Talk:Galilean electromagnetism

This article is only a draft, but both references appear to be primary references, which are OK, but it is harder to establish that the topic is significant and not a mathematical curiosity without reliable secondary sources. A reference that was an actual college textbook, for example, would be more convincing.Constant314 (talk) 20:13, 23 January 2016 (UTC)
 * Agreed, I added a reference to Melcher's book that explains clearly that quasi-static approximations are not appropriately introduced in most books (most avoid any quantitative introduction for non-static cases). I think the next important contribution in this page, before introducing more specific contents, will be to explain how the galilean formalism allows to introduce rigorously the two usual quasi-static approximations (that are in fact dynamic if we stick to the definition) and why they are mutually exclusive (they apply separately in different regions of space in order to describe either the coil or the capacitor but not both). Henri BONDAR (talk)
 * I think you are on the right track, but if the only thing Melcher's book only says about the topic is that it is not appropriately introduced in most books, that is not enough to establish significance.Constant314 (talk) 15:17, 26 January 2016 (UTC)
 * Most reference books in EM were written well before this aspect of EM was revealed (first input was in 1973 and did not spread widely as published in a remote Italian journal). As Melcher stated in his relatively recent contribution, most books introduce quasi-static in an inconsistent way, starting by pure electrostatic and magnetostatic and then a sentence to generalize to slow moving charges without any quantitative considerations, then suggesting falsely that capacitors and coils could be described using the same reduced formalism. Rousseau is the specialist of the domain, he gave many references to books in his 122 ref list. May be you can help to extract appropriate ones. Thanks.Henri BONDAR (talk)
 * Just added a web link to a simple example of the use of the Galilean invariance in the EM frame.Henri BONDAR (talk)
 * Just added a primary source for occurrence of Galilean transformations in a Wiley book for engineers in 1968.--Henri BONDAR (talk) 08:39, 29 January 2016 (UTC)


 * The article is simply wrong and needs to be completely rewritten or removed. It is propagating the myth that the formulations of electromagnetic theory advanced by Einstein's predecessors (e.g. Lorentz, Helmholtz, Maxwell, Hertz) were non-Galilean and starts out by asserting a widespread (and false) myth "In 1905 Albert Einstein made use of the non-Galilean character of Maxwell's equations to develop his theory of special relativity." It was Galilean. It was Einstein who asserted that they can and should be formulated on a non-Galilean framework. That was the innovation of his paper "On the electrodynamics of moving bodies". The "moving" refers to the dichotomy, present in pre-relativistic formulations of electromagnetic theory between the "stationary" and "moving" forms of the theory. All of the pre-1905 formulations had the "moving" versus "stationary" dichotomy, the "moving" forms being relative to a (unique) frame tied to light propagation, because they were all formulated in the Galilean framework, where it is necessary to have this dichotomy owing to the absence of a finite invariant speed. Einstein, himself, as well as Minkowski in 1908, went out of their way to point out that the pre-1905 formulations of electromagnetism were *not* in accord with the Lorentz transformations. You can see more of this under the discussion in the digital archives of Einstein's papers at Princeton (https://einsteinpapers.press.princeton.edu/) in the discussion adjoining Einstein and Laub's reformulation of the classical theory of moving media in a relativistic setting. The constitutive laws, as posed in any of Helmholtz, Heaviside, Hertz, Lorentz are all in accord with the Galilean transforms, not the Lorentz transforms - not even with the fix that Lorentz made. Lorentz's constitutive laws are missing the relativistic correction terms that are present in the Einstein/Laub and Minkowski reformulations of the theory of moving media. As such, even with the "Lorentz transform" fix he posed, they are still non-relativistic and accord with the Galilean group. — Preceding unsigned comment added by 2603:6000:AA4D:C5B8:222:69FF:FE4C:408B (talk) 21:37, 17 December 2020 (UTC)

