Excitingly, I've signed up specifically to answer this question. Well, in so much as real/imaginary space/time are perfectly normal concepts thrown around in physics, and their properties are just useful mathematically. For example, time travel would be described by a "closed timelike curve". I'm sure that's why such things appear in his journal all the time, since whatever physicist the producers get on board to write in such things would know all this stuff relates to what's going on in the show.
That's not to say that this physics in any way explains what is happening on the show, science is a long way from things like that!!
It's just perhaps the most relevant.
It's also, as far as I can see, definitely NOT "advanced quantum mechanics". All these things are more to do with general relativity, it's polar opposite (the Jacob to Quantum Mechanics' MIB). But there you go, they had to put something in the diary!