On 2/17/2021 4:29 PM, Bruce Kellett wrote:
On Thu, Feb 18, 2021 at 10:51 AM 'Brent Meeker' via Everything List
<[email protected]
<mailto:[email protected]>> wrote:
On 2/17/2021 2:07 PM, Bruce Kellett wrote:
On Thu, Feb 18, 2021 at 7:26 AM 'scerir' via Everything List
<[email protected]
<mailto:[email protected]>> wrote:
just few links!
http://users.ox.ac.uk/~everett/docs/Hemmo%20Pitowsky%20Quantum%20probability.pdf
<http://users.ox.ac.uk/~everett/docs/Hemmo%20Pitowsky%20Quantum%20probability.pdf>
This is an interesting paper. I was amused to see that after a
long discussion, their conclusions section says essentially the
things I have been saying for ages.
Bruce
Yes it says what you've been saying, but it's the thing that I
think Hossenfelder said better.
That might be a matter of opinion. Sabine talks about MWI introducing
something equivalent to collapse in the measurement process, I have
said that asking the question "which branch will I end up on?"
introduces a dualist notion of personal identity. This is exactly the
'collapse' that Sabine sees in MWI.
Hemmo and Pitowsky write:
/
// if probability is supposed to do its//
//job, it must be related at least a-posteriori to the statistical
pattern in which//
//events occur in our world in such a way that the relative
frequencies that actually//
//occur in our world turn out to be typical. We take this as a
necessary condition//
//on whatever it is that plays the role of probability in our
physical theory. Now,//
//the quantum probability rule cannot satisfy this condition in
the many worlds//
//theory (nor can any other non-trivial probability rule), since
in this theory//
//the dynamics logically entails that any combinatorially possible
sequence of//
//outcomes occurs with complete certainty, regardless of its
quantum probability./
But Hossenfelder notes, correctly, that advocates of MWI say you
must take the probability of an outcome to be it's relative
frequency as single outcome among all the branches, not just
whether of not it occurred. To may it must be "typical" is
ambigous. Flipping a 100 head in a row, isn't typical, but it's
possible and we have a theory of how to assign a probability to it
and how to test whether that assignment is consistent. It's a
possible sequence, and it "occurs" in the sample space, but that
doesn't make its probability=1.
That is to confuse ordinary probability in a chancy universe with the
fact that these outlying branches certainly occur in MWI. I thought
the point made by Hemmo and Pitowsky was relevant. They pointed out
that no matter what sequence you have observed up to this time, you
have no guarantee that the next N results you observe won't be
contrary to Born rule expectations.
You have not guarantee in one world...if it's probabilistic.
Thus previous experience is no guide to the future in MWI. I know this
is true also in ordinary classical probability theory, but the
difference is that in MWI, one or more of your successors is bound to
see the atypical sequences -- that is not guaranteed in classical
probability theory. It *might* happen, but it is not *bound to*
happen. This difference is important.
I don't think it's even relevant. It isn't "bound to happen" to you.
It's just a possibility for you, just as it is in the Kolmogorov sample
space.
And the statistical limiting theorems that David Albert quotes point
to the significance of this difference.
The statistics are the same the same as the probabilities in the N->oo
limit.
In Sean Carroll's monthly "Ask me anything" blog he wrote this:
/
//0:40:16.3 SC: Sherman Flips says, "How does the weight assigned
to a given branch of the wave function correspond to the number of
micro-states that are in superposition in that branch?" So, you
gotta be a little bit careful. Basically, it is that number, but I
wanna be careful here because number of micro-states is a slightly
ambiguous concept in quantum mechanics. If what you mean is the
number of dimensions of Hilbert space that correspond to that
branch, that's what it means, the number of different directions
in Hilbert space that you can add together in some principled way
to make that particular vector corresponding to that branch.
Whether you wanna call a dimension of Hilbert space a micro-state
or not is up to you.//
//
//
//0:41:00.7 SC: There's another way of thinking about things if
you just had like a bunch of spins. So you have a bunch of
two-dimensional Hilbert spaces, one for each spin, spin up or spin
down, but the dimensionality of the combined Hilbert space is not
2N. If you have N spins, it's 2 to the N. So you don't have one
dimension of Hilbert space for each dimension of the subspaces;
you exponentiate them. That's why it depends on what you mean by
micro-state, but basically, that is what the weight means. You're
on the right track thinking about that./
So he's definitely branch counting, but not describing the
mechanism whereby the amplitude of one component of a
superposition is translated into a different dimensionality of the
combined Hilbert space.
Yes. I think that the idea that Bob has been pursuing is a
definite non-starter. Carroll is smart enough to see this, even though
he does want to finally reduce probability to branch counting. The
real trouble I see with Sean's approach is that he has to call on Born
rule insights to know how many additional branches to manufacture. His
approach is irreducibly circular.
But then he could just postulate the Born rule as the way to partition,
or create, branches and it would work; which is what Sabine says. And
that tells me that the Hemmo and Pitkowsky objection is wrong.
Brent
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