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. 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.
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.
Brent
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