On Friday, April 15, 2022 at 12:41:03 PM UTC-6 [email protected] wrote:
> > > On 4/14/2022 2:00 PM, George Kahrimanis wrote: > > On Wednesday, April 13, 2022 at 8:55:48 PM UTC+3 [email protected] > (Brent) wrote: > > Decoherence has gone part way in solving the when/where/what basis >> questions, but only part way. >> > > As I wrote at the end of my first reply to your message, I share your > concern about decoherence but I see the glass as half-full; that is, with a > little more subtlety I hope that the matter can be formulated in clear > terms. > > Surely collapse is easier to handle as a general concept (except, on the > other hand, that it requires new dynamics). I forgot to mention that *my > argument for deriving the Born Rule works with collapse, too* -- so it is > an alternative to Gleason's theorem. > > Here I define colapse as an irreversible process, violating unitarity of > course, and I keep it separate from randomisation. The latter means that > each outcome is somehow randomised -- an assumption we can do without. > > *Collapse can also be described in a many-world formulation!* It differs > from the no-collapse MWI only in being irreversible. > > > If you can throw away low probability branches, what's to stop you from > throwing away all but one? You've already broken unitary evolution. If > you read Hardy's axiomatization of QM you see that the difference between > QM and classical mechanics turns on a single word in Axiom 5 Continuity: > There exists a *continuous *reversible transformation on a system between > any two pure states of that system. > > My argument in outline is > 1. assessment that MWI-with-collapse is workable; > 2. therefore, outcomes of small enough measure can be neglected in > practice; > > > Yes, I've wondered if a smallest non-zero probability could be defined > consistent with the data. > > 3. now Everett's argument can proceed, concluding that the Born Rule is a > practically safe assumption (to put it briefly). > > So I have replaced two assumptions of Gleason's theorem, randomisation and > non-contextuality, by the assessment of workability only. > > If you don't feel comfortable yet with formulating collapse in a > many-world setting, let us also assume randomisation (God plays dice), for > the sake of the argument, in a single-world formulation. That is, we ASSUME > the existence of probability; then the previous argument just guarantees > that this probability follows the Born Rule. > > > Assume? Randomness is well motivated by evidence. And it's more random > than just not knowing some inherent variable, because in the EPR experiment > a randomized hidden variable can on explain the QM result if it's non-local. > > > Of course I favour the first version of the argument, using the many-world > formulation of collapse, to avoid the "God plays dice" nightmare. > > > Why this fear of true randomness? We have all kinds of classical > randomness we just attributed to "historical accident". Would it really > make any difference it were due to inherent quantum randomness? Albrect > and Phillips have made an argument that there is quantum randomness even > nominally classical dynamics. https://arxiv.org/abs/1212.0953v3 > True randomness implies *unintelligibility*; that is, no existing physical process for *causing *the results of measurements. AG > > > Brent > > > Thanks for the comments so far, because they stirred my thinking and > motivated fresh ideas, some of which I hope will prove helpful and worth > discussing, if and when they mature. > > George K. > -- > 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/06930c0c-5537-4fb7-bf70-fd8c7d9859b0n%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/06930c0c-5537-4fb7-bf70-fd8c7d9859b0n%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/e2a370ad-6787-47cd-95bb-2819484a239bn%40googlegroups.com.
