Has any actual work been done on the idea of traveling to higher dimensions, as a shortcut through space? Plenty of sci-fi books use this concept, but I want to know if there is any research being conducted on this concept. (I'm not talking about all of the warp drive research.)
Imagine two parallel lines. You are a line segment on the lower line, and your perception is completely limited to your line. All objects you are aware of are oriented along the line. You theorize there might be a higher spatial dimension and that there might be another line above you in this second dimension. You would like to construct a bridge to the other line, but you have a problem. In order to bridge the two lines, you have to already have a two dimensional object: an angle. Without an angle, you cannot create a bridge between the two lines. No one has ever observed an angle, and no method to create an angle is known.
This is the problem we are facing with the proposition of hyperspace. No one has ever observed another spatial dimension. We don't know how to access hyperspace, if it exists.