Using observations of distant quasars to constrain quantum gravity

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. (2011, A&A, 533, A71) which claims that Hubble Space Telescope (HST) 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, 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 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.

New Constraints on Quantum Gravity From X-Ray and Gamma-Ray Observations

“…of the PSF is unchanged by the increasing phase fluctuations. The self-similar invariance of the PSF shape (aside from the appearance of the noise plateau) contradicts the expectation from previous work (e.g., Lieu & Hillman 2003;Ng et al 2003;Ragazzoni et al 2003;Christiansen et al 2006Christiansen et al , 2011Steinbring 2007;Perlman et al 2011;Tamburini et al 2011) that phase fluctuations could broaden the apparent shape of a telescope's PSF, thus allowing for tests of spacetime foam models via the Strehl ratio at a level where…”

“…However, Christiansen et al (2011) andPerlman et al (2011), as well as earlier workers (see previous references), adopted the additional hypothesis that the rms phase fluctuations, df, might also be directly interpretable, to within the same order of magnitude, as the diameter of a spacetime-foaminduced "seeing disk" for a distant source, y d . If that were the case, then spacetime foam would have a much more profound effect on the image quality by directly blurring the images (see Figure 1 of Christiansen et al 2011 and Figure 1 of Perlman et al 2011), thereby apparently constraining the allowed parameter space to larger values of the accumulation factor, i.e., a > 0.655, for optical observations (note: by extension, such an interpretation would appear to also allow Chandra X-ray observations to rule out the holographic model (see Figure 1 of Christiansen et al 2011).…”

“…If that were the case, then spacetime foam would have a much more profound effect on the image quality by directly blurring the images (see Figure 1 of Christiansen et al 2011 and Figure 1 of Perlman et al 2011), thereby apparently constraining the allowed parameter space to larger values of the accumulation factor, i.e., a > 0.655, for optical observations (note: by extension, such an interpretation would appear to also allow Chandra X-ray observations to rule out the holographic model (see Figure 1 of Christiansen et al 2011). However, while we can construct several scenarios (see Christiansen et al 2006Christiansen et al , 2011 that suggest df dy » , we do not have a rigorous proof of this hypothesis.…”

“…A number of prior studies have explored the possible image degradation of distant astronomical objects due to the effects of spacetime foam (Lieu & Hillman 2003;Ng et al 2003;Ragazzoni et al 2003;Christiansen et al 2006Christiansen et al , 2011Perlman et al 2011). In particular, most of these focus on possible image blurring of such distant objects.…”

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

“…The theoretical framework used as reference is presented in [1] and references therein [2][3][4][5][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.…”