10-th International Workshop on H.E.S.P. September 16-21, 2003, Dubna, Russia

1. 10-th International Workshop on H.E.S.P. September 16-21, 2003, Dubna, Russia Bradyons and Tachyons S.B. Nurushev Institute for High Energy Physics

2. Contents • Introduction • Classification of particles • Causality Problem • Generalized Galilean Transformation • Where may we look for tachyons? • Charged Tachyons • Cherenkov Radiation Spectrum • Summary

3. Introduction The first discussions of the particles moving with the superluminal velocities were traced back to J.J. Thompson [1], O. Heavyside [2], and A. Sommerfeld [3]. For a long time it was generally believed that the special theory of relativity precludes the possibility of transmitting energy from point to point in space-time at velocities greater than c, the speed of light in a vacuum. .

4. Introduction Such belief stems out from the Einstein conclusion “… velocities greater than that of light … have no possibilities of existence,” [4].Other versions of this statement are presented in the standard textbooks on relativity [5]. At the beginning of the 60’s the interest to the superluminal particles surged among theoreticians [6], [7], [8]. The major theoretical efforts were directed toward a justification of existence of such a particle named as tachyon [9].

5. Classification of particles Three Classes of Particles Based on SR, three classes of particles were proposed by Bilaniuk et al [7]. The Class III particles, i.e. tachyons, would be created in nuclear interactions at superluminal velocities. The sign of 4-D line element, ds2, is associated with three classes of particles. For simplicity, let us put dy = dz = 0, then        > 0    Class I (subluminal particles) ds2 = c2dt2 - dx2 = 0    Class II (photon)     (3)    < 0      Class III (tachyon)

6. Classification of particles Figure 1, Energy vs. velocity for three classes of particles

7. Causality Problem Figure 2, A 2-D diagram for Lorentz transformation

8. Generelized Galileen Transformation • x = r(X - vT)          • t = r- -1T              (6) r=[1-(v/c)2]-1/2 Figure 3, A 2-D diagram of GGT

9. E Figure 4a,4b 2-D diagram of E vs. p for three classes of particles P E E= P

10. Experimental data on the neutrino mass • m2(νe) = -2.5±3.3 eV2 This is from Tritium decay experiment • m2(νμ) = -0.016±0.023 MeV2 Thisis from pion decay experiment

11. Charged Tachyons • The next important item is a way by which tachyon looses its energy. The charged stable tachyon may emit the Cherenkov radiation. The Lorenz - invariant formulation of the Cherenkov radiation by tachyon was given in paper [10]. Tachyon behaving as the deformed sphere looses energy per unit path length in the following way

12. Charged Tachyons • where e – electron charge (assuming that tachyon carries a single electron charge), a0 -radius of sphere, s is the traveling distance. The range of tachyon considered as the distance from the production point to the point of inevitable annihilation with anti-tachyon is defined by a relation R =

13. Charged Tachyons • For numerical estimate it was assumed in paper [10], that tachyon has the same charge and mass as the electron has and the tachyon size is of order of the electron Compton wave length. Then we have R=5.510-9(E/), (In centimeter).

14. Charged Tachyons • Numerically for E it follows R = 5.510-9cm. This estimate immediately leads to two important conclusions: • No way to detect tachyon through its ionization • The only accessable way to detect tachyon is its Cherenkov radiation

15. Cherenkov Radiation Spectrum • For simplicity the Gaussian-like charge distribution was used which gives the following spectral distribution of the tachyons Cherenkov radiation [V.F.P]

16. Cherenkov Radiation Spectrum Where is a frequency of the emitted Cherenkov radiation,  - wavelength, c - speed of light. The maximum of the spectral distribution occurs at frequency

17. Cherenkov Radiation Spectrum • Assuming p= √2 μand a0=λc= hc/mc= 3.8·10-11 cm, one gets

18. Cherenkov Radiation Spectrum • This corresponds to photon energy • E = 11 MeV

19. Table 1. Where may we look for tachyons?

20. Cherenkov Radiation As resume one can list the following important measurements of the Cherenkov radiation which should be done: • The Cherenkov radiation ring should be measured. Tachyon velocity can be extracted from such measurements. • The spectral distribution of the Cherenkov radiation should be measured including its maximum. The size of tachyon can be extracted from such measurement and from point 1 • The Cherenkov radiation absolute intensity should be also measured. Assuming that we can restore a whole tachyon energy by such measurements we can extract the tachyon mass from all listed above measurements.