On Thu, Feb 18, 2021 at 10:51 AM 'Brent Meeker' via Everything List < [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]> wrote: > >> just few links! >> >> >> 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. 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. And the statistical limiting theorems that David Albert quotes point to the significance of this difference. 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. Bruce -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLQwzDrE%2BiWc5dufZ%2B7bA6Xmmnaikc4BeQbwWEQuhdCxYg%40mail.gmail.com.
