On Wed, Nov 06, 2024 at 08:55:15AM -0500, John Clark wrote: > 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. >
No - because the total measure found by summing up the subset measures remains constant. And it is the set measure that is used for probability in branch counting. So even though there is 1 subset in the spin up branch, and 2 in the spin down branch, each subset in the spin down branch has half the measure of the single branch in the spin up branch. -- ---------------------------------------------------------------------------- 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/Zyvi12h3cKyV4EB0%40zen.
