> On 8 Sep 2019, at 16:10, Lawrence Crowell <[email protected]> > wrote: > > On Sunday, September 8, 2019 at 6:00:35 AM UTC-5, Bruno Marchal wrote: > >> On 7 Sep 2019, at 17:17, Philip Thrift <[email protected] <javascript:>> >> wrote: >> >> >> >> On Saturday, September 7, 2019 at 9:25:59 AM UTC-5, Lawrence Crowell wrote: >> On Saturday, September 7, 2019 at 4:09:27 AM UTC-5, John Clark wrote: >> >> On Sat, Sep 7, 2019 'Brent Meeker' via Everything List >> <[email protected] <>> wrote: >> >> >> Sean Carroll is on a nationwide speaking tour now evangelizing Many >> >> Worlds. What is the predictive power of Many Worlds? >> >> > None, unless someone can figure out how to derive Born's rule from >> > it...which I think is impossible. >> >> Many Worlds predicts that the best any observer will be able to do is make >> probabilistic predictions, and Gleason's theorem says that in 3 spatial >> dimensions only the square of Schrodinger's wave (the Born rule), and not >> the cube or anything else, can yield a probability without inconsistencies. >> >> John K Clark >> >> Gleason's theorem is sort of a special case of Born rule for the case an >> operator is the unit operator. There is an interesting chase after the Born >> rule, and some people do think that certain quantum interpretations give the >> added axiomatic "boost" necessary to prove that. I am agnostic about those >> claims. If this does turn out to be the case I would give the best bet to >> either MWI or QuBism. >> >> LC >> >> >> >> >> If the best bet is either MWI or QuBism then theoretical physics is indeed >> doomed. > > Yes. But theoretical physics is not doomed, only physicalism, or the idea > that physics is the fundamental science. As such it is not doomed, but > explain by something non physical, simpler, even if transcendent. > > Bruno > > > > I wrote this not with the expectation that the Born rule will be proven > within either of these interpretations. I think the Born rule should likely > be proven, proven to be false, or shown to be unprovable, outside the context > of any interpretation. My statement is just that if it is proven within the > context of an interpretation these two might have the greatest plausibility.
OK. Note that usually, I use “prove” in the logicien sense. So “proving” (effectively) is the same as showing that the proposition is independent of the choice of any interpretation. I work in “complete” theory: provable is the same as true in all interpretations/models, and consistent means true in (at least) one interpretation/model. Here “complete” is used in the sense of Gödel 1930. Such theories are usually incomplete in the sense of Gödel 1931. To prove in *some* interpretation consists then as adding axioms to the theory. That restricts the interpretations, as suppressing an axioms augments the interpretation. You might look at a theory as a system of (logical) equation, and an interpretation/model as a variety satisfying the equations. In both case there is a sort of Galois connection. Note that once a theory is essentially undecidable (like all the theories allowing the existence of computers) you remain incomplete in all consistent effective extension (including oracles). I thing that the Born rules is basically plausibly imposed by Pythagorus theorem, and the fact that the number 2 has a lot of special and fundamental properties. Gleason theorem illustrates this, but Paulette Février get (in 1920s, she was a student of de Broglie) the simple frequentist justification often given to make it shorts (like in Preskill’s course, or in a book by Selesnick). I don’t worry too much for the Born rules. Like I am open that gravity will be explained by the number 24, like string theory illustrates. The particles are plausibly explained by the number 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000. (The number of elements of the Monster group) What is hard is: to justify this from arithmetical self-reference, to get right the justifiable, the non justifiable, and the plural-(non)-justifiable from the arithmetical self-reference. In that way, the logic of G* - G of Solovay provides the intensional variants making sense of all those nuances, without the need of any ontological commitment other than what we need to define a universal digital machine or universal number. Elementary arithmetic is enough for that. Bruno > > LC > > > >> >> @philipthrift >> >> >> >> -- >> 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] <javascript:>. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/everything-list/710c8709-0a08-454d-930c-8a4f7a04590a%40googlegroups.com >> >> <https://groups.google.com/d/msgid/everything-list/710c8709-0a08-454d-930c-8a4f7a04590a%40googlegroups.com?utm_medium=email&utm_source=footer>. > > > -- > 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 view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/c8445d1b-ebee-4751-b8eb-a31e64c7c596%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/c8445d1b-ebee-4751-b8eb-a31e64c7c596%40googlegroups.com?utm_medium=email&utm_source=footer>. -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/B09AB858-417A-4B2C-8822-487A6E236C2D%40ulb.ac.be.
