Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-11-24
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
15 pages. arXiv admin note: substantial text overlap with arXiv:gr-qc/0602034
Scientific paper
In a recent experiment performed in CERN a faster than light muon neutrino was reported \cite{FTL}. In particular the authors measured a velocity $v$ such that $\frac{v-c}{c}=(2.48 \pm 0.28 (stat.) \pm 0.30 (sys.)) 10^{-5}$. Although the result seems to be in contradiction with the theory of relativity \cite{FTL2}: "The strong constraints arising from these observations makes an interpretation of the OPERA measurement in terms of modification of Einstein's theory unlikely". In truth the result may only represent a difficulty to the {\bf special} theory of relativity, the general theory of relativity allows in addition to the Lorentzian metric of the type $\eta_\mn = \ {\rm diag} \ (1,-1,-1,-1)$ also other flat metrics such as the Euclidian metric: $ {\rm diag} \ (1,1,1,1)$. Naturally an Euclidian metric does not restrict the speed at which a particle propagates. Although only the Lorentzian metric is stable \cite{Yahaloma}, it can not be precluded that an Euclidian metric can be created under special circumstances and persist in a limited region of space-time.
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