I'm going to have to dig further into the attribution of the Telegraphers' Equation to Weber and Kirchhoff in 1857. Prof. Assis has a nice paper on the subject, here:
Assis cites Whittaker as an authority [vol. 1 pp. 230-232]. But by Whittaker's account [pp. 228-229], "...we have an equation first obtained by Oliver Heaviside (1850-1925), namely ... which is known as the equation of telegraphy." Whittaker goes on to describe how Kirchhoff derived a wave equation complete with the speed of light (which may be related to the inductance and capacitance or equivalently the permeability and permittivity), but Kirchhoff's wave equation looks to be a special case that doesn't appear to take into account resistance as in Heaviside's more complete treatment.
I'll see if I can hunt down the other references when I have more time.
The oft-repeated story that Maxwell mathematized Faraday’s ideas may also be incorrect. Herbert Dingle points out that Faraday sought to dismiss the ether. Science at the Crossroads, p. 91. The cited lecture, Thoughts on Ray Vibrations, (1946, two years after Faraday’s 1844 comments quoted above), upon close inspection, looks more friendly to the Ampere-Weber view than what is commonly represented.
Hi Tim, this is an interesting perspective, vis-à-vis Faraday and Clerk Maxwell, that I will examine in the coming months.
Nevertheless, it was clear during the exchanges between Faraday and Ampère around 1822 that there were serious divergences between the two. This can be seen in multiple parts of AKT Assis and JPMC Chaib, Ampere's Electrodynamics, Montreal: Apeiron, 2015. The passages cited below all come from that book.
Savary and Ampère, 1822:
If M. Faraday, in this passage, considered only that the attractions and repulsions between electric currents are complicated facts due to the fact that they result from an infinity of actions between all infinitely small parts of these currents, then he was in agreement with M. Ampère. However, he [Faraday] considered them complicated from another point of view, as he considered as a primitive fact the rotational action and shows quite well that these attractions and repulsions can be reduced to it. But we have just seen that by considering, on the contrary, as primitive facts the attractions and repulsions between the small portions of electric currents, according to the laws given by M. Ampère, one deduces immediately the circular motions of the conducting wires and magnets around each other. [p.252]
Ampère to Faraday, 1822:
A fundamental and obvious principle of physics is that, the action always being equal to the reaction, it is impossible that a rigid system be put in motion in any way by a mutual action between two of its particles, as this action produces on the two particles two equal and opposite forces which tend to move the body in opposite senses. It then follows that, when the particles of a magnet traversed by an electric current which puts them in the same state of the conducting wire act on the pole or on any other part of the magnet, no motion in this body can result from this action, [...]
From this observation, the rotation of a floating magnet around its axis can only be explained as I did in the memoir included in the May issue of the Annales de Chimie et de Physique, which I sent to you recently. [p.271]
I read Faraday’s 1844 and 1846 papers carefully and think what he’s saying is compatible with action-at-a-distance. In his 1844 letter, Faraday argues that if the ether surrounds every atom, how can it be an insulator within insulating materials and yet a conductor within conducting materials? His hypothesis is to treat the action-at-a-distance force as part of matter—indeed, perhaps the most important part because it’s the external force that interacts with other matter or charges.
The intent here is not to attack the thesis of this series, which I think is correct and most helpful. The point is merely to show that Faraday likely stood with the early giants Ampere and Weber and the modern misinterpretations came later.
No, I meant Faraday’s letter to Richard Taylor in 1944 (cited in your footnote 5 I believe). The 1846 is “Thoughts on Ray Vibrations.” I was able to find that on a NASA archive site.
I haven’t seen these other two. How can I find them?
"A speculation touching Electric Conduction and the Nature of Matter" is footnote 5. I gave the initial publication, rather than the reprint in his collected works.
It seems to me that there are two different theories of action-at-a-distance here - Newton's with his invisible hand of gravity theory, and Fresnel's with his interference theory. Newton's equation has the big G, while the following equations seem to be converging on something that actually causes that big G. I'm going to go with Fresnel's.
