On Wed, Aug 01, 2007 at 11:31:51AM +0200, Bruno Marchal wrote: > > > > No, I mean all information known by the observer (including, but not > > exclusively information know by the observer about erself). > > > OK, but then adding "about the universe" is confusing at this stage. > You interpret the quantum state as describing knowledge. (And then I am > not sure I follow what you mean by quantum state: you are supposing the > quantum hyp. here, aren't you (or perhaps your linearity hyp. only? > Again where would that linearity come from?). >

Sorry, I realised I hadn't responded to this before. Things have got away from me, including recovering from a harddisk crash. I am using universe somewhat colloquially here, to help intuition. But sometime it doesn't help. What we have are observer moments, which somehow contain all knowledge, or are circumscribed by all knowledge that an observer has at an instant of time. The use of the word "universe" was meant to make some connection back to discussions of "many universes", or "many worlds", but to be precise we are just talking about observer moments which are in a sense primitive. > > > > >> > >> > >>> this led me to identify the observer moment > >>> and the quantum state vector. > >> > >> > >> ... and the partial relative quantum state vector corresponding to the > >> observer. OK, but at this stage this would be cheating. We can not yet > >> explain why the quantum histories wins over the comp/number relations. > >> > > > > Well I have my own reasons, considering knowledge acquisition as an > > evolutionary process. But I disagree about it being cheating, because > > I don't a priori assume quantum states are elements of a Hilbert > > space. That is a derived property. > > > So, how do you define quantum state? > I don't define quantum state. I use the word state as a synonym of observer moment, again as a means of contact with quantum terminology. I make the statement "identify observer moment with quantum state" as a shorthand for the following argument. Assume that the state (or observer moment) undergoes evolution (I'm refraining from qualifiying this with Darwinian) in that: 1) subsequent OMs (obviously a successor relationship is a prerequisite here - something I call the TIME postulate) are related closely to the previous OM, ie they inherit. 2) There is variation between successor OMs - ie the "many worlds" idea. 3) That a particular successor OM x_i of OM y is what is observed ("anthropically selected"), with a probability P(x_i|y). The probability function P(x|y) satisfies the Kolmogorov probability axioms. This also implies that OMs must satisy set axioms. I also call this third assumption the "PROJECTION postulate". There is a final assumption. The initial OMs are drawn from the set of all OMs according to some sort of measure, which happens to be complex. Since measures can be more general than complex measures, I'm not entirely sure why the measure should be restricted to being complex. And that is it. From this idea (that OMs evolve), the following three postulates of QM follow by a mechanistic proof 1. States are elements of a Hilbert space over a complex field 2. States evolve unitarily (ie according to a Schroedinger equation) i\hbar d\psi/dt = H\psi between measurements 3. The probability function P(x_i|y) satisfies the Born rule P(x_i|y) = |<x_i|y>|^2 / <x_i|x_i><y|y> Now some people have complained about how one can derive quantum probabilities from the Kolmogorov axioms. It seems counterintuitive. But this part is the most rigorous. The argument has been put for the last seven years, and a number of very smart people have looked at it without finding a flaw. Of course that doesn't mean there isn't a flaw, but it would have to be quite subtle. > > > > >> > >> > >>> This is not incompatible with with your > >>> notion of the OM being a Sigma1 sentence, but it places severe > >>> restrictions on the form of the quantum state vector. > >> > >> > >> The OM are the Sigma1 sentences, when they are considered as third > >> person constructs. > > > > Third person is that which is accessible to all observers. > > > ? (This correspond more to the first person plural notion as I have > defined it in most of my papers: observers appeared in the fourth and > fifth hypostases, and perhaps already a part of it appears in the third > one; but there are no observer in the second or first hypostases). > > cf: > 1 p (truth, 0-person) > 2 Bp (provable, 3-person) > 3 Bp & p (knowable, 1-person) > 4 Bp & Dp (observable, measurable; 1-plural-person) > 5 Bp & Dp & p (sensationalisable, feelable, personally > observable/measurable, 1 person again) > Thinking about it, I'm not sure our x-person terminology is completely compatible. And it comes down to the problems I've had even in understanding (or grokking, more to the point) the Theatetus definition of knowledge. I can understand it from a purely intellectual point of view ("henceforth, what we mean by `knowable' is Bp&p"), but I have never grokked it. -- ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://www.hpcoders.com.au ---------------------------------------------------------------------------- --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---