Non-linear wave mechanics

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".

/Talk