I always thought that in naive MWI what matters is not whether something happens in absolute sense, but what Born measure is concentrated on branches that contain good things instead of bad things.
The problem is this requires introducing a special decision-theory postulate that you’re supposed to care about the Born measure for some reason, even though Born measure doesn’t correspond to ordinary probability.
Huh? The whole point of the Born rule is to get a set of ordinary probabilities, which you can then test frequentistically, over a run of experiments. Quantum mechanical measure—amplitude—isn’t ordinary probability, but that’s the thing you put into the Born rule, not the thing you get out of it. And it has it’s own role, which is explaining how much contribution to a coherent superposition each component state makes.
ETA
There is a further problem interpreting the probabilities of fully decohered branches. (Calling then Everett branches is very misleading—a clear theory of decoherence is precisely what’s lacking in Everett’s work)
Whether you are supposed to care about them ethically is very unclear, since it is not clear how utilitarian style ethics would apply, even if you could make sense of the probabilities. But you are not supposed to care about them for the purposes of doing science, since they can no longer make any difference to your branch. MWI works like a collapse theory in practice.
always thought that in naive MWI what matters is not whether something happens in absolute sense, but what Born measure is concentrated on branches that contain good things instead of bad things.
It’s tempting to ethically discount low measure decoherent branches in some way, because that most closely approximates conventional single world utilitarianism—that is something “naive MWI” might mean. However, one should not jump to the conclusion that something is true just because it is convenient. And of course, MWI is a scientific theory so it doesn’t comes with built in ethics.
The alternative view starts with the question of whether a person low measure world still count as a full.person? If they should not, is that because they are a near-zombie, with a faint consciousness that weighs little in a hedonic utilitarian calculus? If they are not such zombies, why would they not count as a full person—the standard utilitarian argument that people in far-off lands are still moral patients seems to apply. Of course, MWI doesn’t directly answer the question about consciousness.
(For example, if I toss a quantum fair coin n times, there will be 2^n branches with all possible outcomes.)
If “naive MWI” means the idea that any elementary interaction produces decoherent branching, then it is wrong for the reasons I explain here. Since there are some coherent superpositions, and not just decoherent branches, there are cases where the Born rule gives you ordinary probabilities, as any undergraduate physics student knows.
(What is the meaning of the probability measure over the branches if all branches coexist?)
It’s not the existence, it’s the lack of interaction/interference.
The topic of this thread is: In naive MWI, it is postulated that all Everett branches coexist. (For example, if I toss a quantum fair coin n times, there will be 2n branches with all possible outcomes.) Under this assumption, it’s not clear in what sense the Born rule is true. (What is the meaning of the probability measure over the branches if all branches coexist?)
I always thought that in naive MWI what matters is not whether something happens in absolute sense, but what Born measure is concentrated on branches that contain good things instead of bad things.
The problem is this requires introducing a special decision-theory postulate that you’re supposed to care about the Born measure for some reason, even though Born measure doesn’t correspond to ordinary probability.
Huh? The whole point of the Born rule is to get a set of ordinary probabilities, which you can then test frequentistically, over a run of experiments. Quantum mechanical measure—amplitude—isn’t ordinary probability, but that’s the thing you put into the Born rule, not the thing you get out of it. And it has it’s own role, which is explaining how much contribution to a coherent superposition each component state makes.
ETA
There is a further problem interpreting the probabilities of fully decohered branches. (Calling then Everett branches is very misleading—a clear theory of decoherence is precisely what’s lacking in Everett’s work)
Whether you are supposed to care about them ethically is very unclear, since it is not clear how utilitarian style ethics would apply, even if you could make sense of the probabilities. But you are not supposed to care about them for the purposes of doing science, since they can no longer make any difference to your branch. MWI works like a collapse theory in practice.
It’s tempting to ethically discount low measure decoherent branches in some way, because that most closely approximates conventional single world utilitarianism—that is something “naive MWI” might mean. However, one should not jump to the conclusion that something is true just because it is convenient. And of course, MWI is a scientific theory so it doesn’t comes with built in ethics.
The alternative view starts with the question of whether a person low measure world still count as a full.person? If they should not, is that because they are a near-zombie, with a faint consciousness that weighs little in a hedonic utilitarian calculus? If they are not such zombies, why would they not count as a full person—the standard utilitarian argument that people in far-off lands are still moral patients seems to apply. Of course, MWI doesn’t directly answer the question about consciousness.
If “naive MWI” means the idea that any elementary interaction produces decoherent branching, then it is wrong for the reasons I explain here. Since there are some coherent superpositions, and not just decoherent branches, there are cases where the Born rule gives you ordinary probabilities, as any undergraduate physics student knows.
It’s not the existence, it’s the lack of interaction/interference.
The topic of this thread is: In naive MWI, it is postulated that all Everett branches coexist. (For example, if I toss a quantum fair coin n times, there will be 2n branches with all possible outcomes.) Under this assumption, it’s not clear in what sense the Born rule is true. (What is the meaning of the probability measure over the branches if all branches coexist?)