Link:     Back     Contents     Next

10. EXPERIMENTS ON CYCLIC PARTICLE ACCELERATORS AND SUPERLIGHT SPEEDS

The main formulas arising from the new space-time theory for particles motion in the cyclic accelerators (for motion at any arbitrary large speed) are the following

...(10.1)

..(10.2)

..(10.3)

where p is the 3-dimensional momentum of a particle;  e_o is the charge of a particle (for immovable particle); m_o is the rest mass of a particle; W is the kinetic energy of a particle; is the rest energy of a particle; B is the induction of transversal magnetic field; R is the radius of a particle circle trajectory;  f = 1/T is the frequency of revolution of a particle along a closed orbit;  Т is the period of  a particle revolution along a closed orbit.

It is not difficult to make yourself sure, that the formulas (10.1) and (10.2) completely coincide with analogous formulas from the special relativity theory (SRT) (see, for example, [59]. Livingston M. S.   High-Energy Accelerators. Interscience Publishers, Inc. New York, 1954). The formula (10.3) is also used for analysing the accelerators operation, but in the SRT is considered to be valid only under condition W < E_o. At W > E_o in the SRT the following formula is considered to be correct

, .(10.4)

where f_SRT is the frequency according to the special relativity theory;  T_SRT is the period according to the SRT.

The formulas (10.3) and (10.4) at W > E_o essentially differ from each other. Let us therefore examine, which of these two formulas is correct, by analysing real expreriments on cyclic particle accelerators.

10.1. Experiment on CERN proton synchrotron [40]         

At first let us consider the experiment carried out on CERN proton synchrotron  [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.]. In the paper [40] the authors assert, that bunches of protons bombarded a berrilium target having a period  Т = 105 ns, and the frequency of accelerating electromagnetic field was in this case equal to 9.5322 МHz. In  [60]. Arutunyan I. N. Accelerators of new generation and their tasks. // Priroda,  1981, No. 12,  p.p.  37 - 48.] we can find a perimeter value for this accelerator 2 p  R = 600 m. From the formula (10.3) we can find (using the known period of revolution of 105 ns)

(10.5)

i. e. W = 16.9 GeV (because for protons E_o = 938 MeV).

In accordance with the formula (9.30) at such kinetic energy the protons must move at a speed 19 times greater than the speed of light in vacuum c_o. According to the formula (10.1) at such kinetic energy the momentum of each proton will be equal to 17.8 GeV/ c_o, but not to 19.2 GeV/ c_o, as it is stated in [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.

Now let us substitute the value of kinetic energy obtained according to the formula (10.5) and the orbit perimeter of 600 m into the formulas (10.3) and (10.4). In accordance with the formula (10.3) and taking into account the formula (10.5) we have

= 9.53 MHz. (10.6)

And according to the formula (10.4) we have

= 0.5 MHz, (10.7)

where f is the value of frequency calculated in the expression (10.6).

It is quite evident, that the frequency value 9.53 MHz is considerably nearer to the experimental frequency value f_exper of  target bombardment by proton bunches

f_exper = 1/T_exper = 1/(105 10^-9 s) = 9.5238 MHz,  (10.8)

That is why 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 can be considered as a confirmation of correctness of the formula (10.3) arising from the new space-time theory.

But, in such a case, why it is considered  that the formula (10.4) arising from the SRT  is reliably confirmed by operation of cyclic particle accelerators [59]. Livingston M. S.   High-Energy Accelerators. Interscience Publishers, Inc. New York, 1954?

In order to answer this question let us consider another cyclic particle accelerator - electron synchrotron  ARUS from Yerevan.

Technical characteristics, which are of interest for us, for electron synchrotron ARUS are as follows  [61]. Bystrov Ju. A., Ivanov S. A. Acceleration and Rentgen devices. Moscow,  Vysshaya shkola, 1983,  pp. 159 - 162.:

- orbit length  2 p  R = 216.7 m;
- kinetic energy of injected electrons W = 50 MeV;
- frequency of accelerating electromagnetic field f = 132.8 MHz;
- multipicity of acceleration g = 96;
- electron rest energy E_o = 0.511 MeV.

