 and 36: since Leonardo 113; the "ad nihilum
Page 37 and 38: But unfortunately for the whole str
Page 39 and 40: The principle of conservation of vi
Page 41 and 42: different from the one joining the
Page 43 and 44: "The equality that exists between e
Page 45 and 46: In virtue of its limitations to New
Page 47 and 48: Helmholtz, while asserting that lig
Page 49 and 50: the temperature of 1 Kg of water ca
Page 51 and 52: In his search for a mechanical equi
Page 53 and 54: had already been achieved in the Be
Page 55 and 56: approach is discussed at length and
Page 57 and 58: and unaware of Green's results190,
Page 59 and 60:
potential function 201. It is worth
Page 61 and 62:
and judged unreliable, despite prov
Page 63 and 64:
The relevance of the first question
Page 65 and 66:
principle taking this potential int
Page 67 and 68:
Finally we get to the real conclusi
Page 69 and 70:
conservation 234, on the theory of
Page 71 and 72:
for the mechanical equivalent of he
Page 73 and 74:
The controversy started with some r
Page 75 and 76:
where μ are immovable masses, m th
Page 77 and 78:
demonstration criticised by Clausiu
Page 79 and 80:
directions that join them and whose
Page 81 and 82:
quotes 288 and criticises a proposi
Page 83 and 84:
motion to all natural forces, the k
Page 85 and 86:
measure this expenditure and compar
Page 87 and 88:
" ...the quantity of force in natur
Page 89 and 90:
forces is constant: but it relates
Page 91 and 92:
experiences in general laws of unli
Page 93 and 94:
"a series of important and difficul
Page 95 and 96:
the Discontinuous Movements of Flui
Page 97 and 98:
methodology. Dühring claimed the c
Page 99 and 100:
The first history of the conservati
Page 101 and 102:
while in Britain for the above talk
Page 103 and 104:
apply it to acoustics (1859), hydro
Page 105 and 106:
magnetic intensity. Maxwell realize
Page 107 and 108:
and the electrostatic In modern not
Page 109 and 110:
of conservation of energy: it is re
Page 111 and 112:
efuted. But again in 1881 Helmholtz
Page 113 and 114:
But was important here is that desp
Page 115 and 116:
The second (1892-94), follows the i
Page 117 and 118:
while the electromagnetic and the s
Page 119 and 120:
can modify its specific theoric for
Page 121 and 122:
considered relevant. In Poincarè
Page 123 and 124:
meaning left is: "There is somethin
Page 125 and 126:
interpretations at the beginning of
Page 127 and 128:
while fighting metaphisicians, he w
Page 129 and 130:
literature 456. There is an intrins
Page 131 and 132:
assertion is surprising: it has lon
Page 133 and 134:
Kant was a Naturphilosophe 480. The
Page 135 and 136:
condition that work done by the for
Page 137 and 138:
histories cites these (Hirn's) arti
Page 139 and 140:
) the experimental determinations o
Page 141 and 142:
force principle 522. Elkana tried t
Page 143 and 144:
Blüh, Otto. "The Value of Inspirat
Page 145 and 146:
Graetz, L. "Das Mechanische Wärme
Page 147 and 148:
Helmholtz, Hermann. "Bericht über
Page 149 and 150:
Helmholtz, Hermann. Wissenschaftlic
Page 151 and 152:
Madison: Wisconsin U.P., 1959. Pp.
Page 153 and 154:
Poincarè, Henry. Electricité et O
Page 155:
Yagi, Eri."Clausius's Mathematical
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