On 21 Apr 2016, at 07:26, 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.
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, the measurement that Bob performs must
then be described as Bob splitting up into many different branches.
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.
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.
Obviously, Bob's brain does not have any information about what
Alice did until the details are communicated to him. So, Bob's mind
is identical across the many branches where Alice and, due to
decoherence, the local environment is different. So, in the
experiment the effectively classical communication is not at all
trivial, in the MWI it is a crucial step localizing the observers in
the multiverse as where the measurements of the spins.
So classical communication has quantum effects? It is the classical
communication that 'causes' the EPR correlations? What about the
effect of the entangled spins -- that is purely quantum, and that
gives rise to the quantum correlations.
The only thing of relevance here is that the classical communication
is a necessary step to get both localized in the same branch. It
doesn't matter whether you invoke decoherence to do this, but
decoherence is still due to local dynamics, so decoherence in
Alice's sector won't affect Bob's sector faster than the speed of
light
What is your reactions to Maudlin's comment
(https://arxiv.org/abs/1408.1826 [1])
"Finally, there is one big idea. Bell showed that measurements made
far apart cannot regularly display correlations that violate his
inequality if the world is local. But this requires that the
measurements have results in order that there be the requisite
correlations. What if no “measurement” ever has a unique result at
all; what if all the “possible outcomes” occur? What would it even
mean to say that in such a situation there is some correlation among
the “outcomes of these measurements”?
"This is, of course, the idea of the Many Worlds interpretation. It
does not refute Bell’s analysis, but rather moots it: in this
picture, phenomena in the physical world do not, after all, display
correlations between distant experiments that violate Bell’s
inequality, somehow it just seems that they do. Indeed, the world
does
not actually conform to the predictions of quantum theory at all (in
particular, the prediction that these sorts of experiments have
single
unique outcomes, which correspond to eigenvalues), it just seems that
way. So Bell’s result cannot get a grip on this theory.
"That does not prove that Many Worlds is local: it just shows that
Bell’s result does not prove that it isn’t local. In order to even
address the question of the locality of Many Worlds a tremendous
amount of interpretive work has to be done. This is not the place to
attempt such a task"
The MWI where you assume branching is only an approximate picture,
in reality there is no such thing (e.g. under unitary time evolution
the entire system can evolve back and eliminate the branches). A
notion of locality can only arise after you have picked some sector
where it has a well defined meaning, so would agree that this is a
nontrivial issue.
The problem is that the notion of world is not defined. I suggest
defining a (physical) world by a set of objects/events close for
interaction.
If Alice and Bob are light-cone separated, it does make sense to say
if they belong to the same world or not. A third observer O, who
participated with Alice and Bob in the preparation of the singlet
state, and moves away so to see Alice and Bob will give the product
OAB l+>l-> + OAB l->l+>, which is still a singlet state, if Alice
measure in some base, and Bob in another base, the wave of splitting/
differentiating of the worlds will eventually reach the third observer
O, splitting him accordingly, and when they meet, they can only agree
on the correlation, due to the linearity of the tensor product.
A more involved treatment of interaction would require a more precise
definition of space-time in quantum physics, but this requires solving
the quantum gravitation problem.
Here we I have used implicitly the Born rule, because we are
discussing only the locality issue, but I do think that the Born rule
can be derived in the MWI by the use of Gleason theorem (but that is
really another (old) topic and I guess Bruce disagrees on this).
(Then with the mechanist hypothesis in the cognitive science, the wave
itself must be derived from the statistics on *all* computations. "All
computations" is a very solid concept thanks to the non trivial
discovery and mathematics of the universal machine (Church-Turing
Thesis, Post law).
The closure of the partial recursive functions (the one semi-
computable by the universal machine) for diagonalization makes the
theoretical computer science a good candidate for an explanatively
close field capable of including the non justifiable, the non
observable, the non knowable, the non memorable, etc.)
Universality entails ignorance, but that ignorance comes with a quite
complex structure.
With the digital mechanist hypothesis, the locality/non-locality issue
is of course an open problem, but a simple Bell's inequality is most
plausibly violated (unless some number conspiration).
Bruno
Saibal
Bruce
Microsoft Word - What Bell Did revised.docx
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[1] https://arxiv.org/abs/1408.1826
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