. (42)10. On Fizeau's experiment and its interpretation
In 1851 a French physicist H. Fizeau published the work "On hypotheses regarding the light ether and on one experiment which is likely to prove that a motion of bodies changes the light velocity inside these bodies" [10]. Using the extracts from this work we shall find the interpretation of this experiment results on the basis of the suggested theory.
At that time there were three hypotheses on interrelation between the light ether and ponderable matter.
1. The ether is rigidly bound with the body molecules and hence participates in the motions that can be given to the body.
Fizeau writes that the third hypothesis was suggested by Fresnel in order to satisfy the phenomenon of aberration and famous Arago's experiment. Arago has proved that the motion of the Earth does not influence the refraction of the star light as the light passes through a prism.
Fizeau designed a device of two glass tubes of L = 1.487 m length and diameter 5.3 mm. The tubes were filled with water. Parallel beams of light were sent into the tubes through faces. One beam passed through both tubes towards the water flow, the second beam passed through both tubes in the flow direction. After the tubes both beams were sent to one and the same glass plate by means of mirrors. On the plate one could observe a shift of the interference bands from the light beams that had passed through the water in the parallel tubes. Then the water in the parallel tubes was set in the opposite motion with the V = 7.069 m/s velocity. The index of refraction for water was n=1.333 and the wave length in the light beam was λ
= 526∙10-9 m.The band shift caused by the water, that was initially at rest and then set to motion, was called an ordinary one by Fizeau. The shift caused by the water, that reversed its direction, was called a double shift by him. Nineteen well-agreed observations resulted in the shift equal to 0.23 of the interference band for the unidirectional water flow and 0.46 for the double one when the flows reverse their direction.
Then Fizeau performed an experiment with moving air. The air was pumped through tubes at 25 m/s. As the air was pumped, no virtual shift of the interference bands was registered.
Let us set up the calculated equation that would meet the hypothesis of fully carried-away ether. Fizeau used this equation when analysing the results of his experiments. Let us define the refraction index of the body, n = С/СT, where C is the light velocity in the free space, CT is the light velocity in a physical body. According to this, for the conditions of Fizeau's experiment, the passage time t1 for the bundle of rays first through one tube of L length and then through the other of the same length in the water flow direction with V velocity will be:
. (42)
For the light beam moving along both tubes in the opposite direction in relation to the flow
. (43)
The difference Δt = t2 - t1 will be:
. (44)
The last mentioned formula fully coincides with the formula presented by U.I. Frakfurt [70].
In relative wave lengths of the registered light, the difference Δ
G, deduced from formula (44) will be
. (45)
Substituting all numerical values L = 1.487 m, C = 2.9979× 108 m/s, V = 7.069 m/s, λ = 526∙10-9 m, n = 1.333 in formula (45) we obtain ΔF = 0.473.
For the experiment with air pumping (n = 1.000292) through the same tubes (L = 1.487 m, C = 2.9979× 108 m/s, λ = 526∙10-9 m) with V = 25 m/s, formula (45) allows obtaining ΔA = 0.942. As mentioned above, when pumping the air, no shift of the interference bands was observed. Thus, formula (45) yields the value that does not comply with the result of Fizeau's experiment.
According to Fresnel's theory (see point 2), the absolute light velocity in a moving body is
U = с1
+ [(m 2 - 1)/ (m 2)]w ,or in the above accepted notation:
U = C/n + [(1-1/n2)V. (46)
A relative shift of the wave length calculated by Fresnel's formula will be
(47)
In numerical expression, after substitution of the data for the liquid moving in Fizeau's experiment (L = 1.487 m, C = 2.9979× 108 m/s, V = 7.069 m/s, λ = 526∙10-9 m, n = 1.333) D R = 0.207. For air calculations by formula (45) allow obtaining D R = 5.51× 10-4.
In 1851 I. Fizeau performed such calculations and concluded that the experiment results comply with Fresnel's theory. A partial drag of the ether is executed by the physical matter that causes an additional part of the refraction index to the unity.
Fresnel's theory suggests "thickening", increasing the density of the ether medium in physical bodies. But after L.B. Boldyreva and N.B. Sotina [71], the development of Fresnel's formula can be carried out on the assumption of photons dynamic interaction with the atoms of a physical body. In this case the light movement in the matter slows down without the ether "thickening" in it. Below we present an outline of Fresnel's formula development from [71].
