Abstract
We discuss the possible breakdown of Lorentz invariance—at distances greater than the Planck length—from both the theoretical and the phenomenological point of view. The theoretical tool to deal with such a problem is provided by a “deformation” of the Minkowski metric, with parameters dependent on the energy of the physical system considered. Such a deformed metric realizes, for any interaction, the “solidarity principle” between interactions and spacetime geometry (usually assumed for gravitation), according to which the peculiar features of every interaction determine—locally—its own spacetinie structure. The generalized theory of relativity, based on the locally deformed Minkowski spacetime, is called “deformed special relativity” (DSR). In the first part of the paper, we give the foundations and the basic laws of DSR. In the second part, we analyze some experimental data, which admit an interpretation in terms of the DSR formalism and are, therefore, candidates for displaying a breakdown of the Lorentz symmetry. They are (i) the superluminal propagation of evanescent electromagnetic waves in waveguides, (ii) the meanlife of the KS 0, (iii) the Bose-Einstein correlation in pion production and (iv) the comparison of clock rates in the gravitational field of Earth. Such analysis provides us with the explicit forms of the related deformed metrics as functions of the energy, thus putting in evidence, in all four cases (and therefore for all four fundamental interactions), departures from the usual Minkowski metric. This preliminary evidence for a broken Lorentz invariance may be regarded as the signature of possible nonlocal effects involved in the processes examined. Moreover, the corresponding deformed metrics obtained by our analysis provide an effective dynamical description of the interactions (at least in the energy range considered).
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REFERENCES
See, e.g., J. D. Bjorken and S. D. Drell, Relativistic Ouantum Fields (McGraw-Hill, New York, 1965), Sect. 11.1.
J. D. Bjorken, Ann. Phys. 24, 174 (1963).
D. I. Blokhintsev, Phys. Lett. 12, 272 (1964); Sov. Phys. Uspekhi 9, 405 (1966).
L B. Redei, Phys. Rev. 145, 999 (1966).
P. R. Phillips, Phys. Rev. 139, B491 (1965); P. R. Phillips and D. Woolum, Nuovo Cim. B 64, 28 (1969).
E. Recami and R. Mignani, Riv. Nuovo Cim. 4(2) (1974) and references therein.
G. Yu. Bogoslovsky, Nuovo Cim. B 40, 99, 116 (1977). For a review, see G. Yu.Bogoslovsky, Fortschr. Phys. 42, 2 (1994).
For a review of Finsler's generalization of Riemannian spaces, see, e.g., M. Matsumoto, Foundation of Finsler Geometry and Special Finsler Spaces (Kaiseisha Otsu, 1986), and references therein.
H. B. Nielsen and I. Picek, Phys. Lett. B 114, 141 (1982). Nucl. Phys. B 211, 269 (1983).
R.M. Santilli, Lett. Nuovo Cim. 37, 337 (1983); 38, 509 (1983).
For a review of isotopic theories, see R. M. Santilli, Elements of Hadronic Mechanics, Vols. I-III (Naukova Dumka, Kiev, 1994).
D. Y. Kim, Hadr. J. 1, 1343 (1978).
S. H. Aronson, G. J. Bock, H.-Y. Chang, and E. Fishbach, Phys. Rev. Lett. 48, 1306 (1982); Phys. Rev. D 28, 495 (1983).
E. Fishbach, D. Sudarsky, A. Szafas, C. Talmadge, and S. Aronson, Phys. Rev. Lett. 56(3), 1427 (1986).
N. Grossman et al., Phys. Rev. Lett. 59, 18 (1987).
F. Cardone, R. Mignani, and R.M. Santilli, J. Phys. G 18, L61, L141 (1992).
S. Coleman and S. L. Glashow, Phys. Lett. B 405, 249 (1997); S. L. Glashow, Nucl. Phys. (Proc. Suppl.) 70, 180 (1998); see also D. Colladay and V. A. Kostelecky, Phys. Rev. D 57, 3932 (1997).
B. Finzi, in Cinquant'anni di Relativitá, M. Pantaleo, ed. (Giunti, Firenze, 1955).pp. 194, 204.
For reviews on both experimental and theoretical aspects of superluminal photon tunneling, see, e.g., G. Nimtz and W. Heiman, Prog. Quantum Electr. 21, 81 (1997); R. Y. Chiao and A. M. Steinberg, in Progress in Optics, E. Wolf, ed. (Elsevier Science, 1997), Vol. 37, p. 346; V. S. Olkovsky and A. Agresti, in Tunneling and Its Implications, D. Mugnai, A. Ranfagni, and L. S. Schulman, eds. (World Scientific, Singapore, 1997), p. 327.
