On 22/04/2016 3:09 am, smitra wrote:
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.
No, that is not the case. I am not throwing anything away. Each copy of
each observer has only one magnet setting in each run of the experiment.
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.
It seems that you have already called on the standard non-local QM
result. The thing that we are concerned with is the situation where both
observers deal with the same entangled pair, and each makes a definitive
measurement in some orientation. So if Alice gets |+>, any branch that
Bob subsequently enters must contain this result, and he can only get
either |+'> or |-'>.
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.
What do you mean "include the polarizer settings"? Of course these must
be recorded so that the relative orientation can be deduced. But there
is only one polarizer setting for A and one for B -- there is no
multiplicity of settings. Because we are measuring just one entangled
pair, there can only be one setting. That measurement destroys the
system at one end, because it distributes the entanglement into the
environment (which includes the observer). That can only be done once at
each end of each entangled pair. I think you are merely confusing
yourself by thinking that there are multiple 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 you agree that that is correct -- for each run of the experiment on
just one entangled pair, there is only one sector in play, that with
only four possible outcomes.
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.
It is no pretence, it is the fact. This is probably the core of our
disagreement. You have not given any reason why there should be more
than four possible outcomes for each run of the experiment on one
entangled pair. You have claimed that this is significant, but you have
given no physical reason why it should be so.
After Alice performs here measurement and she found spin up, her
branch contains some of Bob's branches,
Bob only has one branch before he makes his measurement. After, he has
two branches -- spin up or down along his chose polarizer angle.
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, ->
But, since they both measure the same entangled pair, there can only
ever be just four possible outcomes.
I know I have said this many time, and we go round and round, but you
have not given any solid reason why this analysis might be considered to
be incorrect.
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!.
I find it interesting that you have not commented on this scenario. I
think that it contains all the relevant facts for a full understanding
of the situation at a conceptual level. The point is that some
combinations of results are forbidden. The question, then, is how these
are forbidden? If, as MWI enthusiasts claim, the branch of the mutiverse
you are in only becomes clear when A and B exchange some relevant
information, the question arises as to how it comes about that some
branches are forbidden -- branches that would be perfectly allowed if
the original two measurements were independent in the sense of being
totally local.
It is only because the measurements are made on a single entangled
singlet pair that the (++) and (--) results are forbidden for aligned
magnets. There is no way that an allowed branch that has fully decohered
can suddenly become disallowed, simply by the addition of some
additional information -- decohered worlds do not suddenly vanish.
If we can forget all the other repetitive argumentation and concentrate
on these simple conceptual issues, where there is no multiplicity of
other branches, we might make some progress.
Bruce
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