Talk:Laws of electromagnetism

This article might possibly describe original research.

Therefore: references are needed. Who first posed these laws? Where are they used?
Definition of the quaternion operator is needed.
Is this possibly an application of geometric algebra? I don't understand the notation.
Please review the Wikipedia:Manual of Style (mathematics) and get this article to conform to that.

Thanks. linas 00:07, 4 January 2006 (UTC)[reply]

The quaternion differential operator is implicitly defined in his first equation,

X=({\frac {1}{c}}{\frac {\partial }{\partial t}} \nabla )

.

I haven't gone through this in detail, but I'm assuming it works out to be identical to Maxwell's equations in a vacuum, and is just another mathematical formalism for expressing the same physical laws in a tidy form. I may have seen this treatment or something like it somewhere before. References would certainly be appreciated. Assuming this article is viable, the whole thing needs to be moved to a title that better reflects the content, or perhaps merged into the page on Maxwell's equations, as a section describing this alternate formalism. The title "Laws of electromagnetism" is clearly inappropriate and misleading.--Srleffler 01:59, 4 January 2006 (UTC)[reply]

Some quotes from quaternion:

Some early formulations of Maxwell's equations used a quaternion-based notation (although Maxwell's original formulation simply used 20 equations in 20 variables), but it proved unpopular compared to the vector-based notation of Heaviside. (All of these formulations were mathematically equivalent.)
"Quaternions came from Hamilton after his really good work had been done; and, though beautifully ingenious, have been an unmixed evil to those who have touched them in any way, including Clark Maxwell." -- Lord Kelvin, 1892.
". . .quaternions appear to exude an air of nineteenth century decay, as a rather unsuccessful species in the struggle-for-life of mathematical ideas. Mathematicians, admittedly, still keep a warm place in their hearts for the remarkable algebraic properties of quaternions but, alas, such enthusiasm means little to the harder-headed physical scientist." -- Simon L. Altmann, 1986

--Srleffler 02:15, 4 January 2006 (UTC)[reply]

Thanks.SRleffler

Thankfully. Scientists should not find appeals to Authority impressive. Congress is not able to repeal the "Law of Gravity."

Hamilton, thought otherwise than Lord Kelvin and Simon Altmann. I prefer Hamilton.

Yaw 02:28, 4 January 2006 (UTC)[reply]

Thanks Srleffler. "(All of these formulations were mathematically equivalent.)" This is not true. That is why Heaviside and Gibbs invented Vector Calculus.

The story goes that Maxwell complained that when using quaternions, what he thought would be a maximum turned out to be a minimum. This was the sign problem with quaternions (square of a vector being negative). Heaviside and Gibbs fixed that by making the square of a vector "positive", that is II = 1 while Hamilton's quaternions has II = -1. This difference is HUMONGOUS!!!!

Vectors are not ASSOCIATIVE in that (II)J = J but I(IJ)= IK = -J. This means that when you solve a problem abc=y The answer depends on whether you do (ab)c or a(bc). This is not a problem with Hamiltons Quaternions. This is a problem with vector Calculus and an extra axiom must be added to say how you solve problems.

Maxwell expected that moving a force in the same direction as the displacement that the energy would be positive. The mathematics was smarter and said the energy will be exergy! Namely the sign of the scalar tells what direction the energy is going, in = energy or out = exergy. For example dropping a ball gives exergy, lifting a ball takes energy. The force of gravity is with the drop and against the lift.

There are other problems with Vector Calculus, like non-closure ( a,b members, but ab not member).

Under which operation is there non-closure? In R³, under the cross product, vectors are closed. Masud 05:05, 4 January 2006 (UTC)[reply]

As you can see quaternions and Vector calculus are not mathematically equivalent and the physics they describe are not the equivalent. An mmplosion in one would be an explosion in the other.

Yaw 02:49, 4 January 2006 (UTC)[reply]

Thanks for your answer. Since you assert that this article is not consistent with Maxwell's equations, please provide references where this treatment of electromagnetism has been published previously. If references cannot be provided, this article will, unfortunately, have to be deleted under Wikipedia's policy on original research.--Srleffler 06:52, 4 January 2006 (UTC)[reply]

Form of electromagnetic equations

The most succinct way to express electromagnetic laws are tensorially. The universe appears to be Lorentz covariant, and so are tensors. In my opionion, the only other way to express them is in vector calculus form, since that is what is widely taught, and is less likely to confuse readers.

This article has used numerous unknown conventions, and, in my opinion, either requires lots of cleanup or modified in favour of either vector calculus/tensorial expressions of electromagnetism.

Secondly, if the equations in the article do not represent the same as Maxwell's equations in vector calculus language, then which one correctly describes observed phenomena? Masud 05:01, 4 January 2006 (UTC)[reply]

Redirect

I have redirected this article to Maxwell's equations. Wikipedia should have only one article discussing the rules governing electromagnetism. If Yaw believes that the language and mathematical formalism used to describe that should be changed, then those changes should be made in the existing Maxwell's equations article, perferably after discussing those changes at Talk:Maxwell's equations as he started to. Dragons flight 19:02, 4 January 2006 (UTC)[reply]

Are Maxwell's Equations addressing the Laws of electromagnetism

My article addressed the Laws of Electromagnetism. Does Maxwell's Equations address The Laws of Electromagnetism? I think Maxwell's Equations do address the Laws of Electromagnetism, but they are incomplete and incorrect.

I suggest Wikipedia put Maxwell's Equations under The Laws of electromagnetism.

Yaw 20:38, 4 January 2006 (UTC)[reply]

If you think ME are incorrect, you're waaaaaaayyy out on a limb, and your personal opinions don't belong in wiki. William M. Connolley 23:45, 4 January 2006 (UTC).[reply]

Yaw, you need to find a different outlet for testing your original research. Wikipedia is not that place. try posting to the USENET newsgroup sci.physics.research and see what kind of feedback you get there. you could also submit it to a reputable (or one that is not) journal of your choice. and, of course, you could put it on your own webpage. r b-j 01:09, 5 January 2006 (UTC)[reply]