Well the four-dimensional model is actually based on Special, not General, Relativity and doesn't really have anything to do with curved space and gravity and all that. It's actually, in a way, very simple. I guess it interested me to such a degree because the most complex thing it relies on is Euclidean space. And Euclidean space seems to have some sort of close link with reality for me, at least at the macroscopic level... the three dimensions I live in seem intuitive, not just mathematical. And I guess, for me, that lends special weight to the idea of a fourth, temporal dimension. There just aren't very many ways to understand (special) relativistic effects. I'm not ready to give up on intuition altogether yet...

However I admit that I could be and probably am pretty naive here, having only touched on a series of topics that are themselves huge. Prof. Petkov has a course which is focussed on the philosophical implications of relativity, although it's probably just an extension of what I learned in his intro course. I would like to study Poincaré though... I attended a lecture at McGill by a prof from Oxford (Harvey Brown—really nice, smart guy) about time and relativity, and he mentioned Poincaré several times.

Regarding antirealism (although you didn't use that term specifically), both Prof. Petkov and the introductory text I have say that the word "antirealism" is specifically about "unobservable entities" like electrons and such. I expected it be more general, about the mathematical models used in physics and such. I wonder if this has a different name, or if there's a lot of disagreement about the word "antirealism". Strange. Anyway yet another area I need to look into.