Measuring space-time fuzziness with high energy γ-ray detectors

Abstract

Abstract. There are several suggestions to probe space-time fuzziness (also known as space-time foam) due to the quantum mechanics nature of space-time. These effects are predicted to be very small, being related to the Planck length, so that the only hope to experimentally detect them is to look at particles propagating along cosmological distances. Some phenomenological approaches suggest that photons originating from pointlike sources at cosmological distance experience path length fluctuation that could be detected. Also the direction of flight of such photons may be subject to a dispersion such that the image of a point-like source is blurred and detected as a disk. An experimentally accessible signature may be images of point-like sources larger that the size due to the Point Spread Function of the instrument. This additional broadening should increase with distance and photon energy. Some concrete examples that can be studied with the AGILE and FERMI-LAT γ-ray satellite experiments are discussed. Theoretical frameworkThe theoretical framework used as reference is presented in [1] and references therein [2-6]. A highly simplified view is the following: a unified point of view of general relativity and quantum mechanics implies that at the the Planck scale, P = G c 3 , space-time cannot be treated as smooth and structureless. It would rather appear like quantum foam, whose features are unknown both at the theoretical and experimental levels. Even if a quantitative experimental prediction of the influence of this quantum foam is beyond the existing theoretical framework, some phenomenological approaches are attempting qualitative predictions that are potentially subject to experimental measurements. Following [1,7], we assume that the accuracy with which a length can be measured due to fluctuation of the space-time iswhere N ∼ 1 and α ≤ 1 is a parameter defining different space-time models. The models discussed in [1] suggest values α ∈ ( 1 2 , 2 3 ) depending on the assumptions. The goal would be to study variation of a fraction of wave length over astronomical scale. That seems a Corresponding