On 10 May 2016, at 18:36, 'scerir' via Everything List wrote:
scerir wrote:
If A and B are two wings of a typical Bell apparatus, i the
observable to be measured in A
and x its possible value, j is the observable to be measured in B
and y its possible value,
and if Lambda are hidden variables, we could write
Locality Condition
p_A,Lambda (x|i,j) = p_A,Lambda (x|i)
p_B,Lambda (y|i,j) = p_B,Lambda (y|j)
Separability Condition
p_A,Lambda (x|i,j,y) = p_A,Lambda (x|i,j)
p_B,Lambda (y|i,j,x) = p_B,Lambda (y|i,j)
There is (or was) some agreement that a (phantomatic) deterministic
theory (i.e. one in which
the range of any probability distribution of outcomes is the set: 0
or 1)
reproducing all the predictions of QM, can not violate the
Separability Condition, (the specification of Lambda, i, j, in
principle determines
completely the outcomes x, y, then any additional conditioning on
x or y is superfluous, having x and y just one value allowed, so they
cannot affect the probability, which - in a deterministic theory - can
just take the values 0 or 1) and must violate the Locality
Condition.
Following the above reasoning, MWI (if it is a truly deterministic
theory)
should violate the Locality Condition.
---------------
### Since the Everett faq gives the following .....
"To recap. Many-worlds is local and deterministic. Local
measurements split local systems (including observers) in a
subjectively random fashion; distant systems are only split when the
causally transmitted effects of the local interactions reach them.
We have not assumed any non-local FTL effects, yet we have
reproduced the standard predictions of QM. So where did Bell and
Eberhard go wrong? They thought that all theories that reproduced
the standard predictions must be non-local. It has been pointed out
by both Albert [A] and Cramer [C] (who both support different
interpretations of QM) that Bell and Eberhard had implicity assumed
that every possible measurement - even if not performed - would have
yielded a single definite result. This assumption is called contra-
factual definiteness or CFD [S]. What Bell and Eberhard really
proved was that every quantum theory must either violate locality or
CFD. Many-worlds with its multiplicity of results in different
worlds violates CFD, of course, and thus can be local."
So, I should say that ..... MWI (if it is a truly deterministic
theory, reproducing all the
predictions of QM) should violate the Locality Condition but, in
fact, it violates CFD only :-).
Exactly. I think we are on the same length wave (as we say in french
for assessment). And that is why QM-without collapse needs only the
computationalist First Person Indeterminacy (FPI), making QM facts
confirming mechanism instead of threatening it (which is what would
happen if we allow collapse, or worst, direct action of consciousness
on the physical).
Like with Gödels theorem, QM seems to threat mechanism, but eventually
appears to be an ally, and perhaps a confirmation, (which of course is
not a proof, but we can't prove anything on reality, nor even that it
exists. We can only bet on it.).
Bruno
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