On Tue, Nov 05, 2024 at 07:33:53AM -0500, John Clark wrote: > On Mon, Nov 4, 2024 at 5:18 PM Brent Meeker <[email protected]> wrote: > > > >> Branch counting could never work. > > > > The other advocate of MWI I know insists that it only makes sense for > branch counting. > > > 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. The analogy doesn't quite work, because in QM one has complex measures, not real ones as per the example. -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders [email protected] http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- 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/Zyqi0ZXtycDpH3Oo%40zen.
