January 31, 2012.

THE IVANOV TRANSFORMATIONS AND THE ACOUSTIC DOPPLER EFFECT

The Doppler effect may occur in two different ways. The Relativistic one is the result of the Lorentz Transformations (1904), which are a special case of the Voigt Transformations on the Doppler effect (1887). It definitely applies to light and radio waves. But surprisingly, it was only in 1981 that Mr. Yuri N. Ivanov established the equivalent properties of the regular acoustic Doppler effect. He especially discovered that in the presence of wind, standing waves contract. He found that, in this case, the contraction rate significantly differs from Lorentz's predictions. 

The Voigt Transformations (my corrected version, actually) are shown in the image below. It differs from Lorentz's one because of the presence of Voig'ts constant k, which controls the rate of the transverse contraction. There is no such contraction according to Lorentz: y' = y; z' = z. However, the image below shows that the regular Doppler effect does contract the transverse wavelength in such a way that Voigt's constant k equals Lorentz's contraction factor g. That is why g may replace k in Ivanov's simplified equation set.

  This is verifiable thanks to this program in C language. The Delmotte-Marcotte virtual wave medium (now in 3-D!) proves to be a very convenient laboratory to experiment such wave phenomena. Thanks to the Ivanov Transformations, I did obtain the regular acoustic Doppler effect, which is well known to produce a 1 – beta wavelength contraction forward and a 1 + beta expansion backward. I challenge anybody to obtain a similar almost-perfect Doppler effect without relying on those equations.

The Ivanov transformations produce the regular acoustic Doppler effect.

The wavelength on the vertical axis is contracted from 100 to 86.6 pixels according to Voigt's constant k.

The acoustic Doppler is a special case of the Voigt Transformations (1887) where k equals Lorentz's contraction factor g.

This is shown in this video: 12-01_Ivanov_Transformations.mkv

Compare to the Lorentz Transformations: 12-01_Lorentz_Transformations.mkv

Untransformed spherical standing waves: 12-01_Null_Transform.mkv

The standing wave contraction phenomenon was discovered by Yuri N. Ivanov in 1981.

The image on the left shows the regular untransformed spherical standing wave structure.

The Relativistic Doppler effect (the Lorentz Transformations) does not contract the wavelength on the y and z axes.

The regular Doppler effect (the Ivanov Transformations) contracts the wavelength on the transverse axes according to k .

The squashed ellipsoids (in red) indicate that the standing wave contraction is more severe in this case.

From now on, because it was demonstrated thanks to a true laboratory experiment, the standing wave contraction phenomenon is no longer disputable.

Let's give to Caesar what belongs to Caesar. Matter contraction was proposed around 1900 by FitzGerald, Larmor and Lorentz in order to explain Michelson's null result. The important point is that it was rejected as an absolute fact because none of them could explain why such a prodigy should occur. I am rather surprised that the scientific world is still reluctant to recognize that Mr. Ivanov discovered a fundamental phenomenon. Considering the Lorentz Transformations, it does explain matter contraction and Relativity. I would like to pay tribute to Mr. Ivanov. That is why I worked hard in order to repair this injustice.

And I would also thank him very much for having so pertinently guided me in the past.

January 15, 2012.

The Doppler-moving electron.

Its wave structure is undergoing the Lorentz transformations.

It is now ten years since I published an essay on the wave nature of matter. My book "Matter is made of waves" clearly identified the electron as a spherical standing wave system, which is capable of motion as a result of the Doppler effect. Matter was spontaneously and exclusively constructed out of electrons and hence, electrons are fundamental. The image shown above represents such a system in the vicinity of its center.

The electron is a wave. As such, its motion must obviously produce severe internal transformations involving the Doppler effect. Surprisingly, those effects coincide with the Lorentz Transformations. It is indeed a well known fact that Lorentz's original equation set was much similar to Woldemar Voigt's one, precisely on the Doppler effect (1887). Unfortunately, Voigt's equations were plagued with some anomalies and one error which was not detected by Lorentz and Poincare, the latter being the real author of the latest version.

