On 06-07-2018 14:18, Bruce Kellett wrote:
From: BRUNO MARCHAL <[email protected]>
On 5 Jul 2018, at 17:20, Lawrence Crowell
<[email protected]> wrote:
John Bell proved that any objective theory giving experimental
predictions identical to those of quantum theory is necessarily
nonlocal.
Assuming a unique reality. I prefer the term “inseparable”,
because “non-locality” is often interpreted the existence of FTL
influence (even if they cannot be used to transmit information), but
such FTL influence seems to me suspicious. Some might disagree, but
I have not yet seen a proof that any FTL subsists when we abandon
the collapse postulate. Bell assumes that experiments gives univocal
results.
You might not have seen a proof that non-locality remains when we
abandon the collapse postulate, but that does not mean that no such
proof can be given.
Consider the following scenario. Alice and Bob are given a large
number of entangled pairs, which they measure when they are at large
spacelike separation. Each measurement is made at some angle, and
gives a '1' for 'up' or 'passed', and '0' for the opposite result.
Both record the sequence of such results that they obtain in their
individual lab books, together with the corresponding polarizer
orientations. Their lab books then contain a random sequence of say N,
'1's and '0's. There are 2^N possible such sequences in the
many-worlds case, but since each observer keeps the same lab book for
the whole sequence, each series of measurements is necessarily made in
the same one world. Basically, this is because the worlds are
disjoint, and the observers and/or lab books cannot move between
worlds.
When Alice and Bob meet up at the end of the run of N trials, they
take their lab books with them. When they meet they are clearly in the
same Everettian branch. And since their lab books cannot have jumped
between branches, the sequence of results that they each bring must
also have all been recorded in this same one branch. So when they come
to use their data to calculate the correlations between the
measurements on their individual particles of the entangled pairs,
they are in exactly the same situation as they would be if they had
assumed a collapse model from the outset. The correlations they
observe are necessarily single-world correlations. So the conditions
of Bell's theorem are exactly satisfied, and since the correlations
violate the Bell inequalities, their experiment has demonstrated the
impossibility of a local hidden variable account. They have
demonstrated that the quantum correlations require non-locality, even
with Everett's many-worlds, just as Bell proved.
And all this happens whether they assume many-worlds or a collapse
model.
Bruce
Alice's lab book is not located in a single branch of Bob's lab book and
vice versa. If you consider the entire wavefunction of Alice's sector,
including her lab book and Bob's sector and his lab book, then this is a
complicated entangled wavefunction. If you trace out the environments on
both sides and only consider the contents of the lab books, you're left
with correlated lab books where each entry of one lab book is correlated
with the corresponding entry of the other lab book.
Bell's theorem in general without assuming many or single words, doesn't
directly imply nonlocality, the way the correlations depend on the
relative polarizer orientation shows that there are no local hidden
variables that would have specified the outcome of the measurements.
That leaves us with two options. Either there exists nonlocal hidden
variables, or there are no hidden variables at all. What matters is that
before any measurement where there are multiple possible outcomes
(whether or not that involves entangled pairs where someone else is
measuring the other component), the information about the result of the
outcome is not already present locally.
So, when Alice measures her spin, she gains one bit on information and
that bit of information was not present in her local environment. In
case of entangled pairs that information would have been present at a
spacelike separation, but only if one assumes a single world
interpretation. The thought experiment with lab books doesn't change
this conclusion because the lab books end up in an entangled
superposition with each other, as well as with the local environments.
Saibal
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