Different Routes to Lorentz Symmetry Violations

Recent observations of ultra high energy cosmic rays and gamma rays suggest that there are small violations of Lorentz symmetry. If there were no such violations, then the GZK cut off would hold and cosmic rays with energy ∼10²⁰ eV or higher would not be reaching the earth. However some such events seem to have been observed. This has lead to phenomenological models in which there is a small violation of the Lorentz symmetry or the velocity of light. However recent approaches which no longer consider a differentiable spacetime manifold already predict such violations. Similarly there are other theoretical reasons which also point to this. We briefly discuss some of these approaches and observe that Lorentz Symmetry violations can be tested by data from NASA’s GLAST satellite due for launch. Permanent address: International Institute for Applicable Mathematics & Information Sciences, Hyderabad, India & Udine, Italy. B.M. Birla Science Centre, Adarsh Nagar, Hyderabad 500 063, India.