Do our observations depend upon the quantum state of the universe?

Abstract
Here I shall call elements (1)-(3) the quantum state (or the “state”), since they give the quantum state of the universe that obeys the dynamical laws and is written in terms of the kinematic variables, and I shall call elements (4)-(6) the probability rules (or the “rules”), since they specify what it is that has probabilities (here taken to be the results of observations, Oj, or “observations” for short), the rules for extracting these observational probabilities from the quantum state, and the meaning of the probabilities. What I shall write below is largely independent of the meaning of the probabilities, though personally I view them in a rather Everettian way as objective measures for the set of observations with positive probabilities. Usually it is implicitly believed that the observational probabilities depend strongly upon the quantum state. (Sometimes the Everett interpretation [2] is taken to mean that all of physical reality is determined purely by the quantum state, without the need for any additional rules to extract probabilities, but this extreme view seems untenable [4] and will not be adopted here. Instead, I shall discuss the opposite view, that the probabilities are independent of the quantum state.) However, some advocates of inflation[5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22] often claim that our observations do not depend upon the quantum state at all, but rather that inflation acts as an attractor to give the same statistical distribution of observations from any state. In this note, I shall use the framework of state plus rules to discuss this possibility that observational probabilities might be independent of the quantum state. I shall show that this indeed is logically possible, but apparently only if the probability rules are rather ad hoc. If indeed the rules are this ad hoc, so that the probabilities of our observations do not depend upon a quantum state at all, it would seem to leave it mysterious why many of our observations can be simply interpreted as if our universe really were quantum..
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