On Mon, Jun 26, 2017 at 11:50:45AM +1000, Bruce Kellett wrote: > > You mean your statement about the variation upon which anthropic > selection acts? Does this mean that the continuations that are > anthropically allowed are those the permit the observer's continued > existence? Or is something more implied?
At this point in the argument, there is no discussion of continuations, interesting though that discussion is. We're just talking about an observation that takes place in the context of an Observer Moment. So we should just park that for now. > > That is not what is normally meant by the '+' symbol. You have > simply defined a conjunction to be a disjunction! We are constructively defining +. I would not be so cruel as to use + if the end point were not the usual group operation. > > Bur that does not work for the equations immediately following, > where you simply sum over all the possible outcomes of the operator > 'A'. All the outcomes of A are disjoint. A is a partition, by definition. > Why use the symbol \Sigma if you mean a disjunction? And you > then go on to say that if the outcome is a continuous set, you > replace the sum by an integral with uniform measure. It is difficult > to avoid the conclusion that you do actually mean that '+' implies > standard addition. Not yet at this point. > > Since psi_a is in general just a set of continuations selected by > the operation 'A', it is by no means clear that such a summation has > any meaning in general. A is any partition of the observer moment. + (D.1) is perfectly well defined over any such partition. > Of course, there may be some sets that can > sensibly be summed, but that does not seem a reasonable proposition > for sets of possible continuations such as the one I have given in > terms of cats and dogs, walking, and talking. > Again, why not? The sum simply corresponds to the observation that either of the distinct observation hold. Assuming, for the sake of the argument that walking the dog is mutually exlusive with stroking the cat. > In order for the development you outline to make sense, you would > have to specify the operator 'A' in a lot more detail, so that it > only selected things over which summation was meaningful. IOW, you > actually want 'A' to be a measurement of a quantum state. And you > specifically want a quantum state, because you want there to be more > than one possible result for the measurement 'A'. If 'A' is a > classical measurement of position, for example, then there is only > one possible outcome, and your further development of the situation > becomes trivial, not giving you quantum mechanics at all. > Not so fast. We're situated in a Multiverse, not a class Universe, so talking about an two identical copies seeing different disjoint outcomes is a perfectly reasonable thing to want to describe. > It seems, therefore, that in order to get quantum mechanics out, you > have to essentially assume quantum mechanics right from the start. > You have, at least, to assume that there is variability in the > results of operation 'A', and that this variability can sensibly be > superposed. > Of course. That is reasonable supposition for a Multiverse. The things not assumed are linearity, Hilbert spaces, Born's probability rule, and unitarity, all of which are normally assumed axiomatically in QM, but is derived in this treatment. > >>It is clear that your are trying to introduce the concept of a > >>quantum superposition by the back door, without doing any work, and > >>relying on the inherent ambiguity in the '+' operation. > >Why is this ambiguous? > > Se the above. Does '+' mean 'or', or not? No it does not. In particular it will differ markedly from it when non disjoint events are considered. > > >> If you have > >>nothing but classical outcomes from your observer moment psi(t), > >>then you cannot simply add these outcomes as if they were separate > >>eigenfunctions of a quantum operator. There are no such things as > >>superpositions in classical physics. > >There are, it's just that they're not particularly interesting from a > >physical point of view. > > > >A superposition of a blue ball and a red ball just means that we don't > >know what colour the ball is. > > That is a matter of ignorance, not a superposition of different colours. > In the Multiverse, it is also a superposition. Before a measurement is made, I am both the person who observes a blue ball, and the one who observes a red ball. When we finally get around to the full vector space version, the relevant state vector is a linear superposition of both states. Since it is headed that way, then why not call the state a superposition, even before linearity is proved. Just like it is reasonable to use the symbol +, even though I have only defined (at that time) on a subset of its full range. > >>Sorry, but the whole procedure is nonsense on stilts. It does not > >>get any better from then on in, but I refrain from analysing further > >>-- my blood pressure will not stand it! > >> > >I think what you're reacting to is the transition from D.6 which > >describes what happens in a classical world of a single observer, with > >distinct outcomes, to equation D.7, which is the full linear > >superposition. The reasoning I give goes in two steps - consider a > >whole number of observers of each outcome - eg 2 