On Sun, Sep 6, 2020 at 4:11 AM 'Brent Meeker' via Everything List < everything-list@googlegroups.com> wrote:
> On 9/4/2020 11:27 PM, Bruce Kellett wrote: > > No, listen carefully. Everett predicts that such a sequence will certainly > occur for any N. In other words, the probability of the occurrence of such > a sequence is one. Whereas the Born rule, as we both now seem to agree, > predicts that the probability for the occurrence of such a sequence is > 1/2^N. It is the fact that Everett and the Born rule predict different > probabilities for the same sequence that is the point -- not that either > predicts the impossibility of such a sequence. It is the predicted > probabilities that differ, not the sequences. > > And if you have a theory that predicts two different values for some > result, then your theory is inconsistent. Everett and the Born rule are > inconsistent because they predict different probabilities for this sequence > of N |up>s in N trials (or any other particular sequence, for that matter. > Even though that latter point seems to have confused you!) > > > But you are not using Everett's theory. You're strawmanning Evertt. > It is ultimately a waste of time to argue over exactly what Everett (or any other figure in the history of physics) actually said or thought. That can be the realm of historians of science, but it is not really relevant for the working physicist. What the working physicist is (or should be) concerned with, is the basic ideas; regardless of how the historical figure might have worked with them. So you can think that I am strawmanning Everett -- I actually disagree, but I don't really care. The important point that I am taking from Everett is that the Schrodinger equation is the whole of quantum physics (Carroll's idea). If the wave function of the SE does not collapse (and there is no collapse in the Schrodinger equation), then every possible component of any superposition certainly exists, and continues to exist. This means that when you consider the superposition relevant to a measurement interaction, all possible outcomes of the measurement exist (in separate branches of the universal wave function). > You're saying that since Everett says some sequence occurs he is predicting* > it* with probability 1. But that's only predicting that *it* occurs in > evolution of the wave function. > Sure. I think that is what I just said -- the branch corresponding to any possible outcome exists in the universal wave function. And, ipso facto, by linearity, there is an observer on that branch who sees that outcome. It's not a prediction of the QM probability that is being tested. And it's > not following thru on Everett's interpretation that connects the theory to > observation. It's imposing your idea of how it connects to observation; > essentially cutting off Everett's interpretation part way thru. > I disagree. The existence of observers who see sequences of results far from the relative frequencies predicted by the Born rule is an unambiguous consequence of Everett's approach -- nothing is being cut off, or left out. Everett's theory is deterministic so it's not relevant to criticize it for > "predicting probability 1" when it predicts all the results. > I am not criticizing it for "predicting probability one" -- I see that as a necessary consequence of the theory, since it certainly predicts that every outcome obtains on some branch. I am criticizing the theory for also claiming that the Born rule probabilities obtain. The Born rule predicts low probability for certain sequences, whereas Everett predicts that such sequences necessarily occur. In other words, the charge is one of inconsistency -- I am not objecting to the fact that the theory postulates that all outcomes occur in every interaction. I doubt that that is true, but that is Everett's theory, not mine. > I agree with you that you can't get a probability out of a deterministic > theory unless you put in some additional postulate...like ignorance or > coarse graining...and that's exactly what Everttian's do. They say that > the branches are an ensemble and you have some probability of being the > observer in one of the ensemble...an ignorance based probability measured > by either branch counting or weighting of branches. > Self-locating uncertainty is not resolved by either branch counting or by weighting branches. You, yourself, have pointed to the fact that in the 2^N binary sequences in the repeated two-outcome experiment peak around the centre, corresponding to p = 0.5. If you implement self-locating uncertainty in the abstract as the operation of taking a random history from this set (assuming sampling from a uniform distribution over the set), then you are more likely to end up in a history towards the peak of the distribution rather than in a history far out in one of the tails. If this is what one means by self-locating uncertainty, then this has nothing to do with either branch counting, or with differential weighting of branches. As an interesting aside, it is relatively easy to see that there is no way in this picture for the self-locating uncertainty to favour any probability other that p = 0.5 -- the set of possible histories is independent of the branch amplitudes (weights) so there is no way the Born rule can get any purchase, and branch weights are strictly irrelevant. In other words, for the interpretation to get off the ground at all, one has to deviate considerably from the "purity of the Schrodinger equation". Increasing the number of branches on any interaction according to the desired Born weights simply contradicts the Schrodinger equation, and adding ad hoc weights according to the Born rule and treating these as probabilities also throws the basic assumption that every possible outcome occurs on every interaction under the bus. (In practice, Everettians simply ignore this fact, and treat the Born weights as the full story. It is not surprising that one has to do this, because there is essentially no other way to avoid the glaring inconsistency at the heart of the theory.) It is a bit rich, therefore, for you to criticize me for "departing from the original spirit of Everett." I think this is a kind of cheat, since it is not simply a consequence of > Schroedinger's equation. On the other hand, Gleason's theorem is a > consequence. So once you cheat enough to introduce the probability > concept, getting to Born's rule is just a matter of making up a story you > like. > Exactly. It depends on how much you are prepared to fool yourself into thinking that the MWI makes sense. So my view is that once you've developed decoherence theory and you've > shown that the reduced density matrix is diagonalized, you might as well > then bite-the-bullet and postulate that the theory is probabilistic. Then > the math (Gleason's theorem) forces the interpretation that those diagonals > are the probabilities of results. Then "everything happens" is just a > story attempting to back-fill a picture of how you got there based on > ignorance (self-locating uncertainty). There are some people who can't > abide probabilistic theories and will invent fantastic worlds in order to > have a deterministic ensemble which then must be reduced by ignorance to > agree with observation. They then feel they've made great progress because > they think their theory is deterministic. > So why do you defend Carroll and Everett? Even self-locating uncertainty is an essentially probabilistic idea. 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