On 23-03-2022 02:11, Bruce Kellett wrote:
On Wed, Mar 23, 2022 at 10:26 AM smitra <smi...@zonnet.nl> wrote:
Let's consider this whole non-locality issue right from the start.
Probably a good idea. The discussion has become rather confused. We
should sort out exactly where we agree and where we disagree.
The violation of Bell's inequalities proves that QM cannot have an
underlying local deterministic theory, i.e. one in which the
measurement
outcomes arise deterministically as a result of local interactions.
In
Aspect's experiments, the polarizer angles being set at space-like
separations, rules out local hidden variable theories where the
photons
are still influenced by both polarizers via local interactions.
Yes.
What the violation of Bell's inequalities does not prove, is that QM
is
non-local
Well, these results certainly show that some work needs to be done if
you are to recover a completely local theory.
The unitary time evolution in QM is local. There is only an issue with
collapse, as the mechanism for this is usually left unspecified. But
apart form the issues with collapse QM is a local theory. The violations
of Bell's inequalities have no bearing on QM itself, only on hidden
variable theories that seek to explain QM in terms of classical
deterministic concepts. Such theories cannot be local.
What is true is that there is a problem with collapse
interpretations in precisely the sort of entangled states used in
Bell-type experiments,
I think there are problems in non-collapse interpretations as well. It
is a mistake to put all the problems down to collapse models -- the
collapse in most models can be eliminated, and that does not make
these theories local.
The problems can only be with collapse as without collapse you have a
manifestly local theory. If you think that (unitary) QM is non-local
then you need to prove that, because all the known theorems apply only
to hidden variable theories, not to QM itself.
because the measurement outcome at one location
provides one with information about the other measurement outcome.
That is not true in general. If the polarizers are known to be
parallel, then Alice's result, whatever it may be, tells her that
Bob's result will be the opposite. But this is not the case in
general. If the polarizers are not parallel (and not known in advance
to be parallel), then all Alice can infer from her result is that Bob
could get either up or down. She cannot know which, and she cannot,
without knowing the relative polarizer angle, assign probabilities to
the two possible results. By hypothesis, in this situation, she does
not know the relative polarizer angle, so she has no information about
which result Bob will get.
Yes, I agree, the relative angle must be known and then for every spin
measurement for Alice she'll get some amount if information about Bob's
result, ranging from 0 to 1 bit per bit of her results.
If the polarizers are parallel or antiparallel then the measurement
result
at one site provides one with perfect information about the
measurement
outcome at the other side.
While doing the experiment with parallel or anti-parallel polarizers
does not prove that QM has no underlying local deterministic theory,
that's also unnecessary as this is already an established fact.
I thought that was what was in dispute here.
The violation of Bell's inequalities proves that QM does not have an
underlying local deterministic theory. So, we are then allowed to assume
this and then consider another experiment where the polarizers are
parallel. That experiment then does not have to reproduce this known
fact about there not being a local deterministic theory underlying QM.
We can
then use that fact and say that because we already know that Bob's
photon does not decide in a deterministic way whether or not to move
through the polarizer based on the local physical state, that Alice
having the information on whether or not Bob's photon will move
through
Bob's polarizer, demonstrates a nonlocal feature of QM.
But Alice does not have any such information after her measurement.
She does if both polarizers were agreed to be chosen parallel to each
other, and if there is a real collapse. In that case her measurements
predicts what Bob will find and vice versa. So, Bob then knows that the
violation of Bell's inequality means that before he measures his spin
that the information about what he is about to find does not exist
locally in the physical state of the system, but that it does exist at
Alice's location die to her state collapsing after she performs her
measurement. That's the non-locality in collapse interpretations that
does not exist in the MWI.
But, of course,
this is only true in collapse interpretations where in Bob's sector
there exists a unique result for Alice. This is not the case in the
MWI,
so here there is no issue with non-locality at all.
That does not follow, because, rather than Alice not having a unique
result in Bob's sector, it is the case that Alice has split into two
branches, in each of which she has a definite result. So when she
meets Bob, he also splits into a copy for each of Alice's sectors. So,
for Bob, the Alice he meets will have a definite result. There is no
ambiguity coming from the many worlds situation here. Whenever Bob
looks to Alice, he knows he will see the definite result that she
obtained.
The version of Alice that Bob will mat is undetermined in advance. Bob
splits due to local interactions with Alice's sector.
One cannot avoid the consequences of Bell's theorem by this manoeuvre.
