Limits to Seeing High-Redshift Galaxies Due to Planck-Scale-Induced Blurring

Extract

If spacetime is “foamy” travel along a lightpath must be subject to continual, random distance fluctuations ± δ l proportional to Planck length l_P ~ 10⁻³⁵ m (Lieu & Hillman 2003). Although each “kick” by itself is tiny, these may accumulate. Accounting for redshifted (bluer) emitted photons, over a cosmological distance L = (1+z)L_C for co-moving distance L_C, the resultant phase perturbations Δ φ = 2π δ l/λ at observed wavelength λ could grow independently of telescope diameter D to a maximum of Δφ_max=(1+z)Δφ₀ (Steinbring 2007) where Δφ₀=2π a₀ (l_P^α/λ)L^{1 - α} follows Ng et al. (2003). Here a₀ ~ 1 and α specifies the quantum-gravity model: 1/2 implies a random walk and 2/3 is consistent with the holographic principle; a vanishingly small Δφ_P=Δφ_max/[(1 + z) a₀ (L/l_P)^{1 - α}]=2π l_P/λ is approached when α=1.