When you are interested in physics you must read “Unbelievable“!
The physical aspects of the ether, when required, will be dealt with later in this document. The characteristics dragged ether needs to possess, to explain the stellar aberration, are exactly that of the known vacuum: light moves in a vacuum in all directions with the same speed c and the impulse of photons cannot be altered by vacuum.
Speed, direction and mass determine the impulse of an object.
The mass M, speed V and the direction determine the impulse I. In comparison: a snooker ball will only change direction and/or speed when it encounters the side or other balls. Photons have an impulse If in the direction of movement equal to the energy of the photon divided by the speed of light c.
Where If is the impulse of the photon with frequency v, h is the constant of Planck and c is the speed of light.
Assume a photon coming from the star y-Draconis towards Earth. With dragged ether, a gradual transition can be expected. When the distance to the star y-Draconis increases the influence of the star on the ether will decrease while the influence of the Earth will increase. The influence of the earth on the ether is larger when the ether is closer to the earth. Light coming from y-Draconis will therefore be in transition from ether under the influence of y-Draconis to ether under influence of the earth. A gradual transition from ether under influence of y-Draconis to ether under influence of the earth can be expected.
The physical characteristics of the ether around the star y-Draconis are the same as those of the ether around the earth. The difference is limited to a relative movement of both ethers towards or from each other; comparable with moderate air flows in the atmosphere or ocean currents that gradually merge. For the observed stellar aberration it is of no importance over what distance the transition takes place. The effect will be the same regardless whether or not the transition is sudden.
Figure 2 shows the situation in which a photon suddenly enters the ether under influence of the earth, coming from the ether under influence of the star when the movement of the earth towards the star is maximal. The direction of the photon from y-Draconis has an elevation of 75 degrees with the ellipse of the earth orbit. This angle is virtually constant because the distance to the star y-Draconis is infinitely larger than the distance from the earth to the sun (no parallax). The change of the real angle caused by the orbit of the earth around the Sun, the parallax, is infinitely smaller than the stellar aberration. The parallax, the real change of the angle, is infinite small and independent on the stellar aberration caused by the movement of the earth around the sun.
The impulse of the photon, direction and magnitude is determined in ether I (figure 2). Passage from ether I to ether II brings the photon in ether with exactly the same characteristics. The only difference is that ether II moves in comparison to ether I with a speed of 30 km/second the speed of the Earth around the Sun.
The photon must adjust in ether II to the new situation. If the photon followed the same line, there would be no stellar aberration and the direction and impulse of the photon would be altered and that is not possible with the characteristics of vacuum.
Figure 2. The stellar aberration of a photon in transition from ether I to ether II.
The photon has to have a change in angle when it enters ether II, to maintain the same direction/impulse compared to the direction of the photon in ether I. If there is no aberration β then the photon will move in the same line in ether II. And because ether II is moving compared to ether I with 30 km/s, the photon would be dragged to the right from its original path 30 km each second. The direction and impulse of the photon will then be changed.
This is impossible because vacuum, the ether, has no characteristics to achieve a change in impulse. To comprehend this perception one must understand that an observer in ether II is by definition at rest with the dragged ether II and therefore also moving with 30 km/s in comparison to ether I.
The impulse of a photon in a certain direction can be determined by splitting up the impulse and speed. The speed or impulse of the photon is analyzed in two directions: vertical and parallel to the movement of the earth towards or from the star. The impulse of the photon vertical to the movement of ether II (Y-direction) is unchanged. There is no difference in speed of the two ethers in that direction. For the determination of the impulse and speed of the photon in ether II in the direction of the movement of the earth towards the star y-Draconis, the speed of the earth around the sun has to be added (X-direction in figure 2).
The speed of ether II, compared to ether I in the X-direction is responsible for the apparent change in direction: the stellar aberration. By adding the speed in the X-direction at the moment the photon enters the ether under influence of the earth, the impulse of the photon towards the observer on the earth is kept the same whether the photon is traveling in ether I or ether II. By adding the speed of the earth towards the star in the X-direction when the photon enters ether II we keep the same impulse for the observer, whether the photon is in ether I or ether II.
By adding 30 km/s in the X-direction we however change the speed of the photon. The total speed of the photon, the vector sum of the speed of the photon in both directions, changes when we add 30 km/s in the X-direction. Experience tells us that the measured speed of light in vacuum (ether) never exceeds c.
The transition of the photon entering ether II from ether I, as it is described above, can therefore not be complete. The speed of the photon now exceeds the speed of light. The speed of light has to be adjusted because the observed speed in vacuum is always c.
The correction is achieved by reducing the speed of the photon, after adding 30 km/sec in the X-direction, to c. In figure 2 this is achieved by reducing the vector sum of the speed in X- and Y-direction to the circle with radius c. When we do this we change the impulse of the photon in both directions (X and Y). By looking at the formula of the impulse I of a photon we have only one variable by which we can change the impulse, and that is the frequency v; h and c are natural constants and therefore by definition determined. The impulse of a photon I is:
When we reduce the speed of the photon, after adding 30 km/sec in the X-direction, to c and at the same time increase the frequency v with the same factor the impulse and direction of the photon for the observer in ether II will be the same whether the photon is traveling in ether I or ether II. The increase or decrease of the frequency of the photon when the earth is moving towards and from y-Draconis is called the Doppler effect. In figure 2 we have drawn the situation where the Earth is moving with 30 km/s towards the right-angled projection of y-Draconis on the orbit plane. Imagine that the speed towards the projection of y-Draconis declines from 30 km/s to 0 and after that the speed decreases further to -30 km/s in the opposite direction. The aberration ß will also decline to 0 and further to -ß when the speed is completely reversed.
Figure 3. The theoretical stellar aberration of the inclination of y-Draconis.
The alteration of the elevation angle θ, the aberration of the star y-Draconis measured by Bradley, with dragged ether is theoretically according to figure 3 during the year. The theoretically calculated stellar aberration matches the measured aberration by Bradley perfectly. The chart of figure 3 shows the theoretical changes (ß) of the elevation of the star during the year. Bradley only measured the elevation of the star y-Draconis during the year. The azimuth part of the aberration was initially not recorded by Bradley.
The derived formulas for the stellar aberration are of general use. The stellar aberration of a star is dependent on the elevation (θ) of the star with the orbit of the earth. In figure 4 the maximum aberration of the elevation (θ) of any star is given as a function of the inclination. At 90 degrees the star is vertically positioned to the orbit of the earth around the sun.
Figure 4. The maximum stellar aberration of the inclination of a star as a function of inclination.
When we include the stellar aberration in the orbit plane (the azimuth part) we are able to calculate the exact stellar aberration of any star any time during the year.
Next chapter: The apparent change of angle in a force-free ether