On 2/26/2015 7:10 PM, Jason Resch wrote:
On Thu, Feb 26, 2015 at 5:57 PM, meekerdb <[email protected]
<mailto:[email protected]>> wrote:
On 2/26/2015 3:16 PM, LizR wrote:
On 27 February 2015 at 10:01, meekerdb <[email protected]
<mailto:[email protected]>> wrote:
MWI predicts the same as QM+collapse.
Only because it assumes the Born rule applies to give a probability
interpretation to the density matrix. But Everettista's either ignore
the need
for the Born rule or they suppose it can be derived from the SWE
(although all
attempts have fallen short).
This is an important point. Do /any/ interpretations explain the Born rule?
If so,
that would be a reason to prefer them to the MWI.
Gleason's theorem says the Born rule is the only consistent way to assign
probabilities to states in Hilbert space (showing Born had good intuition).
So then the mystery of the Born rule is solved. I don't see why/how adding collapse
solves anything.
I adds that one of the probable states happens. MWI fails to add that.
So if you can justify placing a measure on the multiple worlds it has to be
Born's
rule. The problem seems to be that branch counting doesn't make sense
unless the
number of branches are infinite.
Why is that?
Branch counting for an up/down measure of a spin 1/2 requires two branches: one up and one
down. But if an instrument bias is added so the probabilities are 0.501 up and 0.499
down, a thousand branches are needed.
But if they're infinite it's not clear how to define the measure.
Why is that?
Because probabilities are M/N where N is the number of possibilities.
Does the size of the infinity matter?
A continuum would be better because is has a natural measure.
Perhaps taking the limit of branch counting as the number of UD threads
goes to
infinity would work, but that seems non-Platonic since it would rely the
threads
coming into existence as on a concrete UD.
This is separate (I think) from the basis problem. Under a computationalist
theory
of mind it would seem that you need to define bases with eigenvectors like,
"I see
the needle pointing up." But we only know (approximately) how to define
eigenvectors for the needle.
Would it be equivalent to the eigenvector of the needle pointing up and you
looking at it?
That's what is assumed in practice, i.e. that the needle collapses/splits the state. But
then the question is why the needle? The needle was moved by a electromagnet...which was
driven by a current...which came from a photoamplifier tube...which was excited by an
electron. But all that instrumentation could be in a superposition (and as Bruce points
out, ARE in a superposition in some other basis).
Brent
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