> On 8 Jun 2018, at 14:55, Bruce Kellett <[email protected]> wrote: > > From: Bruno Marchal <[email protected] <mailto:[email protected]>> >>> On 8 Jun 2018, at 02:32, Bruce Kellett < >>> <mailto:[email protected]>[email protected] >>> <mailto:[email protected]>> 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. > Now that we understand decoherence, the only bases that are useful are those > that are robust against environmental decoherence. That is why we don't see > superpositions of live and dead cats -- that superposition base is not robust. No problem with this. > >> It threats only the naïve conception of “worlds”, which has led to the works >> of Griffith and Omnes (and Gel Mann & Hartle). That works remains still a >> bit naïve with respect of the type of histories we can encounter in >> arithmetic. > > The consistent histories approach is just another way of considering many > worlds. The histories are no more unique than are the worlds. Yes, indeed. Only the math makes more sense here, but many-histories belongs to the "many-worlds” family, I agree. I prefer it, because the word “world” is much ambiguous, and never defined. Bruno > > 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] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- 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.
