Il Nuovo Cimento A (1965-1970)

, Volume 71, Issue 4, pp 509–533

On the shape of tachyons

  • A. O. Barut
  • G. D. Maccarrone
  • E. Recami
Article

Summary

We study some aspects of the experimental behaviour of tachyons, in particular by finding out their « apparent » shape. A Superluminal particle, which in its own rest frame is spherical or ellipsoidal (and with an infinite lifetime), would « appear » to a laboratory frame as occupying the whole region of space bound by a double cone and a twosheeted hyperboloid. Such a structure (the tachyon « shape ») rigidly travels with the speed of the tachyon. However, if the Superluminal particle has a finite lifetimein its rest frame, then in the laboratory frame it gets afinite space extension. As a by-product, we are able to interpret physically the imaginary units entering—as is well known—the transverse co-ordinates in the Superluminal Lorentz transformations. The various particular or limiting cases of the tachyon shape are thoroughly considered. Finally, some brief considerations concerning possible experiments to look for tachyons are added.

О форме тахионов

Резюме

Мы исследуем некоторые аспекты экспериментального поведения тахионов, в частности, посредством нахождения их кажущейся формы. Суперлюминальная частица, которая в своей собственной системе соординат является сферической или эллипсоидальной (и с бесконечным временем жизни), в лабораторной системе координат представляется занимающей всю область пространства, ограниченную двойным конусом и гиперболоидом с двумя слоями. Такая структура (« форма » тахиона) движется со скоростью тахиона. Однако, ески суперлюминальная частица имеет конечное время жизни в своей собственной системе координат, то в лабораторной системе координат эта частица занимает конечное пространство. Как вспомогательный результат, мы можем физически интерпретировать мнимые единицы, входящие, как известно, в попереченые координаты в суперлюминальных преобразованиях Лоренца. Подробно исследуются различные частные и предельные случаи формы тахиона. В заключение, проводится обсуждение возможных экспериментов по наблюдению тахионов.

