Holographic Quantum Foam: Theoretical Underpinnings and Observational Evidence

Abstract

Spacetime is foamy due to quantum fluctuations. Various gedanken experiments show that distances fluctuate by amounts consistent with the holographic principle, hence the name "holographic quantum foam" (HQF). One important prediction of HQF is that necessarily there exists a dark sector in the universe. The resulting cosmology is found (at least qualitatively) to be consistent with observations. Interestingly the quanta of the dark sector are found not to obey the familiar (fermionic or bosonic) statistics, but the exotic statistics known as infinite statistics (or quantum Boltzmann statistics). The most important challenge now is to check if HQF is consistent with experiments/observations. One way is to look for observational evidence of blurred distant point-sources due to physics at the Planck scale. For over two decades it has been debated whether those tiny inherent uncertainties in time and path-length can accumulate in transiting electromagnetic wavefronts from quasars and Gamma-Ray Bursts (GRBs). But a recent event is special: GRB221009A was extremely bright and energetic. That allowed follow-up across the whole spectrum from the optical/near-infrared through to X-rays, and including the highest-ever-recorded energy gamma-rays; all consistent with blurring by HQF. Those data, and a calculation of the HQF-widened point-spread function (PSF) for real telescopes viewing a GRB are presented.

Figures (3)

• Figure 1: Starting from left; reproduced from Steinbring2007: quasar J0836+0054 image with HST; the intrinsic PSF, which includes known instrumental aberrations; and the ideal telescope diffraction pattern (middle panel). This showed a faint PSF residual, with some evidence of Planck-scale induced blurring via a drop in encircled photon flux within the central diffraction spike, when modeled for expected size including foam (right panel). As high-$z$ quasars can be partially resolved, this cannot be called a detection of foam, but did set limits on it.
• Figure 2: Measurements of GRB221009A, reproduced from Steinbring2023. Density contours are of all available, archival GRB data from Fermi LAT (roll-angles and resolutions) or GBM (error-radii) shown in 10% increments, white above 50% for GBM. Note how the broadest case of a real instrumental PSF (white curve; equation 5) nicely matches the roll angle/zenith angle for the Fermi-LAT instrument (shown for $\alpha=0.650$, $z=0.151$, and black-on-white where below Theta; grey-curve: same, $z=1.41$) or the blueward edge of the error radius for the GBM ($\Phi_{\rm FoV}$). The lower limit where blurring must necessarily rise above the nominal resolution ($\Phi_{\rm Res}$) then occurs at $\alpha=0.735$, also shown as a black-on-white curve, where it is less than Theta. In between, scaling from an upper limit of $\Phi_{\rm Hor}$ to $\Phi_{\rm Theta}$, the last term in equation 5 would follow the ratio $1+2\pi/(1.22\times\theta)$, where $\theta$ is $1^\circ$. And so, the half-way point for $\alpha$ (i.e., just scaled instead by the ratio of the resolution to the horizon) happens to coincide with $\alpha=0.667$, which is the holographic value favored by QG models; the associated horizon-crossing angle is also indicated. This limiting behaviour - that an instrument records only the ensemble of wavelength-dependent scattering cases more than its resolution-limit and less than its FoV - is something like the effect of seeing from the ground, and leads to the smooth scaling for the average size of the bluest $\gamma$-ray sources (plotted as a dashed gray curve for the average redshift $z=1.41$). This regime will be scrutinized more carefully in the discussion to follow.
• Figure 3: Same as Figure \ref{['figure_wide']}, now with all individual GRB measurements shown; reproduced from Steinbring2023 and restricted to $\gamma$-ray wavelengths to show the highest-energy LAT photons detected. The down-pointing triangles are all archival roll-angles (black) and zenith angles (grey) available from the Fermi Archive as of 1 November 2022; up-pointing triangles are their corresponding resolutions. Some left-pointing triangles indicate the highest-energy detections from GBM; grey circles indicate the mean energy. At best PSF-sharpness, the open squares are the cataloged Fermi LAT resolutions measured for AGNs (each within a narrow energy range) and colour-coded by its redshift, where known; the PSF scaling behaviour described in Figure \ref{['figure_wide']} is shown colour-coded in the same way. White density contours outline the full sample in 10% increments. To the left, at higher energies than ever detected for AGNs, are TeV sources (black, up-pointing triangles) from the TeVCat catalog (complete as accessed on 1 November 2022 from http://tevcat.uchicago.edu). Model curves are as described before, but here light-grey: $\alpha=0.650$, $z=1.41$; black-on-white: $\alpha=0.735$, $z=0.151$. The most remarkable aspect of this plot is the agreement of the best-resolved highest-energy LAT GRBs with the dark-grey curve labelled "Halo," as this would be the expected result, limited by quantum foam for $\alpha=0.667$.