On 16-03-2022 17:44, Brent Meeker wrote:
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 was
supposed to
banish? 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 be
specified. If Alice uses information from the local environment of the
polarizer that was not available to Bob, then the state must be
specified accordingly. The amplitudes depend on the relative angles.
The superposition over the angles is entirely general, you may replace
that by a single term.
"Relative angles" is a non-local variable. In some of Aspect's
experiments these are determined space-like separately.
Yes, but we have to consider what the relevance of that is for the MWI
picture.
Also, given
the 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 in
the 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 be
aligned, |Alice, up> exists in the branch were Bob found spin down.
Bob's measurement does not change anything for Alice, it only makes
Bob'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.
What matters is that as far as Alice is concerned, Bob's results are a
superposition of both outcomes. There is then no spin measurement
result for Bob's that fixes (in case of perfect correlation) or alters
the probabilities for Alice's result because of that superposition. This
is how the MWI eliminates nonlocality that exists in collapse
interpretations.
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> branch
exists. One can ask how 4 branches get reduced to 2 branches, a point
that you've invoked frequently. The branches that never form are the
ones where both find spin up or both find spin down. But that's
trivial, as we created the entangled spin pairs this way.
That "form" takes place at space-like separation.
Yes, due to the local process of entanglement with the spins, and the
spins in turn where originally created locally.
In the spin up sector, the other spin is spin down and all that
happens is that Alice gets entangled with one spin and Bob gets
entangled with the other spin, which are local processes.
If the angles are unknown to each other but are still
deterministically fixed to some arbitrary values, then all four
branches can form with the appropriate amplitudes. One can then ask
how the values for the amplitudes get fixed as this looks like a
nonlocal process. However, the state describes a nonlocal situation
created by the entangled spin pair. The nonlocal aspects of this state
do not exist in Bob's or Alice's sectors when they perform their spin
measurements. If Alice finds spin up then that doesn't change anything
for Bob because for Bob, the sector where Alice found spin down will
also 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.
Alice and Bob are measuring correlated spins. So, that their measurement
results get correlated is a trivial effect: Alice and Bob get entangled
with the opposite spins. If they measure at different angles, then it's
analogous to Bob and Alice measuring opposite spins at some angle. Of
course the results get correlated, they are essentially measuring the
same thing. In the MWI it's analogous to Alice and Bob reading the same
books.
Saibal
Brent
In contrast, if we don't assume MWI, then Alice finding spin up in
case of parallel polarizers does affect Bob's experiment as there is
then no sector where Alice where she found spin down.
Saibal
To answer Brent's original question, the non-compliant branches are
never formed. They do not magically vanish when Alice and Bob meet.
Bruce
Where 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 visit
https://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
--
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 visit
https://groups.google.com/d/msgid/everything-list/1d86d049e59787a698534d9d23cfe7ac%40zonnet.nl.
