In open-closed string duality, we can reinterpret the one-loop open string diagram (an annulus or cylinder) as a propagating closed string, depending on the direction in which we take time to be. This duality is reflected in the amplitudes we attach to these two different interpretations of the cylinder diagram. My question concerns the interpretation in a target space with Lorentzian signature: surely whether we treat the string worldsheet as a loop of open string or a propagating closed string depends on the reference frame? It could for example be that in one reference frame, surfaces of target space simultaneity intersect the cylinder as (two virtual) open strings, but when we boost to another reference frame, the surfaces of simultaneity intersect the cylinder as a closed string. Is this possible and, if so, what would it mean, if anything?