The Huygens Principle. 

I have been fascinated by optics and wave phenomena since my early age. So I know well that the Huygens Principle is always highly reliable.

Around 1995, personal computers finally became accessible, fast and practical. I then elaborated a new algorithm whose goal was to perform the summation of Huygens' well known wavelets inside a 3-D space. I was working on the Airy disk, which is the 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 shown Airy disk. It should behave like this only for a very wide 180° aperture angle. This means that instead of the usual narrow light cone, the source is a full hemisphere. Look at this!

Discovering the electron.

While working on this, I already knew that matter and especially electrons should be made of spherical standing waves. I was also aware that such waves should undergo the Doppler effect, allowing them to move freely at variable speeds. However, I did not reveal this major discovery because I feared (I was wrong!) that a better knowledge of matter, considering the amazing forces involved, would lead us to a devastating Apocalypse. It is a well known fact that most discoveries such as radioactivity were always followed by more and more powerful weapons.

I could never find any indication that this could be true for the wave nature of matter, though. So, in 2002, I wrote a book which was exempt of any mystery: Matter is made of Waves. It was not the case for another book written in 2000: The Theory of Absolute. I had to make it very evanescent about the wave nature of matter (it is not my discovery, but I was the first and I am still the only person who can explain all about it: electrons, matter, forces, mechanics). My goal was simply to restore Lorentz's Relativity, whose concept is absolute. Although this point of view leads to the same predictions as Einstein's, it should be emphasized that his Relativity, while it proves to be true, is nevertheless the result of our errors while recording phenomena.

LaFreniere's wave.

This Doppler moving electron is my discovery. It was shown in my book and I called it LaFreniere's Wave when I uploaded my first Internet web pages in September 2002. 

The electron can move at any speed from 0 to nearly the speed of light through the aether because it undergoes the Doppler effect (or the Lorentz transformations, which is the same). In spite of my desperate attempts to make him recognize that, M. Wolff never did. 

I also showed before anyone else the correct diagrams for it. Unfortunately, Mr. Marcotte's formulas were missing, but I succeeded anyway. As a matter of fact, the Huygens Principle is far more important and relevant as a tool. The results are a convincing proof that the system should behave this way.

This wave shows all of the electron properties.

The electron's properties are well known. The list is astounding. It is so small that it has no apparent dimension. Its electrostatic charge is negative. There is also a positive antiparticle, the positron, which exhibits exactly the same properties except for the opposite charge. Its wave properties are now a well admitted fact. It can accelerate, slow down and change its direction. It can act and react as a result of an apparent contact, but also at a distance. It contains intrinsic energy according to mc^2, and additional kinetic energy according to m(gamma – 1)c^2 while moving as a result of Lorentz's mass increase. Except for the spin, which is either –1/2 or +1/2, all electrons are rigorously identical.

In addition, the electron is the main player for a lot of phenomena such as magnetic and electric fields, light and radio waves emission, and chemical reactions. It can stabilize itself around the nucleus to form an atom, and it can bind molecules together. Finally, it is a well known fact that electron and positron collisions produce quarks and gluonic fields. This indicates that in this case electrons and positrons involved do not really annihilate. They should most likely be hidden but still present inside quarks and have their standing waves joined together as gluonic fields. This strongly suggests that matter (or any other particle) is solely made of electrons.

This is a huge responsibility for so small a particle, but the electron magnificently takes up the challenge. This web site explains how it is possible.

The moving spherical standing waves calculus.

So the electron appears to be the equivalent of a very special Airy disk whose aperture angle is 360°. As seen above, just one hemisphere becomes the source of traveling waves, but adding the opposite one rather produces standing waves. This is Milo Wolff's unmoving electron. Now let's see how the Doppler effect should transform it.

Using the Huygens Principle, I submitted all of Huygens' wavelets to a Doppler effect. The algorithm then becomes a bit more complicated because the wavelength must shorten regularly from 1–beta forward to 1+beta backward (beta = v/c). The computer produced the following result, which is correct only along the displacement axis:

Marcotte's equations.

Mr. Jocelyn Marcotte informed me in January 2006 that he had found a new simpler algorithm for the aether. It is different from Mr. Philippe Delmotte's, the first inventor, because square or sawtooth waves are propagating normally, while Delmotte's produces some sort of heat, a local vibration of the "aether granules". This does not mean that it is better. It is simply different, but this suggests that many options are possible for an ideal aether. However, in both cases, sine waves behave normally, much like the sound propagates inside a solid and homogeneous substance such as quartz.

It should be pointed out that the cosine indicates quadrature (pi / 2 phase), which is normally the highest amplitude point. However, the electron central antinode is an exception because it is a full wavelength wide. A pi / 2 phase shift occurs in the center, and so the maximum amplitude there is indicated by the sine function while the cosine indicates the zero level. Anywhere else the normal amplitude level according to the distance remains the rule, though.

If all happens like I presume, in the future, those equations will be recognized as the first equations of all. They are fundamental.

