The actual predictions of what we should actually observe are the same for all the various interpretations of quantum mechanics
You are missing MWI’s problem with the Born rule. If each “branch” exists only once, then all outcomes are equally probable, which is empirically wrong.
You are missing MWI’s problem with the Born rule. If each “branch” exists only once, then all outcomes are equally probable, which is empirically wrong.
You keep asserting this, but you have not provided any good reason to believe it. Your assumption seems to be that the counting rule is the natural understanding of probability in MWI. I don’t see this at all. As far as I can tell, there is no “natural” way to interpret probability in MWI.
Consider an analog: a Parfit-esque case of fission, where your body is disintegrated and, instantaneously, two atom-for-atom duplicates are produced in different parts of the world. Call these duplicates Mitchell-1 and Mitchell-2. It certainly does not seem natural to apply the counting rule and say that there is a 50% chance that you are now Mitchell-1. I fail to see why that would be the default position. The appropriate default position seems to be that probabilities are irrelevant here. I think that is the right default position in the MWI case as well, and it is incumbent on all proponents of probabilities in MWI to justify why one should be talking about probabilities at all. I can understand the criticism that talk of probabilites in MWI is incoherent, but I really don’t understand the criticism that probabilities in MWI must be branch frequencies.
As far as I can see, the only way to justify talk of probabilities in the fission case (and, by extension, in MWI) is to think about it from the perspective of the agent’s decision-making process prior to the fission. Perhaps even this is insufficient to get us any coherent notion of probabilities, but it seems like the only semi-plausible candidate. If you’re going to justify the counting rule, you need to tell me why it would make sense for an agent in an Everettian world to organize expectations in accord with the counting rule. And this justification should not sneak in prior probabilistic ideas (like the idea that the agent is equally likely to end up in each future branch). Wallace claims to have provided such a justification for the Born rule. If you want me to take the counting rule seriously, I’d like to see an attempt at a similar justification.
It certainly does not seem natural to apply the counting rule and say that there is a 50% chance that you are now Mitchell-1.
Let’s suppose I am to be disintegrated as you suggest, to be replaced with these atomic duplicates, Mitchell-1 and Mitchell-2. But we add that Mitchell-1 will be gunned down, and Mitchell-2 will not be.
Now suppose you ask me, before this disintegration, “what are the odds that a randomly selected future duplicate of yours will be one that is gunned down?” The answer is 50%.
But this is analogous to the situation in Many Worlds, before a branching. I, here, now, will cease to be; in my place will be a variety of distinct successors. Why is it illegitimate to reason about them in exactly the same way?
Now suppose you ask me, before this disintegration, “what are the odds that a randomly selected future duplicate of yours will be one that is gunned down?” The answer is 50%.
This is true, but irrelevant. There is no random selection going on. By the same token I could say that if you asked “What are the odds that a future self selected according to the Born rule will observe spin-up in this experiment?” you’d recover quantum statistics. But then you’d rightly challenge me by asking why this particular question should matter. Well, I can ask the same of your random selection question.
Here’s one way random selection might be relevant in the fission case. Perhaps, pre-split, the agent should reason as if in a position of complete subjective uncertainty about which future branch is him. If this is right, then it seems reasonable that in a classical world he should assign a maximum entropy distribution over future selves, and so he should reason as if his future self is being randomly selected from all the future duplicates. This sort of argument might justify the random selection assumption. But Wallace makes exactly this sort of argument for the quantum case, except he claims that there are symmetry considerations involved in that case which make it more reasonable to use the Born distribution when one is in a state of complete subjective uncertainty.
The other potential justification I can see for the random selection assumption is that you are using some anthropic selection rule like Bostrom’s Self Sampling Assumption. I think it is far from clear that the SSA is the right way to reason anthropically. In any case, Bostrom himself modifies the SSA to fit Born statistics in his discussion of MWI in his book.
My question was constructed in order to completely sidestep questions of persistent identity (i.e., which future duplicate, if any, is me?). It could have been phrased as follows: “What percentage of my future duplicates will be gunned down?” The answer is 50%, because by hypothesis, there are two duplicates, one is shot, the other isn’t. There is nothing there about random selection or any other sort of selection. There is also no uncertainty about which future copy “is me”; that’s not what I’m asking; a future entity counts for such a question if it is a duplicate of me, and by hypothesis there are two of them.
So why can I not reason in exactly this way about my quantum successors according to MWI? I am not asking “What should I expect to see?”; I am asking, “How many of my decohered successors will have a certain property?”
If each “branch” exists only once, then all outcomes are equally probable,
You keep making this claim, and it keeps not making sense. It isn’t even true for classical mechanics. A coin can have two sides, and it can still be made to favor one side more than the other.
