4) LORENTZ' CONTRACTION. [ return ]

Introduction.

As a calling to mind, I have to say that the study of a classical resonator has produced the time dilation phenomenon, but also surprinsingly the de Broglie wave if the frequency at rest is chosen to be mcc/h where m is the rest mass of the electron.

After, the time dilation in the moving frame from which we consider a divergent and a convergent wave has permitted to derive the wave equations of the electron.

The hypersonic wave structure obtained classically is very interesting, because it contains everything we know about the electron, together with the so-called relativistic phenomenons (except spin).

1) The frequency of the de Broglie wave which increases like the mass in relativity.

2) The de Broglie wave itself.

3) The time dilation in the frame of the electron

4) The Lorentz' contraction

5) A ratio of the de Broglie wave to the De Witte's wave of 137.036 on the first orbit of the Bohr's atom.

6) An hypersonic energy of E=mcc (derived later)

7) Everything we need to derive the Maxwell's equations for vacuum (later).

8) The divergent wave is simply the wave obtained when an oscillator is in motion.

9) The existence of a nucleus of frozen ether is easily justified and explain why the electron appears to have a radius.

Such a simple and convincing structure permits to affirm that we have certainly found the physical reality.

Mechanism for a standing wave structure.

It will be justified later the existence of an ellipsoidal nucleus which needs that a phase constant must be added to one of the two waves which compose the electron.

If we chose to add it to the divergent wave, the constant is: .

With it we obtain a new addition of the waves (standing wave) which is:

Obviously the wave exist only outside the ellipsoidal nucleus.

The reader may test immediately the validity of this equation with t=0 and where it is easy to see that the cosinus factor is nil on the surface of the nucleus. Particularly for y=z=0 and x=ro.sqrt(1-bb) or y=x=0 with z=ro.

That means that the greatest axis (in the yz plane) remains unchanged and is the radius of the electron at rest.

Nevertheles, to account of the exact hypersonic energy of the electron in motion, we will have to consider later a variable length of the greater axis. But I have also the hope that the spinning electron will not need a variable nucleus in addition to the Lorentz' contraction. Unfortunately the theory is not yet ended.

The two waves of the electron are represented below, the divergent in black and the convergent in red. Obviously each wave extents to the infinity in order to be able to generate the other. As it will be shown later, the only mathematical way to justify such a wave structure is to consider that the divergent wave reflects partly on discrete surfaces made of frozen ether or if an interaction exists only between the divergent wave and the convergent one on these discrete surfaces. In fact, these surfaces, if we consider that there are the ellipsoids where the addition of the waves is always nil (cosinus factor in the standing wave above), like on the nucleus, we understand easily that the divergent one is able to generate the convergent one by a simple multiple reflection on them (in yellow on the figure below).

Obviously, the calculation of the reflected wave is not easy and needs the formulas of the Doppler effect established for the theory of the transversal clock.

Such a calculation will be made later.

I have also to say that a beautiful animation of the wave structure of the electron in motion, together with the de Broglie wave (sinus factor in the standing wave above) may be obtained free of charge from me. Simply send an E-mail to roland.dewitte@pi.be to ask it.

Finally the electron may have a standing wave structure, because it is composed of hypersonic waves which reflect on an infinite number of ellipsoidal surfaces including the nucleus, and which are produced by the standing wave itself.

We will have to admit it, because the calculation of the whole energy of the electron with the standard energy density of the sound-waves yields the famous formula: E=mcc.

Lorentz contraction.

The contraction of the energy is due to a change of the direction of the waves which compose the electron when it is accelerated and is clearly and simply explained here.

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