The successes of Astrophysicists

The Michelson experiment

Michelson set out to measure the speed of the Earth in its orbit around the sun using light rays to determine the movement of the light-transporting luminiferous ether relative to the Earth.- If the luminiferous ether were fixed to the Earth, the speed of light at the Earth’s surface would be the same in all directions, just as the speed of sound inside an aeroplane is the same in all directions.

- If the luminiferous ether were stationary and the Earth moved through it, the speed of light would be affected by the speed of the Earth, as shown in the examples in Figures 1, 2, 3:

For the light rays LO travelling in the opposite direction to the movement of the Earth TO, the speed measured on the Earth would be equal to the sum of the speed of light and the speed of the Earth. In effect, one second before they meet the Earth at O the light rays would be 300,000km from O at L and the Earth would be 30km from O at T. The distance L-T would be reduced to 0 in one second, hence the speed of 300,030km per second.

For the light rays L’O’ travelling in the same direction as the movement of the Earth T’O’, the speed measured on the Earth would be equal to the difference between the speed of light and the speed of the Earth. Indeed one second before they meet the Earth at O’ the light rays would be at L at 300,000km from O’ and the Earth at T’ at 30km from O’. The distance L’-T’ would be reduced to 0 in one second, hence the speed of 299,970km per second.

For light rays L’’O’’ diagonal to the direction of the Earth’s movement T’’O’’, the effect of the speed of the Earth on the speed of light would be smaller. It would be equal to the projection of the speed of the Earth over the speed of the light rays: O’’P’’ instead of O’’T’’. It would depend on the angle α between the light rays and the Earth’s movement.

Michelson’s experiment consisted in obtaining interference fringes of light rays from a light source located in his laboratory, using conveniently positioned mirrors, then changing the direction of these rays. This change, which modified the relative length of the trajectories of the light rays, should have brought about a displacement of the interference fringes.

But the experiment failed: there was no displacement of the fringes. Michelson concluded that the speed of light was the same in all directions and that therefore the luminiferous ether was fixed to the Earth like the atmosphere through which sound travels.

Unfortunately, this explanation contradicted the prevailing opinion at the time that the Earth moved through a stationary ether. It was received with reservation and Michelson was led to repeat his experiment. In collaboration with Morley, he began again, this time taking into account the objections that had been raised, and together they confirmed the earlier results. Thus they upheld the conclusion of an ether fixed to the Earth.

Experiments using the same method were repeated throughout the 20th century with increasing degrees of precision, but the result was always the same: the orbital speed of the Earth could not be measured using light rays. It was as though the speed of light were unaffected by the speed of the Earth. If one maintained the common opinion of the time of a stationary ether, this led to a contradiction with the rule of addition of speeds.

The success of astrophysicists

It was another method, namely light spectrometry, that enabled astrophysicists to measure the speed of the Earth in orbit. Michelson and Morley had advocated it to invalidate (or confirm?) their experiment. Still in its early stages at that time, spectrometry made it possible to determine which elements stars were composed of through the characteristic arrangement of their spectral rays. But the movements of the stars displaced the spectra by the Doppler Effect and measurement of this displacement with the Fizeau method using spectral rays gave the radial speed of stars. Thus we learned that the stars were moving away from each other and it is thanks to spectrometry that today most extrasolar planets are discovered and the orbital speed of the Earth can be measured using light rays.

In 1952, Otto Struve set out to demonstrate the existence of extrasolar planets through the observation of stars, since direct observation of the planets was hampered by the dazzle of host stars, a thousand million times more luminous. He advocated searching for fluctuations in the radial speed of stars caused by the rotation of planets. This rotation generates a rotation of the host stars, just as the hammer thrown by an athlete generates through its rotation a rotation of the athlete. This movement is added to the distancing movement of the star. It is very small but its regular periodicity had to indicate the presence of planets. It was necessary to wait until the end of the 20th century for the progress in spectrometry that would make this observation possible.

In 1992, Alexandre Wolszczan discovered the first extrasolar planet using another method. It was orbiting around a pulsar. He demonstrated that the period of its pulses displayed very slight periodic variations, which proved the rotation of a planet.

In 1995, Mayor and Queloz proved the existence of a planet orbiting a “normal” star (one with a constant luminosity, that is), by using spectrometry to measure the radial speed of the star. They found that it displayed periodic variations which corresponded to the rotation of the star brought about by the rotation of a planet. Indeed the orbital speed of the star has a variable effect on its radial speed depending on its angle of projection α (figure 3)

Figure 4 represents the variation in the radial speed of the star during its orbital revolution.

