i like to play a fun game where i try to understand math. this is missing the left side of the equation (S = ...) but otherwise i think it might say
“for an object, action across a trajectory is approximately its mass (m) times the integral of its trajectory, which is [the speed of light squared times (one minus the gravitational potential over 2), minus the speed of light times frame dragging times non-relativistic velocity, minus (the kroenecker delta and gravitational waves), times v sub i (?) times velocity over 2] (... and also, d (?) times time)″
whew. maybe someday i will figure out what v sub i, the kroenecker delta, and d are, or when you’re supposed to multiply things by each other and when not
anyway the point of this equation is that smaller interferometers can be used to detect larger objects (it’s not quite that simple, because larger interferometers can also detect larger gravitational waves)
this paper is about building a 1m “matter wave interferometer”, a mini-LIGO or “MIMAC” (mesoscopic interference for for metric and curvature)
so i think what they’re saying is, a meter-scale interferometer could directly detect the curvature of space, and then use it to detect (supermassive merger scale) gravitational waves, as well as gravitational frame-dragging effects from the earth