Rotation.

Mr. Marcotte soon found that these equations could show the wave rotation step by step from 0 to 2*pi. He had to introduce a t time (also in radians, from 0 pi to 2 * pi), and join them together like this:

y = (cos(t) * sin(x)  – sin(t) * (1 – cos(x) ) ) / x

y = (cos(t) * sin(x)  +  sin(t) * (1 – cos(x) ) ) / x    (opposite direction)

I made two programs showing all this:

Aether06_Marcotte.exe   Source code : Aether06_Marcotte.bas

Aether06_Marcotte_Doppler.exe   Source Code:  Aether06_Marcotte_Doppler.bas

You may freely copy, distribute and even modify them. Please remember that the new 2008 Compiler for FreeBASIC (version 0.20.0b) was released with some new requirements. Gosub keyword is not allowed any more and variables including integer must be declared. However, all previous programs will still work properly on condition that they are edited as follows:

#lang "fblite"

Option Gosub

The FreeBASIC IDE editor is available here: http://fbide.freebasic.net/

The Doppler effect.

The on-axis regular Doppler effect is quite simple: 1 – beta forward and 1 + beta backward (beta = v/c). In addition, the Lorentz transformations indicate that the electron frequency should slow down, producing a longer basic wavelength. I applied those modifications to Marcotte's equations in order to show how its standing waves should behave while the electron is moving. Surprisingly, the well known envelope showing nodes and antinodes is still present.

The electron contraction.

Despite the longer basic wavelength, the envelope containing nodes and antinodes rather contracts according to Lorentz's contraction factor.

This is consistent with Lorentz's first equation.

More energy means more mass for  the accelerated electron.

Lorentz also predicted that the electron mass should increase according to the gamma factor. This was soon verified by M. Kaufmann. The point is: if the emitter accelerates, the forward wave amplitude increases much more severely then it is reduced backward.

The Doppler program (see below) shows that the electron amplitude indeed increases at high speed. So its energy, hence its mass, increases. This also indicates that the gain in mass according to the gamma factor is pure kinetic energy: E = m(gamma–1)c^2, as a consequence of the Doppler effect.

However, this gain in energy must be measured by an observer at rest. Any instrument moving along with the electron would record wrong data because the Doppler effect is unnoticeable inside the same frame of reference. This was discovered in 1842 by Christian Doppler himself...

The Lorentz transformations indicate that a "local time" takes place inside any moving system. Actually, this means that the electron wave phase should vary along the displacement axis. The phase is retarded forward according to the distance to the center. Waves are rather pulsating in advance at the rear.

The effect on the moving electron is obvious. Its standing waves no longer pulsate everywhere simultaneously. So a phase wave whose velocity is 1 / beta (in wavelength per period units) becomes visible. The normalized beta speed equals v / c, hence the speed of light in beta units becomes c = 1.

Electron_Doppler_effect.bas        Electron_Doppler_effect.exe

Relativity.

It should be pointed out that my "Time Scanner" conveniently exploits this phase wave in order to reproduce the Lorentz transformations. For example, scanning concentric waves moving inwards or outwards will add a Doppler effect to them. Surprisingly, it will also transform Milo Wolff's static electron into my moving electron.

This Time Scanner is another invention of mine. It proves that the Lorentz transformations are simply a Doppler effect involving a slower frequency.

Mr. Philippe Delmotte.

The Virtual Aether is Mr. Philippe Delmotte's brilliant invention (June 2005). It is a computerized virtual medium capable of reproducing any wave phenomenon. Its algorithm supposes that the aether is made of an infinite number of "granules", which can vibrate in accordance with Hooke's law. Thus those granules must initially contain kinetic energy, and also inertia, which can be seen as a memory of its precedent energy. In addition, this energy can be transmitted to the nearest neighbors.

The program algorithm is remarkably simple. Believe it or not, this pure jewel needs only three program lines!

M. Jocelyn Marcotte.

On July 10, 2006, Mr. Jocelyn Marcotte succeeded in experimenting my Doppler moving electron. Even better, he used the Lorentz transformations in order to reproduce the Doppler effect. Those transformations are not about a space-time distortion. They more simply predict the way on-axis waves contract and exhibit local phases producing a "phase wave". Mr. Marcotte used his own Virtual Aether algorithm (see WaveMechanics04.bas), which is different from Mr. Delmotte's, in a 3-D space.

In my opinion, this experiment will be related in the future as a memorable achievement. It was the ultimate proof, showing that this amazing wave can exist. Because today's science is afflicted with so many errors, this new discovery will launch a severe revolution in the world of physics. 

Mr. Marcotte's program displays an electron moving as predicted, but alas inside a limited 500^3 granules aether cube. In a few years, computers will run faster using multiple core processors and more memory. Then new programs using advanced code and powerful graphic cards will deliver much better results.

The electron is not infinite.

