As I pointed out, this is the very first experimental demonstration of this most remarkable optical diffraction pattern. You may examine and compile the following program which created those images. The source code is in C. It stands in only one file and it is rather simple, so that it would be easier to analyze how Mr. Marcotte's 3-D wave algorithm works.

11-06_3D_Airy_Disk.zip

Mr. Jocelyn Marcotte elaborated in 2006 a three-dimensional wave algorithm whose engineering is absolutely perfect. It produces a very smooth and accurate propagation whatever the wave direction. The dark side of it is that your computer will have to perform billions of calculations because the program is dealing with a three-dimensional space (1000 x 480 x 480) containing 230 million individual cells. In addition, each cell is surrounded by 26 neighboring ones whose relative influence must be considered. 

This is why you may have to wait for about one hour in order to see the results. Working on a larger volume requires more than 2 GB RAM memory and a 64-bit compiler - and even more time. A sophisticated use of those new graphic cards may also help. Fortunately, more and more supercomputers are becoming available in universities and deliver miracles as they perform parallel calculus.

I don't understand why opticians, acousticians and scientists working in domains such as astrophysics or electronics are still ignoring this new laboratory of the future. Thanks to it, they will be capable of studying any wave phenomena in a much easier way. For example, my hypotheses concerning the "motion optics" are quite reasonable and lead to Relativity. Finally, this prodigy is not that complicated on condition that one is well aware of what is going on. 

The truth takes time. Meanwhile, I will slowly but surely deliver new facts about Relativity. It is all about waves in the presence of motion. In this context, the consequence of motion on waves is obviously the Doppler effect. No mystery there: the Lorentz transformations definitely indicate what sort of Doppler effect is capable of canceling our attempts to detect and measure our absolute motion. As a matter of fact, Lorentz's 1904 title was "Electromagnetic phenomena in a system moving with any velocity smaller than that of light". Believe me, Relativity is explainable without introducing such nonsense as a "space-time" transformation. 

7 June 7, 2011.

Below are two programs showing how Philippe Delmotte's and Jocelyn Marcotte's wave algorithms work.

11-05_Delmotte_Wave_Algorithm.zip

11-05_Marcotte_Wave_Algorithm.zip

Here is another one showing how to use a marginal damping area in order to eliminate annoying reflections at the medium limits.

11-06_Damping_Area.zip

Mr. Marcotte and me are working on a 3-D version of his algorithm, which is especially adapted to the C programming language. Thanks to his particularly brilliant use of pointers, Mr. Marcotte succeeded in eliminating a whole array of variables, which required a huge amount of RAM memory in 3-D mode.

Now, there are only two arrays left and this allows us to work in a much larger 3-D space. I will soon release two videos showing the Airy disk and the Fresnel-Fraunhofer diffraction pattern.

Below is one of my first experiences in 3-D. It shows that spherical standing waves can be created using ingoing regular spherical waves.

11-06_3D_Spherical_Standing_Waves.zip

11-06_3D_Spherical_Standing_Waves.mkv

Spherical Standing Waves.

This is only a preview. Although it is virtual, our wave medium is a genuine laboratory.

In spite of my reaching 70 years of age next year, I have decided to learn the C programming language. It works much faster than Basic. It is also the most used one world wide. I added some basic instructions at the beginning of the source code, which was edited using Code::Blocks. For instance, it requires some SDL functions for graphics and occasionally, the extra SDL_ttf.lib in order to display some text. Learning all this was not a piece of cake (really!) but now I am quite comfortable with it. The programs work fine!

May 13, 2011.

While learning the C programming language, I was helped by MM. Anselme Dewavrin and Jocelyn Marcotte and I finally succeeded in producing an acceptable program using Mr. Marcotte's 2-D wave algorithm. It is quite interesting (results for an omni-directional emitter, a corner primary reflector and parabolic secondary reflector).

Parabolic_Reflector.zip

Le 31 mars 2011.

I added some new information on the expanding universe hypothesis in the page on the  Relativistic Big Bang. Naturally, one speaks here about the aether, not  "space". This is of no consequence because distant galaxies may be considered stationary with respect to the local "space" as well.

In my opinion, the present theory about the acceleration of the expansion of the Universe (according to Mr. Saul Perlmutter) is definitely premature. The expansion phenomenon is still to be studied more carefully, especially when it comes to analyzing the redshift of distant galaxies.

Clearly, a general expansion of a system as a whole, including that of the medium which carries the waves, cannot produce a Doppler effect. In addition, if the medium itself (call it "space" if you prefer) is expanding, the light wavelength must expand proportionally.

However, if the observer and his instruments are also expanding, such a redshift is no longer measurable. In the diagram below, three galaxies A, B and C are moving away from each other at the speed of light, which must accelerate far away from them because of the medium expansion. However, it is postulated that galaxy A only remains truly stationary.

Waves emitted in an expanding universe remain spherical and concentric: especially, there is no Doppler effect.

On condition that everything is expanding at the same rate, all happens as if there were no expansion.

This reasoning leads to a new "Relativity of Expansion Postulate":

The Relativity of Expansion Postulate.

Surprisingly, though, the universe does not obey this principle because we do record a redshift. This is clearly the consequence of an anomaly in the expanding process, but it is unclear what particular variable may cause this. The anomaly could be the consequence of a lot of causes, so that it is definitely unreasonable to explain it right now by an accelerated expansion. For example, matter itself may not expand, or its properties may not evolve proportionally.

Surely, the cause of the redshif is still to be explained. The next step will be to explain why Mr. Perlmutter's observations indicate a departure from Hubble's predictions...

April 4, 2011.

The page on Plane Standing Waves was considerably modified in order to emphasize the effects of motion on standing waves. Mr. Yuri Ivanov called this phenomenon "Lively Standing Waves". In my opinion, though, it should rather be called: "Ivanov's Waves". It is definitely the first step towards a better knowledge of the Lorentz Transformations, and Relativity.

Ivanov's Standing Waves

Gabriel LaFreniere