Directional Entanglement of Quantum Fields with Quantum Geometry

It is conjectured that the spatial structure of quantum field states is influenced by a new kind of directional indeterminacy of quantum geometry set by the Planck length, $l_P$, that does not occur in a classical background geometry. Entanglement of fields with geometry modifies the transverse phase of field states at wavelength $\lambda$ and propagation distance $c\tau$ by about $\Delta \phi\approx \sqrt{l_P\tau}/\lambda$. The new effect is not detectable in measurements of propagating states that depend only on longitudinal coordinates. The reduced information content of fields in large systems is consistent with holographic bounds from gravitation theory, and may appear as measurable quantum-geometrical noise in interferometers.