On 5/4/2022 5:16 PM, Bruce Kellett wrote:
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
Why not? "Being a branch" is only a matter of degree anyway. There are
a bazillion weakly decohered states every second which our instruments
could not distinguish.
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.
If the branches differ by a real parameter, like the time of the
radioactive decay for Schoerdinger's cat, it should work. In general
you might have to come up with something like Zurek's quantum Darwinism
to provide a measure.
Brent
Bruce
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