Detection of discrete spacetime by matter interferometry

TL;DR

This paper proposes using matter interferometry to detect potential discrete structure of spacetime by observing phase shifts caused by direction-dependent dispersion relations, potentially revealing Planck-scale discreteness.

Contribution

It introduces a method to test spacetime discreteness through matter interferometry and calculates expected phase shifts for a specific quantum walk model.

Findings

Large phase shifts can be produced by spacetime discreteness in interferometry.

Current neutron interferometers could set bounds on lattice spacing.

Possible detection of Planck-scale discreteness with scaled-up experiments.

Abstract

If the structure of spacetime is discrete, then Lorentz symmetry should only be an approximation, valid at long length scales. At finite lattice spacings there will be small corrections to the Dirac evolution that could in principle be experimentally detected. In particular, the lattice structure should be reflected in a modification of the free-particle dispersion relation. We show that these can produce a surprisingly large phase shift between the two arms of an asymmetrical interferometer. This method could be employed to test any model that predicts a direction-dependent dispersion relation. Here, we calculate the size of this phase shift for a particular model, the 3D quantum walk on the body-centered cubic lattice, which has been shown to give rise to the Dirac equation in the continuum limit. Though the details of this model will affect the size of the shift, its magnitude is set largely by dimensional analysis, so there is reason to believe that other models would yield similar results. We find that, with current technology, a modest-sized neutron interferometer could put strong bounds on the size of the lattice spacing. This discreteness could possibly be detected even for lattice spacings at the Planck scale by a suitably scaled-up experiment.