A limit on Planck-scale froth with ESPRESSO

Abstract

Some models of quantum gravity predict that the very structure of space–time is ‘frothy’ due to quantum fluctuations. Although the effect is expected to be tiny, if these space–time fluctuations grow over a large distance, the initial state of a photon, such as its energy, is gradually washed out as the photon propagates. Thus, in these models, even the most monochromatic light source would gradually disperse in energy due to space–time fluctuations over large distances. In this paper, we use science verification observations obtained with ESPRESSO at the Very Large Telescope to place a novel bound on the growth of space–time fluctuations. To achieve this, we directly measure the width of a narrow Fe ii absorption line produced by a quiescent gas cloud at redshift $z$ ≃ 2.34, corresponding to a comoving distance of ≃5.8 Gpc. Using a heuristic model where the energy fluctuations grow as σE/E = (E/EP)α, where EP ≃ 1.22 × 1028 eV is the Planck energy, we rule out models with α ≤ 0.634, including models where the quantum fluctuations grow as a random walk process (α = 0.5). Finally, we present a new formalism where the uncertainty accrued at discrete space–time steps is drawn from a continuous distribution. We conclude, if photons take discrete steps through space–time and accumulate Planck-scale uncertainties at each step, then our ESPRESSO observations require that the step size must be at least ≳ 1013.2lP, where lP is the Planck length.

Neutrino signals of lightcone fluctuations resulting from fluctuating space-time

“…n = 0) [4]. Similar arguments also predict the degradation of a narrow FeII absorption line in photon spectra, with a recent study [7] also yielding a natural Planck scale constraint on such effects (again only for energy independent scenarios).…”

“…In the absence of energy dependence (e.g. n = 0), Equation ( 5) reduces to a form used in a number of previous works [4,7,31,32], characterised by single free parameter α, referred to as the accumulation parameter, which is the equivalent of m in this work (where α = 1 − m).…”

“…{L 0 , δL 0 , m, n}, which can then be tested against experimental data. Alternatively, existing constraints on neutrino decoherence can be re-interpreted in terms of this underlying model, and the results compared to corresponding constraints on space-time fluctuations from γ-ray observations [4,5,7].…”

“…The upper panel considers the case of energy independent uncorrelated distance fluctuations, for which sensitivity to natural Planck scale effects (e.g. δL 0 = L Planck ) has been achieved using astrophysical photon observations [4,7]. The y axis indicates the size of fluctuations required for each Planck length travelled to produce strong decoherence effects, which is inversely proportional to energy in this case due to the wavelength-dependence.…”

“…In recent years however, experimental constraints on potential Planck scale quantum gravity effects have been achieved using high-energy particles of cosmological origin, exploiting observations of photons from distant gamma ray bursts (GRBs), quasars and quiescent gas clouds [1][2][3][4][5][6][7], and the high-energy astrophysical neutrinos observed by neutrino telescopes [8][9][10][11] such as the IceCube neutrino observatory [12]. These measurements have achieved sensitivity to very weak effects due to the vast distances traversed by the observed particles, potentially allowing even weak effects to accumulate into measurable signals.…”