Using c = 1, Poincare's equation set (1905) leads to his Relativity Postulate.

Note: k stands for Lorentz's contraction factor. Voigt's constant l is unnecessary because l = 1. 

Nowadays, this one anomaly is rather easy to detect using computers. It is all about the t and t' time variables which must be interchanged. This leads to a reversed version in order to obtain x an t (which apply to the stationary system) on the same side of the equations. One must also distinguish what sort of phenomenon is involved. The point is that those x and t variables may refer to quite different concepts. In the case of Ivanov's waves, the Alpha transformations must deal with an hypothetic wavelength assorted with an hypothetic wave period. The Beta transformations are required for reproducing the relativistic Doppler effect or the electron: then x stands for its wavelength and t for its wave period. It is quite different in the case of matter: x stands for distances in light-second units and the time t (not so surprising) is given in seconds. However, in all cases, we are dealing with the same Lorentz transformations and the same equation set:

The regular acoustic Doppler effect does not behave this way, though, mainly because the frequency remains constant. It may be reproduced using Voigt's corrected and reversed equation set on condition that Voigt's constant k equals g. However, Yuri N. Ivanov's Transformations (also corrected and reversed) do reproduce the regular Doppler effect and additionally, they are simpler.

And so, using this revisited equation set, I could show a long time ago how "my" moving electron should behave. But today, I am very proud to show it using a sophisticated 3-D wave medium, which is a genuine laboratory. Any acoustical or optical experience may be conducted. Thus, the results are undisputable.

It should be emphasized that Mr. Jocelyn Marcotte had already experimented this phenomenon in 2006 using his own 3-D wave algorithm. Now that I finally succeeded in learning the C programming language, I can repeat this exploit, which is rather simple to perform. One must firstly emit a given number of waves undergoing the relativistic Doppler effect (using the Beta transformations). Then the wave direction is reversed so that ingoing Doppler waves encounter outgoing ones. The wave addition is incredibly consistent with Lorentz's predictions. Ten years ago, I called this phenomenon "LaFreniere's wave", that is to say the "moving spherical standing wave" system which is well visible with its stunning phase wave in the video clip below.

12-01_3D_The_Moving_Electron_Clip.mkv

This clip was extracted from the video below.

12-01_3D_The_Moving_Electron.25c.mkv

At half of the speed of light, the contraction becomes more easily observable:

12-01_3D_The_Moving_Electron.5c.mkv

Below it the C program (in English) with all its sub-files. The source code contains some information about the installation of CodeBlocks and especially the SDL graphics library.

12-01_3D_The_Moving_Electron.zip

This is how the electron moves. As a matter of fact, Lorentz's memoir title was: "Electromagnetic phenomena in a system moving with any velocity smaller than that of light". The Lorentz Transformations and Relativity clearly involve motion the same way the Galilean Transformations do. Waves plus motion inevitably suggest the Doppler effect as a consequence. As a matter of fact, Woldemar Voigt released his equation set in 1887 precisely for this purpose: Ueber das Doppler'sche Princip (On Doppler's Principle).

Let's make things clear: the beta speed is the electron speed with respect to the speed of light, which was normalized to: c = 1 by Henri Poincare. Then all is much simpler. In addition, I myself suggested a long time ago to return to Lorentz's contraction factor "g", which is more relevant:

g = (1 – beta ²) ^1/2

 This "moving standing" wave system is really fantastic. Here is a list of its most remarkable properties:

– This wave system is undergoing the relativistic Doppler effect, which is given by the Lorentz Transformations.

– Lorentz predicted that the electron should contract on the displacement axis according to the contraction factor g.

– The contraction is more exactly that if its spherical nodes and anti-nodes, which become ellipsoidal.

