On Sun, Feb 16, 2020 at 6:11 PM 'Brent Meeker' via Everything List < [email protected]> wrote:
> On 2/15/2020 10:03 PM, Bruce Kellett wrote: > > On Sat, Feb 15, 2020 at 3:17 PM 'Brent Meeker' via Everything List < > [email protected]> wrote: > >> On 2/14/2020 2:17 PM, Bruce Kellett wrote: >> >> I attach an extract from Kent's paper. Take up your argument with him if >> you think he has got the statistics wrong. >> >> >> I don't find it very convincing >> > > Whether you are convinced or not does not really affect the logic of > Kent's argument. I think, as I have thought for some time, that your > intuitions are too conditioned by the probabilities of coin tosses in a > single world. You slip single word intuitions into your criticisms of the > many-worlds picture. > > He asserts “After N trials, the multiverse contains 2 N branches, >> corresponding to all 2 N possible binary string >> outcomes." which is not true if pushing the red button produces 0 or 1 >> with some fixed probability p0 (which isn't made clear). >> > > It is true, whatever the probability associated with pushing the red > button. And, in the case I consider, there simply is no matter-of-fact > about such probabilities. > > > I took, " Suppose too that the inhabitants believe (correctly) that this > is a series of independent identical experiments," to mean there there is > some unknown, but fixed probability of writing a 0 or 1. Otherwise I don't > know what "independent identical" means? Those are commonly statistical > terms. > Inpedendent and identical means just that, and no more. Why should there be some notion of a probability associated with it? You are too hung up on single-world statistical intuitions. When the button is pushed, two new worlds are created, one with a 0 written > on its tape and the other with a 1. > > Which implies that number of 0's and 1's will be equal, though not along a > give tape. > Yes, but what are you trying to suggest by this? The button is pushed afresh in each of the created worlds, so in each > world, two new worlds are created. This give 2^N branches or worlds for N > trials. And these worlds will contain tapes, one in each world, on which is > written the binary string corresponding to the history of results for that > world. So there are 2^N different binary strings; that exhausts the space > of possible binary strings of length N. Unless you get hold of this fact, > the rest probably will not make sense. > > Translate the red button into a Stern-Gerlach magnet measuring the x-spin > of an ensemble of particles all prepared in a z-spin up eigenstate. If we > record x-spin up as 0, and x-spin down as 1, we get exactly the same set of > 2^N binary sequences after N trials, all sequences different, as we got > from pushing the red button. The crunch comes when we rotate the S-G magnet > by 10 degrees and repeat. We still get all possible 2^N binary strings -- > the same set of strings as we found before, because this set of exhausts > the space of N binary strings. If If you are still not convinced, rotate > your S-G magnet by a further 20 degrees and repeat the N trials. Do you get > any new binary strings? Of course not, the space of possible strings has > already been exhausted. > > The message is clear, the data that any observer in any world can get is > independent of the coefficients in the original expansion of the prepared > state in an appropriate basis. The Born rule can have no relevance in > many-worlds -- whether Everettian or not. > > > There is nothing which guarantees that all sequences will occur in any >> finite sample. >> > > Think again, all 2^N sequences will occur in any set of N trials. > > > OK, each time the button is pushed and two new worlds created, which are > identical in their records up to the current writing and in one world 0 is > added to the tape and in the other 1 is added to the tape. I understand > that is not consistent with observation. And that there is no mechanism > described in Everett's evolution to deviate from this. That's why I said > that in order to get the Born rule there must be many-worlds before the > experiment which are then divided, possibly unevenly, to produce the Born > rule. > OK. You agree then that Everett is a train wreck. I wish you luck in getting unequal numbers of worlds from unitary evolution via the Schrodinger equation. It is fairly clear that this is impossible. So you abandon unitarity, and undermine the whole reason detere of MWI. But I suppose we can pass over this noting that for large enough N it is >> highly probable, though not certain. >> >> He's right that the citizens of different branches of the multiverse will >> infer different values of p from their experiments. But isn't it also true >> that most of them will infer a value close to the true value. >> > > Close to the true value? Have you not grasped the point that in the red > button case, there is no "true value". And whatever the coefficients in > the original state, the majority of binary strings will have close to equal > number of 0s and 1s -- that is just a fact about the binomial expansion. It > says nothing about the "true value", because no such true value may exist. > > > That's just metaphysical angst. 