On 3/15/2022 10:55 PM, smitra wrote:

On 16-03-2022 04:01, Bruce Kellett wrote:On Wed, Mar 16, 2022 at 11:55 AM smitra <smi...@zonnet.nl> wrote:On 15-03-2022 18:13, Brent Meeker wrote:So it's a collapse of the wave function, which Everett wassupposed tobanish? Can you give a Schroedinger equation evolution of this "determined the moment he sees her notes" change?Alice's notes are in an entangled superposition with the environment. Even though Bob is located in that same environment, and Bob's body will also get entangled, the fact that Bob does not know the content of these notes, means that Bob's mental state described as a bit string containing the information of everything Bob is aware of, can be factored out of this superposition (if this were not true, then Bob could have psychic powers and know what Alice's results are before looking at her notes). From the point of view of a Bob who measured spin up at some polarizer angle beta, the state before he sees the value Alice found, is of the form: |Bob, up, beta> sum_alpha [a(alpha-beta) |Alice, up, alpha> + b(alpha-beta) |Alice, down, alpha>]I don't think this is correct. You are selecting a particular result for Bob, so we can take his polarizer angle for this result as the reference, so Alice's polarizer angle is simply an offset from this reference. You have taken Alice's position as a superposition over different polarizer angles and then summed over this superposition. This is not correct. Alice has a definite polarizer angle when she makes her measurement. Bob does not know this angle, but he does know that Alice is not in a superposition of different angles.The physical process that Alice uses to set her polarizer must bespecified. If Alice uses information from the local environment of thepolarizer that was not available to Bob, then the state must bespecified accordingly. The amplitudes depend on the relative angles.The superposition over the angles is entirely general, you may replacethat by a single term.

`"Relative angles" is a non-local variable. In some of Aspect's`

`experiments these are determined space-like separately.`

Also, giventhe assumptions, the coefficients a(theta) and b(theta) are known. So the correct expression is: |Bob, up>[sin^2(theta/2)|Alice,up> + cos^2(theta/2)|Alice,down>] You appear to be saying that the angle between the polarizers, theta, is not set until Bob looks at Alice's notes. This is, of course, wrong. Alice measures a particular result at a particular angle, so the relative polarizer orientation is set at the time of her measurement. Bob does not know what this is until they meet and exchange notes, but that is not relevant to Alice's situation, which is given by the superposition of \up> and |down> results as shown, with no summation over angles.Yes, if they both choose their angles deterministically (no squares inthe amplitudes, b.t.w.).This is an important distinction, because it leads to important interpretational differences. If the relative orientation theta=60deg, we have: |Bob,up> [0.25|Alice,up> + 0.75|Alice,down>]. If Bob is 'up' in this case, there is a 25% chance that Alice will also be found to be 'up', and a 75% chance that Alice's result will be seen to be 'down'. There is no problem with this for this single case, since we know that all four branches are possible for non-aligned polarizers.Yes (minor point as above: amplities are 1/2 and 1/2 sqrt(3))The problem arises when Alice's polarizer is aligned with Bob's, so theta=0. In that case, sin^2(theta/2)=0, and cos^2(theta/2)=1, and the equation reads: |Bob,up>|Alice.down>. Again, this appears to be OK since we know that for the spin singlet, aligned spin measurements must always give opposite results. The question is, when does the |Alice,up> branch vanish? According to Saibal's account, everything is local, and the relative orientation theta is only obtained locally when Alice and Bob meet. This means that the sin^2(theta/2)|Alice,up> component of the superposition can only vanish when the observers meet. What makes the |Alice,up> branch vanish at that point? There is no appropriate interaction present.In the case where both will choose their polarizers that happen to bealigned, |Alice, up> exists in the branch were Bob found spin down.Bob's measurement does not change anything for Alice, it only makesBob's sector to get located inside Alice's down branch.

`Bob's measurement doesn't change anything for Alice?? You seem to have`

`lost the point that the photons are left and right circularly polarized`

`before they meet the polarizers. They don't have any definite linear`

`polarization.`

The only sensible account is that if the polarizers are aligned, the |Alice,up> branch is never formed. Since the formation (or non-formation) of this branch happens at the time of Alice's measurement, the non-formation of the |Alice,up> branch for aligned polarizers must happen at that time. So information about Bob's polarizer angle must be available at the time of Alice's measurement. Since Alice and Bob are spacelike separated, this information can only have been available non-locally. The |Alice,up> branch cannot vanish at some later time, because there is no appropriate interaction that can make this happen. The only possibility is that the branch was never formed. And this is a non-local phenomenon.There is also a |Bob, down> branch within which the |Alice, up> branchexists. One can ask how 4 branches get reduced to 2 branches, a pointthat you've invoked frequently. The branches that never form are theones where both find spin up or both find spin down. But that'strivial, as we created the entangled spin pairs this way.

That "form" takes place at space-like separation.

In the spin up sector, the other spin is spin down and all thathappens is that Alice gets entangled with one spin and Bob getsentangled with the other spin, which are local processes.If the angles are unknown to each other but are stilldeterministically fixed to some arbitrary values, then all fourbranches can form with the appropriate amplitudes. One can then askhow the values for the amplitudes get fixed as this looks like anonlocal process. However, the state describes a nonlocal situationcreated by the entangled spin pair. The nonlocal aspects of this statedo not exist in Bob's or Alice's sectors when they perform their spinmeasurements. If Alice finds spin up then that doesn't change anythingfor Bob because for Bob, the sector where Alice found spin down willalso exist before he measures his spin.

`Then all four combinations exist in MWI and we need an explanation for`

`how some combinations occur less often than others, including some that`

`don't occur at all.`

Brent

In contrast, if we don't assume MWI, then Alice finding spin up incase of parallel polarizers does affect Bob's experiment as there isthen no sector where Alice where she found spin down.SaibalTo answer Brent's original question, the non-compliant branches are never formed. They do not magically vanish when Alice and Bob meet. BruceWhere we sum over the possible polarizer setting alpha for Alice. |Bob, up, beta> denotes the content of Bob's awareness which should be thought of as a finite bit string. The fact that the description of Alice's sector contains Bob's angle beta, is not a problem. This is not an issue for Alice as she is located inside this superposition. E.g. |Alice, up, alpha> will not be located in a sector with one definite angle beta and measurement result for Bob. The evolution according to the Schrodinger equation then causes this state to change into: sum_alpha [a(alpha-beta) |Alice, up, alpha; Bob, up, beta> + b(alpha-beta) |Alice, down, alpha; Bob, up, beta>] And that then means that Bob splits and ends up in two sectors, one in which he observes that Alice has found spin down with probability |b(alpha-beta)|^2, and one in which he observes that Alice found spin down with probability |a(alpha-beta)|^2. So, the entire process that leads to the correlations is a local process. There is no non-locality implied by the violation of the Bell inequalities in the MWI, because there is no real collapse, only a splitting into different sectors in a purely local way. Saibal-- 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 view this discussion on the web visithttps://groups.google.com/d/msgid/everything-list/CAFxXSLTFQD2AJu9RFbyutYh9iEkNoSib2O584LBsVz6arr_UOg%40mail.gmail.com[1]. Links: ------ [1]https://groups.google.com/d/msgid/everything-list/CAFxXSLTFQD2AJu9RFbyutYh9iEkNoSib2O584LBsVz6arr_UOg%40mail.gmail.com?utm_medium=email&utm_source=footer

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