May 3, 2008.

I am proud to release two new programs explaining the basics of the Wave Mechanics:

WaveMechanics02.bas        WaveMechanics02.exe

WaveMechanics03.bas        WaveMechanics03.exe

The goal was to perfectly reproduce all wave phenomena. I also managed to make the source code the simplest and the clearest possible. Some previous programs which were created two or three years ago in order to test Mr. Philippe Delmotte's algorithm were a bit more complicated. In addition, one could not always obtain perfect results while dealing with problems such as residual reflection. But now the programs work beautifully.

Opticians and acousticians should be highly concerned about the amazing capabilities of this virtual medium, which also works in a two or three dimensional space. In my opinion, a similar but more elaborated algorithm should be be capable of reproducing the free atomic electron behavior for very high frequencies. Clearly, such frequencies are not only caused by an electron flow. Free electrons are mainly moving to and fro on a very short distance. They all together become a genuine and independent wave medium, creating an electronic wave. I also predict that there is no true light propagation inside transparent material such as glass or optical fiber. In such a case, energy transmission is caused by similar electronic oscillations. However, because inner atomic electrons are involved, they can also oscillate in a circular motion in order to produce polarization rotation as well as axial.

It should be emphasized that genuine waves are the result of a mechanical process. Delmotte's algorithm clearly shows that they definitely do not always behave the way mathematicians used to explain. For instance, any fractional step (such as one introduced by a given mechanism) produces quantum effects which become well visible for sawtooth or square waves. Such waves contain harmonics, hence shorter wavelengths which are progressively left behind because they propagate slower. Some energy is also converted into static vibrations, some sort of "heat". We will also show that waves, especially standing waves, can act and react. Thus, matter being made of waves, it surely can act and react the way Newton discovered. A wave is not an equation, it is a physical phenomenon. Physicists should think mechanics. They should be aware that mathematics are just a tool, not a transcendental cause which rules the universe. It is a very bad idea to use mathematics when one simply ignores what is really going on.

Clearly, the Wave Mechanics explains matter mechanics. It is a well known fact that kinetic energy can be stored into fields of force as potential energy. Those are matter's most important properties. Standing waves indeed contain energy, and this strongly suggests that fields of force could be made of standing waves.

This is undisputable: traveling waves do transport energy, and standing waves do contain energy. Physicists discovered not so recently that any intermediate situation also exists: partially standing waves, or standing waves which are actually moving at variable speeds because of the Doppler effect. Let's face it: matter can move, it thus can transport its own energy inside its standing waves, and this energy should be higher (Lorentz's mass increase) because of the wave compression as a result of the Doppler effect. This perfectly explains kinetic energy and Newton's mechanics, even for very high speeds where the Lorentz transformations must be taken into account. This is obvious because the Lorentz transformations are nothing else and nothing more than a Doppler effect. Finally, this also explains Relativity. 

All phenomena can be explained by waves. Thus they can all be explained and demonstrated using this wonderful laboratory.

April 18, 2008.

I invented a new way to produce sounds. Synthesizers do generate similar sounds, but now it becomes possible to let them evolve in order to imitate how true natural waves behave.

While working on the next program from my series on the Wave Mechanics, I noticed that sawtooth waves were not stable. They finally looked much like true sounds, for example that of an organ pipe which contains harmonics, or multiples of the basic frequency. Below is a provisional version which was modified in order to show this:

WaveMechanics03_test.bas        WaveMechanics03_test.exe

Square or sawtooth waves (for instance) truly evolve and progressively eliminate higher harmonics. The result is a natural complex structure capable of imitating that of most music instruments.

The point is that one can easily generate a specific artificial waveform and let it evolve through Mr. Delmotte's algorithm for a few seconds in order to obtain the more natural structure. Then the data can easily be copied to a .wav file. Many sounds and frequencies can be generated simultaneously. I am quite sure that such sounds would be especially enchanting and melodious.

I suppose that this invention was admissible for a patent. I have no money for this, so there is one more now in my drawers among hundreds of them. Some day, Yamaha or others will finally realize that those ideas were interesting, but I will not be in the picture. Sic transit gloria...

April 8, 2008

Mr. Jocelyn Marcotte and Mr. Anselme Dewavrin discovered how to make Euler's method more accurate. Up to now, mathematicians warned that this method yields only approximate results.

For example, one can obtain the sine for 45° this way:

1. Use a 360° scale in order to obtain integers.

2. The required step was once given by:

step = 2 * pi / 360

This step is inaccurate, though. Mr. Dewavrin found the correct one in October 2006, but his formula was too complicated.

Correction on April 17, 2008

A reader informed me today that he had found a simpler formula. He also pointed out that Euler himself was surely aware that his method could yield fairly good results. There is still a small uncertainty remaining for the same reason that one simply cannot draw a perfect sine curve using straight lines.

