On Fri, 7 Feb 2020 at 15:59, Bruce Kellett <[email protected]> wrote:
> From: Bruno Marchal <[email protected]> > > Date: Fri, Feb 7, 2020 at 12:45 AM > Subject: Re: Postulate: Everything that CAN happen, MUST happen. > To: <[email protected]> > > > > On 4 Feb 2020, at 23:13, Bruce Kellett <[email protected]> wrote: > > On Wed, Feb 5, 2020 at 12:13 AM Bruno Marchal <[email protected]> wrote: > >> On 3 Feb 2020, at 22:46, Bruce Kellett <[email protected]> wrote: >> >> On Tue, Feb 4, 2020 at 2:48 AM Bruno Marchal <[email protected]> wrote: >> >>> On 2 Feb 2020, at 12:32, Alan Grayson <[email protected]> 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. > Nevertheless Many Worlds is at least logically possible. What would the inhabitants expect to see, if not the world we currently see? -- Stathis Papaioannou -- 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/CAH%3D2ypX4Sk0X5my1Wf%3Df1RUK4y7JSv2iiY8pJHN0HUJSJ3fw4w%40mail.gmail.com.
