On Tue, Nov 5, 2024 at 5:57 PM Russell Standish <[email protected]> wrote:
*Me: * >> >> >> >> >> >> >> >> >> >> >> >> >> >> >> *> Here's why branch counting won't work: I measure the spin of an >> electron in the > vertical direction and both the electron and I split into >> two, and there's a > 50% chance "I" will see spin up and a 50% chance "I" >> will see spin down. So far > branch counting seems to work. But before I >> started I made up my mind that if I > see spin up I will do nothing, but if >> I see spin down then I will wait for 10 > minutes and then measure the >> electron spin a second time but this time along > the horizontal axis. And >> so the spin down world splits again into a spin right > world and a spin >> left world. So now there's only one branch in the spin up line > BUT three >> branches in the spin down line. If you use branch counting you'd have > to >> say that in the first measurement the probability was not 50-50 as you > >> originally thought, instead there was a 25% chance I would see spin up in a >> 75% > chance I would see spin down. But something I do now can't affect the >> > probability of an experiment I performed 10 minutes ago. > That's why >> when I draw a diagram of the worlds splitting on a piece of paper or > a >> blackboard even though the lines I draw are two dimensional I like to think >> > of those lines is having a little 3D thickness, the total sum of all the * >> >> >> >> >> >> >> >> >> >> * > thickness of all the branches in the multiverse remains constant but >> each time > a world split the resulting worlds become more numerous but >> thinner; although > it always remains true that if you're betting on which >> universe you are likely > to be in you should always place your money on >> being in the thicker one. > > I want to emphasize that this thickness >> business is not to be taken literally, > it's just an analogy that I happen >> to like, you may not and that's OK because > there's no disputing matters >> of taste. But disliking branch counting is not a > matter of taste because >> such a dislike is not subjective, branch counting > objectively doesn't >> work. * > > > > > > > > > > > > > > > * > Maybe we're at cross purposes with what branch counting means. I > always invisaged in branch counting, performing measurements as like > dividing up the unit interval [0,1) into subsets. So if you first divide > the interval into 2 subsets, you'd get [0,0.5) and [0.5,1). Then at the > second step, you'd subdivide [0.5,1) into [0.5,0.75) and [0.75,1). The > measures of the three resultant steps are 0.5, 0.25, 0.25 using the most > naive way of measuring real intervals. The counting comes from attempting > to count the number of subsets of the real interval. Of course, these are > uncountable sets, but if you restrict yourself always to finite partitions > - say all rational numbers with fewer than n decimal places - and perform > counting of the numbers in the subsets - and then take the limit as n goes > to infinity, the naive measure is what you get in the limit.* *I think it's valid for you to divide up the continuum of universes into a finite number of partitions which differ from each other by an arbitrarily small amount, however if we do that then in my example you'd still have more subsets in the spin down branch than the spin up branch because you kept measuring the electron in just one branch. So you'd affect the probability of an experiment you perform 10 minutes ago. And that can't be right. That's why I prefer the thickness analogy, the number of universes increases but their thickness decreases, so the total thickness always remains constant; thus if you're betting on which universe you're in you should always bet you're in the thicker one. * > > *> The analogy doesn't quite work, because in QM one has complex measures, > not real ones as per the example.* *True. **That's the trouble with trying to find everyday analogies to the quantum world, there's always something wrong with all of them (including mine) because quantum mechanics is inherently weird, there's just no getting around that. And yet if we wish to make progress sometimes it's useful to use those analogies in our mental imagery even though they're imperfect. * *John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis>* wv2 -- 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 visit https://groups.google.com/d/msgid/everything-list/CAJPayv2HwDmT9w_FhXo-xVF63MetRMmqW%3Dw1q61BNy8CNJeijg%40mail.gmail.com.