Riassunto

Si studiano alcuni aspetti del comportamento dei taohioni, in particolare trovando quale « apparirebbe » la loro forma. Una particella Superluminale, che sia sferica o ellissoidale (e con vita di durata finita) nel proprio riferimento a riposo, a un osservatore nel laboratorio sembrerebbe occupare Tintera regione di spazio limitata da un doppio cono e da un iperboloide a due falde. Tale struttura (la « forma » del tachione) viaggerà rigidamente con la velocità del tachione. Si noti però che, se la particella Superluminale ha una vita finita (nel suo riferimento a riposo), allora nel laboratorio essa risulta avere un’estensione spazialefinita. Come conseguenza della precedente analisi, siamo in grado d’interpretare fisicamente le unità immaginarie che entrano — come noto — nelle coordinate trasversali per azione delle trasformazioni di Lorentz Superluminali. Si esaminano dettagliatamente i vari casi particolari o casi limite della forma dei tachioni. Infine, si aggiungono alcune considerazioni circa eventuali esperimenti atti alla ricerca effettiva dei tachioni.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. (1).
    G. D. Maccarrone andE. Recami:Nuovo Cimento A,57, 85 (1980);E. Recami andR. Mignani: Riv.Nuovo Cimento,4, 209, 398 (1974), and references therein;E. Recami, Editor:Tachyons, Monopoles, and Belated Topics (Amsterdam, 1978), and references therein;E. Recami: Chapt. 18 inCentenario di Einstein: Astrofisiea e Cosmologia, Gravitazione, Quanti e Belatività netto sviluppo del pensiero scientifico di A. Einstein, edited by M. Pantaleo (Firenze, 1979), p. 1021;E. Recami: Chapt. 16 inAlbert Einstein 1879–1979: Relativity, Quanta and Cosmology in the Development of the Scientific Thought of A. Einstein, edited by F. De Finis, Vol.2 (New York, N. Y., 1979), p. 537.CrossRefADSGoogle Scholar
  2. (2).
    P. Castorina andE. Recami:Lett. Nuovo Cimento,22, 195 (1978), and references (especially ref. (1,4,5)) therein;R. Mignani andE. Recami:Phys. Lett. B,65, 148 (1976);E. Recami: Chapt. 18 in Centenariodi Einstein: Astrofisica e Cosmologia, Gravitazione, Quanti e Relatività nello sviluppo del pensiero scientifico di A. Einstein, edited by M. Pantaleo (Firenze, 1979), p. 1071 and following;E. Recami: Chapt. 16 inBelativity, Quanta and Cosmology in the Development of the Scientific Thought of A. Einstein, edited by F. De Finis, Vol.2 (New York, N. Y., 1979), p. 575 and following;E. Recami: inTachyons, Monopoles, and Related Topics, edited by E. Recami (Amsterdam, 1978), p. 17;P. Castorina andE. Recami:Lett. Nuovo Cimento,22, 195 (1978);M. Pavsic andE. Recami:Nuovo Cimento A,36, 171 (1976), particularly footnotes (17,21,32);E. Recami, R. Mignani andG. Ziino: in RecentDevelopments in Relativistic Quantum Field Theory and its Application, edited by W. Karwowski, Vol.2 (Wroclaw, 1976), p. 269;E. Recami andR. Mignani:Phys. Lett. B,62, 41 (1976), p. 43;R. Mignani andE. Recami:Phys. Lett. B,65, 149 (1976), footnotes at p. 149;Nuovo Cimento A,30, 533 (1975), sect.4, p. 538;M. Baldo andE. Recami:Lett. Nuovo Cimento,2, 643 (1969), p. 646;V. S. Olkhovsky andE. Recami:Nuovo Cimento A,63, 814 (1969), p. 122;E. Recami:G. Fis.,10, 195 (1969), p. 203;Possible... and comments on tachyons, virtual particles, resonances, Report IFUM-088/S.M., University of Milan (August 1968), p. 4.CrossRefGoogle Scholar
  3. (3).
    E. Recami:Found. Phys.,8, 329 (1978), and references therein;E. Recami andR. Mignani: Riv.Nuovo Cimento,4, 209, 398 (1974), and references therein;P. Caldirola andE. Recami: inItalian Studies in the Philosophy of Science, edited by M. Dalla Chiara (Boston, Mass., 1980), p. 249;E. Recami andW. A. Rodrigues:Found. Phys.,12, 709 (1982);E. Recami: inAnnuario ’ 73, Enciclopedia EST-Mondadori (Milano, 1973), p. 85. See also D. M. Bilaniuk, V. K. Deshpande and E. C. G. Sudarshan:Am. J. Phys.,30, 718 (1962).CrossRefADSGoogle Scholar
  4. (4).
    G. D. Maccarrone andE. Recami:Lett. Nuovo Cimento,34, 251 (1982);E. Recami andG. D. Maccarrone:Lett. Nuovo Cimento,28, 151 (1980);P. Caldirola, G. D. Maccarrone andE. Recami:Lett. Nuovo Oimento,29, 241 (1980);G. D. Maccarrone andE. Recami: to be submitted toNuovo Cimento;G. D. Maccarrone, M. Pavsic andE. Recami:Nuovo Cimento B (to appear).CrossRefGoogle Scholar
