The moving electron. A standing wave which is not standing any more.
This wave is an electron.
Mr. Jocelyn Marcotte's equations below are fundamental.
Gabriel uses the term "phase" in the meaning of "in-phase" wave (the direct one) formula, and "quadrature" for "phase quadrature", which is a wave shifted in phase by 90° or π/2 radians. For cosine wave this would be the sine wave. The name "quadrature" comes from the fact that on the phase diagram its phase vector is orthogonal (perpendicular) to the "in-phase" one, making a right angle as in the square (quadrate).
It is also related to the fact that in the old days "quadrature" meant the area. Ancients tried to find for each shape (mostly curved) a geometrical construction which would produce a square (quadrate) of the same area as that shape. This was called "squaring", and the area under the curve was called "quadrature". Now we call it "integral", because we use calculus for finding quadratures. For sine waves, the quadrature (or integral, an area under the curve) gives the same sine wave shifted 90 degrees too.
But there is a couple of problems with Gabriel's approach here:
The word "spin" was first proposed in order to explain some of the electron's properties. It strongly suggests a rotation, but most scientists admit today that the electron does not rotate.
Those properties can rather be explained by a phase rotation:
One must postulate that all electrons inside a rather huge space must be synchronized in order to preserve their spin individuality. Because nodes and antinodes appear simultaneously in both +1/2 and -1/2 electrons, just the central antinode is different and they can stay synchronized using all standing wave sets around.
Positrons cannot survive in such an environment, but one can suspect that, because of the beta-plus and beta-minus decay, the neutron and the proton may contain a certain number of electrons and positrons hided between their three quarks.
While it is perfectly at rest inside aether, the electron is a pure spherical concentric standing wave system. It is then much more simple, but it has nevertheless very rarely been studied. Except for Mr. Milo Wolff, it seems impossible to find any reasonable description on the Internet.
And so, as far as I know, the following diagrams are the nec plus ultra:
I am fascinated by optics and wave phenomena since my early age. So I know well that Huygens' Principle is always highly reliable.
Around 1995 personal computers became finally fast and practical. I then invented a new algorithm, which goal was to perform the summation of Huygens' well known wavelets inside a 3-D space. I was working on the Airy disk, this amazing interference pattern which is present at the focal plane of any convergent lens or telescope mirror.
The program was a hit. The results below represent a very seldom showed Airy disk. It should behave like this only for a very wide aperture angle: 180°. This means that instead of the usual narrow light cone, the source is a full hemisphere. Look at this!
Firstly, here is a diagram for the Airy disk. It is a very special case because the aperture is worth a full 180°.
The 180° aperture Airy disk can be seen as one half of an electron.
The Airy disk, assuming that the aperture angle reaches 180°.
It can also be considered as one half of an electron. The rightwards waves only are present.
Mr. Marcotte's equations can predict exactly the graphics shown in the lower right corner.
The FreeBASIC Airy disk program Ether16.exe Ether16.bas is still available only in French.
Sorry. I simply cannot write all my work in English, so I need help in order to translate it.
Waves are adding themselves in a rather complex way.
This 3-D view is very interesting, albeit it is artificial.
The electron amplitude values.
Matter is made solely of electrons.
The electron explains matter and all forces. This is very demanding for a simple wave.
But the point is
that this wave does explain everything.