Do you have access to Classical Electromagnetics, 3rd ed. by Jackson? Perhaps his discussion of Faraday's Law of Induction and Galilean Transformation on page 208-211 might be relevant. Constant314 (talk) 22:38, 29 January 2016 (UTC)
 * Thanks for your precious help, I only have the 1st ed., I will get the 3rd one soon. I think that some Galilean transformations could be explicitly written in this page later on, especial in order to justify rigorously quasi-static approximations (I never liked that name "quasi-static" both in EM and in thermodynamics frame as they involve dynamic behaviors (even if non-radiative in the EM frame), and because the conditions for their validity are rarely quantified). If you have time, please also look at my talk about non-radiating near-field and health issues Talk:Wireless power. Regards --Henri BONDAR (talk) 08:24, 30 January 2016 (UTC)
 * This third edition is indeed useful. Not only Jackson introduces a Galilean transformation for the Fraday's equation (p209-210) but he also demonstrates without saying it clearly (p515-p516) that a situation described by a scalar potential V (then in the quasi-electrostatic near-field frame)can be seen as Galilean, whereas wave propagation (the far-field) could not. So by combining the two aspects, Faradays and quasi-magnetostatics and Scalar potential and quasi-electrostatics, you already see the whole picture taking form. The idea that they are two mutually exclusive Galilean approximations for the near-field is however missing in Jackson's work.--Henri BONDAR (talk) 09:00, 30 January 2016 (UTC)


 * So, Jackson got a result consistent with quasi-electrostatics? In Jackson's treatment E' = E + k (v x B) but B'= B.  By symmetry, you would expect a (v x E) term added to B to give B'.  The following is speculation: (v x B) is the force felt by an electric mono-pole (an electron).  (v x E) would give rise to a force on magnetic mono-poles which do not exist so the (v x E) term can be ignored and we can take B' = B.  Is that perhaps what you previously meant by magnetic free? Constant314 (talk) 18:48, 30 January 2016 (UTC)


 * Yes indeed but only in the specific case he cited as an example (Potential Vij between two charges). The whole story is indeed to compare electrical and magnetic contributions to the force and to show that they are two mutually exclusive limiting cases when v<<c.

I used the expression "Magnetic free" in the Poynting vector page. This vector can be derived in the quasistatic frame through only electrical quantities (Scalar potential times the gradient of D). Applied to the capacitor this vector leads to the same balance than the usual vector (it is well known that you can add any divergence field to the Poynting vector without changing the meaningful balance). Applied to the two flat disk capacitor, you can easily demonstrate that you get the same result, but energy flow instead of spreading radially from the capacitor axis is parallel to it and then somehow more realistic (demonstrated in annex2 of Bondar-Bastien article in the AFLB (Association Française Louis de Broglie)). The proposal (with due reference to a book not our article) was removed by Interferometrist because this vector was not relativistic :-) (he also stated falsely that waves in piezo-electric materials are only of the acoustic type). Not an easy task to bring a structured knowledge here, it is why it is so interesting.--Henri BONDAR (talk) 11:38, 31 January 2016 (UTC)

I found a possibly useful reference. Page 77 of Electromagnetic Theory by Julius Adams Stratton, 1941. Stratton is even referenced by Jackson. He says “The Galilean transformation of classical mechanics represents the limit approached by  when v << c and may be interpreted as the relativity principle appropriate to a world in which electromagnetic forces are propagated with infinite velocity.

An intuitive way to present the background ideas
There is a very simple way to present the ideas behind the Galilean formalism: In the Maxwell equation frame you have two dynamic coupling terms involving respectively: $$\frac{\partial\mathbf B}{\partial t}$$ and $$\frac{\partial\mathbf E}{\partial t}$$, if you remove a single one, you still have a dynamic behavior but no waves (besides the speed of light disappears in the equations). Galilean formalism shows how and when these approximations are licit and that they lead to two types of dynamic but non-radiative behaviors in the EM frame. Of course you cannot remove both terms and keep a dynamic behavior as well as you cannot keep both without involving propagation at the speed of light. If you remove both terms, the situation becomes quasi-static in the strict acceptance of the term (situations where quantities allowed to vary with time are described by equations where the time is not explicitly present). But sensu stricto you cannot consider quasi-static Maxwell equations without removing the current in the capacitor and the voltage on the coil.

