Talk:Gauss's law for magnetism
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Faraday's Electrotonic State
Steve, Yes that is correct , Maxwell did indeed believe that A corresponded to something physical, although he was not altogether clear himself how to accurately describe it. He saw it as a kind of 'momentum' in Faraday's lines of force, corresponding to what Faraday referred to as the 'electrotonic state'. In the 1864 paper it starts to take on the role of a fly-wheel. Imagine the magnetic field like fly-wheels which store rotational kinetic energy, and when the current is switched off, the fly-wheels unload their kinetic energy back into the wire for the final kick.
Anyway, that source which you supplied  is excellent. It openly states that the Lorentz force appeared in Maxwell's 1864 paper. I wish you had supplied this source a few weeks ago. Nobody was in any doubt about the fact, but there was an argument over the issue that it wasn't stated in any secondary sources, and as such, couldn't be mentioned in the Lorentz force article. That's twice in two days that secondary sources have conveniently turned up confirming issues about which I had been accused in the past of original research. David Tombe (talk) 01:22, 9 November 2010 (UTC)
The Helmholtz decomposition theorem
Steve, I realize now why my mention of Maxwell's original equations was put into a special history section to segregate it from the Helmholtz decomposition theorem. It's because the Helmholtz decomposition theorem actually reverses Maxwell's argument. Therefore I want to ask, 'if the vector B is eligible for the Helmholtz decomposition theorem, what are its properties which make it so eligible?' We know that the divergence of B is zero, but we only know that because it is the curl of A. How do we reason this in reverse? What is the initial reason why we know that the divergence of B is zero if we are going to work backwards like this? A divergence could be zero for one of two reasons, (1) because it is the curl of another vector, or (2) because it is an inverse square law function. But can it be for both of these reasons simultaneously? I would doubt it, because reason (1) is solenoidal with no singularities, whereas reason (2) necessarily has a singularity. I would say that in the case of B, we are dealing with reason (1). So how can we use this reasoning backwards? I know that we have touched on this subject before, but I hadn't realized until now how significant it is in relation to the order of the logic. I think that the last time that we touched on this subject, the issue was that I was suggesting that curl A = B was a more specific equation than div B = 0, hence calling into question whether or not the name Gauss's law for magnetism was really giving justice to the significance of the equation. David Tombe (talk) 21:41, 9 November 2010 (UTC)
- I am not quite sure what you are trying to say on everything, but there are some things I think I can answer. First, Helmholtz decomposition works on all vector fields (probably with some exceptions that physicist don't care about ;) ). Basically it says that all vector fields can be broken into a curlA + gradV. (There are some additional subtleties with boundary conditions I think.) Maxwell's B=curlA is equivalent mathematically to the divB = 0. We know the divergence of B is zero because we have never seen a magnetic monopole. It should be seen as an experimental fact. I am not a historian so I don't know if there was an initial reason for divB=0. I trust your knowledge on the subject.
- In answer to why a vector field can be divergence-less. First the inverse-square law is not divergence-less at the origin. Second there are many functions that are both curl-less and divergence-less over a region, besides the inverse square law. The grad of any scalar function whose Laplacian is zero for example will work. (There are many of these harmonic functions.)
- As far as curlA being more specific than divB = 0, that depends on A having a physical meaning. The current accepted view is that A is used simply to make the equations easier. I am inclined to believe that A has a physical meaning as a 'generalized momentum per charge'. But WP is not the place to make that argument or to right wrongs.
- I agree with Steve that that statement belongs in the history section. I don't think that the statement that follows accurately reflects the modern view of A, but I don't know how to fix that. I don't think the statement is any less for being there. TStein (talk) 22:45, 9 November 2010 (UTC)
Tstein, I would also agree with Steve that the statement about Maxwell belongs in the history section, and with regret. Just like yourself and Maxwell, I believe that A has a physical meaning such as I described above. But sadly that is now history. I believe, just as you do, that A is a momentum per unit charge. Maxwell saw A as being the momentum which was the driving force behind the time varying aspect of electromagnetic induction. It was like as if space was densely packed with fly-wheels such that their rotation axes traced out the magnetic lines of force. He linked A to Faraday's electrotonic state. And of course from curl A = B, it follows that div B = 0. What nowadays seems to have happened is that the logic has been reversed, and that they deduce from div B = 0 that there is a vector A such that curl A = B. But how did they deduce in the first place that div B = 0 other than that it was one of Maxwell's equations (one of the Heaviside four and also equation (56) in the 1861 paper)? I see a bit of a tautology going on here. And with the new reversal of logic, there is a constant of integration. And from that they further conclude that rather than A being a quantity with a definite value whose value we don't know, it is a quantity which has freedom to have an arbitary value. That's a bit like being in a car in which we can't see the speedometer, and rather than concluding that we don't know the speed, we conclude that the speed is free to have any value. There is a subtle difference. David Tombe (talk) 00:43, 10 November 2010 (UTC)
Name for 'Gauss' law for magnetism'
While I am here, something else has been bothering me about this article, the name. The problem is that this equation doesn't really have a name. 'Gauss' law for magnetism' is in my opinion more of a description than a name. While I know we can't read peoples minds and help them find a nameless law, we need to mention that it has no name. I would mention it myself in the article, except that there is some possibility that the name is catching on a little. Griffiths page 326 specifically writes (no name). TStein (talk) 22:56, 9 November 2010 (UTC)
- Tstein, I would agree with you that the equation div B = 0 has traditionally had no name. Gauss's law was originally intended for electrostatics, and I can accept its extension to gravity on the grounds that the relevant mathematical principles are identical. But magnetism is a more tricky issue. If the basis for div B = 0 was that B is an inverse square law, then I would accept that we are looking at Gauss's law for magnetism. But clearly, with a singularity in the inverse square law, that cannot possibly be the reason why div B = 0, such that curl A = B. Yet on the other hand it does look like Gauss's law if magnetic charge where to be equivalent to an electric dipole with net zero charge.