The correct step (in radians) is given by:

step  =  2 * sin(pi / 360)

3. Also in October 2006, Mr. Dewavrin discovered a simplified algorithm capable of listing the whole sine and cosine scale (hence sinusoidal oscillations) using two iterative program lines only:

sine = sine + cosine * step 
cosine = cosine – sine * step

4. One should initialize the sine to 0 but not the cosine to 1 as it would seem logical. Mr. Jocelyn Marcotte discovered last week that the cosine needs a slight advance in order to cancel the retardation firstly introduced by the algorithm. The correct cosine initialization is given by:

cosine = Cos(step / 2)

Then the sine scale becomes perfectly accurate up to 9 digits for double precision variables. The cosine scale is also perfectly accurate, yet all angles are 1 / 2 shifted as a result of cosine initialization offset. Below are two programs showing this:

Euler.bas        Euler.exe

Improving_Euler_s_method.bas      Improving_Euler_s_method.exe

Nobody can state that Euler's method is inaccurate any more. It does firstly introduce a specific error, but this error is foreseeable and verifiable. So one may add the equivalent correction which will cancel it (well, almost). Here, one obtains a surprising accuracy up to 9 digits, which is fantastic.

Such achievements are important for us because oscillations are the very basis of waves' behavior. Each new element helps us to understand what is truly going on. We already created or improved algorithms reproducing virtual waves, but some of the effects are still to discover. Especially, genuine waves (not equations) are never perfectly sinusoidal, and this strongly suggests that they may not behave exactly the way equations indicated. It should be emphasized that Mr. Philippe Delmotte's and Jocelyn Marcotte's virtual wave algorithms use a similar step, so they are likely to produce the same unpredictable effects.

It turns out that any granular medium (made of electrons, atoms or molecules, for example) clearly exhibit quantum properties. As explained above, energy transmission must be performed in a step-by-step process, and the step vs. wavelength ratio is not linear. A specific energy transmission constant should be considered. This means that ultrasonic waves behave differently for shorter wavelengths where very few molecules are involved.

Clearly, genuine waves do not behave exactly the way equations indicate. They truly exhibit unusual and surprising properties. Especially, waves can act and react with other waves, and such a behavior was surely not foreseeable using wave equations. Thus, being made of standing waves, two material bodies can act and react according to Newton's laws.

March 17,  2008

Mr. Anselme Dewavrin discovered in Decembre 2006 an algorithm which produces oscillations. It derives from the I.I.R. (infinite impulse response) electronic filter and also from Mr. Jocelyn Marcotte's algorithm, which produces computerized virtual waves. These three program lines must be repeated in a computer loop:

y1 = step * y3 – y2
y2  =  y3
y3  =  y1

step  =  sin(4 * pi / lambda) / sin(2 * pi / lambda)

I found yesterday that the equivalent step also works for Euler's method:

step  =  sqr(2 – (sin(4 * pi / lambda) / sin(2 * pi / lambda)))

instead of : 

step  =  2 * pi / lambda

So this new calculus was integrated to my new program (see March 14 below):

WaveMechanics01.bas      WaveMechanics01.exe

Surprisingly, in October 2006, Mr. Anselme Dewavrin was also the discoverer of another oscillation algorithm based on Euler's method. It is amazingly simple:

sine  =  sine – cosine * step
cosine = cosine + sine * step

step  =  sqr(2 – (sin(4 * pi / lambda) / sin(2 * pi / lambda)))

Although Euler's method is not accurate, the program indicates that it can now deliver the exact wavelength thanks to this new calculus for the step. But the sine and cosine magnitudes are still not perfectly accurate, though. I presume that this residual anomaly will also be corrected some day, making Euler's method finally "perfectly accurate".

March 14, 2008

Below is the first one of a series of FreeBASIC programs on wave behavior. They will especially demonstrate that waves and standing waves are capable or interaction. Thus, because matter is made of standing waves, its whole mechanics will become obvious.

WaveMechanics01.bas      WaveMechanics01.exe

I already wrote 21 programs in French and the goal is to translate them all before releasing new ones.

As a science, the Wave Mechanics is all about Matter Mechanics. Waves explain all: energy, forces, action and reaction, motion, inertia, etc. I wrote somewhere that today's invasion of physics by mathematicians is a plague. A wave is not an equation. It is a mechanical phenomenon which can be more or less predicted by an equation, which remains an approximation despite its perfection. The real thing is much better. In my opinion, Mr. Philippe Delmotte's and Jocelyn Marcotte's computerized virtual mediums are perfect.

I strongly suspect the so-called "error" of Euler's method to be actually the most basic property of waves. Because energy transmission is performed step by step in all well known waves such as sound, this obviously "quantum-like" anomaly (especially for shorter wavelengths) should be present.

It turns out that true waves are not perfect. As a consequence, matter standing waves should oppose a very weak resistance to traveling waves emitted by all matter in the universe. They should be progressively scattered. The result after millions and millions of wavelengths is matter's standing wave amplification. Thus matter standing waves can constantly emit energy without fading out.

