Okay, this is really interesting stuff. I am learning something usefull, which I will noodle through. But, when I am told I am not understanding something correctly, I go find out.
Sooooo..... I sent an e-mail to a respected pulmonary cardiologist, who is a pulmonary specialist/professor of medicine, and wrote a really great book some years back on the subject. I asked him the basic question orginally posed; i.e. "would you redescend if you blew a safety stop?". I further clarified my question to him in that you knew nothing about the diver, their repetitive dive history, depth, bottom time, nothing.
The responses were as follows (please note this is NOT a recommendation from a doctor, and I am answering this as a point of discussion, NOTHING MORE, and and offering this only as a point of discussion):
It is really two questions, involving in-water recompression:
1. When you miss a recommended safety stop,
2. When you have (or about to develope) the bends
1. A safety stop in recreational diving is recommended because it builds a margin of safety; by definition, in recreational diving (i.e. diving by the tables) you will not get bent without a safety stop. It is 'no-decompression' diving. So if you missed a safety stop, and are worried about it, no harm at all in going back down and recompressing. Your theory is correct; it is the same (physics-wise) as the chamber in terms of increasing the pressure.
2. If you miss a decompression stop that is built in because it is necessary to avoid the bends (i.e., by definition not
recreational diving), then you have a problem. The problem is that if you get acutely ill (pain or mental confusion or whatever) and go back down, you could drown. This is probably why the docs recommend not to go back down - if the diver is unstable in any way, it could be a disaster. Controlled recompression is theoretically much safer.
So to answer your question, going back down is a good idea if there is no threat of illness (bends) that would lead to possible drowning AND (I should add) you have enough air to stay down awhile. In the real world I imagine there might be a lot of confusion over these issues if a diver surfaces without a stop and he/she asks 'what should I do?' Best to know and be prepared ahead of time.
So, I think there is lots of discussion left on this issue, and no clear consensus in the medical field. But my original point was that the physics and gas law properties do not change, but as pointed out, the controlled enviroment of a hyperbaric chamber does.
