New Constraints On The Nature Of Space-Time Planck Scale Fluctuations Using X-ray and TeV Gamma-Ray Ob- servations

The space-time metric is widely believed to be subject to stochastic fluctuations induced by quantum gravity at the Planck scale. This paper describes a work based on two different phenomenological approaches to this topic. By interpreting the ideas developed in these two approaches in the light of each other, it is shown that the constraints on the nature of Planck scale space-time fluctuations already set by the observation of very high energy electrons and gamma-rays are much stronger than have been shown so far. It appears that for the kind of Planck scale fluctuations implied by several models, including the most naive one, to be consistent with the observations, the transformation laws between different reference frames must be modified in order to allow the Planck scale to be observer-independent. 1. First approach: the effects of Planck scale space-time fluctuations on kinematics A general way of describing the space-time fluctuations at the Planck scale is to write σx/x = f (xP /x), where x stands for the length l or the time t, with