February 20, 2008

The page on fields of force was updated.

This is the debut of a new era. The unification of forces is now complete. Energy, forces and matter mechanics are systematically linked to fields of force. Here is the electrostatic field responsible for the Coulomb force, the simplest and most common field of force:

The "biconvex" ellipsoid electrostatic field of force generated by two electrons.

All distances between antinodes and electrons are integer multiples of the wavelength.

This is possible thanks to the ellipse's amazing properties (see below).

The field is the result of the wave addition between two electrons or positrons. Like electrons and matter, it is made of standing waves whose amplification returns energy equally towards both particles. The force is exerted equally in two opposite directions as a result of the radiation pressure.

As seen from this field's point of view, there is no action and reaction any more, but rather two opposite and equal actions. So Newton's well known third law is still valid but it should rather be called the principle of Double Action.

Moving matter undergoes a mass gain as kinetic energy according to Lorentz's gamma factor. When two electrons collide, the field of force becomes an energy reservoir which is capable of accelerating them back in opposite directions. Thus, a collision between two billiard balls creates billions of temporary fields of forces whose total energy according to mc^2 is finally returned to the balls. The calculus below could be achieved thanks to the active and reactive mass method, which is based on Lorentz's Doppler effect.

This calculus is not disputable because it matches all well accepted and verified observations. 

M = a + r

T = M₁ + M₂

Total constant energy (law of conservation of energy) = M₁ + M₂ + delta

The field's energy (delta) is given by:

Delta = Total energy – (M₁ + M₂)

As far as I know, I was also the first one (in 2002) to point out that all of the ellipse's magnitudes are directly linked to the Lorentz transformations. Below is my most recent diagram:

January 21, 2008

A decisive test was added to the second page on Lorentz's Relativity. One can check that the Lorentz transformations prevent moving observers from detecting their absolute speed with respect to the aether. They will rather transpose the Lorentz transformations to the system at rest.

I am especially proud of these diagrams because they display the situation as seen by A and B in accordance with both Lorentz and Einstein. Thus the results are not disputable. Below are the four separated images:

http://www.glafreniere.com/images/relativity04a.gif

http://www.glafreniere.com/images/relativity04b.gif

http://www.glafreniere.com/images/relativity04c.gif

http://www.glafreniere.com/images/relativity04d.gif

Lorentz's reversed equations below are not disputable either because they are also consistent with both Lorentz and Einstein's point of view. I am very surprised that nobody ever put them down this way.

Clearly, Lorentz's point of view is valid as an alternative to Einstein's Special Relativity. If the transformations really occur, a moving observer cannot establish his true speed anyway. All observers must deal with a perfect reciprocity. Einstein was correct on the principle, but he was wrong on the true events.

Relativity is definitely true. It is not a theory any more. It is possible because moving matter and forces are involving waves. Now, there is a new theory to discover: the New Mechanics. It is much more important than Relativity because it is how matter truly behaves.

Matter mechanics is solely the result of Lorentz's very special Doppler effect applied to electrons.

Matter structure is solely the result of Fresnel's diffraction patterns for multiple emitters. 

January 12, 2008

The second page on Lorentz's Relativity was updated again. I added a clock synchronization procedure which is consistent with the Lorentz transformations.

The calculus is quite simple. Now Relativity can be easily demonstrated. It is not a dogmatic and complex theory any more. Starting from now, scientists can no longer ignore this hypothesis because it works, and also because everybody can examine it and understand it.

I will add many similar experiences, but making all this simple needs a lot of thinking. I am prepared to work on this for a long time, but it is worth the effort because Lorentz's Relativity leads to the New Mechanics, which is much more important. 

January 3, 2008

The first page on Lorentz's Relativity was updated. After so many years of intense thoughts, I finally affirm that the Lorentz transformations and Relativity are strictly based on the fact that the electron frequency slows down in accordance with Lorentz's contraction factor:  g = sqr(1 – beta ^ 2).

The electron frequency slows down according to Lorentz's factor.

This phenomenon alone causes the Lorentz transformations and explains Relativity.

This is truly the "formula of the century". It turns out that the Lorentz transformations are much more important than Relativity (which is all about mystification) because they explain matter mechanics. Matter true behavior is important, indeed capital, and Newton's laws can now be upgraded by adding the Lorentz transformations effects and the mass gain, which is responsible for kinetic energy according to the gamma factor (1 / g).

There is no "General Relativity". Gravity is definitely not linked to Relativity. It is just a force like other ones, which all act through fields of force, albeit they are submitted to the Lorentz transformations.

The second page on Lorentz's Relativity was partially updated. The goal is to examine many situations and experiments (such as the Michelson interferometer) which systematically yield a null result. Finally, one should draw the conclusion that one's velocity with respect to the aether is not measurable.