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Experiment of Alvager, Farley, Kjellman and Wallin [40] on Geneva proton synchrotron

In the experiment [[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.], which was carried out on Geneva proton synchrotron, they measured the speed of gamma quanta born at decays of neutral pi-mesons. Generation of neutral pi-mesons was performed  using  bombardment of  immovable beryllium target by protons having after acceleration the momentum of 19.2 GeV/c_o. In the experiment they used gamma quanta flying at an angle near 6° to the direction of protons flight. Across the path of gamma quanta flying out from the beryllium target two deflection magnets were installed near the beryllium target and one deflection magnet was installed at a distance near 50 m from the beryllium target. These magnets were intended for deflection of charged particles generated during bombardment of the target by protons from trajectory of gamma quanta flight. Before the third deflection magnet a leaden collimator with diameter of 5 mm was placed. After the third deflection magnet gamma quanta passed through a window in concrete wall, which had thickness of 6 m, and hit a detector of gamma quanta. That detector consisted of the following parts placed each after another:
          - A large scintillation detector;
          - A leaden plate  4 mm thick;
          - A small scintillation detector;
          - Cherenkov's detector.

The large scintillation detector was intended for eliminating registration of charged particles using a method of anticoincidence. The leaden   plate 4 mm thick was intended for conversion of high-energy gamma quanta into electron-positron pairs.The small scintillation detector registered electron-positron pairs generated in the leaden plate. The moment of appearance of a pulse at an output of the small scintillation detector was considered as the moment of coming gamma quanta to this compound detector.Cherenkov's detector was intended for selection of gamma quanta with energy exceeding 6 GeV

Measurement of gamma quanta speeds in experiment [40] was performed by   time-of-flight method using only one detector of gamma quanta. Only one detector of gamma quanta was used in experiment [40] in order to eliminate possible objections that gamma quanta coming to the second detector are gamma quanta re-transmitted by the substance of the first detector (which is at rest relatively the second detector), but not the gamma quanta radiated by a source moving at a great speed. In order to provide mesurement of gamma quanta speed by time-of-flight method using only one gamma quanta dectector, in the experiment [40] they used the effect of protons groupping by a synchrotron into compact bunches. That proton bunches bombarded the beryllium target with a period of 105 nanoseconds and the time interval, during which one bunch bombarded the target, was equal to some nanoseconds. For providing the bunch stucture of the accelerated beam, during a time interval of the order of 100 milliseconds (in each acceleration cycle), within which bunches repeatedly bombarded the target, the frequency of accelerating electromagnetic field of the accelerator was maintained constant and equal to 9.53220 ± 0.00005 MHz.

Dt = (t_T + t_delay) - (t_T + s/c_u) = t_delay - s/c_{u ,} (4.9)

where t_T is  the moment of gamma quantum generation in the beryllium target at its bombardment by protons;  t_delay is a time interval between generation of a gamma quantum in the target and the moment of sending the stop pulse to time-pulse-height converter (delay time);  s is the distance from the beryllium target to detector;  c_u is an  unknown speed of gamma quanta radiated by a source moving at a speed u.  

At first in the experiment [40] they measured a magnitude Dt₁ corresponding the distance s_A from the target to gammas detector  placed into position A

Dt₁ = t_delay- s_A/c_u , (4.10)

after that the distance between the target and the detector was smoothly increased up to such value s_B, at which the time interval

Dt₂ = t_delay + T - s_B/c_u     (4.11)

was equal to the time interval Dt₁ with error d t 

t_delay - s_A/c_u= t_delay + T - s_B/c_u + dt , (4.12)

where T = 1/f is  the period of beryllium target bombardment by proton bunches. 

               From expression (4.12) we can obtain the formula for calculation the value of light speed from a moving source

c_u= (s_B - s_A)/(d t + T) = D s/(d t +1/f), (4.13)

where D s  is   the distance between two fixed positions of the detector (in points A and B). 

In the experiment [40] at Ds = 31.45 m, d t = 0 and  f = 9.53220± 0.00005 MHz they obtained

c_u= (2.9977±0.0004)·10⁸ m/s. (4.14)

For checking the obtained result the detector from position in point A was moved at a distance of  4.5 m in the direction "from the target". In this case they considered that the measure the value

Dt₃ = t_delay - (s_A + 4.5 m )/c_u . (4.15)

From position B the detector was moved at a distance of  4.5 m in the direction "to the target". In this case they considered that they measure the value

Dt₄ = t_delay + T - (s_B - 4.5 m )/c_u . (4.16)

For the values 

Dt₁ - Dt₃ = 4.5 m/c_u,       Dt₄ - Dt₂ = 4.5 m/c_u 

in the experiment [40] they obtained the value 15 ·10^-9 seconds complying with value (4.14). On this basis the authors of the experiment [40] made a conclusion, that if the speed of light from a moving source depends upon the speed of light source according to formula c_u = c_o + k u, then from the experiment [40] it follows, that k = (-3 ± 13)·10^-5. And this means that experiment [40] contradicts the existence in nature of dependence c_u = c_o(1 + u²/c_o²)^1/2.

