SPHERICAL STANDING  WAVES

The electron is a spherical standing wave system.

Surprisingly, spherical standing waves can move, thanks to the Doppler effect.

Then they are not "standing" any more.

 The phrase "standing waves" is misleading because such waves can move. Then each wavefront remains perfectly spherical in spite of the Doppler effect. However, the system's nodes and antinodes undergo a contraction according to the Lorentz transformations. It is clearly visible in the animation shown above. The most ignored and scorned science. I never could find any practical information about spherical standing waves, except for Milo Wolff's web site. So I had to develop the whole science by myself. It was a time consuming task, but it was worth the effort because I could explain matter and all forces. However, many people such as MM. Serge Cabala, Philippe Delmotte, Anselme Dewavrin and Jocelyn Marcotte helped me. I suppose that some pioneers did find interesting equations and properties in the past, but where are they?The wave science is the most ignored and scorned of all. This attitude is especially hard to explain because nuclear physicists know since many decades that matter exhibits wave properties. Clearly, such waves cannot be plane. They should be spherical, and more likely spherical standing waves. In addition, because matter can move, a Doppler effect should occur. This is quite obvious. So scientists should be aware that spherical standing waves explain matter, especially the electron. But they never dare to show such waves or speak about them.The unmoving concentric system. Firstly, one must examine the unmoving system, which is simpler.

Regular spherical standing waves.

This 3-D view is interesting, albeit it is artificial.

 The animated diagram above displays standing waves with a 3-D effect. Standing waves on water should look like this, but electrons are actually spherical standing waves.The Huygens Principle reveals that the energy incoming from only one half of a sphere should cross the focal plane in a very special way, explaining why the central antinode diameter is a full lambda wide. Then adding the second half produces the whole system:

The wave addition is rather complex.

The result is an amazing full lambda wide core, where a pi phase shift occurs.

The electron amplitude.

THE  NON-CONCENTRIC  SYSTEM

The moving electron undergoes the Doppler effect.

Waves are not concentric any more, but they remain perfectly spherical.

The wave addition reveals a stunning "phase wave", which speed is given by:  1 / beta.

The moving electron diagram (speed : .5 c), showing its characteristic envelope still present.

NO  INCOMING  WAVES.  JUST  OUTGOING  WAVES.