2015ApJ...805...10P

One aspect of the quantum nature of spacetime is its ''foaminess'' at very small scales. Many models for spacetime foam are defined by the accumulation power α, which parameterizes the rate at which Planck-scale spatial uncertainties (and the phase shifts they produce) may accumulate over large path lengths. Here α is defined by the expression for the path-length fluctuations,, of a source at distance l, wherein, with being the Planck length. We reassess previous proposals to use astronomical observations of distant quasars and active galactic nuclei to test models of spacetime foam. We show explicitly how wavefront distortions on small scales cause the image intensity to decay to the point where distant objects become undetectable when the path-length fluctuations become comparable to the wavelength of the radiation. We use X-ray observations from Chandra to set the constraint, which rules out the random-walk model (with). Much firmer constraints can be set by utilizing detections of quasars at GeV energies with Fermi and at TeV energies with ground-based Cerenkov telescopes: and, respectively. These limits on α seem to rule out, the model of some physical interest.