versions of me decide > >to observe a, and versions decide to observe b. Then the combined > >projection 2\P_A + 3\P_B plausibly describes this (multiverse) > >situation. > > I think that rather than imagining an arbitrary number of observers, > what you are actually wanting is to count the number of > continuations of your observer moment that give the each particular > result, psi_a = \P_A psi. You need to imagine an arbitrary number of observers in order to make sense of the '+' operator over its full range. > In other words, you are using a simple > branch counting algorithm to get quantum weights, measure, or > probabilities -- whichever you are trying to derive. It is known > that branch counting is not a good way to derive quantum > probabilities. > False as charged. I'm not using branch counting, which as you point out, doesn't work too well. (Although, IIRC, Tegmark came up with a version of branch counting that did seem to work - but in any case, that is not what I'm doing). > > >Then the next move is to consider the sets of observers to > >be drawn from a complex set. Quite what this means is a little hard to > >wrap your head around (since we're used to reasoning about whole > >numbers of people), but a) it is clear that we don't end up with QM > >wihout it, > > Yes, there's another rub! You simply assume what you need to get the > result you want. That scarcely counts as a derivation from general > principles. The general principle is to choose the most general thing, unless there is good reason for choosing something more specific. The most general thing in this case is a spectral measure, which have a Banach space range. I make some noises in my book about why the measure needs to be a field value, but I have always been open that this is a bit of a kludge, and that I'm not happy with it. Quite possibly, QM will need extending to Quarternions, or Octonions, in which case I will have missed a trick (like Einsteins famous "blunder" re the Cosmological Constant). The trouble is that nobody knows how to even do QM over the quarternions, although there have been some attempts. It is always possible that when done correctly, there is no physical difference between QM over quaternions and the usual complex valued theory. In which case we may as well stick with the complex theory for ease of use. On the other hand, if there are physical differences, then we can settle that by experiment. An experiment ruling in favour of the complex version of the theory over the quarternionic one will be a definite setback for my programme. Note that in my first presentation of this argument (Standish (2004), Foundations of Physics Letters, vol 17, p255), I state that the complex measure is the most general. Well that is just wrong. I'm aware of the error when I came to writing the book a couple of years later, but perhaps I was overly optimistic about how to resolve it. > > >and b) complex measures are more general than positive real > >(or whole number) measures. One had better have a good reason to > >impose a more specialist measure, and being comfortable with our usual > >notions of discrete persons is not good enough. Particularly when the > >universe doesn't agree. > > Well, the universe is quantum, and you are not going to get quantum > behaviour unless you either assume it, or take the empirical > approach that science has used in the past. > > >The problem is why don't we have an even more > >general measure, such a quaternions. The answer I give in my book > >doesn't satisfy me, even though true, and probably part of the solution. > > Pragmatism is actually the answer -- you use what you need to get > results that fit with observation. And that does not count as a > derivation from first principles. > You have to get your first principles from somewhere! But once they are found, they have to make sense. All of the first principles I use are well argued for in my book - except for the complex measure thing, which I remain conflicted about. There is possibly an analogy with Euclid's fifth axiom here. BTW - an anonyous reviewer of my paper stated that e thought my derivation seemed wrong because it appeared to derive quantum mechanics from classical probability theory, but e couldn't find a logical fault with my argument, which is why e ultimately agreed for it to be published. I have never claimed that I do any such thing, of course, whilst admitting that it does look a bit like it. What I suspect the case is, is that I've started with a different set of metaphysical assumptions, namely that we live in a Multiverse, and that observer moments are drawn from a much more general measure than classical probability theory allows. I still claim that my argument needs to looked at seriously on its own terms, rather than trying to interpret it in terms of other failed attempts (eg branch counting). It is also possible that Gunther Ludwig also came up with an equivalent argument published in a German language book in 1983, however the presentation is so obscured by dense formal mathematical treatment, that I can't be sure. -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Senior Research Fellow hpco...@hpcoders.com.au Economics, Kingston University http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. 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