On Thu, May 5, 2022 at 9:57 AM Brent Meeker <meekerbr...@gmail.com> wrote:

> On 5/4/2022 4:01 PM, Bruce Kellett wrote:
>
> On Thu, May 5, 2022 at 8:04 AM Brent Meeker <meekerbr...@gmail.com> wrote:
>
>> On 5/4/2022 12:27 PM, smitra wrote:
>>
>> In fact, that idea introduces a raft of problems of its own -- what is
>> the measure over this infinity of branches? What does it mean to
>> partition infinity in the ratio of 0.9:0.1? What is the mechanism
>> (necessarily outside the Schrodinger equation) that achieves this?
>>
>> That simply means that there is as of yet no good model for QM without
>> the Born rule.
>>
>>
>> But there is no mechanism for the Born rule.  It is inconsistent with
>> pure Schroedinger evolution of the wave function.  I think the problem of
>> measures on infinity is overcome if you simply postulate a very large but
>> finite number of branches to split.
>>
>
> The trouble if the number of branches is finite is that, given the large
> number of splits since the beginning of time, you will eventually run out
> of branches to split.
>
>
> There's always a bigger, but still finite number.  Hilbert space already
> assumes continuous complex values.
>

You cannot adjust the total number of branches as you go: you can't
manufacture more branches if you run short

>
> Or why not not an continuum probability and just measure by the density
>> around the eigenvalue
>>
>
> How do you measure the density? You still need to impose a measure on an
> infinite set.
>
>
> The reals have natural measurable subsets which define the Lebesque
> measure.
>
> https://e.math.cornell.edu/people/belk/measuretheory/LebesgueMeasure.pdf
>


Can you put the infinite set of branches in one-to-one correspondence with
the reals? Are these, in fact, equivalent sets. What is the length of a set
of branches?

I think there might be problems with using the Lebesgue measure over sets
of branches. You can define a Lebesgue measure over the real line because
there is a natural concept of the length of an interval. There is no such
natural concept of length over a set of branches.

Bruce

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