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Thanks, Ken. I now read your work with Price, and indeed my point above largely overlaps with your discussion there.
Regarding consciousness, please don’t bring that into the discussion – I’m sure it won’t help, just like the introduction of the concept of “free will” led to much discussion, with only a fraction pertaining to the relevant quanum phenomena. These notions are too human, and therefore much harder to understand than physical phenomena, even quantum phenomena! And for the purposes of discussing and studying quantum phenomena, measuring devices which irreversibly register the results (in their memories) are completely sufficient (in the other case, “free variables” is a completely well-defined mathematical concept which plays the relevant role in the discussion, without leading one astray from quantum physics into human affairs).
That said, I completely agree with you that one needs to spend some time clarifying these issues for oneself. I did so recently, re-reading parts of Price’s book in the process. The upshot is that the fact that we can only remember the past and not the future (or, to be more careful, our computer memories can only register information from their past…) is yet another instance of the Principle of Independent Incoming Influences, and is tightly related with the fact that there are sources of low entropy in the past. For example, if you want to store a bit A in memory, you can take a blank bit M=0 of memory, and perform a controlled-not operation, with A your control. After this, M will “remember” A. The controlled-not operation is reversible, but you can’t run the procedure in reverse because there’s no way to bring in a blank (low entropy) bit of memory from the future.
I hope this helps. Nathan.