On 4/06/2017 10:05 pm, Bruno Marchal wrote:
On 02 Jun 2017, at 03:01, Bruce Kellett wrote:
In QM, with or without collapse, decoherence and the transition from
the pure state to a mixture gives a definite measurement result.
In particular branches only. When looking at the whole wave including
the observers, decoherence explain why it *looks*, to all observers in
the different branches, that mixed states have been obtained, but that
is not the case in the global description.
The transition to the mixed state is essential for one to get a definite
experimental result. Physicists realized a long time ago that the pure
unreduced state of the MWI does not work. The difficulty is known as the
'basis problem'. If you retain the full superposition of the pure state,
there is no preferred basis, and expanding this superposition in terms
of different bases gives different -- usually nonsensical -- physical
results. It is only when you reduce to a mixed state that the basis is
fixed, and results are definite. This does not mean, as you appear to
think, that you have lost the other branches. All the branches of the
MWI are still present, except that now there is a different definite
measurement result in each branch.
Without collapse, different branches get different results, but once
obtained, these results are fixed, and are not affected by whether
Alice and Bob exchange information or not.
I agree. That is used in the fact that in EPR like situation, when
Alice and Bob are space-time separated, what we have is "only" an
infinity of Alices and Bobs,
This is wrong. There is no "infinity of Alices and Bobs".
all with their spin correlated, and when Alice makes her measurement,
at any angle, she will know Bob's possible result,
Bobs possible results, as far as Alice knows, is 50/50 for '+' or '-'.
without needing any action at a distance. She just localize herself,
and her corresponding Bob, in which branch they belong.
That is not correct. You keep saying it, but you offer no proof or
mechanism whereby such a thing could happen.
There is no influence at a distance, although we would need it to talk
of token unique Alice and Bob in case there would be only one universe.
That is a total misunderstanding as well. All branches might exist (two
for Alice in this case, one where she got '+' and one where she got
'-'), but we need consider only one typical branch to get the general
result -- that is how things are done in physics when you have
superpositions.
........
But there is non-locality -- non-local influence -- in all
interpretations since it is inherent in the quantum formalism.
I don't see any non-locality in the MWI. EPR, Bell, assumes always one
Alice and Bob, and as Everett shows, decoherence explains the
manitenance of coherent first person plural description, and the
absence of collapse prevent any non-local influence.
That is not the case either. Bell does not assume a necessary collapse.
Bell's theorem is a mathematical theorem, it is true whatever
interpretation of QM you adopt. You seem to be suggesting (and you are
more explicit in this suggestion elsewhere) that Bell's theorem is
invalid for MWI.
1. That is not true -- Bell's theorem is valid in all interpretations.
2. Even if you did find an error in Bell's theorem, all that that would
get you is the possibility of a local hidden-variable account of the
correlations. If you think such a local hidden variable account is
possible, then give it - in full mathematical detail - and we might
begin to think that you know what you are talking about.
You cannot get away by reversing the onus of proof. Bell's theorem is
independent of whether or not a collapse is assumed,
To interpret the experimental violation, you need to identify the
Alice and Bob you talk about. But EPR and Bell talk of Alice and Bob
like if they were in a definite universe all along the experience,
when that is never the case. They do assume implicitly one physical
universe.
Not true. See above. Even if this were the case so that the theorem was
not valid in MWI, that actually does not get you anywhere --
non-locality would still exist, except that now you could give a local
hidden variable account. I see no sign that you are actually doing this.
so if you want to argue that MWI removes the non-locality proved by
Bell, then the onus of proof is very much on you: you have to
demonstrate how this can be possible.
It is a trivial consequence of the linear differential shroedinger
equation. Or of the fact that the evolution is a rotation (unitary) in
Hilbert space.
Rubbish. If you remain with the linear Schrödinger equation, you cannot
get definite results for experiments. Once you have definite results, as
you need to calculate correlations, the non-locality is evident.
You say that Bell's theorem relies on the unicity of outcomes. By
this, I presume you mean that Bell assumes counterfactual
definiteness (in the usual terminology). If by counterfactual
definiteness you mean that a measurement gives a definite (though
unknown in advance) result, even if that measurement is not performed.
This does not make sense in the MWI. If I measure a alive+dead cat, it
is only a "first person illusion, 1p" that such an experience gives a
definite result. In the 3p picture, both results must be said to obtained.
Again, you have a fundamental confusion between the 3p account of the
situation and the 'bird' view from outside space and time. There is no
'person or persons' who have the bird view. The 3p account still gives
just one definite result for each observer -- even though these results
may be different on different branches. Both results are obtained only
on the "1-plural" view, if I have understood what that piece of jargon
means.
Then I accept that counterfactual definiteness is assumed in quantum
mechanics. Without such an assumption, the whole notion of an
expectation value would collapse.
