Wikipedia: Non-linear wave mechanics/Talk

I really quite dislike this article. There is no explanation of what non-linear means, and a decided impression that non-linear, dispersive and non-harmonic waves have all been confused by the author, and the comments about UP are just wrong (at least UP in the sense of [P,Q] = i h, with [,] being the commutator). Plus UP is nothing to do with non-linearity, and can be derived in a straightforward way from the linear Schrodinger equation. The last example is thin to the point of not being there, and the last paragraph is a rant.

Can someone who knows about non-linear wave phenomena refactor this.

GWO

I rather agree with the above, and add my plea to his.

I'm having a hard time believing in this whole project, I must say, and I think this page is a fine example of what's bound to go wrong when you have a totally open-source encyclopedia that can be edited by anyone, with no clear way of enforcing any sort of standards (besides the obvious objection that it's redundant with, and vastly inferior to, the information that already comprises the web itself). The majority of the physics pages contain things that are just plain wrong (who says indices of refraction can't be less than 1, anyway?), from what I can see. I can't imagine why I would come here for information rather than anywhere else.

Bryan

: But you see, Bryan, that due to your own comment, the offending article has been removed. If you think you can accomplish more as part of an open content project that does have official standards (wait a second--Wikipedia doesn't have standards?--what a strange thing to say), you are invited to visit http://chalkboard.nupedia.com/ and http://www.nupedia.com/ . We will create a huge, high-quality, open content encyclopedia one way or another. --LMS

Mea Culpa. I saw this, hated it, but left it up too long, thinking that someone more qualified could fix it. It's better nothing than nonsense, so I removed the main page and added it here, just in case someone wants to make some use of it when they really write the page up. AN

Wavelength is much more complex for non-harmonic waves. For example;

                                  .****.
                                *        *
            .***.              *          *             .***.
   ..      *     *            *            *           *     *      ..
 **  *    *       *          *              *         *       *    *  ***
      `**'         *        *                *       *         '**'
                    *      *                  *     *
                      '**'                      '**

In this case, we speak of a spectrum of wavelengths. Many people mistakenly speak of an "uncertainty" in the wavelength. Waves such as the ones depicted above and below, have a position though again it is a spectrum of positions and not any "uncertainty" in the position. If a "detector" stretches out the above wave in order to "determine" its wavelength, then this new wave would look more like a classical harmonic wave. The "uncertainty" in its wavelength (energy, momentum) would decrease while the "uncertainty" in its position would commensurately increase. Conversely, if the "detector" compacts the wave then the new wave looks more like a point-like particle. Speaking of the "dual wave and particle" nature of such waves is mistaken but physicists have been clinging to such archaic and obsolete concepts ever since Quantum Mechanics was invented. The Heisenberg Uncertainty Principle was specifically invented as a way for classical physicists to understand quantum mechanics. The original version of the HUP has no place in modern quantum mechanics and the modern version of the Heisenberg "uncertainty" principle says nothing more than the above figure demonstrates.

Another important non-linear wave is:

                                  .******************************
                                 *
                                *
                               *
                              *
                             *                                 
                            *
 **************************'

Harmonic waves barely scratch the surface of wave mechanics. Knowledge of solitons has been traditionally restricted by physicists who only begin to teach about the subject to second year physics students. The mathematics of non-linear waves is difficult and physicists confuse doing mathematics with deep knowledge of a field. The "shallow" non-mathematical knowledge of laypeople is deprecated by most physicists, hence there is no interest in teaching the subject to non-physicists although doing so would require minimal effort. Pictures of solitons and spherical waves can be easily grasped by school children but the knowledge is hoarded with the excuse that "non-linear math is too hard for most people"

I think removing the main page was a good choice. I tried a google search: http://www.google.com/search?q=non-linear+wave+mechanics and found the wikipedia article as number one on the list!