Changing field for PhD - How much do I need to know before I start talking to advisers/applying? I finished an integrated masters program in physics last summer, and I plan on doing a PhD on the coordination of autonomous agents, particularly in the field of automated vehicles.

I was excited after having a discussion with a  top professor in the field at a university I wanted to go to. I was told to read some more of his work to see if I could understand it, and get in contact in a few weeks. I did the reading, with some basic understanding afterwards, but the position I was pursuing was given away while I did this reading before I had the chance to prove my knowledge. 

When I read papers in this field, which incorporate set theory and graph theory as well as other areas I have no background in, how much of the material do I need to 'get' before I can seriously apply? I find myself understanding the ideas and the processes, but I get tangled in the maths. How much training would somebody with a good academic record, but from a different field, get on a PhD program like this? Would I get time to get up to speed by reading seminal textbooks?

This sort of move into a new field is scary, and even with my good academic record, I am terrified of being completely useless.
First of all, do you have enough time to change your topic? If so, I would strongly recommend to talk to your supervisor first. If he/she knows you and your abilities, he/she can guide you on choosing a topic; you can finish up and get a PhD. Second of all, with a good help of your supervisor and your commitment you can finish a PhD.

Note on "Scary Parts": Nothing is scary!. I myself had no idea about a subset of computing semantics, and it felt like jumping from an airplane when I started to learn about it. However, at the end of the learning period, I realized why I was so afraid? Don't be scared, it will take your focus away, on doing your job. Your new slogan should be: Keep calm and learn!