On Sun, Feb 9, 2020 at 9:48 AM 'Brent Meeker' via Everything List < [email protected]> wrote:
> On 2/8/2020 2:12 PM, Bruce Kellett wrote: > > On Sun, Feb 9, 2020 at 6:38 AM 'Brent Meeker' via Everything List < > [email protected]> wrote: > >> On 2/7/2020 11:00 PM, Bruce Kellett wrote: >> >> >> It is an indexical theory. The problem is that in MWI there will always >> be observers who see the sequences that are improbable according to the >> Born rule. This is not the case in the single-world theory. There is no >> random sampling from all possibilities in the single-world theory. >> >> >> ?? There's something deterministic in single-world QM? You seem to have >> taken the position that MWI is not just an interpretation, but a different >> theory. >> > > That is a possibility. I do think that MWI has difficulty with > probability, and with accounting for the results of normal observation. > > That some very improbable results cannot occur in SW QM. I think you are >> mistaken. >> > > I don't know where you got the idea that I might think this. > > > No matter how low a probability the Born rule assigns to a result, that >> result could occur on the first trial. >> > > > Yes, but in SW the probability of that is very low: in MWI the probability > for that is unity. > > > You keep saying that; but you're misreferencing what "that" is. The > probability of any given observer seeing the low probability event is just > that low probability. "That" isn't unity. > It is unity if the hypothesis is that every outcomes occurs for every trial. It is not a matter of any arbitrary observer -- it is that there is an observer who definitely sees that result. However, we seem to be in danger of going round in circles on this, so it > might be time to try a new tack. > > As I said, I have difficulty understanding how the concept of probability > can make sense when all results occur in every trial. If you have N > independent repetitions of an interaction or experiment that has n possible > outcomes, the result, if every outcome occurs every time, is a set of n^N > sequences of results. The question is "How does probability fit into such a > picture?" > > In any branch, when the experiment is performed, that branch is deleted > and replaced by n new branches, one for each possible outcome of the > experiment. This is clearly independent of any model for the probability > associated with each outcome. In the literature, people speak about > "weights of branches". But what does this mean? -- that there are more of > some types of branch?, or that some branches are more 'important' that > others? It does not seem clear to me that one can assign any operational > meaning to such a concept of "branch weights". > > > That's why I said that to make it work one needs to postulate that there > are many more branches than possible results, so that results can be > "weighted" by having more representation in the ensemble of branches. Then > probabilities are then proportional to branch count. That gives a definite > physical meaning to probabilities in MWI. It's a physical model that > provides "weights". BUT it's a cheat as far as saying MWI implies or > derives the Born rule. The rule has been slipped in by hand. > It certainly is a cheat. And it is a different model. It is not just an interpretation of QM -- it is a different model, incompatible with Everett. Everett is quite clear: he postulates one branch -- one 'relative state' -- for each component of a quantum superposition. This is incompatible with multiple branches for each such component. > In this situation, the set of n^N sequences of results for this series of > trials is independent of any a priori assignment of probabilities to > individual outcomes > > > I don't understand what you mean by that. Are you limiting this to a > binomial experiment, with H's and T's? And are you assuming that at every > trial each outcome occurs exactly once in the multiverse? > Did you not see that I speak of 'n' possible outcomes for every experiment? It is by no means limited to binary outcomes. And yes, I am following Everett and assuming that each trial outcomes occurs exactly once in the multiverse. If you go beyond this, then you are talking about a different, non-Everettian model. I think that most of your comments are based on your assumption that an uncountable infinity of branches is associated with each possible outcome (to accommodate all real weights). That is why we seem to be constantly talking at cross purposes -- you have not made you assumptions clear. : whatever the probabilities or weights, the set of sequences of results is > the same. In other words, for the experimentalist, the data he has to work > with is the same for any presumed underlying probabilistic model. > > > Are you saying the data he obtains has no probabilistic relation to the > ensemble of possible outcomes? You seem to be putting the Bayesian > inference backwards. The data he has is in some sense independent of any > model. But he's evaluating his model given the data. That fact that this > doesn't change the data is the same in any interpretation. > The point is that the data are independent of any probabilistic model -- given a strict Everettian interpretation of the relative states and branching. Thus the data cannot be used to evaluate any such model. Consequently, experimental data cannot be used to infer any probabalistic > model. In particular, experimental data cannot be used to test any prior > theory one might have about the probabilities of particular outcomes from > individual experiments. > > > Sure it can. The data can imply a low posterior probability for a given > model. The experimenter has gotten one particular result. It is > irrelevant that other results occurred to other copies of the experimenter. > That is only if probabilities and branch weights have an objective meaning. My contention is that they do not in a strictly Everettian model. > The conclusion would be that such a model is unable to account for > standard scientific practice, in which we definitely use experimental data > to test our theories, and as the basis for developing new and improved > theories. This is impossible on the above understanding of MWI. > > So this understanding of MWI is presumably flawed. But how? I do not see > any other realistic way to implement the idea that all possible results > occur in any trial. Talking about branch weights and probabilities seems to > be entirely irrelevant because these things have no operational > significance in such a model. > > > They are parameters to the hypothetical model to be evaluated by > calculating their posterior probability given the observed results. All > possible results don't occur in any branch. They occur in other branched > to other observers and that influences the result no more than supposing > the results are drawn from some ensemble. > Again, you seem to be implicitly relying on the assumption that branch weights actually exist and have objective meaning. In other words, your comments presume your idea of implementing probabilities as branch counts. This is a different model. It is not implicit in the Schrodinger equation, and it is certainly not what Everett envisaged. Bruce -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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