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 \alpha , which parameterizes the rate at which Planck-scale spatial uncertainties ( and the phase shifts they produce ) may accumulate over large path-lengths .
Here \alpha is defined by the expression for the path-length fluctuations , \delta \ell , of a source at distance \ell , wherein \delta \ell \simeq \ell ^ { 1 - \alpha } \ell _ { P } ^ { \alpha } , with \ell _ { P } being the Planck length .
We reassess previous proposals to use astronomical observations of distant quasars and AGN 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 \alpha \gtrsim 0.58 , which rules out the random walk model ( with \alpha = 1 / 2 ) .
Much firmer constraints can be set utilizing detections of quasars at GeV energies with Fermi , and at TeV energies with ground-based Cherenkov telescopes : \alpha \gtrsim 0.67 and \alpha \gtrsim 0.72 , respectively .
These limits on \alpha seem to rule out \alpha = 2 / 3 , the model of some physical interest .