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-  [[38]. Sadeh D. Experimental evidence for the constancy of the velocity of gamma rays, using annihilation in flight // Physical Review Letters. – 1963 .-v. 10. - p. 271 - 273.];

-   [[39]. Fillipas T. A., Fox J. G. Velocity of gamma rays from a moving source // Physical Review. - 1964. - v. 135.-p. 1075];

-   [ [40]. Test of the second postulate of special relativity in the GeV region / Alvager T., Farley F., Kjellman J., Wallin J. // Physical Letters. - 1964. - v. 12. –No. 3. - p. 260 -262.].

Experiment with alpha particles by Alvager, Nilsson and Kjellman [37]

In the experiment  [ [37]. Alvager T., Nilsson A., Kjellrian J. On the independence of the velocity of light of the motion of the light source // Arkiv fur Fysik. - 1964.- B. 26.-No. 16. - S. 209-221; A direct terestrial test of the second postulate of special relativity // Nature. - 1963. -v. 197. -p.1191] targets made of carbon С¹² and oxygen О¹⁶ were bombarded by alpha particles with kinetic energy of 14 MeV accelerated in a cyclotron. In the result of such bombardment, excited nuclei  with a certain recoil speed appeared. Excited carbon nuclei radiate gamma quanta before they come to a standstill having a speed of  0.018 с_o measured using doppler shift of frequency. And oxygen nuclei radiate gamma quanta after they come to a standstill (doppler frequency shift was not detected). Radiated gamma quanta were received by two detectors. The first one was placed at a distance of 1 meter from the targets, and the second one was placed on the same line with the first detector at a distance of 5 m from the targets. The targets were placed at a distance of 30 cm one from other and it was possible to change their places quickly.

In this experiment the time moment of gamma quanta passage through the detectors were measured and after that  experimentators calculated the value

D = { [ (t₂^O16- t₁^O16) - (t₂^С12- t₁^С12) ] - [ (t₂^O16 - t₁^O16) - (t₂^С12- t₁^С12) ] }, (4.6)

where t₁, t₂ are measured moments of gamma quanta hitting into the first and into the second detectors, respectively, in a case when alpha particles fly at first through the oxygen target and then through the carbon target; t₁, t₂ are   measured moments of gamma quanta hitting into the first and into the second detectors, respectively, in a case when alpha particles  at first fly through the carbon target and then through the oxygen target, and the upper index shows which of nucleus the detected gamma quantum was radiated.

If you will determine the moments of gamma quanta hittings into detectors, then using known distance between the detectors and the supposed speeds of gamma quanta, instead of expression (4.6) you will have

D = 2 s (c_o^-1- c_u^-1), (4.7)

where s = 4 m is a distance between the detectors; c_o  is speed of gamma quanta radiated by immovable oxygen nuclei; c_u is speed of gamma quanta radiated by moving carbon nuclei.

Substituting expression (4.2) into formula (4.7) we have

D = 2 s k u c_o^-2, (4.8)

where u = 0.018 c_o is speed of motion of carbon nuclei;  k = 1 if dependence c_u = c_o + u·cosa exists in nature;   k is determined by expression (4.4) if dependence c_u = c_o·(1 + u²/c_o²)^1/2 exists in nature.

Substituting into expression (4.8) numerical values of magnitudes and k = 1, we shall have D_(4.1) = 0.5 10^-9 seconds, corresponding to existence in nature of dependence c_u = c_o + u cosa. Substituting into expression (4.8) numerical values of magnitudes and value k from expression (4.4), we shall have D_(2.1) = 0.5 10^-11 seconds corresponding existence in nature of dependence c_u = c_o(1 + u²/c_o²)^1/2.

The value D_exp calculated according to formula (4.6) and measured in the experiment [37] moments of gamma quanta hitting into detectors after statistical processing is equal to D_exp = (0.2 ± 0.2) 10^-9  seconds.

So, because of the result  D_exp < D_(4.1), experiment [37] prooves that dependence c_u = c_o + u cosa is absent in real nature.

But dependence c_u = c_o(1 + u²/c_o²)^1/2 is neither confirmed nor disproved by the experiment [37] too. It is conditioned by the fact that root-mean-square error of measuring the value D_exp,   which in this experiment is equal to 0.2 nanoseconds, is two orders (100 times) greater than the value D_(2.1) resulting from the dependence c_u = c_o(1 + u²/c_o²)^1/2.

Experiment  [37] has one more drawback - gamma quanta hitting into the second detector come through the substance of the first detector. Therefore one can suppose that gamma quanta coming to the second detector are not primary gamma quanta radiated in the targets, but secondary gamma quanta re-radiated  by the substance of the first detector. If this effect exist in reality, then experiment [37] has no probative force with respect to dependence c_u = c_o + u cosa too.

Experiment with positrons by Sudeh [38]

            In the experiment [[38]. Sadeh D. Experimental evidence for the constancy of the velocity of gamma rays, using annihilation in flight // Physical Review Letters. – 1963 .-v. 10. - p. 271 - 273.] a beam of positrons was directed to a target of 1 mm thickness made of acrylic plastic. In this target the annihilation of positrons with electrons being components of acrylic plastic target  occurs. Two gamma quanta appearing at annihilation fly away at an angle of 180° in the positron and electron centre-of-mass system, and at less angle, depending upon the positron  momentum,  in the laboratory system. In experiment [38] two detectors of gamma quanta were placed at the same distance (equal to 60 cm) from targets in directions making up angles of 20° and 135° with the direction of positrons flight. Under such conditions the detectors detected only those gamma quanta, which were formed at a certain speed of motion of the electron-positron system centre of mass equal to approximately 0.6·c_o . Special electronic circuit provided measuring the difference in time between registration of these gamma quanta by the detectors with an accuracy of 0.2 10^-9 seconds. Within the limits of measuring errors any difference in time of gamma quanta registration in the experiment [38] was not detected, whereas, if dependence c_u = c_o + u cosa exists in nature, between the moments of gamma quanta hitting into the detectors a time interval of the order 0.2·10^-9 seconds should be observed. So, experiment [38] reliably confirmed the absence in nature of dependence c_u = c_o + u cosa.

  As to the dependence c_u = c_o·(1 + u²/c_o²)^1/2, the experiment [38] does not disprove it, and can not disprove it in principle (even if the accuracy of measuring the difference between the moments of gamma quanta registration by the detectors will be some orders greater). This is conditioned by the fact that according to the formula c_u = c_o(1 + u²/c_o²)^1/2 the speed of light depends only upon absolute (modulus) of the source velocity vector, and does not depend upon an angle between a direction of a source motion and a direction of gamma quanta motion. Indeed, if the dependence c_u = c_o(1 + u²/c_o²)^1/2 exists in nature, then gamma quanta must hit detectors simultaneously, if they were emitted simultaneously from a point equidistant from the detectors .

Experiment by Fillipas and Fox [39]

Just because of the same reason the experiment [ [39]. Fillipas T. A., Fox J. G. Velocity of gamma rays from a moving source // Physical Review. - 1964. - v. 135.-p. -1075] also can not disprove in principle the existence in nature of the dependence c_u = c_o(1 + u²/c_o²)^1/2. In experiment [39] the experimentators checked simultaneity of gamma quanta (appearing at decay of neutral pi-mesons) hitting detectors  placed equidistantly from a point, in which the gamma quanta were born. But  absence in nature of dependence c_u = c_o + u cosa the experiment [39] prooves with high degree of reliability.

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