– Surprisingly, the electron standing waves remain perfectly concentric in spite of the Doppler effect.

– Lorentz predicted that the electron would not contract on orthogonal axes: y' = y; z' = z as a result of Voigt's constant k = 1.

– That is why moving matter, which is solely made out of electrons, contracts only on the displacement axis.

– Lorentz also predicted that the electron "time" would slow down according to the contraction factor g.

– As a result, the electron oscillation frequency slows down in such a way that the transverse wavelength remains constant.

– Additionally, Lorentz predicted that the electron should exhibit a "local time".

– The local time induces a local phase shift explaining deBroglie's "phase wave" along the displacement axis.

– Louis deBroglie predicted that the phase wave speed should be given by: 1 / beta.

– He also predicted that it should become shorter at high speed. The full phase inversion distance is indeed: g * lambda / beta.

– By predicting additional diffraction effects, which were soon demonstrated, he discovered that the electron is a wave.

– Lorentz predicted that the electron should undergo a gain in mass according to the gamma factor, which is given by: 1 / g.

– I demonstrated a long time ago that this gain in mass (or energy) is merely the result of the Doppler wave compression.

– In 2006, Mr. Jocelyn Marcotte demonstrated that the electron amplitude curve is given by the cardinal sine (sinc).

– The distance to the center being equal, the amplitude is symmetrical forward and backward in spite of the Doppler effect.

– The Inverse Square Law no longer applies unless one considers that distances are contracted according to Lorentz's factor g.

The Inverse Square Law violation in a moving system is a striking novelty. On the one hand, it is a clear demonstration that Lorentz's length contraction is a true fact. On the other hand, one is still entitled to consider that, from an absolute point of view, the wave energy truly falls off according to the square of the distance. Consequently, I am of an opinion that Mr. Saul Perlmutter must reconsider his theory of an accelerated expanding universe. Considering today's well-demonstrated Doppler laws, it is unlikely to be correct.

Let's take a simple, especially eloquent example. Suppose that a far distant Type Ia supernova is moving away at 86,6% of the speed of light. In this case, beta = 0.866 Lorentz's contraction factor g is .5. Its brightness is well known to be constant and hence, its distance appears to be easily measurable using the Inverse Square Law.

But actually, it is not that simple because of the the Relativistic Doppler effect. At such a speed, because of the Lorentz transformations, all galaxies in the vicinity are squashed and packed together in the direction of their motion to 50% of their normal size. The contraction is even more severe for all the area in front of them because the speed there is nearly that of light. If Lorentz is right, this area would end (seem to end, more exactly) in a sort of "time wall" so that no more galaxies could exist beyond it. Its distance would be about 13.7 light-years away, but this is uncertain. See the page on the Relativistic Big Bang for more details.

Moreover, the relativistic mass is doubled at .866 c so that electrons in that supernova emit light which is two times brighter. Its wavelength is also two times longer because the oscillation period of those electrons is two times slower. This calculus indicates that no material body can reach the speed of light, a law which was stated implicitly in the title of Lorentz's memoir released in 1904. So, the "time dilation" produces a first 2x redshift. It is not related to the regular Doppler effect, which is given by: 1 + beta = 1.866 times the wavelength. Finally, the total relativistic redshift is 2 * 1.866 = 3.732 times the regular wavelength (at rest) for this speed. It is measurable and so, the speed of the supernova can be known. But when it comes to establish its distance by measuring its brightness, applying the Inverse Square Law appears rather tricky.

At such a speed, as seen above, the light from a fast-moving galaxy fades out according to the square of the double of its distance.

Obviously, it is also possible to consider that the light energy is truly fading out according to the square of the distance to the point where it was emitted. If the galaxy speed was constant, it is now situated 0.866 time beyond this point. The problem is that, if the galaxy was accelerating and is now moving at 99.9% of the speed of light, it simply cannot go on accelerating significantly. It must stabilize its speed ultimately because no matter can reach the speed of light.