Hows does a processor physically do calculations?
There's basically two concepts you'll have to explore. 

First, how does the digital logic work? Using logic gates, you can basically build up whatever mathematical logic engine you want (theoretically). This rough generalization won't really change, but in the future we may have more than just binary logic (1 and 0).

Second, how do those gates actually operate from a analog physics standpoint? This is basically the IEEE article, etc. This will potentially change with time, too.

It'll be difficult to find one source that puts it all together (outside of a textbook) because they are different EE fields of study.