On 16-03-2022 12:11, Bruce Kellett wrote:
On Wed, Mar 16, 2022 at 4:55 PM smitra <smi...@zonnet.nl> 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.
No, there is no need for this. The final polarizer angle is all that
matters.
There is always a need to fully specify everything that is done in the
measurement process. Not doing so makes things obscure and doesn't allow
you to draw rigorously valid conclusions.
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.
There is no superposition over angles -- there is only one relative
angle between the polarizers for each entangled pair.
There may not be, but, in principle, there always is a superposition
over angles.
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.).
OK. The squares were a confusion between amplitudes and probabilities.
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.
"Makes Bob's sector to get located inside Alice's down branch"? What
the hell is that supposed to mean? Bob's sector does not get relocated
anywhere. If Bob found up, Alice finds down for aligned polarizers.
The branch in which Bob found down is the one in which Alice finds up.
For aligned polarizers, sin(0) = 0.
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. 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.
Except that when the measurements are local, the relative angle is
unknown to both participants. So neither knows locally that the
polarizers are aligned. That knowledge can be available only
non-locally. And that is how it happens.
It's then not clear that the polarizers will actually be aligned. The
information about the angles cannot appear out of thin air, the laws of
physics conserve information. Not specifying the process, assuming that
it's not known but then later assuming the case of the relative angle
being zero is an invalid way of reasoning.
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.
Of course they do. Otherwise the correct correlations cannot be
formed. The correlations cannot wait until Alice and Bob meet because
in general there is no interaction there that could reset things.
Remember, the results could be exchanged by email, with no direct
interaction at all.
They are measuring spins that were correlated at the point of creation,
so due to local interaction. The mere fact that their results get
correlated is then not a nonlocal effect, at least not in the MWI. It's
not different from Alice and Bob reading the same books and then noting
that what they read is correlated. True, but utterly trivial.
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.
If Alice finds spin up, then the particle that Bob measures is known
to have spin down. And this can only be known non-locally. Bob does
not know it at the time of his measurement. The same happens if Alice
finds spin down. The particle Bob measures is known, non-locally, to
be spin up. That is what the entanglement implies. The process is
non-local because the entangled, non-separable, wave function is
non-local.
As I pointed out above, it's not a valid argument to one hand assume
that the angles are not known and then on the other hand, assume that
the relative angles are exactly zero. One has to specify a rigorously
well defined experiment and discuss that.
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.
Huh? Of course there is a branch for Alice finding spin down, just as
much as there is a branch for Alice finding spin up. For non-aligned
polarizers, there are always four branches on an individual trial.
Right? It is just that for repeated trials, some of the branches are
redundant and need to be eliminated (or never formed).
Yes, but not in collapse interpretations where only one branch really
exists.
Saibal
Bruce
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