Branch counting (was: Spin Superposition)

[John Clark]

On Mon, Nov 4, 2024 at 5:18 PM Brent Meeker <meeke...@gmail.com> 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. 

John K Clark    See what's on my new list at  Extropolis

cjj

[Russell Standish]

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.

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[John Clark]

On Tue, Nov 5, 2024 at 5:57 PM Russell Standish <li...@hpcoders.com.au> wrote:

Me: > Here's why branch counting won't work: I measure the spin of an electron in the

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

wv2 

 

 

[Russell Standish]

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.

[John Clark]

On Wed, Nov 6, 2024 at 4:42 PM Russell Standish <li...@hpcoders.com.au> wrote:

> So even though there is 1 subset inthe 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.

OK, but that's pretty much what I was doing, except that I use the word "thickness" instead of "measure".  

John K Clark    See what's on my new list at  Extropolis

4m2

 

[Russell Standish]

On Wed, Nov 06, 2024 at 04:49:36PM -0500, John Clark wrote:
> On Wed, Nov 6, 2024 at 4:42 PM Russell Standish <li...@hpcoders.com.au> wrote:
>
>
> > So even though there is 1 subset inthe 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.
>
>
> OK, but that's pretty much what I was doing, except that I use the word "
> thickness" instead of "measure".  
>

Sounds like it. Our difference, I think, is that we assigned different
meanings to the term "branch counting".

So when I hear "You can't get the Born rule from branch counting", to
me that means you can't get the complex measure from simple
considerations of dividing up sets of "descriptions" (naively thought
of as bit strings) and counting their elements.

I had quite a long discussion with Bruce Kellett about this some time
back. We ended in an impasse.

There's another fly in the ointment - in my book, I stated that
complex measures were the most general type of measure, but it aint
so. In fact a quaternionic measure seems to fit the bill:
arxiv:hep-th/0110253v2