My recollection is that Jaynes deals with this point. He discusses in particular time varying lambda (or I'd say maybe space-time varying lambda). As a general proposition, I don't know how you could ever rule out a hidden variable theory with time variation faster than your current ability to measure.
He has another paper, where he speculates about the future of quantum theory, and talks about phase versus carrier frequencies, and suggests that phase may be real and could determine the outcome of events.
The obvious way to get "random" detection probability deterministically would be the time varying dependency on the interaction of photon polarization, phase of the wavefront, and detector direction.
If you'd like to discuss this in more detail, I'd keep this thread alive for a while, as it's an issue I'd like to clear up for myself.
(I'll look up the paper when I have more time. EDIT - paper put in first post.)
Today's post, Bell's Theorem: No EPR "Reality" was originally published on 04 May 2008. A summary (taken from the LW wiki):
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