The Fizeau and Sagnac experience from quantum positions

The experiments of Fizeau and Sagnac will soon be 200 years old, and their exact meaning is still incomprehensible. The scheme of the Fizeau experiment is shown in Fig. 10.

1 - light source, 2 - translucent mirror, 3 4 5 - ordinary mirrors, 6 - interferometer, 7, 9 - pipe sections, 8 - water, V - water velocity .

The essence of experience is as follows. The beam from the light source is split by a semitransparent mirror 2 into two beams. One beam (solid line) is reflected from the mirror 3, passes through the water in the section of the pipe 7, is reflected from the mirrors 5, 4, passes through the section of the pipe 9, the translucent mirror 2 and hits the interferometer 6. The second ray reflected from the mirror 2 (dashed line) passes through the water in the pipe at section 9, is reflected from the mirrors 4 and 5, passes through the water column 7, is reflected from the mirrors 3 and 2, and then hits the interferometer. Two beams on the interferometer create a corresponding interference pattern.

First, the interference pattern is recorded with still water. Then the water is given speed v . The interference pattern is a uniform alternation of dark and light stripes. As a result of the experiment, it turned out that the distances between the dark stripes and the light ones with stationary water are one, and with moving water others. This is possible in the case when the time of arrival of the beams at the interferometer will be different. On mirror 2, the outgoing rays have one phase, and on mirror 5 one ray turned out to be shifted relative to the other, that is, the speed of light moving behind the flow of water and against the flow of water is not the same. It turned out as if it were a stream of water, capturing photons and increasing or decreasing their speed.

According to the classical theory, the propagation of light in a certain medium was assumed in the form of re-emission of photons between atoms. Each act of re-radiation requires a certain time, and the light, instead of moving, carried out the re-radiation procedure. In each substance on the path of movement of light, there are a different number of atoms, which leads to a different time delay in the speed of light. This delay is called the refractive index of the medium n . The speed of light in such a medium is represented by the expression v=c/n , where c is the speed of light in vacuum. Which is true and consistent with Huygens' hypothesis.

Classical physics suggested that if water moves against the flow of light, then each photon will meet a larger number of water molecules than in the case when the water is stationary, and as a result, the speed of light will be less than in stationary water. If light moves in the direction of movement of water, then on the contrary, it spreads faster than in still water. With the speed of water equal to the speed of light, the photon would fly after the molecule, and would not be able to catch up it.

But such an explanation for the delay is questionable. And this is a doubt of this kind. Let's imagine that we are emitting only one photon in each beam. We place in the section а , only one water molecule in each section of the pipe, which the photons cannot pass, that is, both photons will surely meet the molecules. Let's assume that at first the molecule is motionless, in this case we get some kind of interference picture. Each photon lingered on its molecule for the same amount of time. And now let's give the molecules a speed V , so that the full cycle of interaction of photons with molecules ends without going beyond the tube, for example, in sections b and c .

In both cases, the photon interacted with only one molecule. Question: will the pictures be the same or different in both cases? It is impossible to answer this question, within the limits of Fizeau's experiments, and it is impossible to stage such an experiment. If the experiment was successful, and we got the same pictures in both cases, then the classical theory, the number of repeaters, would be correct. The Sagnac experiment in Figure 11 answers this question.

The beam of light from the generator is divided by a translucent mirror 4 into two beams. One beam (solid line) passes through semitransparent mirror 4, being reflected from mirrors 1, 2, 3, arrives at mirror 4, passes it and hits interferometer 5. The second ray (dashed line), reflected from mirrors 4, 3, 2, 1 and 4 again, arrives at the interferometer. Mirrors 1, 2, 3 can be rotated as shown by the arrow.

With stationary mirrors, we have some kind of interference picture. Then we set the mirrors in motion. Experience shows that interference fringes spread, which indicates a delay of one beam relative to the second. Almost the same as in Fizeau's experiment with one exception. Each photon on each movable mirror interacts everything and always, if there is no scattering, with one atom of the mirror. Each photon on its way will meet only three atoms, regardless of whether the mirrors are moving or not. At the same time, the interference patterns of the moving and stationary states of the system are different. We would see the same different pictures in Fizeau's experiment with one atom.

Thus, we see that the classical model of light delay is not entirely correct. It takes into account the speed delay due to the change in the number of atoms encountered in the path of light propagation, but does not take into account the addition of the speed delay from the very speed of the atom. And what to do in this case? Attempts are being made to rely on Lorentz's theory (Wikipedia):

“According to the electron theory of Lorentz, the effect of light entrainment by a moving medium is due to the following: the medium's dipoles induced by a passing wave produce secondary radiation, which is dragged along with the dipoles when the medium moves” .

