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Thank you for your helpful comments and the important issues they raise.
As Eli and I are now commenting separately, we can allow ourselves to diverge somewhat from the essential points of agreement on which our papers are based. So this is also a dialogue between the authors.
Indeed, both TI and TSVF seem to be more compatible with the Block Universe view. However in both cases their originators explicitly distant themselves from this view, even sympathizing, to a lesser or greater degree, the notion of Becoming, namely some Bergsonian/Whiteheadian picture within which the “now” moving from past to future is not a subjective illusion but rather an essential aspect of time which still lies outside of physical theory. I already mentioned a recent paper of Cramer http://arxiv.org/pdf/1503.00039 which presents this shift in his thinking. And of course Ruth Kastner’s version of TI suggest a revision in this direction. As for Yakir Aharonov, with whom we are in close contact, he often says that his TSVF is equally compatible with Block Universe and Becoming, but his own sympathy is strongly with the latter. He is actually planning a paper on this issue.
I am adding a PPT file of my talk on these issues
– see especially slides 9-10.
More comments are to follow.