Without incoming energy, the electron would still emit spherical outgoing waves. So it would rapidly fade out. Obviously, it needs replenishment. This is accomplished by powerful and constant aether waves. Traveling waves penetrating through standing wave antinodes are deviated because of a lens effect. A small part of the energy is transferred to the standing waves. This constantly refilled energy allows the electron to exist forever. 

Outgoing spherical waves weaken according to the square of the distance law. In spite of this, the light from a star, for instance, can travel for billions of years, almost infinitely. It never totally disappears.

The electron too produces outgoing spherical waves. Those are regular traveling waves. Because the electron is rather made of standing waves, amplitude can no longer be the same everywhere in both directions, making them "partially standing waves". Finally, even farther, just outgoing traveling waves remain.

The diagram below shows how the transition between those three states is possible:

Radiation pressure.

Obviously, while it is accelerating, slowing down or changing its direction, the electron cannot use its incoming waves any more. Its focal point is not compatible with their future position any more.

However, the radiation pressure mechanism can overcome this problem. Waves emitted by an electron will inevitably encounter those incoming from all other electrons, especially on the axis joining them. This will produce a very special set of standing waves, a field of force, which will also be amplified by aether waves. Half of the resulting energy is then returned and focused directly towards both electrons which created the field.

Programs to come will show clearly how and why this phenomenon is possible. Those fields of force are emitting focused and powerful traveling waves towards the electron. And because their phase and wavelength do not necessarily coincide, the electron will progressively change its position according to them.

Because the wave's amplitude is higher near the center, it turns out that half of the electron energy may be present inside a very small sphere, maybe the size of an atom. There is enough space for thousands and even millions of wavelengths, though. The other half may expand inside a much wider sphere.

The amplification process can be seen as the production of an infinite number of Huygens' wavelets. According to Huygens, the wavelets' addition must create a wave front wherever their phases coincide. Clearly, incoming wavelets can produce standing waves, but outgoing ones can only produce outgoing wavefronts.

It turns out that the wavelets' summation, hence new energy, is far greater near the center. It does not obey the square of the distance law. This indicates that very far from the electron, permanent standing waves compatible with the core phase cannot exist any more.

The Virtual Aether is a new tool which can show how a limited number of wavelets will behave. The diagram below is a good example:

One wave. Two particles. Four phases.

Standing waves exhibit nodes where the medium pressure remains constant, and antinodes where negative and positive energy alternate. They produce regularly spaced nodes and antinodes whose distance is a half-wavelength, but in the meantime the medium pressure is the same everywhere and the system seems to disappear.

The point is that such antinodes appear twice per period. This means that while a standing wave system is producing a positive antinode at a given x coordinate, another perfectly synchronized system placed crosswise can rather produce a negative antinode there. Both systems being identical, their pulsating period is not for an observer placed there. 

So this is a relative point of view. All electrons are perfectly identical, but their unique central antinode is a privileged one. The amplitude there can be positive while it is negative inside another one, although all antinodes will be present simultaneously.

This means that while one core is positive, another one can be negative. In other words, its phase  is pi shifted with respect to the other one. In the meantime, all other antinodes are present, but their position is lambda / 2 shifted. Finally, two sorts of electron are possible. The electron spin does not refer to a mechanical rotation. It is the consequence of a phase rotation, and in order to achieve this all electrons must be perfectly synchronized.

In addition, two times per period, such synchronized standing waves seem to disappear because the medium pressure is uniform everywhere. This is called quadrature, which can be either pi / 2 or 3 pi / 2. This indicates that there is some place for two other particles, two sorts of positrons, whose antinodes also appear simultaneously.

Assuming that electrons can synchronize themselves mutually, all positrons in the vicinity will less or more rapidly transform their phase and become electrons. The atomic structure makes it so that electrons are always nearer one from another, while positrons are also grouped. Moreover, the proton structure supposes that its three quarks should produce a pi / 2 phase shift in its center, making a hidden positron very stable and comfortable there.

The spin effect.

Two electrons close together behave normally in spite of the spin difference. But up and down spin produce opposite magnetic fields when the electron standing waves are adding to the positron's. A surprising unidirectional radiation appears, whose direction determines the north and south pole. This means that one hydrogen atom alone is certainly magnetic. It is a dipole, and the sun's surface clearly proves this. However, the hydrogen molecule is made of two hydrogen atoms. Because it is not magnetic, it should contain two electrons whose spin is +1/2 and –1/2.

For the same reason, any atom should contain an equal number of spins, which should be placed on opposite sides. Otherwise, the resulting atom shows a residual polarity which modifies its chemical properties. This is partially the cause of Pauli's Exclusion Principle.

The electron spin (up and down, or +1/2 and –1/2) is the consequence of a phase rotation. It can be either –pi/2, pi/2, 3pi/2, etc. The positron's quadrature is rather 0 pi, pi, 2 pi, etc. The word spin indicates a mechanical rotation, but this would suggest an axis which was never demonstrated. Moreover, such a real spin is unlikely to be possible because the electron is so small that it can be seen as a point.

So the spin is the wave period. Here is a diagram showing this: