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At present time it is a matter of common knowledge   (for example, see [[20]. Frankfurt U. I., Frenk A. M. Optics of moving bodies. Мoscow: Nauka, 1972. pp. 113 - 124., [ [26]. Goldenblat I. I., Uljanov S. V. Introduction into relativity theory and its applications to new engineering. Moscow: Nauka, 1979. p. 17.]), that the law of independence of light speed upon light source speed (Einstein's second postulate) is reliably prooved by experiments, which are listed, for example, in papers:
 [18]. Molchanov A. G. Experimental checking of special relativity theory postulates // Achievements of physical sciences.-1964.-v. 83.- issue 4.  pp. 753 - 755.
[19]. Frenk A. M. Some problems of experimental basics of relativity theory// Frankfurt U. I. Special and general theory of relativity.  Мoscow: Nauka, 1968. p. 250.
[20]. Frankfurt U. I., Frenk A. M. Optics of moving bodies. Мoscow: Nauka, 1972. pp. 113 - 124.
[21]. Mandelshtam L. I.   Lectures on optics, theory of relativity and quantum mechanics.  Мoscow: Nauka, 1972. p. 161.
[22]. Goldenblat I. I. Time paradoxes in relativistic mechanics.  Мoscow: Nauka, 1972. p. 66.
[23]. Satsunkevich I. S. Current experimental confirmation of the special theory of relativity.  Мinsk: Vishejshaja shkola, 1979. p. 8.
[27]. Strakhovsky G. M., Uspensky A. V. Experimental checkout of relativity theory// Achievements of physical sciences. 1965. v. 86. p. 421 - 432.
[28]. Baranov A. G. About some experiments on testing the postulates of special relativity theory // Einstein's collection. 1966,  Moscow: Nauka, 1966. pp. 284 - 297.
[29]. Anisovich K. V. To experimental basics of the special relativity theory// Einstein's collection. 1973,   Moscow: Nauka, 1974. pp. 360 - 395.
[30]. Frankfurt U. I. Optics of moving media and special relativity theory// Einstein's collection. 1977. - Moscow: Nauka, 1980. - pp. 321 - 326.
[31]. Shmidt-Ott V. D. Some new measurements in connection with confirmation of rightness of the special relativity theory// Achievements of physical sciences. - 1968. - v.  96.  issue  3. - pp. 519 - 527].

Therefore it should seem that existence in nature of dependence of light speed in vacuum upon light source speed in the form

c_u = c_o (1 + u²/c_o²)^1/2    (4.1)

is not confirmed by experiments. But if we shall consider each of these experiments separately, we shall find that even a single of them does not contradict the existence in nature of square-law dependence (4.1), that they disprove only existence in nature of a dependence, which is a consequence from Newton's mechanics and has the form   c_u = c_o + u cos a, where a is an angle between direction of light propagation and direction of the light source velocity vector.

At that it is easily to prove that unability of dependence (4.1) to be disprooved  by the majority of experiments on checking the correctness of Einstein's second postulate is a consequence of two specific peculiarities of dependence (4.1) in comparison with dependence

The first peculiarity of formula (4.1) consists in its low sensitivity to small  values of source speed (with respect to value c_o). Indeed, even if  a source speed is equal to such tremendous for the Earth    value as 30 000 m/s, the speed of light emitted by such source is   according to formula (4.1) only 1.5 m/s greater than the speed of light from an immovable source. And taking into account that at present time the root-mean-square error of measuring value c_o is equal to 1.2 m/s  [ [24]. Sazhin M. V. Light speed// Space Physics. Small Encyclopedia. Мoscow: Soviet Encyclopedia, 1986. p. 622 (in Russian)], to detect the existence of dependence (4.1) in experiments on the Earth with comparatively small speeds of light sources is practically impossible.

The second peculiarity of formula (4.1) consists in its non-sensitivity to a direction of source motion. Indeed, the formula (4.1) does not comprise the angle between a direction of source motion and a direction of light propagation. Moreover, according to formula (4.1) the light speed does not depend upon the sign of source speed: the light speed from a moving source is always greater than the value c_o, both in case if a source is receding from a measuring instrument and in case if a source is nearing a measuring instrument. Because function (3.13) is an even increasing function of its argument - the speed of source motion.

Let us now show that namely these two peculiarities of dependence (4.1) are the main cause of the fact that up to the present time dependence (4.1) is not neither confirmed, nor disproved be experiments on direct test of Einstein's second postulate.

As far back as in 1914  de-Sitter [[32]. De-Sitter W. Ein astronomischer Beweis fur die Konstanz der Lichtgeschwindigkeit // Physikalisch Zeitschrift.-1913.-B.14.-S.429; S. 1267-1268.] has analysied the results of astronomcal observations of a binary star from the Auriga asterism with nearly circle orbit (with ellipticity of  0.005)   and average speed of 110 km/s and has proved, that dependence c_u = c_o + u cos a is disproved by these astronomical observations, and even if any dependence of light speed upon source speed exists in nature and has a form

where k is an unknown coefficient, then it follows from astronomical observations that k < 0,002. But if in dependence (4.1) we shall expand  the square root    and confine ourselves only to two first members of decomposition, then we shall have

c_u = c_o + (0.5 u/c_o)·u . (4.3)

This means that at small speeds of sources motion (as compared with the constant c_o = 299792458 m/s) the formula c_u = c_o (1 + u²/c_o²)^1/2 may be substituted by expression (4.2), in which

k = 0.5 u/c_o. (4.4)

Substituting into the formula (4.4) the average speed u = 110 km/s for motion of a binary star from the asterism of Auriga, we shall have k = 0.0002, i. e. ten times less than the value, which is admitted by astronomical observations of binary star analysed by de-Sitter.

Therefore, astronomical observations of binary stars analysed by de-Sitter do not contradict the existence in nature of the square-law dependence of light speed upon source speed of the form c_u = c_o (1 + u²/c_o²)^1/2.

Majorana's experiment [[33]. Majorana Q. Experimental demonstration of the constancy of velocity of light emitted by a moving source // Lincei Rendues. - 1918. - v.27. - p. 402 - 406; Physical Review. - 1918. v. 11 –p. 411 - 420; Philosophical Magazine. – 1919. – v. 37. p. 145 - 150.] was one of the first attempts to test the Einstein's second postulate rightness in a laboratory. This experiment showed the absence in nature of dependence c_u = c_o + u cos a using the shift of interference fringes in Mikelson's interferometer with unequal arms if immovable source of light  is replaced by a source moving at a speed of approximately 80 m/s. But, as Majorana himself have noticed, the result obtained in this experiment should not be considered as completely convincing proof of absence of light speed dependence upon light source speed. Because in this experiment he measured the speed of light, which penetrated through a beam splitter and which was reflected from the beam splitter,  and, as a result, the light can (because of its absorption and subsequent re-emission of light quanta by the beam splitter substance) be re-emitted at a speed equal to c_o  even if a certain dependence of light speed upon light source exists in nature.

The same demur can be made with respect to argumentativeness of some other experiments on direct test of Einstein's second postulate. Moreover, as it was shown by Fox [[34]. Fox J. Experimental evidence for the second postulate of special relativity // American Journal of Physics.-1962. v. 30. - p. 297 - 300; Evidence against emission theories // American Journal of Physics. - 1965. - v. 33. - p. 1 – 17; Constancy of the velocity of light // Journal of Optical Society of America. – 1967. - v. 57. - p. 967 - 968.], molecules of air also absorb light quanta with their subsequent re-emission, i. e. they are light retransmitters, and under ordinary air pressure   it is sufficient to have air layer of 1 mm thickness in order to  have the majority of photons moving at constant  speed of c_o. That is why in all experiments, in which across the light path from a moving source there were retransmitters (mirrors or beam splitters) or in which the light beam from a moving source propagated through some substance (for example, through air), it is impossible in principle  to detect any dependence of light speed upon light source speed.

Consequently, in order to obtain convincing experimental confirmations   of presence or absence in nature of some dependence of light speed upon light source speed, it is necessary, first of all, to exclude from the process of transmission of electromagnetic oscillation from a moving source to a measuring instrument the participation of molecules of any substance, which are immovable relatively to the meassuring instrument.   On this basis we may exclude from further consideration (even without specific mention) all those experiments, in which this requirement is not fufilled. Experiments, which meet this requirement, can be separated into two groups: experiments in vacuum and experiments with gamma-rays.

Among experiments in vacuum we can see:

- Experiment executed by Babccock and Bergman [[35]. Babcock G. C., Bergman T. G. Determination of the constancy of the speed of light // Journal of Optical Society of America. - 1964. - v. 54. No. 2. – p. 147 - 151.];

- Experiment execcuted by Beckman and Mandix [[36]. Beckmann P., Mandics P. Test of the constancy of the velocity of electromagnetic radiation in high vacuum // Radio Science Journal of R.N.B.S.. - 1965. -v. 69D.- No. 4.-p.623-628.].

Experiment of Babcock and Bergman [35]

In this experiment [ see [35]. Babcock G. C., Bergman T. G. Determination of the constancy of the speed of light // Journal of Optical Society of America. - 1964. - v. 54. No. 2. – p. 147 - 151.]  Kantor's experiment was repeated, which allegedly confirmed the existence  in nature of dependence c_u = c_o + u cos a. But unlike Kantor's experiment in the experiment [35]  all equipment was placed in vacuum and the light path length was increased. The speed of a light source in experiment [35] was equal to  50 m/s.

Having obtained interference fringes shift 240 times less, than the shift resulting from dependence c_u = c_o + u cos a, Babcock and Bergman made a conclusion, that dependence c_u = c_o + u cos a does not exist in nature, and that Kantor's exxperiment was erroneous.

But the possibility of exictence in nature of the dependence (4.1) Babcock and Bergman did not foresee. And the experiment [35] in principle does not permit to confirm or to disprove the existence in nature of dependence (4.1). It is conditioned by the fact, that in the experiment [35] they compared the speed of light beam emitted in the direction of  light source motion  with the speed of light beam emitted in the direction opposite to the direction  of light source motion. But in accordance with formula (4.1) the speeds of the both these beams should be equal. So, the experiment performed by Babcock and Bergman  [35] in principle can not either confirm or disprove the existence in nature of the square-law dependence of light speed upon light source speed  according to the formula c_u = c_o (1 + u²/c_o²)^1/2.

In this experiment [[36]. Beckmann P., Mandics P. Test of the constancy of the velocity of electromagnetic radiation in high vacuum // Radio Science Journal of R.N.B.S.. - 1965. -v. 69D.- No. 4.-p.623-628], which was also performed in vacuum, a flat mirror fastened to a gyroscope rotor was used as a moving source of light. In this experiment they photographed a fringe pattern, which was formed as a result of interference of a light beam reflected only from a moving mirror and a light beam reflected  in series from the moving mirror and from an immovable mirror (Lloyd's mirror). Arrangement of equipment  used in this experiment is shown in fig. 4.1. In order to facilitate measuring the small shift of fringes, which could appear if the dependence c_u = c_o + u cos a exists in nature, they photographed on one half-frame of a photographic plate an interference pattern formed during rotation of the gyroscope rotor in one direction and on the second half-frame of the same photographic plate (with small overlap of the first half-frame) they photographed  an  interference pattern formed during rotation of the gyroscope rotor in the opposite direction, but at the same rate of rotation. Distance between a moving mirror (fastened to the gyroscope rotor) and the photographic plate, on which the fringes patterns were formed, in this experiment was equal to 4.25 m. The rate of the gyroscope rotor rotation was increased to a value, at which linear speed of the mirror motion was equal to 50 m/s.

(1 - light source; 2 - mirror fastened to the gyroscope rotor, 3 - immovable mirror (Lloyd's mirror) , 4 - photographic plate)

Any fringes shift was not detected in this experiment, that was a convincing confirmation of absence in nature of the dependence c_u = c_o + u cos a.

Touching dependence (4.1), this experiment also does not either confirm or disprove it. It is conditioned by the fact that according to formula (4.1) the speed of light from a moving source does not change its value at reversing the direction of source motion.   In order to obtain convincing confirmation of existence or absence in nature of dependence (4.1) in this experiment it is necessary to photograh on the first half-plate the fringes pattern formed at rotation of gyroscope rotor with maximal possible speed, and on the seconf half-plate - at rotation of gyroscope with angular velocity sufficiently  (some hundred times) less than maximal velocity with simultaneous increasing the distance between moving mirror and photographic plate.

It is not difficult to show that convincing experimental confirmation of presence or absence in nature of dependence c_u = c_o (1 + u²/c_o²)^1/2 you can obtain in an interference experiment with moving mirror only under condition

L > 2 c_o² l D/u_m², (4. 5)

where L is the distance between a moving mirror and photographic plate; l is  wavelength of electromagnetic oscillations used for forming the fringes pattern;  u_m is maximally possible linear speed of  motion of the mirror fastened on the gyroscope rotor; D > 0.1  is  relative shift (in wavelengths) of fringes, at which this shift can be reliably measured.

For example, at u_m = 300 m/s, l = 0.3 micrometers and D = 0.1 from the formula (4.5) we shall have L > 60 km. But in the experiment [36] this distance was equal only to 4.25 m. Consequently, the experiment [36] also does not either confirm or disprove existence in nature of dependence c_u = c_o (1 + u²/c_o²)^1/2.

In other experiments with moving mirrors the distance, through which the light passed in vacuum, did not exceed 100 m, and mirror speed did not exceed 300 m/s. As a result, these experiments do not meet the requirement of condition (4.5) and do not have probative force with respect to square-law dependence c_u = c_o (1 + u²/c_o²)^1/2. The main reason is small value of source speed.