hossi said:
I have observers A and B, measuring alpha and beta when not in causal contact. That does not neccessarily have to be the same time (which is not well defined anyway), but let's say in whatever slicing its the same time t_0. We know the total spin is zero. Let us say they measure
S_A,alpha = 1
S_B,beta = 1
I think that the point of Rovelli is, that you have to look at things from the point of view of one observer at a time. As there is no SINGLE observer who can see both S_A and S_B at this moment (in whatever frame), it doesn't make sense for him to talk about "S_A has measured 1 and S_B has measured 1". You have to put yourself into the skin of A OR of B because there's no single observer seeing both.
So, S_A ONLY knows about "A saw 1", not about B and vice versa.
which is not a problem, because they have not compared their stuff.
Exactly.
Now go to time t_1 when they are in causal contact and measure the other part of the previously entangled state. They find
S_A,beta = 1 [note: I corrected this, think it was a typo to say -1]
S_B,alpha = -1
Now, I would have thought S_B,beta is what B has measured for beta at t_0. According to Rovelli, the important thing is now to let A ask at t_1 what B has measured. This is
S_AB = S_A,beta = -1
which is not what B has measured at t_0. Has B changed his mind concerning the measurement of beta from 1 to -1? Or has he not changed his mind but A always hears the answer he wants to hear? If so, does that make sense macroscopically?
Again, I think you have to see things from the PoV from ONE single observer, even when they meet.
Let's pick A. Back when A did his measurement, A knew of HIS result, but didn't know anything about B, so from A's PoV, B was in a superposition of states. And when A met B, this resulted in a kind of collapse, which put B into one definite state. So first A had his result (+1), and next, he meets B which has a result (-1). No problem. The -1 of B comes from the collapse of the superposition of B (before measurement by A) and its measurement by A.
So from A's PoV everything is ok.
You could do a similar reasoning from B's point of view.
And this is what I've been claiming all along: if you step back, and you consider ALL of these PoV's together, you have MWI.
Because from B's PoV, we first had +1. Ok. And from B's PoV, A was in a superposition until they met. So B will "measure" A in the -1 state when he meets. But that means that the "B" of the second story is NOT THE SAME B as the B in the first story (written from A's PoV).
In other words, they are in different branches. But as long as you look upon things from a single observer viewpoint, you don't have to think about this and this is what Rovelli does. He works from the PoV of ONE observer, for which the second observer is still in a superposition until he's observed by the first observer. And then he says that this is not something that happens to that second observer, but a description from the PoV of the first observer. This argument comes close to "Wigner's friend" (Eugene Wigner, 60ies).
So in a certain sense, Rovelli's viewpoint, that quantum states (using projection and all that) have only a meaning relative to an observer, is very similar to saying that coordinates in relativity have only a meaning relative to an observer. This is very true of course. But in relativity, one doesn't reject, because of that, the *underlying* geometrical object of spacetime, which is simply differently explored by different observers. So it is not because Rovelli rightly gives us a view on how "standard quantum theory with projection" is something which is relative to an observer, that this implies that the underlying objective structure does not exist.
And in an MWI view, that's exactly what happens. So it seems that Rovelli says something which is the equivalent of "(x,y,z,t) coordinates are to be seen relative to the observer" and MWI says the equivalent of "there is an underlying geometry from which we can derive that for each observer, things appear in an (x,y,z,t) coordinate frame".