- At the end of the day however, more and more modern sources are starting to use the name 'Gauss's law for magnetism'. I think they have missed the point, but since wikipedia goes by the sources, I think that the name 'Gauss's law for magnetism' is going to have to remain here.
- Yes, go ahead and mention in the article that this equation has traditionally had no name, but that in recent times, more and more sources have begun to call it 'Gauss's law for magnetism'. David Tombe (talk) 00:52, 10 November 2010 (UTC)
There are some major problems with this name! The primary one being that the physical law was discovered by the French knight Petrus Peregrinus of Mericourt in 1269. It was then brought into the scientific lexicon by Roger Bacon and then championed by Michael Faraday. By then, it was just well known and the origin in the West was not, so it got no name.
Sir Peter of Mericourt also introduced the idea of a pole and built the first model of the Earth as a magnet. It is the greatest piece of western science between the Ancient Greeks and Galileo. And it was done while waiting out a siege under the service of King Charles I of Naples, as a Muslim city was rebelling in support of a German pretender.
The paper by Peregrinus in translation is here: http://books.google.com/books?id=ePdUAAAAMAAJ&source=gbs_slider_user_shelves_7_homepage
Basically, it has a eloquent thought experiment of slicing a magnet into two, and both halves having a north and south pole. Then in the mathematical limit of slicing forever, all would have north and south poles. Its style is very Einstein like in approach and thought. All in 1269!
So, given that this is one of the oldest, and best verified (except the spurious measure by SLAC in the 1980s) laws in all of physics, it should have a name that is physical. It should be called "Peregrinus's Principle," and hopefully textbooks will soon adopt that name.
The other problem with this name is that Gauss himself did not believe in Peregrinus's Principle, as is clear from his scalar potential idea, which was mathematically beautiful and physically totally wrong.
So, naming the law after Gauss is like naming the particle model of light after Huygens. Totally wrong in every way.
But, it does look like Gauss's law --- so physicists who know no history whatsoever sometimes call it this because it has no name.
I say that we should boldly call it:
or take the more Wikipedia-like conservative course of action, and call it: "The Maxwell Equation with no name."
But redirect other stuff here. That way Gauss's law and be called Gauss's law.
If people agree on the bold course of action, I would write it up. If not, I have better things to do with my time ...
No matter what, the name Gauss's Law of Magnetism should go ....
- You are welcome to discuss Perigrinus in a history section (especially if you can cite a secondary source). Also check out Magnetic monopole#Historical background, which is closely related. You may want to edit both, or link one from the other. :-D
- But as for changing the article title, I strongly disagree.
- See Stigler's law of eponymy. The complaint you have here, you could raise at almost every eponymous thing in science (and elsewhere). It doesn't mean we should coin new names for everything. If Stigler's law is a problem, then the solution is to educate the public better about Stigler's law. Personally, if I learn that there's a law called "Flo's law", I would never assume that Flo invented the law. If I wanted to know the history of Flo's law, I would look it up, instead of guessing. Anyone who is familiar with Stigler's law would do the same thing.
- So I'm all for providing good historical information, but please put it in the history section, not the article title.
- Why is "Peregrinus's principle" a bad choice for a wikipedia article title? Because you just made it up, obviously. WP:NOR etc.
- Why is "The Maxwell equation with no name" a bad choice? For one thing, you made up that specific phrase, whereas the exact term "Gauss's law for magnetism" really exists in the literature. For another thing, if the text of this or another article mentions "the Maxwell equation with no name" it is more long-winded and less clear and descriptive than "Gauss's law for magnetism". For another thing, "the Maxwell equation with no name" still violates Stigler's law because it suggests that Maxwell invented it. For another thing, "the Maxwell equation with no name" is not a literally correct description of the law, as the law surely has at least one name. --Steve (talk) 23:25, 27 August 2014 (UTC)
It would be nice to add the orignial references
Does anyone have orignial references to this? All we have is a collection of references to modern books, but not to the original work. Whilst I have no objection to having references in modern books, as they are possibly easier to get hold of, it would be nice to add the original references. I've been trying to research the history of EM theory, and find Wikipedia is pretty much useless for this, as generall all it has are references to modern material, but no references to the original work. Drkirkby (talk) 10:08, 29 November 2011 (UTC)
- If you read a modern book on the history of EM, it will say who published what and when. Then, using that knowledge, you can flesh out the history section yourself. :-) Just be sure that everything you write is based on the modern history books, not the historical documents, WP:PRIMARY. --Steve (talk) 13:19, 29 November 2011 (UTC)