He is "carried away" again. Moreover, it is not the original light that is carried away, but the induced light and the dipoles captured by the medium, in this case by water. I wonder what these dipoles are? Special water molecules? Or are they all water molecules? Not entirely clear.

R. Feynman tried to clarify the matter (Refractive index. Chapter 31. How the refractive index arises):

“Now let's try to understand how a decrease in the speed of light occurs. In particular, it is especially important to trace the connection of this fact with some physical assumptions or laws that were previously expressed and boil down to the following:
a) the total electric field under any physical conditions can be represented as the sum of fields from all charges in the Universe;
b) the radiation field of each individual charge is determined by its acceleration; acceleration is taken taking into account the delay arising from the final propagation velocity, always equal to с

Further it is warned that this delay is not the delay that is responsible for the speed of light in the medium c/n . And now it is proposed to connect the decrease in the speed of light with the physical law of retardation, which is not responsible for the speed of light in the medium. A little further it says:

“Our task is to understand how the apparent lower speed arises” .

Interesting: is the speed still less objectively or so it just seems? Then came such formulas that it’s scary to read. Probably few people understand them.

Wikipedia advises everyone who does not understand:

“For a consistent description of the Fizeau experiment, a special theory of relativity is needed” .

And the special theory of relativity says that the faster the inertial system moves, the slower flows time . Why a moving atom holds a photon longer than a stationary one nobody knows, and even hypotheses on this phenomenon are neither good nor bad. To understand this, you need to know the structure electron and photon .

It is not known how the delay in the time of “entrainment” of a photon by an atom can be explained from the standpoint of the theory of relativity, proceeding from the structure of a frequency-dependent quantum model ( E = hv ), but if we proceed from the photon model proposed by us, then we can represent the model of the interaction of a photon and an electron in this form.

According to our assumption, with an increase in the speed of an electron, a part of its charge is lost. And since the density of intensity is not linearly distributed along the radius of the electron, it increases towards the center of the electron, then the intensity increases per unit area around the electron. And if we assume that photons are packed in an electron in the form of layers, then we can assume that the higher the electron's speed, the more efforts a photon needs to exert in order to penetrate inside the electron. For the proposed model, this looks like an elastic collision. An elementary photon is a chain of vortices. If the field of the electron is dense, the first vortex cannot overcome this potential, and it waits for the approach of the next corresponding vortex of another quantum, then the vortex of the next quantum, etc. And so on until the required potential is formed. Only after this will the actions in the electron begin, such as occur in a motionless electron.

According to this amount of delay, the refractive index changes. After the photon is absorbed and it turns out that there is a place for it in this electron, it is suitable for it, it will be accepted into the body of the electron. Resonant absorption will occur, the electron's velocity will change, and the photon will exit the experiment. If the photon is not resonant for a given state of the electron, the electron will emit it. It is possible that the radiation mode will also be delayed. Nature loves symmetry. In this case, the status of the electron will not change in any way, and the photon will be “carried away” by the electron for some time (the time of absorption and emission).

It would seem that the model of photon delay due to absorption and radiation also does not stand up to criticism, because we can say that this happens with both beams, and they should be delayed in the same way. But they are delayed in different ways. This can be explained by the electron spin. It is known that in a magnetic field all magnets are oriented in the same way, and each of the rays interacts with electrons in the same way. But one of the rays interacts with the incoming electrons, and the other with the outgoing ones, as shown in Fig. 11a.

This difference in interaction leads to different times of interaction of photons with electrons. After the interaction, the speed of the photons naturally remained the same.

The propagation delay of light, depicted in Figure 11a, represents the classic view of this process, and it seems to exist, but the quantum view of this process is more interesting. Let us change the Fizeau experiment so that the water in the pipes moves not in the direction of propagation of light, but transversely to the movement of light (Fig. 11b).

Will the interference pattern change in this experiment when the water flow rate changes? It is not known exactly, because the author did not find a description of such an experience. It is very likely that such an experiment was not carried out by anyone. If a system with a transverse motion of water behaves in the same way as with a longitudinal motion of water, then this phenomenon cannot be explained from the standpoint of classical physics. The water velocity vector does not play a role in the change in the speed of light, in contrast to the modulus of the water velocity. And this means only one thing, the speed V changes the absolute speed of the electron in the atom so that it increases or decreases the rate of absorption and emission of photons. In whatever direction the light passes through the water moving with the speed V , it will be delayed by the same amount. This is possibly the isotropy of space.

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