I disagree that using the latter to generate a sensory stream from a quantum state yields reasonable predictions—eg, taken literally I think you’re still zeroing out all but a measure-zero subset of the position basis
The observation you got from your sample is information. Information is entropy, and entropy is locally finite. So I don’t think it’s possible for the states consistent with the observation you got from your sample to have measure zero.
When you’re using TMs to approximate physics, you have to balance the continuity of physics against the discreteness of the machines somehow. The easy thing to do is to discuss the limiting behavior of a family of machines that perform the simulation at ever-finer fidelity. I was doing this implicitly, for lack of desire to get into details.
And as I’ve said above, I’m not attempting to suggest that these naive approaches—such as sampling a single classical state and reporting the positions of some things with arbitrary fidelity in the limit—are reasonable ideas. Quite the opposite. What I’m trying to point out is that if all you have is a quantum state and the Born rule, you cannot turn it into a hypothesis without making a bunch of other choices, for which I know of no consensus answer (and for which I have not seen proposals that would resolve the problem to my satisfaction, though I have some ideas).
I agree that the correct way of making these choices will almost surely not involve recording any observation with infinite precision (in the limit).
The observation you got from your sample is information. Information is entropy, and entropy is locally finite. So I don’t think it’s possible for the states consistent with the observation you got from your sample to have measure zero.
When you’re using TMs to approximate physics, you have to balance the continuity of physics against the discreteness of the machines somehow. The easy thing to do is to discuss the limiting behavior of a family of machines that perform the simulation at ever-finer fidelity. I was doing this implicitly, for lack of desire to get into details.
And as I’ve said above, I’m not attempting to suggest that these naive approaches—such as sampling a single classical state and reporting the positions of some things with arbitrary fidelity in the limit—are reasonable ideas. Quite the opposite. What I’m trying to point out is that if all you have is a quantum state and the Born rule, you cannot turn it into a hypothesis without making a bunch of other choices, for which I know of no consensus answer (and for which I have not seen proposals that would resolve the problem to my satisfaction, though I have some ideas).
I agree that the correct way of making these choices will almost surely not involve recording any observation with infinite precision (in the limit).