Using Observations of Distant Quasars to Constrain Quantum Gravity

TL;DR

This paper critiques previous methods of using distant quasar observations to test quantum gravity models, emphasizing the importance of correct distance measures and analysis techniques to avoid overstating constraints on spacetime foam.

Contribution

It clarifies the proper use of comoving distance in such tests and discusses methodological considerations for accurately constraining quantum gravity models.

Findings

Incorrect distance measure leads to overstated constraints.

Proper analysis requires careful selection of comparison stars and measurement methods.

Reevaluation of previous constraints on spacetime foam models.

Abstract

Aims. The small-scale nature of spacetime can be tested with observations of distant quasars. We comment on a recent paper by Tamburini et al. (A&A, 533, 71) which claims that Hubble Space Telescope observations of the most distant quasars place severe constraints on models of foamy spacetime. Methods. If space is foamy on the Planck scale, photons emitted from distant objects will accumulate uncertainties in distance and propagation directions thus affecting the expected angular size of a compact object as a function of redshift. We discuss the geometry of foamy spacetime, and the appropriate distance measure for calculating the expected angular broadening. We also address the mechanics of carrying out such a test. We draw upon our previously published work on this subject (Christiansen et al. 2011), which carried out similar tests as Tamburini et al. and also went considerably beyond their work in several respects. Results. When calculating the path taken by photons as they travel from a distant source to Earth, one must use the comoving distance rather than the luminosity distance. This then also becomes the appropriate distance to use when calculating the angular broadening expected in a distant source. The use of the wrong distance measure causes Tamburini et al. to overstate the constraints that can be placed on models of spacetime foam. In addition, we consider the impact of different ways of parametrizing and measuring the effects of spacetime foam. Given the variation of the shape of the point-spread function (PSF) on the chip, as well as observation-specific factors, it is important to select carefully -- and document -- the comparison stars used as well as the methods used to compute the Strehl ratio.