Energy structure at 3.2 1020 eV in special scale-relativity

Details Energy structure at 3.2 1020 eV in special scale-relativity Energy structure at 3.2 1020 eV in special scale-relativity

Dec 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004sf2a.conf..373n&link_type=abstract

SF2A-2004: Semaine de l'Astrophysique Francaise, meeting held in Paris, France, June 14-18, 2004. Edited by F. Combes, D. Barret

Mathematics

Logic

Scientific paper

In scale relativity, one considers a space-time geometry that is continuous but non-differentiable, which implies its fractality (i.e., a structuring of the scale-space). One can show that the standard laws of dilation correspond to a "Galilean" version of the theory. Their Lorentzian generalization involves the appearance of two length-scales, invariant under dilations and unreachable, one toward the small scales that can be identified with the Planck length-scale and the other toward the large scales that can be identified with the scale L of the cosmological constant (Lambda=1/L2). One of the consequences of these new laws of dilation is the existence of a very high energy structure at E = (3.2 +/- 0.2) 1020 eV, generated when the SU(2) running coupling reaches the critical value 1/4 pi2. This predicted energy is precisely the maximal energy observed for ultra-high energy cosmic rays by the Fly's Eye detector, at E = (3.2 +/- 0.9) 1020 eV.

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