This resembles the misleading dichotomy between “observation” and “existence”, discussed elsewhere. If you want to talk about bias in the coin, then we should be talking about the existence and the number of coin flips.
You are missing MWI’s problem with the Born rule. If each “branch” exists only once, then all outcomes are equally probable, which is empirically wrong.
You keep asserting this, but you have not provided any good reason to believe it. Your assumption seems to be that the counting rule is the natural understanding of probability in MWI. I don’t see this at all. As far as I can tell, there is no “natural” way to interpret probability in MWI.
Consider an analog: a Parfit-esque case of fission, where your body is disintegrated and, instantaneously, two atom-for-atom duplicates are produced in different parts of the world. Call these duplicates Mitchell-1 and Mitchell-2. It certainly does not seem natural to apply the counting rule and say that there is a 50% chance that you are now Mitchell-1. I fail to see why that would be the default position. The appropriate default position seems to be that probabilities are irrelevant here. I think that is the right default position in the MWI case as well, and it is incumbent on all proponents of probabilities in MWI to justify why one should be talking about probabilities at all. I can understand the criticism that talk of probabilites in MWI is incoherent, but I really don’t understand the criticism that probabilities in MWI must be branch frequencies.
As far as I can see, the only way to justify talk of probabilities in the fission case (and, by extension, in MWI) is to think about it from the perspective of the agent’s decision-making process prior to the fission. Perhaps even this is insufficient to get us any coherent notion of probabilities, but it seems like the only semi-plausible candidate. If you’re going to justify the counting rule, you need to tell me why it would make sense for an agent in an Everettian world to organize expectations in accord with the counting rule. And this justification should not sneak in prior probabilistic ideas (like the idea that the agent is equally likely to end up in each future branch). Wallace claims to have provided such a justification for the Born rule. If you want me to take the counting rule seriously, I’d like to see an attempt at a similar justification.
Let’s suppose I am to be disintegrated as you suggest, to be replaced with these atomic duplicates, Mitchell-1 and Mitchell-2. But we add that Mitchell-1 will be gunned down, and Mitchell-2 will not be.
Now suppose you ask me, before this disintegration, “what are the odds that a randomly selected future duplicate of yours will be one that is gunned down?” The answer is 50%.
But this is analogous to the situation in Many Worlds, before a branching. I, here, now, will cease to be; in my place will be a variety of distinct successors. Why is it illegitimate to reason about them in exactly the same way?
This is true, but irrelevant. There is no random selection going on. By the same token I could say that if you asked “What are the odds that a future self selected according to the Born rule will observe spin-up in this experiment?” you’d recover quantum statistics. But then you’d rightly challenge me by asking why this particular question should matter. Well, I can ask the same of your random selection question.
Here’s one way random selection might be relevant in the fission case. Perhaps, pre-split, the agent should reason as if in a position of complete subjective uncertainty about which future branch is him. If this is right, then it seems reasonable that in a classical world he should assign a maximum entropy distribution over future selves, and so he should reason as if his future self is being randomly selected from all the future duplicates. This sort of argument might justify the random selection assumption. But Wallace makes exactly this sort of argument for the quantum case, except he claims that there are symmetry considerations involved in that case which make it more reasonable to use the Born distribution when one is in a state of complete subjective uncertainty.
The other potential justification I can see for the random selection assumption is that you are using some anthropic selection rule like Bostrom’s Self Sampling Assumption. I think it is far from clear that the SSA is the right way to reason anthropically. In any case, Bostrom himself modifies the SSA to fit Born statistics in his discussion of MWI in his book.
My question was constructed in order to completely sidestep questions of persistent identity (i.e., which future duplicate, if any, is me?). It could have been phrased as follows: “What percentage of my future duplicates will be gunned down?” The answer is 50%, because by hypothesis, there are two duplicates, one is shot, the other isn’t. There is nothing there about random selection or any other sort of selection. There is also no uncertainty about which future copy “is me”; that’s not what I’m asking; a future entity counts for such a question if it is a duplicate of me, and by hypothesis there are two of them.
So why can I not reason in exactly this way about my quantum successors according to MWI? I am not asking “What should I expect to see?”; I am asking, “How many of my decohered successors will have a certain property?”
If that’s the question you’re asking, then it’s obvious frequencies are the way to go. But why is this a problem for the MWI?
You keep making this claim, and it keeps not making sense. It isn’t even true for classical mechanics. A coin can have two sides, and it can still be made to favor one side more than the other.
This resembles the misleading dichotomy between “observation” and “existence”, discussed elsewhere. If you want to talk about bias in the coin, then we should be talking about the existence and the number of coin flips.