July 28, 2008.

Here is another complementary program showing how to produce a variety of reflection and damping effects. One can even obtain adjustable transparent mirrors or amplification screens, and all those procedures are compatible with Mr. Marcotte's 8 neighbor 2-D optimized algorithm. 

WaveMechanics05_Reflections.bas        WaveMechanics05_Reflections.exe

The goal is to show that MM Philippe Delmotte's or Jocelyn Marcotte's algorithms are very simple to deal with. Most of these effects need not more than two elementary variable modifications.

July 20, 2008.

We are about to release a new program which will surely be a must in the future for everybody interested in waves.

Below is a complementary program. It contains basic procedures and should be useful for those who simply cannot wait.

WaveMechanics05_Wave_Generator.bas        WaveMechanics05_Wave_Generator.exe

Clearly, MM Philippe Delmotte's and Jocelyn Marcotte's algorithms yield flawless, perfect results. They do work in accordance with Huygens' Principle and Fresnel's integrals. This is very comforting because the waves are simply standard, normal waves. Our new laboratory reveals itself to be a great, indeed respectable one, and now the experiment results can hardly be disputed.

The 2-D Wave Generator

The goal is to obtain a powerful laboratory capable of experimenting any wave phenomenon. So the very first step is to generate waves inside the virtual medium (a two-dimensional one here, hence circular waves, not spherical). Thanks to my previous programs using the Huygens Principle, and more recently Ether06 below (to be translated soon), I was well aware that the 2-D core diameter exhibits a 3/4 wavelength diameter instead of the full lambda core for spherical waves.

Ether06.bas    Ether06.exe

The medium reacts rather capriciously to any energy input. It must be very smooth and progressive, so I desperately tried all kind of distribution curves inside a 3/4 lambda circle. Finally, I realized last week that the simpler solution, the elementary sine curve inside a 1/2 lambda circle instead of 3/4, could also be the best one. As a matter of fact, the results perfectly mach the curves given by the Huygens Principle, and the smaller circle is much faster to scan (1.5^2 = 2.25 less surface).

Mr. Jocelyn Marcotte's optimized algorithm.

Firstly, it should be pointed out that Mr. Marcotte's algorithm in one dimension, which is obviously the simpler and most efficient one, was invented in January 2006. I challenge anybody to find any consistent proof indicating that it existed in 2005 or before. It should be put down exactly in the following form and sequence:

past(x) = present(x)

present(x) = trend(x)

trend(x) = present(x–1) + present(x+1) – past(x)

Please stop repeating that it existed well before unless you do have this proof. There should be a maximum of 8 variables without any additional procedure. I acknowledge that many algorithms existed before, especially Mr. Philippe Delmotte's one, which also yields perfect results. Unfortunately, Mr. Paul Falstad does not know the name of the author of his method. I could check that all those algorithms contain additional variables or procedures, and sometimes the results are wrong or problematic.

But secondly, Mr. Jocelyn Marcotte went further. During the same year 2006, he elaborated a more complex but very efficient 2-D version using 4 additional neighbors on the diagonals, but with half of their influence only. This is an application of the normal square of the distance law. The diagonal neighbors being 1.414 times farther, their influence is indeed theoretically two times weaker.

I would like to apologize here to Mr. Marcotte for not realizing during at least two years that his enhanced method is really great. While using only 4 neighbors, the energy transfer on the diagonals is reported to the next sequence. This produces more or less squarish waves, especially near the pulsating center and for very short wavelengths. I did myself try to use 8 neighbors, but this did not significantly accelerate the waves. Mr. Marcotte's magnificent idea was to take the central energy into account on a negative basis, as it had already been observed that the positive value could rather produces variable but slower speed, which is useful for simulating lenses.

Finally, in spite of its complexity, this optimized algorithm is still faster because the wave velocity is accelerated to 1 pixel per loop exactly instead of .707. What is more, this procedure is transposable in 3-D. Then it also yields a velocity of one pixel per loop, which is very comforting and convincing. In such a case, one must use the square root of 3 for the neighbors placed on the vertices of a cube. This leads to an even more complex but highly dependable calculus using three different levels of influence and 26 neighbors. During the same year 2006, Mr. Marcotte used this optimized algorithm in order to reproduce my 3-D Doppler moving electron. It was definitely a memorable World's Premiere.

The c = 1 normalized speed.

The interesting point for me is that this 1-pixel velocity is consistent with Henri Poincare's c = 1 normalized speed of light. This convention allowed him to elaborate a considerably simplified version of the Lorentz transformations. So we will use the simplified equation set without any additional correction, making our demonstrations much more convincing. Here is a copy from Poincare's 1901 (four years before Einstein!) book "Electricity and Optics" :

Actually, this is a simplification of the Voigt Transformations (1887), where Voigt's constant "l" is useless. Lorentz found that it could be removed from the equation set because the null result for the Michelson interferometer is obtained only if  l = 1. 

