So, as many of you know, Doctor Who was on tonight. There was a small section near the end that had my emergency-response-aid brain slightly baffled, but I can skip over most of that. What I am more concerned with is why the Doctor didn't do anything in that particular situation.
Under the cut is a less-cryptic, more-spoilery discussion that offers a possible explanation as to why the Doctor stood there and didn't help.
Let's face it, Amy was being pretty rubbish with her CPR, but the Doctor was being even worse, just sitting there like a lemon. What if it's because he can't give a human CPR, even if he tried?
In Classic Who, we are told that the Doctor and all other Time Lords have a respiratory bypass that allows them to go without breathing for a significant length of time. He has used this skill to escape strangulation, hanging, and being in the vacuum of space. It's one of those nice little oddities of his biology that allow writers to get him in some unusual situations.
I believe that this system also makes it impossible for him to perform CPR.
In order to survive for a long time without breathing, you need a high saturation of oxygen in your bloodstream. I highly doubt any of you will have seen it, but a few years back there was a TV show called
Invasion where water-dwelling aliens systematically cloned and replaced humans. Because the aliens were water-dwelling, the clones had the ability to stay underwater for a very long time. This was because they had high o2 sats, and there was even a point where a doctor who didn't realise she was a clone tried to donate blood to her son. Her son nearly died because the blood was too oxygenated and was poisoning him.
So, the Doctor needs to have this system too. He will have a very high o2 saturation in his bloodstream, which also means that when he breathes in air his lungs are removing a lot more oxygen than ours would. CPR still gets oxygen into the body of the person because when we exhale there is still plenty of oxygen in there - we don't strip it completely out when we breathe. Maybe the Doctor does.
When Martha was performing CPR on the Doctor, she was taking breaths from an oxygen cannister, which has a far higher concentration of oxygen than air (I don't remember if they were 100% oxygen or a lower concentration), so there wouldn't be any problems with him not getting enough oxygen from her breaths to wake up. It's possible that, if she was trying it normally, he would have either taken far longer or not woken up at all and simply regenerated.
So the reason the Doctor didn't help Rory might be because he was worried that it wouldn't work at all if he tried, and while Amy might have been captain of the HMS Failwhale, she could at least give oxygen. Maybe they should have switched it up so that the Doctor did reps and Amy did breaths, but you can't win them all.