Directional Entanglement of Quantum Fields with Quantum Geometry

Understand

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.