﻿ Spherical Standing Waves

4: SPHERICAL STANDING  WAVES
Plane Standing Wave

The electron is a spherical standing wave system.

Surprisingly, spherical standing waves can move as a result of the Doppler effect.

They are not "standing" any more.

 The phrase "standing waves" is misleading because such waves can move. Then the node and antinode pattern undergoes a contraction according to the Lorentz transformations. It is clearly visible in the animation shown above. Please observe that the first black antinode near the center is contracted horizontally as well as subsequent layers. The faster they move, the more they become elliptic. But they never contract transversally. Exactly the way Lorentz predicted. The most ignored science. There was almost no practical information about spherical standing waves on the net, except for Milo Wolff's site. So I had to develop the whole science by myself. It was worth the effort because I could finally explain matter and all forces. I would like to give a special thanks to MM. Serge Cabala, Philippe Delmotte, Anselme Dewavrin and Jocelyn Marcotte, among others, who supported and helped me in this enterprise. I suppose that some ancient pioneers did find interesting equations and properties in the past, but up to now there was very few evidence of them. The wave science is the most ignored and scorned of all. It is 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. If waves are involved, the first thing to do should be to study waves. But curiously, there is some sort of taboo regarding matter waves. Nobody ever dares to show them. The unmoving concentric system. Firstly, one should examine the unmoving spherical standing wave system, which is simpler.

Regular spherical standing waves.

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

 The animated diagram above artificially displays spherical standing waves with a 3-D effect for the central plane only. Standing waves on water should more or less look like this, but electrons are actually spherical standing waves. The Huygens Principle reveals that 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.

Theoretical incoming and outgoing wave fronts are not concentric any more, but they remain perfectly spherical.

The wave addition reveals a stunning "phase wave", whose speed is given by:  1 / beta in wavelengths per period units.

The .5 c moving electron diagram showing its characteristic envelope still present.

NO  INCOMING  WAVES.

The core is capable of building up considerable pressure.

The fifth (green) spherical layer is 5 wavelength distant to the center.

The core pressure is: 5 * 2 * pi = 31 times higher than in this layer.

A doubled frequency would double the pressure for the same distance.

A doubled distance would also double the pressure for the same frequency.

 The  x  variable is given by: 2 * pi * distance / lambda, and so the wavelength is important. On the other hand, a bigger core should produce more heat and energy. The core pressure is normalized to 1, but the goal is to obtain the required pressure for the fusion to become possible. The equation indicates which pressure should be applied on the inner side of the sphere. Obviously, the amplitude is always positive for a compressed medium because vacuum is the lower limit. An asymmetry appears for very high amplitude levels. So, before proceeding, the hydrogen overall pressure should already be very high. The device also needs a chimney for collecting heat, and a system for recycling the hydrogen. The sphere can be replaced by an ellipsoid with two focus cores, producing a sort of "artificial quark" with high amplitude plane standing waves in-between. Then those standing waves may participate to the fusion process and greatly improve the device efficiency. I presume that engineers will find a practical way to produce Huygens wavelets on the inner surface of the sphere. Technically, most of the energy produced by at least one thousand loudspeakers regularly spaced should be transferred to the central core. I could check this with my own computerized medium without any surprise, because it is simply the Huygens Principle. A chain reaction. It should be emphasized that a chain reaction and self-amplification occurs. The resulting heat causes additional reactions to take place, allowing the standing wave system to oscillate permanently.

 Gabriel LaFreniere, On the Internet since September 2002. Last update December 3, 2009.