On 16/04/2016 12:20 am, Bruno Marchal wrote:

On 14 Apr 2016, at 14:31, Bruce Kellett wrote:Although all possible combinations of measurement outcomes exist inMWI, it is not clear what limits the results of the two observers toagree with quantum mechanics when they meet up in just one of thepossible worlds.Because they have separated locally, and Alice's measurement justinform both of them (directly for Alice and indirectly for Bob oncesome classical bit of information is communicated by Alice to Bob bythe usual means).

`This is the purported solution given by Deutsch and Hayden, amongst many`

`others. Unfortunately, it does not work, as can be demonstrated by`

`working through a specific example.`

`Consider the usual case of a spin singlet that splits into two spin-half`

`components that separate and are measured by A and B at spacelike`

`separation. There are two possible measurement results for each`

`observer, call them |+> and |->. The entangled state can then be written as:`

|psi> = (|+>|-> - |->|+>).

`ignoring normalization factors for simplicity. The first ket applies to`

`observer A and the second to observer B.`

`This is the general expression for the singlet state in any basis, such`

`as would be define by the orientation of the measuring magnets. We`

`denote the measurement results in some other direction as |+'> and |-'>.`

`A and B perform their measurements at spacelike separation, but each`

`chooses the measurement orientation outside the light cone of the other.`

`There are four possible combinations of results, corresponding to four`

`worlds in the MWI: |+>|+'>, |+>|-'>, |->|+'>, and |->|-'>. Since each`

`observer has a 50% chance of getting |+> and 50% of getting |->, and the`

`two measurements are completely independent of each other, it would seem`

`that each of these four worlds is equally likely.`

`But this conclusion is contradicted by quantum mechanics: if the two`

`observers, by chance, have their magnets aligned, then the |+>|+'> and`

`|->|-'> combinations are impossible. In general, the probabilities of`

`the four possible joint outcomes depend explicitly on the relative`

`orientation of the magnets of the A and B -- they are seldom all equal.`

`How is this taken into account in the formalism?`

`In the formalism of QM, the answer is clear enough. Given the expression`

`for |psi> in an arbitrary basis, as above, we can choose the basis for`

`this expansion to be that for the orientation of magnet A. But then, in`

`order to get the relevant outcomes for B, we have to rotate this`

`expansion to the basis corresponding to the orientation of magnet B. But`

`we have to do this rotation before B makes his measurement! How does B`

`know the necessary rotation angle? Recall that both A and B make`

`independent arbitrary rotations at spacelike separations.`

`After the measurements are complete, A and B communicate their results`

`to each other, so the branch of B that measured |+'> communicates this`

`to both copies of A, to get the combinations |+>|+'> and |->|+'>.`

`Similarly, the branch of B that got the result |-'> communicates this to`

`both copies of A, to get the remaining two combinations |+>|-'> and`

`|->|-'>. Deutsch and Hayden propose that non-locality is eliminated by B`

`communicating his orientation angle as well as his result to A. But`

`adding the angle theta to the information transmitted does not change`

`the fact that one copy of B transmits a |+'> result and one copy`

`transmits a |-'> result. In other words, this extra orientation`

`information is completely irrelevant to the outcomes of the`

`measurements, and also irrelevant to the relatives probabilities for the`

`our possible worlds.`

`Deutsch and Hayden have not shown that this EPR experiment is local in`

`MWI -- they still have to use the rotation of the wave function basis`

`for B's measurement /before/ that measurement is made, and that`

`information is not locally available to B, it can only have been`

`transmitted non-locally.`

So MWI does not give a local account of the EPR results on entanged states. 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.