Wikipedia: Non-linear wave mechanics

Difference (from prior author revision) (major diff, minor diff)

Changed: 1,51c1

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

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