Indeed, the gamma quanta source in the experiment [40]  moved   (according to author's opinion) at a speed of 0.99975 c_o and in accordance with formula (4.4) resulting from dependence c_u = c_o(1 + u²/c_o²)^1/2 it is expected that k = 0.5. Having foreseen possible objections against argumentativeness of their experiment the authors of the experiment [40] analysed (using Fox's aborption theory ([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.]) and rejected appreciable influence on the results obtained in the experiment [40] of the gammas retransmission  effect by the substence immovable relatively the detector, through which  gammas fly from the moment of their generation in the target to the moment of their coming to detector (beryllium target, window of vacuum chamber of the acelerator, air layer of 60 m thick).

a) Reaction, which are called proton capture gamma,  in which a target atom nucleus captures a proton. In the result of this reaction a compund nucleus in excited condition is formed, which passes from excited state to normal state by way of gamma quantum radiation  ([ [41]. Kolpakov P. Ye. Basicss of Nuclear Physics.  Мoscow: Prosveshchenije, 1968. p. 284.]); 

b) Reaction [ [42]. Mukhin K. N. Introduction into nuclear physics. - Moscow: Gosatomizdat,  1963,  p. 503.]  

p ^- +  p ®  n  +  g ; (4.17)

c) Reaction [[43].   Valter A. K., Zalubovsky I. I. Nuclear Physics, Kharkov, Vyshcha shkola, 1974. - p. 285.]  

p ⁺   +  n ®  p  +  g ; (4.18)

d) Reacrion [[44]. Lebedev A. I. Pi-mesons// Micro Physics. Small Encyclopedia. Chief editor D. V. Shirkov,  Moscow: Soviet Encyclopedia, 1980. p. 308.]  

p^± ® m^± + n_m ( anti-n_m) + g ; (4.19)

e) Breaking radiation of charged particles, generated at bombardment of the target by protons. The spectrum of breaking radiation gamma quanta  is continuous with maximal energy equal to kinetic energy of breaked particles (см. стр. 405 - 406 в [[42]. Mukhin K. N. Introduction into nuclear physics. - Moscow: Gosatomizdat,  1963,  p. 503.) . 

Indeed, if the target diameter is 1 mm, the interior diameter of the collimator tube is 5 mm, a distance between the collimator and the target is 50 m, then the angle of incidence of gamma rays onto the interior surface of the collimator will be of the order of 10^-4  radians. And this means that a distance between the projections of atoms of the lead crystal lattice on a plane perpendicular to the direction of gamma rays flight will be 10^-4 times less than the real distance between atom nuclei in the lead crystal lattice along the interior surface of the collimator tube. It is conditioned by the well known statement that at small incidence angle a the crystal lattice of period d acts as a lattice of period d sin a [[45]. Shpolsky E. V. Atom Physics, v. 1. - Moscow: Fizmatgiz, 196З,  p. 136]. Then, if the average distance between atom nuclei in the crystal lattice of lead is equal to 5Ч10^-10 m (see p. 457 in [45]), the average distance between projections of atom nuclei centres on the plane perpendicular to the direction of gamma rays flight will be of the order 10^-14 m, while the lead atom nucleus diameter is also of the order of 10^-14 m [[46]. Barrett R., Jackson D. Nuclear sizes and structure. Clarendon Press, Oxford, 1977,  p. 46]. It means that all gamma quanta getting through to the interior surface of the collimator tube will be reflected from this surface as from solid wall made of nucleus matter.

That is why, even if in the experiment [[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] the gamma quanta were emitted by neutral pi-mesons moving at a speed of 0.99975 c_o, after their reflection from the interior wall of the lead collimator tube they will move at a speed of  c_o.

And if the gamma quanta after the collimator move at a speed of c_o, then instead of expression (4.9) the following formula will be valid

So, as the result of the above consideration the experiment [[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] should not be treated as a reliable proof of absence in the nature of the square-law dependence c_u = c_o (1 + u²/c_o²)^1/2.

Thus, not a single of the experiments, which were carried out earlier on testing the validity of the second Einstein's postulate, does not disprove the existence in nature of the square-law dependence c_u = c_o (1 + u²/c_o²)^1/2 of light speed upon the light source speed. Those experiments reliably proove only the absence in nature of dependence c_u = c_o + u·cosa. Consequantly, it is necessary to find and to carry out such an experiment, which could confirm or disprove the existence in nature of the square-law dependence c_u = c_o (1 + u²/c_o²)^1/2. And up to the moment, when such experiment will be carried out, the square-law dependence   c_u = c_o (1 + u²/c_o²)^1/2 is to be considered as a hypothesis, which does not contradict either the principle of relativity, or results of experiments on testing the validity of the second Einstein's postulate, or astronomic observations of binary stars considered by de-Sitter (see chapter 3).

That is why let us now consider the effects, which can be consequences from the square-law dependence c_u = c_o (1 + u²/c_o²)^1/2 when binary stars orbits are not circles, but ellipses with various eccentricity..

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