Not in the 1-views. It continues to make sense, and the contagion of
superposition (the linearity of the tensor product) even prolongate
the 1-views into 1-plural views, that gives the
siplitting/differentiation/decoherence, which needs only to propagate
at the speed of light or below.
That is very confused.
So if you abandon counterfactual definiteness, you have a different
theory -- you have abandoned standard QM, and you then have to
explain how you can get and use expectation values.
We got them in the memories of the person's involved. Not from looking
at the whole universal wave. It is again like with computationalism.
Your claim appears to be that Bell's theorem is not valid in MWI.
Bell's theorem is valid. His inequality does not even assume QM, but
just locality.
I agree, but that is not what you were implying above. It seems that now
you agree that the Bell inequalities assume only locality. But these
inequalities are violated by experiment. That can only mean that the
assumption of locality was wrong -- whatever interpretation of QM you adopt.
It is violate when we do the experience, like Aspect, and this shows
non-locality in our branch,
When you make measurements, you get definite results. When you measure
an intrinsically non-local entity such as the singlet state of two
electrons, you get non-local results.
but when looking at the big picture, we see that this non-locality has
a local origin.
No, it has its origin in the fact that the state Alice and Bob are
measuring is intrinsically non-local.
It would need an action at a distance to destroy the alternante
branches alwailable to Bob,
Not at all. There are only ever two branches available to Bob and Alice,
and thus only four possible combinations of results, each combination
occurs in a single world, and the non-locality is evident in every such
world.
but without collapse, non-locality is a local, branch-owned,
phenomenon. I take Bells theorem + Aspect as a quasi definite proof
that if there is one universe, then there are many universes.
That can work only if you insist on locality, and that MWI preserves
locality. Both these assumptions are wrong.
This is nonsense. Bell's theorem is a theorem of quantum mechanics,
and it is therefore valid in all interpretations of that theory.
Yes, in all interpretation of quantum mechanics, the relevant branches
violate the inequality, but they do that without involving an action
at a distance when we look at the entire wave. It is phenomenological.
If it is not valid in MWI, then Many-Worlds is a different theory,
and not just an interpretation of standard QM.
It is valid in the MWI, but interpreted differently than in a
mono-universe interpretation which requires non local action at a
distance to get the same non-locality.
(with or without hidden variables).
That is what making a measurement means. It is what happens in all
interpretations. It makes no sense to deny counterfactual
definiteness -- that is not QM.
It is QM without collapse, and using the simple mechanist FPI.
You must have some strange understanding of what counterfactual
definiteness means.
Alice and Bob get *all* (always correlated) answers, but when
light-separated, it make no sense to compare them. They can only
make comparison with the person accessible in their light cone,
where the contagious superposition spread out.
I presume you mean "space-like separated". Alice and Bob do their
measurements;
The infinities of Alices and Bobs do their measurements.
they get their results and write them in their lab books. They meet
years later and compare lab books. Are you trying to suggest that
they do not have definite answers in their lab books before then?
The infinities of Alices and Bobs get their infinities of definite
results.
In MWI (with two-outcome experiments), there is a copy of Alice that
writes '+' in her lab book, and a copy who writes '-' (for a given
orientation theta). Similarly for Bob. There are, therefore, only
four possibilities when they meet: '++', '+-', '--', and '-+'. The
non-locality is necessary to set the probabilities for each of these
four possible combinations of results. If you want to eliminate the
non-locality, you have to give a non-magical way of establishing the
necessary probabilities. You have never been able to do this.
QM does that, and without collapse, I don't see how any influence
leaking at the speed of light need to be introduced.
Remember that in a sequence of such experiments, the probabilities
for '+' and '-' are 50/50 for both Alice and Bob.
OK.
The joint probabilities, or correlations, depend on the relative
orientations of their polarizers.
Right.
It is information about this relative orientation that must be
conveyed non-locally for the correlations to come out correctly when
they meet.
Why? That would be the case if you think that it is the same Bob and
Alice all along the experiences, but that cannot be the case.
It is not sufficient for them simply to exchange this information
later, because their results at particular orientations are already
fixed when they meet.
I don't see this. If the angle is some theta different from 0° or 90°
they will both split/differentiate, and whoever they will meet later
will be the correspond partner with the correct correlation, obtained
by the decoherence local to their respective branch. In this case, it
is clear that it does not make sense to attribute to "Alice and Bob"
the same identity than the initial one.
You are just resorting to unexplained magic again. The Alice and Bob
that meet to compare results are simply the original Alice and Bob that
got particular results -- in MWI there are two copies of Alice and two
of Bob, with just four possible combinations. The correlations must be
correct for each branch of the combined wave function (each of the
possible combinations). There are no "infinities of Alices and Bobs".
That is not in the quantum formalism. I think it is clear that you are
working in some theory that is different from quantum mechanics, but are
unwilling to spell out what that theory is.
Bruce
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