1/2 is as "true" a value as science can > ever infer. That's why I find these two paragraphs misleading: > That is just not the case. If observers in each world rely on their data to infer probabilities, they will get all values from 0 to 1. Saying that 50/50 is the preferred value is just to confuse the 3p picture with the 1p picture, as Bruno would say. There is no reason to suppose that 1/2 id the "true" probability -- the preponderance of branches with approx.mately equal number of 0 and 1 is just a consequence of the fact that there are only two possibilities -- the binomial theorem gives you this -- it has nothing to do with the physics. * “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.”* > These two paragraphs are perfectly claear, and completely correct. The "all of them" who conclude a branch weighting very different from 0.5 > will be a vanishingly small fraction. > You are brining in one-world intuitions again -- to say nothing of the 1p/3p confusion. The number of branches with particular outcomes is irrelevant. The point is that from each 1p perspective, the data that observer obtained is typical of the majority. That is what the calculations given by Kent mean. > The whole argument is "There will necessarily be outliers and they can't > tell they are outliers. Therefore science is impossible because we can > never be certain we are not misled into seeing patterns were none exist." > > And the fact that 50/50 seems to be obtained on the majority of branches > is true, even if the true probabilities are 0.99 and 0.01. > > > But you postulated that every time a 0 is printed on a tape, a 1 is > printed of the other world's tape. So every tape will be a branching graph > with 0 and 1 at each branch point. > Not really. At each branch point there will be two new worlds, one with 0 on its tape, and the other with 1 on its tape. Almost all paths thru this tree will have approximately equal numbers of > 0s and 1s per the binomial theorem. Each path corresponds to an > experimenter. So almost all experimenters will estimate P(0)=P(1)=0.5 or > nearly so. > But that is merely a consequence of the fact that we are considering only two possibilities for each trial. You confuse the 3p and 1p pictures, again. You have to focus on what each observer sees and can infer. He cannot know what other observers get. And the larger is N, the greater the percentage of branches within a small >> interval around the true value. Are there some branches in which the >> citizen infer values very different from the true value p0? Sure. But in >> a single world where N experiments have been performed to use in estimating >> p, there is a probability that some value far from p0 will be observed. >> > > > This is where you fall back on your single-world intuitions about > probability. You have to get away from this, those intuitions fail in the > many-worlds case. > > This is untrue: "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" If they have any understanding of >> statistics they will infer that it is highly probable that most other >> universes obtained a value close to theirs. >> > > > That is rather like Bruno's "frequency operator". Sure, they infer that it > is highly probable that most other universes obtained a value close to > theirs -- that is another simple property of the binomial expansion. But > everyone infers this -- even those with widely disparate observed relative > frequencies. They can't all be right, so the inference along these lines > that any individual makes is clearly wrong. > > Of course some of them will be wrong about that...some of them will be >> outliers. >> > > How do they know that they are outliers? Or how can you even define an > "outlier" when there is no underlying probability -- as in Bruno's WM > duplication scenario. > > > So Kent's argument is really that in a universe with randomness we can >> never be sure we're not an outlier. But as Ring Lardner would say, "But >> that's the way to bet." >> > > You are basing probabilities on a one-world model again. You can't really > mean that everyone in the two-outcome case should bet 50/50, regardless of > the data? > > > No. I'm arguing they should bet p/(1-p) for whatever p they observe. > It's inductive inference. > Right. So they will not agree about the results of the same series of experiments. The problem I see with this is that it would then require a miracle for some particular observer to confirm his results if he ran another series of N trials, especially if the actual probabilities are (0.99, 0.01). Note that this exact same argument could be made in which there is a "true > value" p=0.5. Would you then conclude that it is impossible to > experimentally infer p=0.5? > Not impossible. Just unreliable, since any input state would lead to that result. That is why I say that Everett is inconsistent with normal scientific practice. That is not to say I don't agree with the point that for MWI to work the > value of p must depend on the prepared system; which brings me back to the > idea there must be many (infinitely many) branches or weights which just > get divided proportionately at measurement. It must be MW+Born. > Just adding Born to MWI gets you nowhere, because there is no place for Born to influence the outcome of the 2^N binary strings. If you want a new, different, many-worlds theory, then go for it. I wish you luck, but I predict that you will not succeed. There is no real way to make the number of branches in MWI depend on the amplitudes of the initial state. People like Carroll and Wallace assume that if they get the Born rule from somewhere, it will just plug in. The considerations above show that this is a vain hope. Bruce -- 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/CAFxXSLRMXXJokthMg1ezvEMFJjw1GTApa_p4nSDM6%2BwFcN%2BrZA%40mail.gmail.com.