Even if one can claim that the fact that Alice splits into two copies,
one for each result she could get, means that she does not (from Bob's
perspective) get a definite result voids the applicability of Bell's
theorem, this still does not provide a local explanation for the
violation of the Bell inequalities. The violation of these
inequalities is an established experimental fact, and an explanation
of this fact is required. If it is claimed that many worlds can
provide a local explanation, then it is up to those who make this
claim to provide this local explanation.
This you have failed to do. Merely claiming that Bell's theorem does
not apply in many worlds theories (non-collapse theories) is not an
explanation of anything. The correlations are still there, and still
in need of explanation.
Bell's theorem doesn't even apply to QM itself, let alone the MWI.
Bell's theorem applies to local hidden variable theories. And the
nonlocality issue with collapse is also a different thing than what
Bell's theorem is about.
Unitary QM is a manifestly local theory, so there is nothing to explain.
If you believe that (unitary) QM is nonlocal, you ought to prove this.
One can then say that there is still an issue with locality in
Bell-type
experiments due to the correlations depending on the relative angle.
The
relative angle is only available non-locally.
Only in Aspect-type experiments where the polarizer angles are set at
spacelike separations. This was done to rule out the possibility of
some local influence on the hidden variables that might be possible if
the detector angles were known at the time of the creation of the
entangled pair, as in the original Freedman-Clauser experiments. This
was always a somewhat extreme possibility, and no attempt has ever
been made to provide a hidden variable theory (local or not) that
could achieve this. So the fact that the polarizers are set
non-locally is not really an issue, apart from ruling out some
somewhat bizarre possibilities.
However this sort of
non-locality is put in by hand, and what you put in must come out in
the
final results.
This is just silly. This non-locality is not "put in by hand". It is
either inherent in the experiments on non-separable entangled pairs or
it is not -- nothing is put in by hand.
Of course, the entangled state is a nonlocal object that is used in the
experiment, but this is also created using local interactions.
Take e.g. this trivial experiment. Two copies are made of
a file containing a random bitstring and given to Alice and Bob.
Alice
and Bob move away from each other, and at a spacelike separations
they
both apply a random cyclic permutation to the bitstrings and save
the
results in their file, overwriting the old data by te new data. They
then meet each other and compute the correlations of their
bitstrings.
Obviously, the correlation will be (almost) zero unless they have
chosen
the same cyclic permutation. And this is also information that is
only
available non-locally.
No, it is not available only non-locally. They might have agreed
before the experiment on a cyclic permutation that both could use. In
your toy example, such a possibility is not as bizarre as the thought
that something similar could enable a local explanation of the
Freedman-Clauser results.
So, the mere fact that a correlation depends on
nonlocal information that was put into the experiment, does not
demonstrate that there is an essential non-local feature in the laws
of
physics. What you out into an experiment that affects the results
must
come out.
Your simple example is not really appropriate, and it does not
demonstrate that the non-locality was put in by hand.
It demonstrates that the mere fact that a correlation depends on
nonlocal information in an essential way, does not prove that there is
anything nonlocal about the processes that explains the correlation.
In the Bell-type experiments this is a useful method to
demonstrate to rule out a local dependence on both polarizer
settings.
The mere fact that the correlation then depends on a non-locally
chosen
relative angle is not the argument here.
No, the real argument here is the provision of an actual account of
how the correlations are formed in a many worlds setting if one is not
to rely on the inherent non-locality available in the so-called
'collapse' models. Your claim is that many worlds can provide this
local account. So far you have not provided any such account.
The account exists in the form of the unitary time evolution of the
state describing the entire system. This is local. It is your assertion
that unitary QM is nonlocal.
Merely claiming that many worlds theories violate the assumption that
Bell made that experiments have definite results does not amount to an
account of anything.
Bell's theorems do not apply to QM, only hidden variable model. What
matters is that QM violates Bell's inequalities, which then proves that
QM does not have an underlying local deterministic model. QM itself is
local except possibly for the collapse part depending on how you model
that, or if collapse happens at all.
It can readily be argued that, while Bell
probably thought that experiments gave unique results, that assumption
did not invalidate the main conclusions of his argument. After all,
Alice and Bob can only meet in one world, and in that world in which
they do meet, each had definite results for their measurements. The
fact that there are several copies of both Alice and Bob, does not
alter the fact that only one copy of one can meet only one copy of the
other. The correlations have to be explained for each such pairing of
Alices and Bobs.
Those correlations then imply that there is no local hidden variable
theory possible that can explain the individual measurement outcomes.
Saibal
Bruce
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