World selection in case of entanglement measurement

[entropy1]

Suppose we have a pair of spin entangled electrons, measured by resp. Alice and Bob. The basises of Alice and Bob make an angle of α=10°. If Alice and Bob wind up in a joint world where Alice measures $|u\rangle$, then the probability that, in that world, Bob measures $|d\rangle$ is $\cos^{2}\alpha$. So does that mean that the physical oriëntation of the SG machines determine which world(s) we end up in?

If there is a correlation by definition, how is it realized if MWI is local?

(How) Does the correlation follow from the (MWI) formalism?

 

[PeterDonis]

If Alice and Bob wind up in a joint world where Alice measures $|u\rangle$, then the probability that, in that world, Bob measures $|d\rangle$ is $\cos^{2}\alpha$.

No, it isn't. If you're talking about the MWI, there is no "joint world" where Alice measures some definite result but Bob's result is somehow unknown and there are probabilities for different ones. There are just worlds in which Alice and Bob measure some particular pair of results.

does that mean that the physical oriëntation of the SG machines determine which world(s) we end up in?

There is no such thing as "which world(s) we end up in". In the MWI all of the worlds exist.

 

[PeterDonis]

If there is a correlation by definition

There is no "correlation" in the MWI if you are talking about a single run of the experiment. If $\alpha$ is 10 degrees, as you say, then there will be four worlds after the experiment is over, corresponding to the four possible pairs of results that Alice and Bob can get. In the complete wave function for the whole system, which includes all the worlds as terms in a superposition, the terms will have different amplitudes, but the "copies" of Alice and Bob in each world have no way of measuring or knowing those amplitudes, so they have no way of knowing what the overall wave function actually is. All they know is the particular results they both observed.

 

[entropy1]

In this document, I read on page 12:

"Thirdly, in any case, no physical meaning has been attached to the constants |a|² and |b|² . They are not to be interpreted as the probabilities that their respective branches are realized; this is the whole point of Everett’s proposal. It can not be said that a proportion |a|² of the total number of worlds is in state φ₀ ⊗ Φ₀; there is nothing in the axioms to justify this claim. (Note that if the two worlds picture were justified, then each state would correspond to one world, and it must be explained why each measurement does not have probability $\frac{1}{2}$ .) Nor can one argue that the probability of a particular observer finding herself in the world with state φ₀ ⊗ Φ₀ is |a|² ; this conclusion again is unsupported by the axioms."

I have to read the entire document, but if this quote cuts wood, doesn't that mean that there are no physical probabilities assigned to the worlds, so that correlation is left in the dark?

 

[PeterDonis]

doesn't that mean that there are no physical probabilities assigned to the worlds, so that correlation is left in the dark?

This is basically what I was saying in post #2, yes.