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

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solve the difficulty of the elastic-solid theory of reflection and refraction of light. This footnote was the starting point of H. Lorentz’s 1875 doctoral thesis. A clear schematization of the physical model of Helmholtz’s theory was given by Hertz in 1892 388. Hertz distinguished two limiting cases, both refer to a conception of action-at-a-distance starting from the charges on the plates that polarize the dielectric between the plates. In the first case, the energy is supposed to be concentrated on the plates and the actions (at a distance) produced by the polarised dielectric are comparatively small. Ideally, removing B leaves some action-at-adistance. In the second case, the energy is supposed to be concentrated in the dielectric particles and so the dielectric action is the prevailing one. This second case is mathematically equivalent to Maxwell’s. Helmholtz himself was quite clear about the physical differences between his and Maxwell’s theory: "The two theories are opposed to each other in a certain sense, since according to the theory of magnetic induction originating with Poisson, which can be carried through in a fully corresponding way for the theory of dielectric polarization of insulators, the action-at-a-distance is diminished by the polarization, while according to Maxwell’s theory on the other hand the action-at-a-distance is exactly replaced by the polarization" 389 and "It follows from these investigations that the remarkable analogy between the motion of electricity in a dielectric and that of the light aether does not depend on the particular form of Maxwell’s hypothesis, but results also in a basically similar fashion if we maintain the older viewpoint about electrical action-at-adistance" 390. Helmholtz’s comparison between the three theories had already led to remarkable results: he judged Weber’s theory untenable (for the instability of the equilibrium given by K < 0) and instead showed great interest in Maxwell’s limit of his own theory. In addition, he considered this last approach suitable to solve the difficulty of optical theory. For my purposes, it is relevant to notice Helmholtz's shift of criticism towards Weber’s law. Weber’s law is no longer considered inconsistent with the principle 388 Hertz, H. Untersuchungen über die Ausbreitung der elektrischen Kraft. Leipzig, 1892. Tr. by D.E.Jones Electric Waves. London: Mac Millan, 1892. Repr. New York: Dover, 1962. Pp.23-5. 389 Helmholtz "Beweg Elektr" pp.556-7. 390 Helmholtz "Beweg Elektr" p.558.
of conservation of energy: it is recognised that the work done during a complete cyclical operation is zero, in other words the existence of a potential is recognized. What is criticized now is the possibility of deducing absurd consequences from the law. In 1872, Helmholtz modified his PCE with the explicit requirement that T > 0 (T = kinetic energy), in order to theoretically disregard the supposed inconsistencies derivable from Weber’s law 391. What was Weber answer? As mentioned in previous sections, in 1846 Weber published his non-positional force law and in 1848 he published a derivation of this law from the expression of a potential. Both these results contradicted Helmholtz’s 1847 formulation of PCE. In Weber’s case the forces were not central and there was no clear distinction between kinetic and potential energy. So the problem was: had Weber’s law to be considered in agreement with a general PCE, despite its contrast with Helmholtz's PCE? Still in 1867 Thomson and Tait gave a negative answer to this question: "... the conclusion (of Weber’s theory) would stand in contradiction with the ’Conservation of Energy’ which we take to be a general law of nature from innumerable experiments. Such theories are all the more dangerous if they accidentally explain other phenomena, as Weber’s explain induced currents" 392. Tait again in 1868: "But the investigations of these authors (Riemann and Lorenz) are entirely based on Weber’s inadmissible theory of the forces exerted on each other by moving electric particles, for which the conservation of energy is not true, while Maxwell’s result is in perfect consistence with that great principle." 393. Tait’s (and Thomson’s) objection refers to the contradiction between Weber’s law and Helmholtz’s PCE, but cannot be accepted as an objection that Weber’s law is incompatible with the impossibility of perpetual motion. The existence of a potential for Weber’s law implies that the work done by the electric forces is a perfect differential. This means that in a cyclical process an indefinite amount of work cannot be generated by a particle moving under the action of the force assumed by Weber. Thus work is not created out of nothing. Finally both Helmholtz (in 1870 and 1872) and Maxwell (in 1873) agreed on this important 391 Helmholtz, Hermann. "Ueber die Theorie der Elektrodynamik." Berlin Monats April 1872: 247-56. Repr. in WA 1 : 636-46. Pp.645-6. 1877. P.318. 392 Quoted in Neumann, Carl. Die Gesetze von Ampére und Weber. Leipzig: Teubner, 393 Tait,P.G. Sketch of Thermodynamics. Edinburgh, 1868. P.76.
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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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