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I’ve finally read not only your “information” article but also your 1307 arXiv preprint, which indeed required some “wading.” I must say I think you’re on the right path, with the most appropriate motivations I’ve seen yet (that is, of course, to the best of my judgement). And there’s a lot to do. I wonder why there aren’t more people working along such lines. For example, do you know what Rob Spekkens thinks about your line of argument? Does he accept now that retrocausation is worth pursuing?
Two things on the technical level: (a) I think you will need a measure for paths, as in Feynman path integrals; they’re not discrete, and you can’t just count them with integers; (b) Even accepting your idea of an entropy for 4D histories, I still think we’ll need the 3D concept in addition, e.g., so as to be able to identify low-entropy past boundary conditions, etc.
And one more thing: I think that by the time we’ve learned how to describe a measurement in a retrocausal theory of local beables, we will see that our ontic variables describe waves (with quantum noise, not just a solution of a PDE), but our epistemic variables are nevertheless “corpuscular,” in the sense that once something has been measured irreversibly, even just a single click in the detector, it’s either there or it isn’t. So the “it from bit” ideas will still apply in some sense, but only in the limited sense relevant to the epistemic variables. (And, of course, unitary evolution will be natural – you simply can’t change the information in your epistemic state between updates).
OK, I guess that’s it. Thank you very much for your efforts in oganizing this, and especially for inviting me to join in. Please tell me if you’d like to look at the stochastic quantization ideas and discuss them as well.