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

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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
can modify its specific theoric formulation, but not its validity, that Planck considers true as far as numerical results are concerned 415. Following Planck in fact the numerical value of the work equivalent of a transformation of a system between two states is always the same, independently of the way in which the transformation takes place. This he considers as an experimental result. But the theoretical interpretation of the energy terms can be achieved in different ways in different theories: the process of "substantialization" is open to a certain arbitrariness, always useful for the progress of knowledge 416. Planck ends his 1887 analysis pointing to one of this progress, the overcome of the action at a distance approach in electrodynamics, based on the (theoretical) success of the new version of the principle of conservation: the local conservation of energy. There is not a unique way to apply the general framework and thus a great part of the success relies in the ability of the scientist to use this new powerful theoretical tool: thus Helmholtz's 1847 success is due not only to his theoretical formulation but to his widespread and deep knowledge of the most various branches of natural science, a fact often overlooked by commentators. Only when his empirical knowledge fails, as in the case of electromagnetism, the methodological problems of the theory/experiment interplay in the formulation and application of the principle become evident. So far Planck's warnings. A different approach is outlined by Helm: of the two roots of Helmholtz's principle he accepts the first one (impossibility of perpetual motion) and denies the validity of the second (central forces). Thus Helm, while accepting a principle of conservation and a concept of energy, refuses as unnecessary Helmholtz's two main energy forms: tension and living forces. For Helm there is no theoretical nor practical reason to specify in an energy balance which is a tension force and which a living one, given that what matters is the work equivalent of a specific energy term. Helm denies 417 both the central forces hypothesis and the mechanical view of nature. Energy conservation means energy correlation and the equations are nothing else that sums of work equivalents. The mechanical view of nature, Helm asserts in line with Mayer's approach, does not add anything to the constancy of the sum of the work equivalents. I want to underline that the refusal of the privileged status of the central forces does not necessarily imply the rejection of the mechanical view: Clausius, as discussed 415 Planck Prinzip p.99, see also the Introduction to the 1887 edition. 416 Planck Prinzip Pp.104-5. 417 Helm Energetik p. 41.
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Fabio Bevilacqua Conservation and I
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different formulations 4 and priori
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and interesting results, despite th
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principle of correlation is express
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principle to the existing empirical
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the origin and meaning of the princ
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Whether physiological research, apa
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In a discussion on the origins of a
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his "Wärme" that one of the differ
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generate a determined equivalent of
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"Bericht", despite the application
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experiments in the most disparate b
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The premise reveals that the struct
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intelligible if it can be referred
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elevant consequence of the deductio
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Needless to say the plan was to be
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and from here that the direction an
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since Leonardo 113; the "ad nihilum
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But unfortunately for the whole str
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The principle of conservation of vi
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different from the one joining the
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"The equality that exists between e
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In virtue of its limitations to New
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Helmholtz, while asserting that lig
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the temperature of 1 Kg of water ca
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In his search for a mechanical equi
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had already been achieved in the Be
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approach is discussed at length and
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and unaware of Green's results190,
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potential function 201. It is worth
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and judged unreliable, despite prov
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The relevance of the first question
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principle taking this potential int
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Page 127 and 128: while fighting metaphisicians, he w
Page 129 and 130: literature 456. There is an intrins
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Page 133 and 134: Kant was a Naturphilosophe 480. The
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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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