Lucinda from Knox County,
You mentioned the Styrofoam cups that collapse at great depths. Would the same phenomena occur with a basketball, tennis ball or balloon? Would a ball reinflate when it returned to the surface? Have you experimented with the behavior of any other objects at great depths?
A basketball, tennis ball or balloon would all contract when exposed to great pressure in the deep ocean. In theory, if any of these was a perfect sphere, they could reinflate upon resurfacing. In reality, these would tear at depth and thus would not reinflate. If a ball could be taken down at pressure (one atmosphere) and released at depth, it would not shrink, but shoot to the surface where it would promptly explode.
As you descend in the ocean, pressure increases by one atmosphere for every 10 meters of depth. The air in the submersible is calibrated to one atmosphere for the entire dive, hence avoiding any pressure problems for the human lungs within. Since styrofoam is lightweight and easy to handle, it makes the ideal "shrinking under pressure" experiment. Besides cups, we have a couple of styrofoam mannequin heads to take down. We have fun using Sharpie markers to identify the cups as coming from "Life on the Edge."