How seriously is the idea taken that the passage of time is a purely subjective phenomenon? (I just read Palle Yourgrau's book on Gödel, who apparently came to such a conclusion via the theory of general relativity.) How might such an interpretation relate to Kant's view of time?

Many philosophers in the past half-century or so, especially those influenced by physics, have taken the passage of time to be wholly subjective. Physics (Newtonian as well as Einsteinian) appeals to temporal relations like 'earlier than' or 'simultaneous with', never to an ongoing now that passes. (Minkowski diagrams use 'now' as a label for a point of origin, but that's a far cry from passage of time.) Recently, some philosophers have turned the tables, and taken 'past','present' and 'future' to be fundamental (and not merely subjective). So, there is a lively debate now about the status of the present moment. For references on the contemporary debate, see the entry on "Time" in the Stanford Encyclopedia of Philosophy. (It's free on the internet, and a great resource.) Kant doesn't exactly fit into the terms of the contemporary debate. I'm no Kant scholar, but I think that Kant took time to be something like succession--we experience one thing after another. Kant took time to be...