 According to the formula (10.4) arising from the SRT the frequency of electron bunches rotation along the orbit of ARUS accelerator at the moment of electrons injection with the electrons kinetic energy of W = 48.55 MeV will be equal to

= 1.3843 MHz. (10.9)

And according to the formula (10.3) arising from the new space-time theory the frequency of electron bunches rotation along the orbit of the ARUS accelerator at the moment of electrons injection with the electrons kinetic energy of W = 48.55 MeV will be equal to

= 132.8 MHz, .(10.10)

But if you will place a target on the trajectory of electron bunches motion in the ARUS accelerator, then the period of target bombardment by electron bunches (at kinetic energy of each electron in a bunch of  W = 48.55 MeV) will be equal not to the value

T_SRT = 1/f_SRT = 1/(1.3843 MHz) = 722.39 ns  (10.11)

corresponding to the bunches rotation frequency of 1.3843 MHz, but to a value

T = 1/f = 1/(132.8 MHz) = 7.53 ns,       (10.12)

But the period of 7.53 ns for electron bunches rotation along the orbit with a length of 216.7 m would mean, that electrons move at a speed, which is 96 times greater than the speed of light in vacuum c_o. And according to the SRT the superlight speeds of electrons are impossible.

Indeed, having divided the value from the expression (10.11) by the value from the expression (10.12), we shall obtain g = 96, which is the multiplicity of acceleration for the electron synchrotron ARUS. And, having divided the value from the expression (10.6) by the value from the expression (10.7), we sshall obtain, that the multiplicity of acceleration for the CERN 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] is equal to19.

But absence of superlight speeds in the modern particle accelerators is proved also by direct measurements of particles speeds by means of measurement of particles time of flight between two points, distance between which is known.

One of such experiments is carried out on the same CERN proton synchrotron aand its results are published in the paper [63]. Mass analysis of the secondary particles produced by the 25-GeV proton beam of the CERN proton synchrotron // Physical Review Letters. –1960. V. 5. No. 1. p.19 – 21.

The results of measuring the transit time by various particles over a fixed distance of L = 27 m at different values of particles momentums, which are represented in the article [63], confirm the dependence of transit time upon particle momentum  arising from the special relativity theory 

.(10.13)

where    and do not confirm dependence of transit time upon particle momentum arising from the new space-time theory

..(10.14)

where, as before, .

One more of such experiments is the experiment described in a paper [64]. Measurement of average momentum and composition of secondary beams of particles from accelerator// Koptev V. P., Kruglov S. P., Kuzmin L. A., Malov Ju. A., Strakhovsky I. I., Shcherbakov G. V. // Devices and technique of experiment, 1976, No. 4,  pp. 55 - 58. It has been performed on a synchrocyclotron  of Leningrad Institute of nuclear physics with particles generated at bombardment of a poliethilen target by protons with kinetic energy of 1 GeV.   In this experiment they measured difference of transit times t₂ and t₁ over a distance of  L = 21 m for particles with diffefent masses m₁ and  m₂, aand then they calculated the momentum of a particle wwith greater mass m₂ using the formula

....(10.15)

where Dt₂₁ = t₂ - t₁, and during derivation of the formula (10.15) it was supposed, that a particle with smaller mass m₁ (electron or pi-meson) at great momentums ( р > 100 MeV/c_o) moves at a sspeed, which is practically equal to the speed of light in vacuum c_o. As a result the formula (10.15) is derived by substituting the values

...(10.16)

But in the experiment [64] the calibration of time scale for time-of-flight spectrum was performed using the period of target bombardment by proton bunches, which was not measured directly, but was accepted as equal to the period of accelerating electromagnetic field of the accelerator (based upon the accelerator operation explanation within the framework of the SRT). And because of the fact that the period of target bombardment by proton bunches in the experiment [64] was not measured, the values Dt₂₁ obtained in the experiment [64] can not be considered as experimentally measured ones. In order we should be able to consider these values as experimentally measured, it must be confirmed that the period of target bombardment by proton bunches is equal to the period of accelerating electromagnetic field of the accelerator. Indeed, under the formula (10.3) from the new space-time theory the period of proton bunches rotation on the output radius of the synchrocyclotron equal to 3.165 m (see p. 138 in  [61]. Bystrov Ju. A., Ivanov S. A. Acceleration and Rentgen devices. Moscow,  Vysshaya shkola, 1983,  pp. 159 - 162) should be equal to 36.69 ns, but not to 75.27 ns, as it is considered by the authors of the article [64].

In other experiment  [65]. Bertozzi W., “Speed and Kinetic Energy of Relativistic Electrons”, American Journal of Physics, 1964, v.32, p. 551 - 555 with high-energy electrons the superlight speeds of electrons were not detected only because of the fact, that electrons trajectories passed inside accelerating section of a linear accelerator of electrons. In the experiment [65] its authors did not take into consideration, that this accelerating section is a very effective device for decelaaration of electrons (in accordance with the principle of reversibility the more effective is the electrons accelerator, the more effective it decelerates  the same electrons when accelerating voltage is taken off from the acceleration section).

Link:     Back     Contents     Next