R. M. Santilli, Hadr. J. 15, 1 (1992).
F. Cardone and R. Mignani, JETP 83, 435 (1996) [Zh. Eksp. Teor. Fiz. 110, 793 (1996) ].
C. O. Alley, “Relativity and Clocks,” Proceedings of the 33rd Annual Symposium on Frequency Control ( Elec. Ind. Assoc. Washington, DC, 1979).
R. Penrose, The Emperor's New Mind (Oxford University Press, 1989).
J. A. de Azcarrage and F. Rodenas, J. Phys. A 29, 1215 (1996).
F. Cardone and R. Mignani, On a nonlocal relativistic kinematics, INFN preprint 910 (Rome, Nov., 1992).
F. Cardone, R. Mignani, and V. S. Olkhovski, J. de Phys. I (France) 7, 1211 (1997).
For experimental as well as theoretical reviews, see, e.g., B. Lörstad, Correlations and Multiparticle Production (CAMP), M. Pluenner, S. Raha, and R.M. Weiner, eds. (World Scientific, Singapore, 1991); D. H. Boal, C. K. Gelbke, and B. K. Jennings, Rev. Mod.Phys. 62, 553 (1990), and references therein.
See M. Fincke-Keeler, Bose-Einstein Correlations in Proton-Antiproton Collisions at ℚs= 200 to 900 GeV, Ph.D. thesis (University of Victoria, Canada, 1989).
C.M. Will, Theory and Experiment in Gravitational Physics, (Cambrdidge University Press, 1993), and references therein.
F. Cardone and R. Mignani, Int. J. Modern Phys. A 14, 3799 (1999).
T. Damour and J. Taylor, Astrophys. J. 366, 501 (1991), and references therein.
M. Ferraris, Proc. of Journe es Relativistes, S. Benvenuti, M. Ferraris, and M. Francaviglia, eds. (Pitagora, Bolagna, 1983), p. 125; M. Ferraris and J. Kijowksi, Gen. Rel. Grav. 14, 37 (1982).
M. Gaspero, Sov. J. Nucl. Phys. 55, 795 (1992); Nucl. Phys. A 562, 407 (1993); ibidem, 588, 861 (1995). M. Gaspero and A. De Pascale, Phys. Lett. B 358, 146 (1995).
CPLEAR collaboration, R. Adler et al., Nucl. Phys. A 558, 43c (1993); Z. Phys. C 63, 541 (1994).
F. Cardone, M. Gaspero, and R. Mignani, Eur. Phys. J. C 4, 705 (1998).
G. Amelino-Camelia, J. Ellis, N. E. Mavromatos, D. V. Nanopoulos, and S. Sarkar, Nature 393, 763 (1998).
P. Kaaret, Astron. Astrophys. 345, L32 (1999).
P. A. M. Dirac, Nature 139, 323 (1937).
J. K. Webb, V. V. Flambaum, C. W. Churchill, M. J. Drinkwater, and J. Barrow, astroph/9803165 (1998). M. J. Drinkwater, J. K. Webb, J. Barrow, and V. V. Flambaum, Mon. Not. Roy. Astron. Soc. 295, 457 (1998).
See e.g., A. V. Ivanchik, A. Y. Potekhin, and D. A. Varshalovich, Astron. Astrophys. (1998), and references therein.
See, e.g., M. B. Green and J. H. Schwarz, Superstring Theory (Cambridge University Press, 1987). P. Sisterna and H. Vucetich, Phys. Rev. D 41, 1034 (1990).
F. Cardone, M. F. Francaviglia, and R. Mignani, Gen. Rel. Grav. A 30, 1619 (1998); Found. Phys. Lett. 12, 281 (1999); Gen. Rel. Grav. 31, 1049 (1999); Energy as fifth dimension, Found. Phys. Lett. (in press).
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Cardone, F., Mignani, R. Broken Lorentz Invariance and Metric Description of Interactions in a Deformed Minkowski Space. Foundations of Physics 29, 1735–1783 (1999). https://doi.org/10.1023/A:1018825930183
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DOI: https://doi.org/10.1023/A:1018825930183