Curve of the variation of radial speed of the star during an orbital revolution.
- HH’ corresponds to the period of one rotation of the star (and the planet).
- H ordinate of B and D corresponds to the average radial speed of the star.
- IH and HA correspond to the maximum effects of the orbital rotation of the star on its average radial speed.

Figure 5 shows the effect of the orbital speed of the star on its radial speed when the star’s orbit plane passes through the Earth. In B and D, the orbital speed is perpendicular to the radial speed and its effect on the radial speed is null. In C the orbital speed has the same direction as the radial speed: it is added to the average radial speed and corresponds to HI in Figure 4. In A the orbital speed has the opposite direction to the radial speed: it is subtracted from the average radial speed and corresponds to HA in Figure 4.

The orbital plane of the star passes through the Earth. Aa, Bb, Cc, Dd represent the orbital speed of the star. AA’, CC’, DD’ represent the axial speeds.
CC’ = DD’+ Cc; AA’ = DD’- Aa

When the orbital plane of the star does not pass through the Earth, the effect of the orbital speed is smaller. It depends in addition on the angle β between the radial speed and the orbit plane of the star (Figure 6).

The orbital plane of the star does not pass through the Earth. It makes an angle β with the axial speed. The projection of the orbital speed onto the radial speed is carried out in two stages: 1) through the projection Mm of the orbital speed MM’ onto xx’ which is the intersection of the orbital plane of the star and the perpendicular plane passing through the radial speed 2) through the projection Mm’ of Mm onto the radial speed, which depends on the angle β.

The radial speeds of stars often display variations of a period of one year. They are therefore synchronous with the orbital movement of the Earth. They translate the effect of the orbital speed of the Earth (and not of the star) on the axial speed of the star. The closer the star is to the ecliptic plane, the greater these variations are. The highest values of variation when the star is in the ecliptic plane correspond to the orbital speed of the Earth (Figure 7).

Star in the orbital plane of the Earth. Aa, Bb, Cc, Dd correspond to the orbital speed of the Earth.
GH is the radial speed of the star when the star is in B or D and the orbital speed of the Earth is perpendicular to the radial speed and has no effect on it.
EF is the radial speed of the star when the star is in A and the orbital speed is in the opposite direction to the radial speed and is subtracted from it. EF = GH – Aa. IJ is the radial speed of the star when the star is in C and the orbital speed is in the same direction as the radial speed and is added to it. IJ = GH + Cc

This is what was demonstrated by I.A. Bonnel (1), who set his students the task of “determining the speed of the Earth in its orbit by means of a series of observations of Aldebaran (a Tau), a bright star near the ecliptic plan” as part of their practical work designed to familiarize them with celestial mechanics. The students had to measure the spectral shift of this star for several months over a-one year period and, based on the different values obtained, construct a curve comparable to the one in Figure 4 in which the values HI or HA corresponded to the orbital speed of the Earth.

I.A. Bonnel pointed out that these measurements provided a good approximation of this speed and that within the framework of this practical work it was possible to omit corrections due to:

- the rotation of the Earth on itself,

- the variations in the orbital speed of the Earth according to Kepler’s second law, and

- the position of Aldebaran, slightly outside the ecliptic plane.

Thus, through applying the rule of addition of speeds to light rays, and thanks to the precision of current measurements, the method of radial speeds has made it possible to discover most of the extrasolar planets known today and to measure the orbital speed of the Earth, something Michelson was not able to achieve.

This success supports Michelson’s hypothesis of an ether fixed to the Earth

Measurement of the speed of the Earth using light rays calls into question the Michelson experiment. But rather than its experimental results, which have been confirmed throughout the 20th century, it is their interpretation that must be reconsidered.

In the 19th century Fresnel’s hypothesis of a stationary ether was preferred over Michelson’s conclusion of an ether fixed to the Earth. Now a rereading of the original texts shows that Fresnel’s demonstration contains an assertion that leads to a contradiction (2).

This error undermines the credibility of the stationary ether hypothesis.

It is the origin of the difficulties experienced by Fizeau (2) and Michelson (2).

On the other hand, Michelson’s hypothesis of an ether fixed to the Earth not only explains (2) the results obtained by Michelson and Morley without contradicting the rule of addition of speeds, but also those obtained by astrophysicists like I.A. Bonnel without contradicting those of Michelson and Morley :

- In the Michelson and Morley experiment, the light rays remain confined to their laboratory. The Earth and the neighbouring ether form a whole in which everything takes place as though the Earth were stationary. The rule of addition of speeds need not be applied.

- In the measurements made by astrophysicists, light rays travel through intersidereal spaces where the ether is stationary and the rule of addition of speeds must be applied when the Earth moves.