<p>Like doing the SM in physics and PhD in computer science at the same time?</p>
<p>No. Not without the express consent of both departments, which is unlikely to be granted – each department wants to spend its limited resources on students who are fully committed to its own graduate program. As I’ve said before, there is not enough time in the day to be working full-time as a graduate student in two programs simultaneously.</p>
<p>The appropriate route, if you are interested in both physics and computer science, is to find a faculty member doing research at the interface of these fields, and to join one of the programs and do your thesis work in his/her lab. It’s not necessary to be enrolled in two graduate programs in order to get an education in two fields – the point of an academic graduate degree is that you are able to think and do research, not that you are being trained as a practitioner of a particular subfield.</p>