On Thursday, February 6, 2020 at 10:59:27 PM UTC-6, Bruce wrote: > > From: Bruno Marchal <[email protected] <javascript:>> > > Date: Fri, Feb 7, 2020 at 12:45 AM > Subject: Re: Postulate: Everything that CAN happen, MUST happen. > To: <[email protected] <javascript:>> > > > > On 4 Feb 2020, at 23:13, Bruce Kellett <[email protected] <javascript:>> > wrote: > > On Wed, Feb 5, 2020 at 12:13 AM Bruno Marchal <[email protected] > <javascript:>> wrote: > >> On 3 Feb 2020, at 22:46, Bruce Kellett <[email protected] <javascript:>> >> wrote: >> >> On Tue, Feb 4, 2020 at 2:48 AM Bruno Marchal <[email protected] >> <javascript:>> wrote: >> >>> On 2 Feb 2020, at 12:32, Alan Grayson <[email protected] <javascript:>> >>> wrote: >>> >>> On Saturday, February 1, 2020 at 11:42:12 PM UTC-7, Brent wrote: >>> >>>> First, it's false. You can make it true by interpreting "can happen" >>>> to mean "can happen according the prediction of quantum mechanics for this >>>> situation", but then it becomes trivial. Second, it's not "at the heart >>>> of >>>> MWI"; the trivial version is all that MWI implies. Read the first few >>>> paragraphs of this paper: >>>> >>>> arXiv:quant-ph/0702121v1 13 Feb 2007 >>>> >>>> Brent >>>> >>> >>> In posing the question, I want to give its advocates such as Clark the >>> opportunity to justify the postulate. It goes way beyond the MWI and QM. >>> E.g., it means that if someone puts on his/her right shoe first this >>> morning, there must be a universe in which a copy of the person puts on >>> his/her left shoe first. It seems way, way over the top, but oddly many >>> embrace it with gusto. AG >>> >>> >>> >>> That is already completely different, as it seems to say that everything >>> happen with the same probability, but that is non sense, >>> >> >> No, it is exactly what Everett predicts. >> >> >> If that was the case, I don’t think we would still be here discussing >> Everett. >> >> Everything that happens happens with probability one. >> >> >> Everett insists, perhaps wrongly (but then that is what should be >> debated) that he recovers the usual quantum statistics, where the >> probability is given by the square of the amplitude of the wave. >> > > It turns out, in fact, that Everett did not prove this result. As in > conventional QM, he just asserted it. > > > > He provides argument, which actually were already found by Paulette > Février-destouche in France 20 years before Everett, and correspond more or > less to the argument made by Graham in the selected paper by DeWitt and > Graham on the MWI, and by Preskill in his textbook in Quantum Mechanics. > Is that argument totally convincing? Perhaps not, but let us say that I > think it is improvable, and it is going in the direction that we can expect > when postulating Mechanism (as do Everett, and many others, consciously or > unconsciously). > > > Everett's argument is far from convincing. It is criticized by Simon > Saunders in the book "Many Worlds?: Everett, Quantum Theory, & Reality", > and by David Wallace in his book on "The Emergent Multiverse". Perhaps the > most telling critique of Everett's idea has been given by Adrian Kent in > his contribution to the book, cited above, that he edited with Simon > Saunders and David Wallace. I give extensive quotations below, and attach a > pdf with these comments in a more friendly format. Note that Kent's > critique also undermines any idea that you can attach probabilities to > outcomes in your W/M duplication scenarios in Step 3. > > > Born Rule in Everettian Many Worlds Theory > > Everett gives an argument for the Born rule in his 1957 paper. Simon > Saunders (in his introduction to the volume of essays: "Many Worlds?: > Everett, Quantum Theory, & Reality", OUP 2010) gives the following summary > of Everett's argument: > > "But Everett was able to derive at least a fragment of the Born rule. > Given that the measure over the space of branches is a function of the > branch amplitudes, the question arises: What function? If the measure is to > be additive, so that the measure of a sum of branches is the sum of their > measures, it follows that it is the modulus square---that was something. > The set of branches, complete with additive measure, then constitute a > probability space. As such, version of the Bernouilli and other large > number theorems can be derived. They imply that the measure of all the > branches exhibiting anomalous statistics (with respect to this measure) is > small when the number of trials is sufficiently large, and goes to zero in > the limit---that was something more." > > This account can be criticized on several grounds. Firstly, it relies on > the limit of infinitely many trials, whereas in practice, we only ever have > a finite number of such trials. Another criticism is that there is not any > solid basis for the assumption that the measure should depend only on the > branch weights---why should it not depend on the actual structure of the > branches themselves? The other main line of objection relates to the simple > application of Everett's rule in the case where all possible outcomes occur > on each trial. In that case, all possible sequences of results occur, so > that predictions using this rule would have been wildly contradicted by the > emperical evidence---which only goes to show that the Born Rule, far from > being an obvious consequence of the interpretation of the quantum state in > terms of many worlds, appears quite unreasonable. > > > This latter point is made very strongly by Adrian Kent in his contribution > to the above cited volume of collected essays (pp. 307--354). > > Kent considers a toy multiverse, which is classical, but in which branches > are multiplied to record all possible results. The first such world he > considers includes conscious inhabitants, but which also includes a machine > with a red button on it, and a tape emerging from it, with a sequence of > numbers on it, all in the range 0 to (N-1). When the red button is pressed > in some universe within the multiverse, that universe is deleted, and N > successor universes are then created. All the successors are in the same > classical state as the original (and so, by hypothesis, all include > conscious inhabitants with the same memories as those who have just been > deleted), except that a new number has been written onto the end of the > tape, with the number 'i' being written in the 'i'-th successor universe. > > Suppose, further, that some of the inhabitants of this multiverse have > acquired the theoretical idea that the laws of