Came across this reading La Berge Lab testing...

[i]..if the lucid dreamers are actually sharing a dream-world, they would show simultaneous eye-movement signals in their polygraphic recordings. If on the other hand, they report carrying out this task in a mutual lucid dream and do not show simultaneous signals, we would have to conclude that they were at most sharing dream plots. Let us be sure to appreciate the significance of such an experiment. If the mutual lucid dreams fail to show simultaneous signals, it would be neither surprising or especially significant. However, if the mutual lcud dreamers did prove to produce simultaneous eye movement signals, we have incontrovertible proof for the objective existence of the dream world.

Stephen LaBerge (1985) Lucid Dreaming, NY Ballantine