14. A NEW EXPLANATION OF FIZEAU'S TEST RESULT
 
   As is well known light moves at a lower velocity through transparent bodies than through vacuum. The velocity of light decreases in inverse proportion to the index of refraction, and is expressed in the following way

(14.1)

   The question is: "Why does light propagate more slowly through a material environment than through a vacuum?" The following may be an answer to this question.
   During motion through a transparent substance photons are absorbed by that substance (atom or molecule), to be emitted later on, after a very short time, and after some time they are absorbed again, and so ceaselessly, until they leave the environment. The emission of a photon is stimulated by another photon, which comes across an excited atom or molecule. In this way the direction of motion of the emitted photon and the photon which stimulates this emission is the same. Because of this the direction of radiation through transparent substances does not change. This phenomena is well known in the case of lasers as a stimulated emission of radiation.
   The total period of time the photon spends in the states of absorption is proportional to the index of refraction of the body. The total period of time the photon takes to pass through the transparent body is the sum of the time of the photon motion through that body at a velocity which is equal to the velocity of light in vacuum and the time of the photon's detention in a state of absorption. From there we have

(14.2)

where is the total period of time that the photon needs to pass through the transparent body, is the time that the photon needs to pass through the body at the velocity of light in vacuum, is the total period of photon detention in a state of absorption and is the length of the photon's path through that body.
   Using Eqs. (14.1) and (14.2) we obtain

(14.3)

(14.4)

   What happens to the velocity of  light in a transparent body when it is in motion? In order to give an answer it is necessary to analyze the process of the photon's motion through a moving body.
   Fig. 14.1 shows a photon's motion through water which moves at speed . For a greater part of the way, the photon passes as in a vacuum in the form of radiation and at a velocity which is equal to its velocity in vacuum. On the other considerably shorter part of the way, the photon is carried in an absorbed state at speed , that is, at the speed of the water which carries it. As can be seen in Fig. 14.1, the photon is carried in the direction of the water's motion from position 1 (the position of photon absorption) to position 2 (the position of photon emission). This process is repeated until the photon leaves the pipe.

Fig. 14.1

   During the photon motion through the pipe containing water the layer of the water, whose thickness , flows out in a lateral direction, and the photon does not succeed in reaching and passing trough it, so the shortening of the path on which the process of absorption and emission will not happen is given by equation

(14.5)

   For the same reason there is a shortening of the absorption time . This shortening of the absorption time is proportional to the thickness of the out flowing water layer , like the total absorption time is proportional to the total length of the water column, that is, the pipe length containing water through which light rays pass, so we have

(14.6)

From Eqs. (14.3), (14.4), (14.5) and (14.6) we have

(14.7)

and

(14.8)

From Eqs. (14.1), (14.3), (14.5), (14.6) and (14.7) it follows that

(14.9)

   During the free motion through the water the photons (from emission - the position 2 in Fig. 14.1, to repeated absorption - the position 1 in Fig. 14.1) do not pass the way they passed in the absorbed state. Because of this, the time shortening of the free passing in a form of radiation is proportional to the way , into which the photons have been carried in an absorbed state. This means that it is proportional to the total period of time that the photons spend in an absorbed state and to the speed at which they are carried - the water speed. So from Eqs. (14.4) and (14.8) we have

(14.10)

   The total shortening of time that the photon takes to pass through the water, which moves in the direction of the photon motion, on the way length is

(14.11)

   Fig. 14.2 shows the motion of a photon through water flowing in the opposite direction to the motion of the photon.

Fig. 14.2

   We can see that, in this case, the time is increased for , in which the photon is in an absorbed state, due to the arrival of a new water layer during the time the photon passes through the pipe containing water. Also the time of the photon's free passage through the water in the form of radiation is increased for . This appears due to an increase in the length of the photon's path through the water, because of its return, in an absorbed state, in the direction of the water's motion. Because of this, the photon must once again travel this additional distance, which has already been passed.
   So, the time taken by a photon, to pass downstream, through the pipe with water, is shortened and the time needed to pass upstream is increased.
   The increasing of times passing , and are calculated in a similar way to the shortening of times , and , in the previous case. At that it is taken

In this way we get

(14.12)

and

(14.13)

and from there

(14.14)

   Using Eqs. (14.11) and (14.14) we find that the ray, which propagates downstream, reaches the interference shift measurer before the ray which moves up stream for the time

(14.15)

Considering that we can write

(14.16)

This time difference corresponds to the shift of the ray relative to the ray which is measured by the interferometer

(14.17)

   From this it results that the speed of light in water, which is moving in the same direction as that of the light is defined by the equation

(14.18)

and the speed of light travelling in the opposite direction to the water flow is defined by the equation

(14.19)

   So, according to the given postulate Eq. (14.17) has been derived in order to calculate the interference shift. Fizeau's test completely confirmed the correctness of that shift calculation by using Eq. (14.17). This is the confirmation of the correctness of the previously given hypothesis that light propagates more slowly in a transparent body than in a vacuum, because of the time which the photons spend in the state of absorption on their way through that body, when their motion in the form of radiation is stopped.
   The new hypothesis about light propagation through moving transparent bodies and this calculation which proves the correctness of that hypothesis, exclude any connection of the ether with the speed of light in moving transparent bodies, as Fizeau, Fresnel and Hertz asserted.
   In estimating the reliability of the given hypothesis we should bear the following in mind. The law on the conservation of momentum is not satisfied when considering the transition of a photon from air ( = 1) to water ( = 4 / 3) and vice versa

(14.20)