This study at the University of Missouri is making its way around the blogosphere:

While completing the first puzzle, the researchers recorded participants’ heart rate and blood pressure responses. Participants then reported their levels of anxiety and how unpleasant or pleasant they felt during the word search puzzle. Next, and while in possession of their iPhones, participants were informed that their iPhones were causing “Bluetooth interference” with the wireless blood pressure cuff, and that they needed to be placed further away in the room for the remainder of the experiment. The researchers then provided the participants a second word search puzzle. While working on the puzzle, the researchers called the participants’ iPhones. After the phones finished ringing, researchers collected blood pressure and heart rate responses. Participants then reported their levels of anxiety and how unpleasant or pleasant they felt during the word search puzzle. The researchers found a significant increase in anxiety, heart rate and blood pressure levels, and a significant decrease in puzzle performance when the participants were separated from their iPhones as compared to when iPhone users completed similar word search puzzles while in possession of their iPhones.

Seems to me the anxiety was driven not by the absence of the iPhone, but by being able to hear a call coming in and not being able to do anything about it. Not sure what that proves.