My PhD was in biophysics and the questions ranged widely outside my dissertation (in my case, you actually do a defense to proceed to work on your PhD, then write your dissertation and give a final talk; there's no way, unless your advisor rejects your dissertation, that your phd wouldn't be awarded. Other programs rear-load the process and have a real "defense" at the end, which is crazy if you think about it.
At one point in my thesis defense, I derived several equations I hadn't seen before, on the fly, such as "What is the time resolved fluorescence of a fluorophore in 4-dimensional space?" and finally understanding ergodicity (https://en.wikipedia.org/wiki/Ergodicity).
My defense wasn't about determining if I was an expert and qualified to write a dissertation in my field (my questioners already knew that), but to determine if I was a well-rounded general intelligence capable of out-of-task prediction.
In my phd experience in the USA we had oral qualifying examinations which involved whiteboard derivations. The thesis defense after writing was really mostly focused on probing the results in the thesis.
At one point in my thesis defense, I derived several equations I hadn't seen before, on the fly, such as "What is the time resolved fluorescence of a fluorophore in 4-dimensional space?" and finally understanding ergodicity (https://en.wikipedia.org/wiki/Ergodicity).
My defense wasn't about determining if I was an expert and qualified to write a dissertation in my field (my questioners already knew that), but to determine if I was a well-rounded general intelligence capable of out-of-task prediction.