  5. (5).
    E. Recami: inToxhyons, Monopoles, and Belated Topics, edited by E. Recami (Amsterdam, 1978), p. 16;V. De Sabbata, M. Pavsic andE. Recami:Lett. Nuovo Cimento,19, 441 (1977);E. Recami andK. T. Shah:Lett. Nuovo Cimento,24, 115 (1979).Google Scholar
  6. (6).
    M. H. Cohen, K. I. Kellermann, D. B. Shaffer, R. P. Linfield A. T. Moffet, J. D. Romney, G. A. Seielstad, I. I. K. Pauliny-Toth, E. Preuss, A. Witzel, R. T. Schillizzi andB. J, Geldzahler:Nature (London),268, 405 (1977).CrossRefADSGoogle Scholar
  7. (7).
    A. O. Barut: inTachyons, Monopoles, and Related Topics, edited by E. Recami (Amsterdam, 1978), p. 148.Google Scholar
  8. (8).
    R. Mignani andE. Recami:Nuovo Cimento A,30, 533 (1975);Phys. Lett. B,62, 41 (1976);E. Recami: inTachyons, Monopoles, and Related Topics, edited by E. Recami (Amsterdam, 1978), p. 3;E. Recami andR. Mignani: inThe Uncertainty Principle and Foundations of Quantum Mechanics, edited by C. Price and S. S. Chissick (London, 1977), p. 321.CrossRefADSGoogle Scholar
  9. (9).
    E. Mignani andE. Recami:Lett. Nuovo Cimento,7, 388 (1973).CrossRefGoogle Scholar
  10. (10).
    It is interesting enough that a similar hehaviour, associated with solitonic solutions of nonlinear equations, was already considered from the mathematical viewpoint in A. O. Barut:Phys. Lett. A,67, 257-(1978). See also Ø. Grøn:Lett. Nuovo Cimento,23, 97 (1978).Google Scholar
  11. (11).
    E. Recami andR. Mignani:Lett. Nuovo Cimento,4, 144 (1972);L. Parker:Phys. Rev.,188, 2287 (1969). See also V. S. Olkhovsky and E. Recami:Vis. Kiiv. Univ. Ser. Fiz. (Kiev),11, 58 (1970); preprint ITF/70, Ukrainian Ac. Sc. (Kiev, 1970);E. Recami andR. Mignani: Riv.Nuovo Cimento,4, 209, 398 (1974), and references therein;H. C. Corben:Nuovo Cimento A,29, 415 (1975);Int. J. Theor. Phys.,15, 703 (1976).CrossRefGoogle Scholar
  12. (12).
    C. C. Chiang: private communication;V. A. Gladkikh:Fizika (Is. Tomsk Univ.), No. 6, p. 69 (1978); No. 6, p. 130 (1978); No. 12, p. 52 (1978); Ya. P. Terletsky: inTachyons, Monopoles and Belated Topics, edited by E. Recami (Amsterdam, 1978), p. 47;H. C. Corben:Lett. Nuovo Cimento,11, 533 (1974);Nuovo Cimento A,29, 415 (1975). See also N. Fleury, J. Leite-Lopes and G. Oberlechner:Acta Phys. Austriaca,38, 113 (1973);J. E. Gott III:Nuovo Cimento B,22, 49 (1974). For the different case of the spherical electromagnetic waves actually emitted by a source, cf. fig. 1 in E. Recami and G. D. Maccarrone:Lett. Nuovo Cimento,28, 151 (1980).Google Scholar
  13. (13).
    A. O. Barut: inTachyons, Monopoles, and, Related Topics, edited by E. Recami (Amsterdam, 1978), p. 143.Google Scholar
  14. (14).
    J. M. Jauch:Foundations of Quantum Mechanics (London, 1968);A. J. Kálnay: inTachyons, Monopoles, and Related Topics, edited by E. Recami (Amsterdam, 1978), p. 53, and references therein;Phys. Rev. D,7, 1707 (1973);J. C. Gallardo, A. J. Kálnay, B. A. Stec andB. P. Toledo:Nuovo Cimento A,48, 1008 (1967);A. J. Kálnay andB. P. Toledo:Nuovo Cimento A,48, 997 (1967);V. S. Olkhovsky andE. Recami:Lett. Nuovo Cimento,4, 1165 (1970);E. Recami: inQuarks and the Nucleus (Progress in Particle and Nuclear Physics, Vol.8), edited by D. Wilkinson (Oxford, 1982), p. 401;P. Calderola, M. Pavsic andE. Recami:Nuovo Cimento B,48, 205 (1978);Phys. Lett. A,66, 9 (1978);Lett. Nuovo Cimento,24, 565 (1979);P. Caldirola: Riv.Nuovo Cimento,2, No. 13 (1979).Google Scholar
  15. (15).
    E. Recami andG. D. Maccarrone:Lett. Nuovo Cimento,28, 151 (1980).MathSciNetCrossRefGoogle Scholar
  16. (16).
    E. Recami, K. T. Shah andW. Yourgrau:On a possible experiment concerning tachyons, unpublished preprint (August 1978).Google Scholar

Copyright information

© Società Italiana di Fisica 1982

Authors and Affiliations

  • A. O. Barut
    • 1
  • G. D. Maccarrone
    • 2
    • 3
    • 4
  • E. Recami
    • 2
    • 3
    • 4
  1. 1.Department of PhysicsUniversity of ColoradoBoulderUSA
  2. 2.Istituto di Fisica Teorica dell’ UniversitàCataniaItalia
  3. 3.Sezione di CataniaIstituto Nazionale di Fisica NucleareItalia
  4. 4.Centro Siciliano di Fisica Nucleare e di Struttura della MateriaCataniaItalia

Personalised recommendations