On 21-04-2016 08:15, Bruce Kellett wrote:
On 21/04/2016 3:26 pm, smitra wrote:
On 20-04-2016 07:36, Bruce Kellett wrote:
On 20/04/2016 3:21 pm, smitra wrote:
On 20-04-2016 03:02, Bruce Kellett wrote:
On 20/04/2016 6:56 am, smitra wrote:
The mistake made is to invoke classical reasoning after the
measurements are made. If the choice for the orientation of the
polarizers were not made in advance, then Alice and Bob cannot have
said to have made any definite choices at all.
I think you need to learn something about decoherence , and the
emergence of the 'classical' from the 'quantum'. In the final
analysis, Alice and Bob meet to compare their results. By that
stage,
their results, and their relative magnet orientations, are definite
and classical (FAPP if you wish). And that is the end result we
have
to explain. All else is boondoggle.
Invoking FAPP is precisely where your argument goes wrong.
Actually, I think that in order for MWI to make any sense at all,
the
separation of worlds has to be absolute, not just FAPP -- but that is
another argument.
While due to decoherence the macroscopic world looks classical, in
reality (assuming MWI) it not classical. This means that when Bob
meets with Alice that the settings Alice chose are still not
determined. It is only when Alice communicates to Bob what her
polarizer settings were
If Alice's setting are not determined, how can she communicate to
Bob
what they were? Decoherence works for both Alice and Bob separately,
and long before they meet. Both have definite magnet settings and
definite results by then -- that is decoherence at work.
They get split up in different branches where they make definite
choices and find definite outcomes. From Bob's perspective all the
different sectors for Alice are in play until he hears from her what
she did and what she found. Decoherence does not get rid of the
different branches.
No, of course not, but only two branches exist for each experimenter.
You're throwing away information about the polarizer settings here, but
it's via this that the branches of the other observer are correlated.
that Bob becomes localized in that particular sector of the
multiverse where this is now fixed.
So, decoherence ensures that long before A and B meet, there are
only
ffour worlds in the general case, ++, +-, -+, and --. It is the fact
these these possibilities have different probabilities that is to be
explained, and you have not explained that.
The mistake made here is to write down the global situation like this.
Locally Alice finds herself in one particular situation where she made
a particular choice for the polarizer and found a particular outcome
of the spin measurement result. If she found spin up with her
polarizer oriented in some particular direction, then from the
perspective of her branch, Bob is to be described by a state of the
form:
|Bob>|->
where |-> is the spin state relative to Alice's polarizer setting.
Now Bob and his local environment are in some unknown quantum state.
When doing practical calculations in quantum mechanics we would use
density matrices to calculate probabilities, but in principle we have
to assume that Bob's sector is described by some unknown pure state
which evolves in time,
That is quite wrong. Bob is not in some unknown pure state. He is in
an entangled state with Alice at all times, and that cannot be
described as a separate pure state -- that is the separability issue,
and it is basic to the quantum description of the entangled singlet
state that neither participant can be described separately, either by
a pure or by a mixed state. They are irre4ducible entangled.
Yes, but I did describe this situation correctly. If you project that
full state out on Alice's sector where she has chosen a definite setting
and has obtained spin up, then in that sector, Bob's spin is: |Alice
z-direction, ->. As far as Alice is concerned, the Bob she'll have to
deal with is boxed in in this sector.
the measurement that Bob performs must then be described as Bob
splitting up into many different branches.
Not many. In the spin-half case under discussion, there are only two
possible states for Bob after he measures his side of the entangled
state, |+'> and |-'>. This is why I insist that there are only four
possible combinations of states for Alice and Bob, (++'), (+-'),
(-+"), and (--'). This is a clear consequence of the non-separability
of the entangles state they both measure.
But you need to include the polarizer settings, this may sound trivial,
but it plays a nontrivial role as far as addressing the apparent problem
with nonlocality in the form of the correlation between what Alice and
Bob can find. When the entangled state is destroyed by the measurements,
the information is present in the measurement outcomes and the chosen
polarizer settings.
Bob's sector after Bob performs his measurement is thus described by
Alice as a superposition of many different effectively decoherent
branches, in each branch Bob chose some definite polarizer setting and
found some result. But Alice cannot pretend that in her sector, only a
single branch for Bob exists.
No, for the one entangled state that they both measure, there is only
one magnet setting for each observer. Before they exchange notes, they
do not know each other's setting, but they do know that they have only
one setting each.
This doesn't actually matter, because that's equivalent to having a
choice and then focusing on the sectors where they made the choices
consistent with the fixed settings in the other scenario.
So, all the different Bob's with different probabilities of finding
spin up and spin down depending on his choice of the polarizer exist.
If you pick only that branch where Bob happens to have chosen his
polarizer setting in the same or opposite way as Alice, then that Bob
could only have found one particular result. But that's not the
physical situation that Alice is dealing with. And Bob's own
perspective is different from Alice, as from his point of view he
finds himself in some branch where Alice exists in many different
branches.
Only when they communicate can each branch of Alice contain only one
branch of Bob and vice versa. Even if you assume that decoherence
would lead to this, which is in principle possible, then one still has
to take into account that decoherence can only act within the future
light cone, so Bob's sector won't decohere all the way into Alice's
sector until that time that Alice could have send a message at the
speed of light to Bob. The possible elimination of two out of the four
possibilities can thus only happen in a local way.
None of the four possibilities present in the MWI is eliminated. There
are four possibilities, agreed, but they continue to exist
indefinitely because the Alices and Bobs in each of the four meet, and
exchange information. When they meet, they discover facts about the
correlations between them, but those correlations must have existed
before they met. The reason for this is that the four possible A/B
states are of different probability. Those probabilities are set by
the relative orientations of the magnets used to measure the entangled
singlet state.
As is usual in these discussions with MWI believers, you have
multiplied the number of copies that lie around, quite illegitimately,
but still fail to explain how the correlations arise. You seem to
think it comes from some magic in the exchange of information when A
and B meet, but that can't be the case, because the probabilities for
the four possible worlds are set long before this happens. Some of the
possible worlds actually have zero probability, and in those, Alice
and Bob never meet because they no longer exist.
That's an artifact of pretending that there are four independent
branches. After Alice performs here measurement and she found spin up,
her branch contains some of Bob's branches, these will evolve from from
the state: |Alice's polarizer setting, ->
There is no issue with nonlocality here, because Bob is not boxed in by
what Alice has done, from Bob's perspective, if he finds spin up, then,
Alice is to be described as:
|Bob's settings, ->
Saibal
I dream of some "XKCD-style" cartoon. Alice and Bob perform their
experiments with particular settings and get particular results, which
they separately record in lab books. Several weeks later, they meet up
in a cafe down the street for a coffee. Alice puts her lab book with
her results on the table, "Look", she says, "I got |+> with my magnet
set at zero degrees to our agreed reference orientation." There is a
pause.......then Bob slowly lays out his lab book. "Holy shit!", he
says, "I also got |+> at zero degrees to our agreed reference." They
look at each other with gradually increasing dismay........ "Fuck!",
they say in unison. "That means that we don't exist..........." Their
voices fade into silence, and then...........Nothing!.
Bruce
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