I'm going to have to dig further into the attribution of the Telegraphers' Equation to Weber and Kirchhoff in 1857. Prof. Assis has a nice paper on the subject, here:
https://www.researchgate.net/publication/3452171_Telegraphy_equation_from_Weber's_electrodynamics
Assis cites Whittaker as an authority [vol. 1 pp. 230-232]. But by Whittaker's account [pp. 228-229], "...we have an equation first obtained by Oliver Heaviside (1850-1925), namely ... which is known as the equation of telegraphy." Whittaker goes on to describe how Kirchhoff derived a wave equation complete with the speed of light (which may be related to the inductance and capacitance or equivalently the permeability and permittivity), but Kirchhoff's wave equation looks to be a special case that doesn't appear to take into account resistance as in Heaviside's more complete treatment.
I'll see if I can hunt down the other references when I have more time.
The oft-repeated story that Maxwell mathematized Faraday’s ideas may also be incorrect. Herbert Dingle points out that Faraday sought to dismiss the ether. Science at the Crossroads, p. 91. The cited lecture, Thoughts on Ray Vibrations, (1946, two years after Faraday’s 1844 comments quoted above), upon close inspection, looks more friendly to the Ampere-Weber view than what is commonly represented.
Hi Tim, this is an interesting perspective, vis-à-vis Faraday and Clerk Maxwell, that I will examine in the coming months.
Nevertheless, it was clear during the exchanges between Faraday and Ampère around 1822 that there were serious divergences between the two. This can be seen in multiple parts of AKT Assis and JPMC Chaib, Ampere's Electrodynamics, Montreal: Apeiron, 2015. The passages cited below all come from that book.
Savary and Ampère, 1822:
If M. Faraday, in this passage, considered only that the attractions and repulsions between electric currents are complicated facts due to the fact that they result from an infinity of actions between all infinitely small parts of these currents, then he was in agreement with M. Ampère. However, he [Faraday] considered them complicated from another point of view, as he considered as a primitive fact the rotational action and shows quite well that these attractions and repulsions can be reduced to it. But we have just seen that by considering, on the contrary, as primitive facts the attractions and repulsions between the small portions of electric currents, according to the laws given by M. Ampère, one deduces immediately the circular motions of the conducting wires and magnets around each other. [p.252]
Ampère to Faraday, 1822:
A fundamental and obvious principle of physics is that, the action always being equal to the reaction, it is impossible that a rigid system be put in motion in any way by a mutual action between two of its particles, as this action produces on the two particles two equal and opposite forces which tend to move the body in opposite senses. It then follows that, when the particles of a magnet traversed by an electric current which puts them in the same state of the conducting wire act on the pole or on any other part of the magnet, no motion in this body can result from this action, [...]
From this observation, the rotation of a floating magnet around its axis can only be explained as I did in the memoir included in the May issue of the Annales de Chimie et de Physique, which I sent to you recently. [p.271]
I read Faraday’s 1844 and 1846 papers carefully and think what he’s saying is compatible with action-at-a-distance. In his 1844 letter, Faraday argues that if the ether surrounds every atom, how can it be an insulator within insulating materials and yet a conductor within conducting materials? His hypothesis is to treat the action-at-a-distance force as part of matter—indeed, perhaps the most important part because it’s the external force that interacts with other matter or charges.
The intent here is not to attack the thesis of this series, which I think is correct and most helpful. The point is merely to show that Faraday likely stood with the early giants Ampere and Weber and the modern misinterpretations came later.
Hi Tim, are you referring to the following papers?
A speculation touching Electric Conduction and the Nature of Matter, Lond. and Edinb. Phil. Mag., 1844, vol. xxiv. .p 136.
On new magnetic actions, and on the magnetic condition of all matter-continued...., Philosophical Transactions, 1846, p. 41.
No, I meant Faraday’s letter to Richard Taylor in 1944 (cited in your footnote 5 I believe). The 1846 is “Thoughts on Ray Vibrations.” I was able to find that on a NASA archive site.
I haven’t seen these other two. How can I find them?
"A speculation touching Electric Conduction and the Nature of Matter" is footnote 5. I gave the initial publication, rather than the reprint in his collected works.
Michael Faraday, Experimental Researches in Electricity, 3 volumes (1839, 1844, 1855).
It seems to me that there are two different theories of action-at-a-distance here - Newton's with his invisible hand of gravity theory, and Fresnel's with his interference theory. Newton's equation has the big G, while the following equations seem to be converging on something that actually causes that big G. I'm going to go with Fresnel's.
Fresnel's theory is not based on action-at-a-distance, but, rather, local action.
Thanks John, that makes more sense.