On Monday, June 11, 2018 at 1:37:53 AM UTC, Bruce wrote: > > From: Bruno Marchal <[email protected] <javascript:> > > On 8 Jun 2018, at 14:55, Bruce Kellett < <javascript:> > [email protected] <javascript:>> wrote: > > From: Bruno Marchal <[email protected] <javascript:>> > > On 8 Jun 2018, at 02:32, Bruce Kellett < <javascript:> > [email protected] <javascript:>> wrote: > > > The SWE does not give a preferred basis. Basing MWI on the Schrödinger > equation runs into the basis problem. Few MWI advocates actually take this > seriously. And they should. > > > The relative proportion of histories do not depend on the choice of the > base, so the base we use are chosen endemically, like the present moment > for example, in the whole of physics. Obviously, we needs brain to assess > our results and communicating, and some works, like sure and others, > justify the indexical importance of the position base, with respect to the > branch where intelligence can develop. > > > What on earth are you talking about? The position basis is not > well-defined either. The Hilbert space corresponding to the position > operator X has an infinite number of possible bases -- just like any other > Hilbert space. Any linear vector space has an infinite number of possible > bases. How do you choose which one you are going to use? Talking about the > relative proportion of histories sounds just like the long-since refuted > branch counting approach to probabilities. > > > Measure is quite different from counting. > > > And the probabilities for various outcomes most certainly depend on the > chosen base, as do the outcomes themselves. > > > Well, we can use what we call in French “le peigne de Dirac”. To make that > precise Laurent Schwartz has invented the theory of distribution. I > simplify things here. Consider that space has been quantised, like in > Loop-Gravity or something. Here, you do a 1004 fallacy, with respect to the > goal (helping Grayson to have an idea of what is QM-without-collapse). > > > ? > > > * In this situation, what is the role of the SWE since the wf is usually > asserted without any reference to it? Now consider a general case where the > wf for a system is determined using the SWE. Since the solution can be > expanded using difference bases, say E or p, does each possible expansion, > each implying a different possible set of measurements, imply a different > set of worlds using the SWE? TIA, AG* > > > The Schrödinger equation merely gives the time evolution of the system. To > define the problem you have to specify a wave function. It is in the > expansion of this wave function in terms of a set of possible eigenvalues > that the preferred basis problem arises. So it is not really down to the SE > itself, it is a matter for the wave function. Each expansion basis defines > a set of worlds, and all bases give different worlds. > > > That is correct, but the choice of the basis don’t change the relative > “proportion of histories”. > > > The choice of basis makes all the difference in the world. > > > Everett prove the contrary, and he convinced me when I read it. I found > “his proof” used in many books on quantum computing, although with > different motivation. Thee result of an experiment, obviously depend of > what you measure, but when you embed the observer in the wave, you get that > what they find is independent of the choice of the base used to describe > the “observer” and the “observed”. If not, the MW would already be refuted. > > > In that case, MW is refuted. Clearly, what the observer finds is dependent > on the basis in which he is described. Or else experiments would not have > definite results when described in the laboratory from the 1p perspective. > Even if you take the 'bird' view of the whole multiverse -- which is, I > agree, independent of the basis in which it is described -- the view of any > observer embedded in the multiverse is totally basis-dependent. That is, > after all, what we mean by 'worlds' -- the view from within, or the 1p > view. But that view depends on how you describe it: the way in which you > partition the multiverse itself. Only certain very special bases are robust > against environmental decoherence -- how else do you resolve the > Schrödinger cat issue? > > Bruce >
*So you find the resolution in the fact that according to decoherence theory, the cat is simultaneously alive and dead for only short time? AG* -- 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 post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
