EXPERIMENT 4 , POSITIVE RESULT, (performed 20/08/99).

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It is travelling wave experiment, where the variations of the wavelength is directly measured as a consequence of the anisotropy of the light speed in vacuum.

If I were using free electromagnetic travelling waves, due to the fact that the GTWMC one-way velocity is [c-v]/(1-bb) in front of an oscillator and [c+v]/(1-bb) with b=v/c at the rear of it, the wave equations of the counter travelling waves in the direction of the ether-wind are: sin[2.pi.f.[t-(1-bb).x/(c-v)]] and sin[2.pi.f.[t+(1-bb).x/(c-v)]] with the different wavelengths: [c-v]/(1-bb).f and [c+v]/(1-bb).f.

f is the frequency of the oscillator in the moving frame.

But, as it is difficult to produce in free space a good TEM wave, I have preferred to use the electromagnetic field in a standard rectangular X band waveguide (WR 100) at the frequency of 9.192 Ghz.

1) ABSOLUTE WAVEGUIDE THEORY

I consider a waveguide (see figure below) with a centered antenna producing a signal of frequency fo. The waveguide and the antenna are in absolute motion.

Due to the classical Doppler effect, the TEM waves produced by the antenna at the frequency fo have a frequency f which is : f = fo.[c/(c-v.cos(a))].

But these TEM waves may propagate into the waveguide, if the angle a obeys the following equation: sin(a)=c/2.d.f

We have thus, the equation in a: sin(a)=[(c-v.cos(a))/2.d.fo] which is the same as:

.

The two solutions for the two ways and the same direction are for cos(a): .

If we consider one way, the TEM wave equations are:

and

.

Thus, the standing-travelling wave (mode TE01) is:

.

The second factor is simply cos[pi.y/d] and becomes cos[pi.y'/d] in the moving frame (in introducing GTWMC) where we see that the electric field is nil for y'=d/2 and y'=-d/2, that is to say on the walls of the waveguide.

The first factor is a travelling wave whose equation in the moving frame is:

. (GTWMC has been introduced).

Thus, the wavelength in the moving frame is: .

As for v= 360 km/s, fo= 9.192 Ghz, d=22.86mm, the values of cos(a) for the positive way is: 0.7014154 and -0.70019335 in the negative way, the wavelengths are:

lambda+ =4.64589 in the positive way and lambda- = 4.66184 in the negative way.

The following experiment permits a direct measurement of these travelling wavelengths and thus the ether-wind detection.

THE EXPERIMENT.

The experiment uses a standard rectangular X band waveguide (wr100, wg16) of a length of 3 m.

At each end, there is a waveguide switch which may be connected to a low vswr load or to the output of a microwave oscillator (see figure below). The waveguide is orientated in the direction of Leo (11h of right ascension) and the two ways for the travelling waves are obtained in changing the end used to send the wave.

When the wave travels from left to right the left input is connected to the microwave oscillator and the right end to the low vswr load.

The microwave oscillator is made of quartz oscillator controlling a PLL with a frequency of 1.3131 Ghz at the output. A step recovery diode is used to produce harmonics whose the 7 th is selected by a band-pass filter.

A microstrip power divider followed by several isolators produces the different signals needed for the experiment. One signal is used to power the long waveguide through a faraday effect variable phase shifter, and the other two to bias the double balanced mixers used as phase detectors.

The experiment is performed as follow:

The left end of the waveguide is connected to the microwave oscillator and the right end to the low vswr load.

Then, the phase shifter is adjusted, in order to obtain a nil DC signal at the output of the left double balanced mixer (with the signal from the left antenna in the waveguide). After, the right antenna in the slotted waveguide part is adjusted in order to obtain a nil DC signal at the output of the right double balanced mixer.

The distance between the antennas is measured to be:297.3 cm

Now, the right end of the waveguide is powered and the left one connected to the low VSWR load.

The phase shifter is again adjusted in order to obtain a nil DC signal at the output of the left double balanced mixer. But this time, we see that the right double balanced mixer don't yield a nil DC signal, simply because the number of wavelengths between the antenna has changed.

In fact, in order to obtain a nil DC signal, I have to move the antenna in the slotted line (on the right) of about one centimeter towards the right. There the distance between the antennas is: 298.3 cm.

Such a beautifull result is in good agreement with the fact, that there are 64 wavelengths of the travelling wave travelling towards the right: 64x (4.64589)= 297.33 cm and 64 wavelengths of the travelling wave travelling towards the left:

64 x[4.661847]= 298.35.

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