In Post #21, Chalnoth claimed the block universe view to be "widely discredited", although the Wikipedia piece he refers to seems noncommittal, and I've never heard of the guy who texted Brian Greene with some objections to it. (Sorry, Chalnoth; the quotes editing doesn't seem to be working right now.) I googled this issue extensively this past week, and that's not my impression.at all.
The most comprehensive discussion I found is on Stanford's encyclopedic site, heavily revised in 2013 and found here:
http://plato.stanford.edu/entries/spacetime-bebecome/
The block universe view can be traced back to Einstein, both through his own writings and through a biographer who was a friend of his. "Andromeda Paradox" brings up a raft of sites referring to some of the situations that resulted in it, and I'd say it's at the heart of Special Relativity, or, at least, of the diagramming taught to Einstein by his physics teacher, Minkowski, who developed the method for it.
I'm sure that that view (that the past, present, and future all exist) is vastly stronger than it was before it started taking shape with the 1918 experimental confirmation of relativity (which integrated time with space), and much stronger than it was even as recently as 1981, because of inflationary theory that (together with limits on the relevance of spatial separations below a certain tiny size that result from Heisenberg's Uncertainty Principle) leaves it perhaps looking kind of unlikely that there aren't innumerable replicas of ourselves living in innumerable replicas of our "observable region" right at this instant, and that there won't be even (vastly) more replicas of the entire "local universe" (including that entire "observable region") scattered through a multiverse between now and the infinite future, although most of those replicas may be on scales of size that are self-consistent, but different from our own.
The view that the past, present, and future all exist seems counterintuitive because it doesn't explain the sensation that time flows. Thing is, since electrons do circulate through our nervous system, our impressions do flow, and the Stanford piece concludes with a description of light cones on a very small scale, moving along world lines, as possibly the best explanation of that flowing sensation.