Approaches to Quantum Gravity

538 J. Collins, A. Perez and D. Sudarskyquantum geometry [65]. Similar constraints can be placed on the effects that arisein the string theory scenarios [44; 66].A further source of severe constraints uses the possibility that different particlespecies have different values of their limiting velocity, as in the SME. Tests aremade by examining the resulting changes in thresholds and decay properties ofcommon particles. Coleman and Glashow [19] obtained a dimensionless bound of10 −23 on this kind of Lorentz violation. Other related arguments connected to theexistence of a bound to the propagation velocity of particles for modified dispersionrelations have been used by Jacobson et al. [36; 37; 38]. These authors noted thatthe 100 MeV synchrotron radiation from the Crab nebula requires extremely highenergy electrons. They combined the upper bound on the frequency of synchrotronradiation for electrons with a given velocity in a given magnetic field with thefact that there would be an upper bound for any electron’s velocity if ξ for theelectron had a particular sign. In fact the analysis, carried out within the Myersand Pospelov framework, indicates that at least for one of the electron’s helicities acorresponding ξ parameter, if it had a particular sign, could not have a magnitudelarger than about 10 −7 .Finally there is the reported detection of cosmic rays with energies beyond theGZK cutoff. We recall that these ultrahigh energy cosmic rays are thought to beprotons whose interaction with the photons of the cosmic microwave backgroundwould prevent them from traveling more than about 50 Mpc, while the likelysources are located much further away. This anomaly is often presented as candidateobservational evidence for LIV [13; 26; 70; 1; 12; 10]. Our own feelingis that the list of unexplored alternative explanations of this anomaly, even if oneneeds to go beyond established physics, is much too broad at this time, and thus itsinterpretation as a signature of a LIV – given the difficulties we discussed here – isat best premature. Fortunately the Auger Experiment will become fully operationalsoon and its results should help clarify the situation.27.7 Evading the naturalness argument within QFTSeveral proposals have been made to evade the naturalness problem for Lorentzviolation.One argument relies essentially on the possibility that a fiducial symmetry wouldprotect Lorentz symmetry. Jain and Ralston [40] and Nibbelink and Pospelov [55]argue that supersymmetry could be such a symmetry. At the one-loop level thisindeed works: contributions to self-energy graphs with particles and their superpartnershave the same couplings but opposite signs. This cancellation is veryreminiscent of the one for the cosmological constant in the same theories. However,the authors note that, as the Lorentz algebra is a subalgebra of the supersymmetry