The same situation exist in fluid mechanics: If a tank is filled with water, the pressure at the bottom is given by $$\ p - p_0 = \rho g h,$$. This formula can be applied even if h varies slowly with time (quasi-hydro-statics). But you also have dynamic situations such as a converging diverging flow that involve $$\frac{\partial\mathbf v}{\partial t}$$ terms without involving waves and finally far field situations where you only find acoustic waves.

The two Galilean frames can be seen to be related to non compressible cases, it is why Maxwell and later Lorentz have introduced the idea of some kind of ethereal fluid.--Henri BONDAR (talk) 12:37, 30 January 2016 (UTC)


 * I’m going to pick on your lede paragraph. Take this as a suggestion. Your first sentence is “Galilean electromagnetism is the study of Electromagnetic fields that fulfill the Galilean invariance.”   We know that electromagnetic fields do not fulfill the Galilean invariance, so, as written, it will be a red flag.  Someone will immediately label it as fringe science and nominate it for deletion.  Let me suggest a different sentence that would be less likely to provoke a knee jerk reaction: ”Galilean electromagnetism a formal electromagnetic field theory that consistent with Galilean invariance.  It is useful for calculating electromagnetic effects when objects are moving with low velocity.”  Feel free to do anything you want with those sentences.  The important points are that Galilean electromagnetism is not a replacement for ordinary EM theory and it is useful for calculations. Constant314 (talk) 02:53, 1 February 2016 (UTC)


 * Fully agreed my introduction is provoking as such, the word approximation is missing. Why not simply "Electromagnetic fields that fulfill approximately the Galilean invariance", I will think some more before making the changes. Thanks for both inputs (Stratton and awkward intro)--Henri BONDAR (talk) 08:54, 1 February 2016 (UTC)


 * I see that I left out the word is in my suggestion:”Galilean electromagnetism is a formal electromagnetic field theory that consistent with Galilean invariance.". Anyway, I suggest that you rework the first sentence so that it starts with "Galilean electromagnetism is ...".  Constant314 (talk) 19:34, 3 February 2016 (UTC)


 * Done, much clearer now, thanks --Henri BONDAR (talk) 10:35, 4 February 2016 (UTC)
 * About the idea that quasistatic regimes are obtain by neglecting one of the two coupling terms $$\frac{\partial\mathbf B}{\partial t}$$ or $$\frac{\partial\mathbf E}{\partial t}$$ but not both (obvious but not explained so clearly in Melcher book and lectures) you can see for instance : Melcher lectures in MIT (see page 16) http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-007-electromagnetic-energy-from-motors-to-lasers-spring-2011/lecture-notes/MIT6_007S11_lec17.pdf. By the way I have started to improve the Quasistatic approximation page(if you have some time).--Henri BONDAR (talk) 15:02, 4 February 2016 (UTC)

Mathematical formalism
I planned to add such a section, where the Galilean formalism could be introduced in the EM frame. The main idea is to show that the two Galilean limits can be obtained by going to the limit of infinite light speed. To do so, I will use the Stratton reference kindly provided by Constant314 as well as Levy-leblond and Rousseau articles. According to a recent mail from Rousseau, the two quasi-static domains are also quite well introduced in the recent Melcher's book using instead of the Galilean formalism, time constants evaluations. This should also be mentioned in this page, I guess.--Henri BONDAR (talk) 11:15, 3 February 2016 (UTC)


 * Yes, you need equations that show precisely what the subject is about. Description only goes so far. Constant314 (talk) 19:37, 3 February 2016 (UTC)

What Jackson and others do not cover
Consider deleting the sentence about what Jackson does not discuss because 1) it’s irrelevant, 2) it’s virtually impossible to find a citation that says Jackson doesn’t otherwise discuss a topic. If it were a three-page paper, it might be acceptable to say that it did not cover a particular topic, but Jackson is an 800-page book. It becomes WP:OR to say that you read the whole book from cover to cover and understood everything and attest that there is no other coverage of Galilean invariance. As long as the lede establishes significance, you do not need further justification to discuss the topic.

