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Fig. 1

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The detectability of various models of foamy spacetime for existing and planned telescopes. We show the diagonal tracks for halo size δψ for an unresolved, z = 6.3 source, using the comoving distance [Eq. (5), dashed lines], naive application of the luminosity distance [i.e., not redoing the integral I(z,α) as per Eq. (9), in dotted lines], and correct application of the luminosity distance (dash-dot lines). Tracks are shown for α = 0.6,2/3, and N = 1.8. See Sects. 2, 3 for discussion. It appears to us that Tamburini et al. (2011) used the phase uncertainty Δφ = 2πδψ as a measure of halo size, which would exaggerate the expected halo size by nearly an order of magnitude. This displacement would make it appear that quantum foam may be easily tested by HST imaging, which it is not.

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