I myself found that the normal Doppler effect occurs when l = g (This is Lorentz's g contraction factor, see below). If l = 1 according to Lorentz, the simpler equation set rather involves a slower frequency. I also found that one must swap x, x' and also the t, t' variables in order to produce this slower Doppler effect. Lorentz and Poincare preferred the inverted version in order to obtain a perfect invariance when applying them to Maxwell's equations. In practice, this simply will modify the x coordinates and the t period or phase (not the time!) of the Wave Generator in the program available above. More exactly, those equations simply describe the electron behavior at high speed. Thus, speaking of space contraction and time dilation appears ridiculous. This interpretation was certainly the most catastrophic error in Physics ever. No doubt, it originated from Poincare's reticence about matter contraction, which was Lorentz's bright idea at that time.

The inverted Lorentz transformations produce a Doppler effect instead of correcting it.

The x and t symmetric equations on the right hand side were adapted from Poincare's version. 

I discovered a new improved damping screen.

The wave algorithm simply transfers energy from one "granule" to its neighbors without any loss, with the inevitable consequence that the waves undergo a hard reflection when they reach the medium limits. Most often, the reflections must be eliminated and Mr. Philippe Delmotte succeeded as soon as 2005, thanks to a relatively wide damping zone (100 pixels or more). It is a tough and time consuming method, though.

Fortunately, I had to review the whole set of screens and mirrors because Mr. Marcotte's optimized algorithm works differently. I accidentally found an amplifier screen and a phase inverter. I also noticed that one must use progressively the soft reflection instead of the full damping procedure when the incidence angle becomes important. So I followed this Ariadne's thread and I finally elaborated last week a very simple damping screen which is successfully in use in the above-mentioned program.

But unfortunately, this damping screen becomes more difficult to deal with when the incidence angle cannot be known for sure. This is especially the case when the source is moving, when there are many sources, or when other reflections occur. The situation near the reflection point surely can be analyzed, but the smaller error produces a faint reflection which complicates ulterior interventions and finally ends up with a disaster. I am confident that a simple and trouble-free all-azimuth damping screen is possible, but I am afraid that finding it requires a better I.Q. than mine.

June 13, 2008.

Below is my fourth program on the Wave Mechanics. This one explores the capabilities of Mr. Jocelyn Marcotte's wave algorithm, which was created in June 2006. We worked closely together and the final result appears quite remarkable. We can now very easily generate and handle all kinds of waves. We also elaborated more simple and efficient procedures. This invention has now reached a very high degree of perfection.

WaveMechanics04.bas        WaveMechanics04.exe

Please note that Mr. Marcotte does not necessarily agree with my own theories about the wave nature of matter. The important point is that this algorithm produces absolutely normal waves. No theory there. No fantasy. Just waves.

Thus, I am confident that people interested in waves, especially opticians and acousticians, will realize soon that MM. Philippe Delmotte and Jocelyn Marcotte invented something important. This new computerized virtual wave medium proves to be a powerful tool, a genuine laboratory. Scientists will obtain a much better comprehension of all wave phenomena. There is a huge difference between theory and practice because facts are not disputable. Although virtual facts may appear quite evanescent, this wave algorithm will on the contrary yield very reliable results. As a matter of fact, all wave phenomena can otherwise be experimented through material waves such as sound, and yield the same results. For instance, hundreds of loudspeakers connected to the same sinusoidal source and evenly distributed on a circular spherical surface will produce a genuine (but noisy) Airy disk. The Huygens Principle (Fresnel integrals) can also predict this but scientists will finally prefer the algorithm because it is much easier to handle.

Let's face it: physics deviated from its logical course one hundred years ago because this tool was absent. Look at this:

Michelson_orthogonal_forward_51_angle.avi

The virtual medium can easily reproduce what is really going on inside the Michelson interferometer. I simply applied the Lorentz transformations. In 1895, Lorentz was on the right track, but he finally gave up on matter contraction because all scientists (especially Poincaré and Einstein) rejected this idea.

And this is only the tip of the iceberg. Thanks to this algorithm, I will slowly but surely produce more and more demonstrations. I admit that my hypotheses about the wave nature of matter definitely look weird, but they will prove to be correct and consistent with Lorentz's Relativity.

From my point of view, here is what is really weird. Since one hundred years, thousands and thousands of scientists studied and spoke about motion and Relativity without ever taking the Doppler effect into account. So I strongly suggest that you firstly examine my Time Scanner and compare the results to the Lorentz transformations (as seen by Lorentz himself). No doubt, Relativity is all about the Doppler effect, is it not so complicated, and our new virtual medium can handle it magnificently.

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.