Similarly, it is irrelevant that “Quasi-static approximations are often poorly introduced in literature as stated for instance in Hauss & Melcher.” Again, you don’t need to justify the existence of this article on the grounds that it is poorly covered elsewhere. I suggest that this statement be replaced with something affirmative about the topic from that book. Constant314 (talk) 19:09, 6 February 2016 (UTC)


 * Thanks for your inputs and corrections. Concerning Jackson, agreed to remove this personal and awkward comment. Concerning Melcher comments, I think they are more relevant and can be sustained by solid references (book and page reference). Levy Leblond, Rousseau, Melcher and many other sustain the idea that quasistatic regimes are badly introduced in literature. Besides it contributes to set the usefulness of the topic. --Henri BONDAR (talk) 07:51, 8 February 2016 (UTC)


 * Well, it is not fatal, but being poorly covered elsewhere is not a justification for an article. In fact, it is a justification to not have an article.  WP:GNG calls for significant coverage rather than insufficient coverage.  Can you find at least one statement in Melcher's book that Galilean electromagnetism is useful for something more than being a mathematical curiosity? Constant314 (talk) 16:02, 8 February 2016 (UTC)


 * Jackson comment removed. I continue to think that the idea that the two Galilean limits are mutually exclusive should be more developed especially if we remove also Melcher comments. It is important that this inherent difficulty of the "going to the limits" process in the electromagnetic frame should be emphasized, as it explains why such developments where not made earlier. One possibility is to consider that the four vector "density, current" cannot vanish, but I am still searching for a clearer introduction of the idea.--Henri BONDAR (talk) 08:13, 8 February 2016 (UTC)

Establishing notability
I added a quote from Rousseaux to the lede that I think goes a long way toward establishing notability. However best practice is to have at least two independent reliable sources to establish notability. Rousseaux makes heavy use of Levy-Leblond, so those are not independent sources. Melcher’s MIT course notes do not contain the word “Galilean” and they do not mention velocity. Not having two sources does not de-establish notability, but if there are two independent sources, it is very unlikely that anyone will attempt to delete the article on the basis of being not notable. Can you find a second, independent source that discusses Galilean electromagnetism? Constant314 (talk) 21:00, 8 February 2016 (UTC)


 * We may separate the wording "Galilean electromagnetism" first introduced quite recently by Levy-Leblond (it explains why so many articles refer to it), from the content behind that was present well before their article. The same topic hides behind expression such as "Galilean transformation", "Galilean invariance" or simply "low velocity transformation rules" as soon as applied in the EM context. These ideas can be traced back down to Maxwell himself (According to Rousseaux). I am still searching for a clear reference in Maxwell's work.
 * It is true that recent Melcher's MIT course does not contain any direct reference to a Galilean aspect. This document is aimed for a non-specialize audience and contains an alternate smooth way to introduce quasistatic domains based on time scales and space scales. It is not intended to establish notability but as a didactic work that helps to introduced, in an engineer point of view, the same ideas. By the way, In the quasistatic approximation page I have introduces the two ways on the same footing (here again the question to know if it was made appropriately or not before Melcher/Levy-Leblond remains). In the Haus & Mecher old book (well before Levy-Lebond article), the Galilean transformations for both limits are clearly written (however I don't know if they are said to be "Galilean", but it is obvious for the specialist).
 * Anyway, the occurrence of the expression "Galilean Electromagnetism" is quite limited in literature, the background ideas are long present in many sources but also cannot by said to be really wide spread because according to Levy-Leblond, Melcher and Rousseaux of the aforementioned difficulties. On the other hand, I never saw a critic against such an approach that is generally well received by most specialists as it enlightens why "quasi-static" approximations for the fields can be related to dynamic behaviors for the charges and currents.--Henri BONDAR (talk) 10:28, 10 February 2016 (UTC)