First they consider the case with a transparent medium being at rest in relation to the observer connected with the earth. The time to = L/C is designated as the duration of the light pass of the distance L in the vacuum (in the same frame of reference but out of the medium). The duration of the light pass of the same distance inside the transparent medium is defined as:
to + DT = l/c1 , (48)
where C1 is the average velocity of light in the transparent medium at rest, C1 = C/n, and D T is the total time of the photon delay at the L length due to the interaction of the photon with the atoms (molecules) of the matter.
Another case was considered with a transparent medium moving with the V velocity relative to the earth (the motion of the medium from the source corresponds to the positive V value). In the system related to the moving medium the photon velocity is equal to C-V, and the duration of the photon pass over the length L in the vacuum
T'o = L/(C - V) . (49)
The duration of the light pass over the same distance will be:
T'о + DT = l/c* , (50)
where C* - is the average light velocity in the system related to the moving medium.
It is known from the experiments that the refraction index depends only slightly on frequency. From the viewpoint of the proposed model it means that the mean duration of the light delay at the length unit D T/L to a first approximation by b = V/C may be considered to be independent of the source relative velocity. With this assumption from formulae (48)-(50) we obtain:
l/c* = L/(C - V) + L/C1 - L/C . (51)
Hence in [71] for the light velocity U in relation to the immovable observer, after all the necessary substitutions and expansion the result into a series we obtain:
U = C* + V = C1C(C - V)/(C1V +C(C - V) + V) =
= (C1C2 - C1CV +C1V2 +C2V - V2C)/(C1V + C(C - V)) »
» C/n +(1 - 1/n2)V. (52)
According to the authors of this conclusion, Fresnel's formula describing Fizeau's experiment can be obtained within the model of the three-dimensional Euclidean space and independent time as a result of interaction of photons with the medium atoms.
This explanation is most logic among others including the one suggested by Fresnel. The concept of the ether "thickening" inside material bodies cannot be accepted with the understanding that the ether existence is denied by the special theory of relativity. We think that the ether medium providing a basis for the light propagation is displaced near atomic nuclei in physical bodies (Fig. 12). Deceleration of the light velocity in physical bodies occurs due to the effect of bending around the areas near the atomic nuclei. We believe that the light in a physical body propagates in the ether medium with the velocity equal to that in the free space C. But the distance of electromagnetic waves transmission in a body is greater than the length of this body due to the processes of bending around the areas where the ether medium is displaced by nuclear forces. Elongation of this distance is proportional to the refraction factor of the body.
Thus, the real light velocity as the ratio of duration of the wave pass to the body length, is equal to some value СТ = L/t = C/n, that is less than C. Recall that as follows from the light refraction formulae, no jump in the ether density occurs on the boundary of a transparent body (see Sect. 3), only the "apparent" light velocity changes. This "apparent" velocity is a result of elongation of the photon distance in a physical body. Every photon of the visible light diffracts on an obstacle that is, for instance, an electron or atomic nucleus, since the wave length of the visible light is much greater than the size of such an obstacle. If the wave length approaches the nucleus size, the phenomenon of beam diffusion and reflection is observed. These phenomena are used during X-ray diffraction analysis of substances.
The acoustic signal velocity decelerates in the medium saturated with inclusions which size is much less than the length of propagating waves. This phenomenon is well known in acoustics [72]. The carrier of the light electromagnetic oscillations in physical bodies is all-penetrating ether. In physical bodies the refraction factor can, to some extent, vary due to manifestation of the effects of photon re-emission, recombination and luminescence.
Thus, Fizeau's experiment is not evidence of the ether partial entrainment by a physical body. This experiment should be explained by the fact that the light velocity is less decelerated (or accelerated) in a moving body than in a body at rest. In this case the ether medium remains immobile.
Massive physical bodies that greatly deform the ether medium supposedly "fasten" the shell from the ether medium in their environment. A recent discovery of the dark mass filling the universe [73] provides a basis for the conclusion that the Earth as a massive body has its own "atmosphere" of the ether medium that is entrained in the movement together with our planet. It is believed that the influence of this "atmosphere" supposedly extends to the Lagrange point, where the gravitation fields' influence of the Earth and the Moon is divided.
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