their multiverse might > attach 'weights' to branches, i.e., a number p_i is attached to branch 'i', > where p_i >= 0 and Sum_i p_i = 1. They might have various different > theories about how these weights are defined.... To be clear: this is not > to say that the branches have equal weight. Nor are they necessarily > physically identical, aside from the tape numbers. However, any such > differences do not yield any natural quantitative definition of branch > weights. There is just no fact of the matter about branch weights in this > multiverse. > > Kent goes on the say: > > "Everettian quantum theory is essentially useless, as a scientific theory, > unless it can explain the data that confirm the validity of the Copenhagen > quantum theory within its domain---unless, for example, it can explain why > we should expect to observe the Born rule to have been very well confirmed > statistically. Evidently, Everettians cannot give an explanation that says > that all observers in the multiverse will observe confirmation of the Born > rule, or that very probably all observers will observe confirmation of the > Born rule. On the contrary, many observers in an Everettian multiverse will > definitely observe convincing 'discomfirmation' of the Born rule. > > "It suffices to consider very simple many-worlds theories, containing > classical branching worlds in which the branches correspond to binary > outcomes of definite experiments. Consider thus the 'weightless > multiverse', a many-worlds of the type outlined above, in which the machine > produces only two possible outcomes, writing 0 or 1 onto the tape. Suppose > now that the inhabitants begin a series of experiments in which they push > the red button on the machine a large number, N, times, at regular > intervals. Suppose too that the inhabitants believe (correctly) that this > is a series of independent identical experiments, and moreover believe this > 'dogmatically': no pattern in the data will shake their faith. Suppose also > that they believe (incorrectly) that their multiverse is governed by a > many-worlds theory with unknown weights attached to the 0 and 1 outcomes; > identical in each trial, and seek to discover the (actually non-existent) > values of these weights. > > "After N trials, the multiverse contains 2^N branches, corresponding to > all 2^N possible binary string outcomes. The inhabitants on a string with > pN zero and (1 - p)N one outcomes will, with a degree of confidence that > tends towards one as N gets large, tend to conclude that the weight 'p' is > attached to zero outcome branches and weight (1 - p) is attached to one > outcome branches. In other words, everyone, no matter what string they see, > tends towards complete confidence in the belief that the relative > frequencies they observe represent the weights. > > "Let's consider further the perspective of inhabitants on a branch with > 'pN' zero outcomes and '(1 - p)N' one outcomes. They do not have the > delusion that all observed strings have the same relative frequency as > theirs: they understand that, given the hypothesis that they live in a > multiverse, 'every' binary string, and hence every relative frequency, will > have been observed by someone. So how do they conclude that the theory that > the weights are '(p,1 - p)' has nonetheless been confirmed?. Because they > have concluded that the weights measure the 'importance' of the branches > for theory confimation. Since they believe they have learned that the > weights are '(p,1 - p)', they conclude that a branch with 'r' zeros and '(N > - r)' ones has importance p^r(1 - p)^{N-r}. Summing over all branches with > 'pN' zeros and '(1 - p)N' ones, or very close to those frequencies, thus > gives a set of total importance very close to 1; the remaining branches > have total importance very close to zero. So, on the set of branches that > dominate the importance measure, the theory that the weights are (very > close to) (p,1 - p) is indeed correct. All is well! By definition, the > important branches are the ones that matter for theory confimation. The > theory is inded confirmed! > > "The problem, of course, is that this reasoning applies equally well for > all the inhabitants, whatever relative frequency 'p' they see on their > branch. All of them conclude that their relative frequencies represent (to > very good approximation) the branching weights. All of them conclude that > their own branches, together with those with identical or similar relative > frequencies, are the important ones for theory confirmation. All of them > thus happily conclude that their theories have been confirmed. And, recall, > all of them are wrong: there are actually no branching weights." > > > This argument from Kent completely destroys Everett's attempt to derive > the Born rule from his many-worlds approach to quantum mechanics. In fact, > it totally undermines most attempts to derive the Born rule from any > branching theory, and undermines attempts to justify ignoring branches on > which the Born rule weights are disconfirmed. In the many-worlds case, > recall, all observers are aware that other observers with other data must > exist, but each is led to construct a spurious measure of importance that > favours their own observations against the others', and this leads to an > obvious absurdity. In the one-world case, observers treat what actually > happened as important, and ignore what didn't happen: this doesn't lead to > the same difficulty. > > Bruce >
This appears to argue that observers in a branch are limited in their ability to take the results of their branch as a Bayesian prior. This limitation occurs for the coin flip case where some combinations have a high degree of structure. Say all heads or a repeated sequence of heads and tails with some structure, or apparent structure. For large N though these are a diminishing measure. An observer might see their branch as having sufficient randomness to be a Bayesian prior, but to derive a full theory these outlier branches with the appearance of structure have to be eliminated. This is not a devastating blow to MWI, but it is a limitation on its explanatory power. Of course with statistical physics we have these logarithms and the rest and such slop tends to be "washed out" for large enough sample space. No matter how hard we try it is tough to make this all epistemic, say Bayesian etc, or ontological with frequentist statistics. LC -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/fb75f022-9f9a-453b-905b-bdcfcabef740%40googlegroups.com.