Section 3 of Le Bellac, M.; Levy-Leblond, J.M. (1973). "Galilean Electromagnetism"
What do you make of section 3? It appears to be a discussion showing that a Galilean electromagnetism that satisfied both the electro quasi-static and the the magneto quasi-static at the same time would lead to counter factual conclusions such as capacitors do no work, there is no force between currents, E fields are everywhere the same value, there is an absolute rest frame. Is that your interpretation? Constant314 (talk) 15:56, 10 February 2016 (UTC)


 * Yes it is the idea behind mutual exclusion, a system both quasi electro and magneto static is simply static (i. e. no displacement currents in capacitors, no electro-motrice force in coils). Quasistatic approximations only apply in different space or time regions. Well, this is not exactly true, uncoupled superposed situations exist when fields are parallel everywhere ( The Poynting vector vanishes everywhere and mixed coupling $$k=\frac{k_L+k_C}{1+k_Lk_C}.$$ can be defined and measured). But such a situation is not related to any specific approximation and also exists for antennas. Back to our topic, in contrary to classical mechanics, a single Galilean approximation has no meaning in EM. This explains on one side why quasistatic approximations are often pretty badly introduced in most books and on the other side the late introduction of the idea of Galilean electromagnetism. As explained previously, a clearer explanation for this idea (other than nebulous quadrivector considerations) should be provided if existing. I have a very simple one but it is not supported by any reference.--Henri BONDAR (talk) 07:47, 11 February 2016 (UTC)


 * It would be very helpful if there is an example in one of the references where using the older non-Galilean low velocity approximation


 * $$ B' = B - \epsilon_0 \mu_0  v  \times E   $$


 * $$ E' = E + v \times B   $$


 * for a calculation gets a answer with significant error (perhaps 10%) and one of the Galilean low velocity limits gets an answer with substantially less error (perhaps 1%). Constant314 (talk) 15:24, 11 February 2016 (UTC)


 * Perhaps you can also get a better accuracy in some cases as you have more correcting terms. The answer I get from Rousseaux is that such a transformation has no physical meaning as it doesn't lead to a group structure. May be you will find more insight in http://www.pprime.fr/sites/default/files/pictures/pages-individuelles/D2/germain/PRL2008.pdf
 * Galilean transformations seems to be directly useful only in cases of solid moving frames (for instance charges stuck in a solid moving dielectric).--Henri BONDAR (talk) 07:25, 12 February 2016 (UTC)
 * There is also an interesting reference to Galilean transformation in Maxwell Treatise on Electricity and Magnetism: https://en.wikisource.org/wiki/A_Treatise_on_Electricity_and_Magnetism/Part_IV/Chapter_VIII (see section 600]: On the Modification of the Equations of Electromotive Force when the Axes to which they are referred are moving in Space). --Henri BONDAR (talk) 09:47, 12 February 2016 (UTC)
 * That's a good one. It make very clear the problem of using a non-Galilean transformation. Constant314 (talk) 15:21, 12 February 2016 (UTC)


 * I've added to and modified the history section based on my understanding of the references you have provided. I also removed some language that sounded like editorializing.  Feel free, of course, to change it.Constant314 (talk) 16:32, 12 February 2016 (UTC)


 * Wonderful job Constant, I am totally comfortable with it. --Henri BONDAR (talk) 08:37, 13 February 2016 (UTC)


 * Could I prevail on you to add a citation to Rousseaux’s comment in PHYSICAL REVIEW LETTERS June 2008 to the simple example of inconsistency in the history section? Constant314 (talk) 17:40, 13 February 2016 (UTC)


 * No problem except that I am a little busy today, I'll try to do it tomorrow. --Henri BONDAR (talk) 16:03, 15 February 2016 (UTC)

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