On 24 June 2017 at 11:36, Russell Standish <li...@hpcoders.com.au> wrote:
> On Sat, Jun 24, 2017 at 06:29:54PM +1000, Bruce Kellett wrote: > > On 24/06/2017 5:23 pm, Russell Standish wrote: > > > > OK, it was possibly the case that you gave arguments earlier in the > > book. But I was going on the basis of the Appendix "Derivation of > > Quantum postulates". > > > > But the problems only begin with the assumption of a probabilistic > > model. Psi(t) is the set of possibilities consistent with what is > > known at time t. But how do you limit this set? At the moment, I > > could go to the pub for a drink, could open a bottle of wine at > > home, stroke the cat, turn on the telly, talk to my wife, etc, > > etc,..... The possibilities consistent with what is known at this > > time is not a well defined set, or limited in any way. > > The everything is the set of all infinite length strings, each of > which describes a universe to infinite detail. I always wondered about this aspect of your theory Russell. I assume that you mean "describes under some interpretation". If so, the only available interpretation (whether explicitly computationalist, a la UDA, or otherwise) would have to be intrinsic to the strings themselves. Hence some interpretative scheme or other must also be implicitly assumed. Isn't that so? David Some of these strings > will describe universes compatible with our current observer moment - > an infinite number even, as the information content of our OM is > finite. Others will not. It is a well defined subset of the everything. > > > > > Because you then go on to define projection operators in terms of a > > sum over the members of this set of possible outcomes. That is > > meaningless unless you are already assuming the the outcomes are > > just possible results for a well-defined measurement, and that this > > measurement process can be defined in a linear vector space. > > > > Summation of the projection operators is defined in equation D.1 for > disjoint observations a and b (ie where it is impossible to observe a > and b simultaneously). Linearity is not assumed at this point. > > > Another problem occurs further down when you seem to have complex > > numbers of observers observing an observer moment. Why you should > > have more than one observer for any observer moment is a mystery yet > > to be solved. > > It's more a measure over observer moments. In a branching multiverse, > not all observer moments are equally likely, but one would expect > across a branching point, measure should be conserved. > > Why the measure is complex, not real is more tricky. With the > everything, subsets naturally induce a real valued measure. But we do > know that complex measures are more general, and we need a good reason > not to choose the most general. But complex measures are not the most > general. I do say "more general division algebras cannot support > equations of the form (D.7)", but I confess, I'm still not completely > happy with that line. > > > But then you go on, in eq. B8 to define the inner > > product in terms of the probability function. But you have merely > > multiplied together two expansions in terms of projections over > > possible outcomes -- assuming that there is a linear span over the > > space in the process. This gives the Born rule, sure, because you > > have built it into your derivation of the inner product. > > > > By the time we get to equation D.8, we have proved that the set of > observer moments is a vector space, so yes, this construction is > allowed. We are entitled to define any real-valued bilinear operator on > that space and call it an inner product. > > By using that particular inner product, you get the Born rule in the > usual form. If we'd chosen another, we'd have a different expression > that is equivalent to the Born rule. > > > > > >>So you know about QM from the start, and devise a strategy to get > > >>you there. One of the problems that many-worlders face in their > > >>attempts to derive the Born rule from within MWI is that they cannot > > >>independently justify a probabilistic model. > > >Yes, but I don't start with the MWI (namely, I don't start with a > > >Hilbert space and unitary equation of motion - ie Schroedinger's > > >equation). I start with evolution in a generic multiverse. > > > > Why a multiverse? You no doubt argue for it elsewhere, but that is > > not apparent in your quantum derivation. > > > > Yes - of course. The whole book is premised on it. > > > And I do not understand why the most general equation for computing > > psi as a function of time is a first order differential equation. > > The equation could clearly be non-linear in psi -- such things have > > been postulated after all, as in general relativity and GRW for > > instance. > > > > A first order differential equation needn't be linear. Linearity comes > from assuming that the laws of physics don't change every time you > observe something, more specifically the solutions ψ_α are also solutions. > > A higher order equation can be transformed into a first order equation > by adding new variables - a trick commonly done in dynamical systems > theory. > > Perhaps there's an implicit assumption that the evolution should be > Markovian. I think one could make a convincing case that it should be, > but perhaps that assumption needs to be made explicit. > > > Besides, you do not show that the operator H is the Hamiltonian and > > the energy operator. You do not derive the basic commutation > > relations between position and momentum operators -- a relation that > > is central to the whole of QM. > > > > The commutation relations between x and i∂/∂x follow > mechanically. That i∂/∂x can be identified with p (modulo a constant > multiplier) is the correspondence principle, which I discuss on page > 120. Vic Stenger has an argument for it, based on Noether's theorem. > > > > > >>If you have a > > >>probabilistic model in 3 or more dimensions, Gleason's theorem tells > > >>you that the Born rule is the only consistent model for > > >>probabilities. > > >My arguments go through in fewer than 3 dimensions as well, AFAIK, > > >although that would a relatively uninteresting world - very black and > > >white :). Which is why I suspect it is independent of Gleason. > > > > > >>But you have to say why you want a probabilistic > > >>interpretation in the first place. Deutsch's attempts founder on the > > >>fact that he has to assume that small amplitudes have small > > >>probabilities, even to get started, so his argument is manifestly > > >>circular. > > >> > > >Yes - I think the problem with those approaches is that they start > > >with a Hilbert space and unitary equation of motion (ie a classic > > >MWI), and then fail to generate the Born rule because there is no > > >observer in their mechanics. > > > > > >>As I said, you build a probabilistic model in at the start, so > > >>Gleason's theorem is going to get you the Born rule automatically. > > >>Or if you don't assume Gleason, you have an equivalent result by > > >>another route. Assuming a probabilistic model is a very powerful > > >>starting point...... > > >Sure - but it is necessary. If evolution did not work the way it did, > > >we could only ever be Boltzmann brains, isolated observers existing > > >fleetingly, barely having time to consider what to have for lunch, let > > >alone figuring out the meaning of the universe. Fortunately for us, > > >evolution does work to generate complex worlds from simple beginnings, > > >meaning an evolved world is overwhelming more likely to occur in the > > >Multiverse of Everything than Boltzmann brain existences. > > > > Why do you have to have evolution? > > My 2 sentence summary is as above. If you want a more detailed > portrayal, read my book :). > > > It seems to me that you are > > allowing enough empirical science to creep into your deliberations > > to give you the results you want. > > For guidance, perhaps, but I don't think I've built a just-so story here. > > > I don't think Boltzmann brains are > > the only alternative to evolution. > > The only alternative to it arising through an irreversible process is > de novo creation. > > > Evolution could work in all sorts > > of different ways -- such as Lamarkianism, etc. The only reasons we > > rule these out are empirical. > > So? - I make no comment on the central dogma of biology. > > > Similarly, the only reason for going > > to quantum mechanics is solidly empirical -- classical physics just > > does not work all the way down. So one will never be able to derive > > quantum mechanics from general, non-empirical considerations. It is > > just too weird for that! > > > > If true, then point to which assumption I use that is too weird. > > > -- > > ------------------------------------------------------------ > ---------------- > 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. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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