Cosmic Rays and Tev Photons as Probes of Quantum Properties of Space-time

It has been recently observed that small violations of Lorentz invariance, of a type which may arise in quantum gravity, could explain both the observations of cosmic rays above the GZK cutoff and the observations of 20-TeV gamma rays from Markarian 501. We show here that different pictures of the short-distance structure of space-time would lead to different manifestations of Lorentz-invariance violation. Specifically, the deformation of Lorentz invariance needed to resolve these observational paradoxes can only arise within commutative short-distance pictures of space-time. In noncommutative space-times there is no anomalous effect, at least at leading order. Also exploiting the fact that arrival-time delays between high energy photons with different energies would arise in both the commutative and the noncommutative Lorentz-violation pictures, we describe an experimental programme, based on time-of-arrival analysis of high energy photons and searches of violations of GZK and TeV-photon limits, which could discriminate between alternative scenarios of Lorentz-invariance breakdown and could provide and unexpected window on the (quantum) nature of space-time at very short distances. A rather robust expectation that is emerging from theory work on short-distance (so called, “quantum gravity”) properties of space-time is that space-time symmetries may require modification. In particular, quantum-gravity effects inducing some level of nonlocality or noncommutativity would affect even the most basic flat-space continuous symmetries, such as Lorentz invariance. This has been recently emphasized in various quantum-gravity approaches [1-14] based on critical or noncritical string theories, noncommutative geometry, canonical quantum gravity. While we must be open to the possibility that some symmetries be completely lost, it appears plausible that some of them be not really lost but rather replaced by a Planck-scale-deformed version, and some mathematical frameworks which could consistently describe such deformations have emerged in the mathematical-physics literature [15, 16, 3, 6, 7]. We shall here focus on quantum-gravity motivated violations of Lorentz invariance, but of course Lorentz-invariance violations do not have to be necessarily associated with quantum gravity and in fact even outside the quantum-gravity literature there is a large amount of work on the theory and phenomenology of violations of Lorentz invariance (see, e.g., the recent Refs. [17, 18], which also provide a good starting point for a literature search backward in time). Since quantum-gravity formalisms are still too complex to allow definite quantitative predictions of the effects, possible deformations of Lorentz invariance have been investigated through phenomenological models. In particular, the investigation of the Lorentz-violating class of dispersion relations