DrChinese said:
This was the EPR argument. Local causality + HUP -> (QM is incomplete) or (Reality is observer dependent - in this case Alice).
Yes. The only essential difference between the argument I have given and that of original EPR lies in the "completeness" condition.
I agree. Even if the argument I have posed can go through, its 'lesson' can be
no different from that of original EPR.
So ... I see then ... as far as original EPR is concerned, you have no objection to the type of CF used. Okay. That helps clarify for me your position on CF. Good.
So, we are left with the question of which notion(s) ought to be relinquished:
Eye_in_the_Sky said:
... one of the following must be relinquished:
(i) 'free-choice' ,
(ii) QM is "local" ,
(iii) QM is "complete" ,
(iv) some other (implicit, currently unidentified) assumption .
You suggest:
DrChinese said:
... Bob's reality is dependent on a choice made by Alice if QM is complete. I would say this is a generally accepted conclusion: that either locality does not hold, or reality is dependent on observeration.
Okay. Let us write this as:
(QM is complete) Λ (local causality) → Bob's 'reality'
depends on Alice's choice ,
where the 'reality'-
dependence is "non-causal".
_________
For clarity, let us consider an example.
Suppose Alice measures S
x and gets the result "+". Then Bob's 'reality' is such that
if Bob measures Sx then he cannot obtain the result "+".
On the other hand, if Alice had measured S
y (
instead of S
x), then Bob's 'reality'
would have been such that
if Bob measures Sx then he can obtain the result "+".
... DrC, is this example included in what you mean by "Bob's reality is dependent on a choice made by Alice"? ... or is it not?
__________________________
Only now is it beginning to become clearer to me (although, not yet quite 'altogether') what is going on here.
First, let me explain the two motivations I had for my having posed the argument in the manner I did:
motivation 1: Somehow, vaguely, I felt that by stripping the
microsystem of all 'reality', then (as a consequence) the "nonseparability" issue would – simply –
disappear; [... Now, however, I see it seems that the issue has
not just
disappeared, but rather, it has been
transferred over to the
macroscopic experimental arrangement;]
and
motivation 2: Since Bell's "local causality" criterion is about 'probability' 'assignments' made on the basis of "complete" 'information', I suspected that by couching the
quantum state in terms of 'information', then somehow, a previously hidden insight would emerge. [... And indeed (... I think)...
I see it now.]
Bell's "local causality" criterion goes like this ["types" of
emphasis added] (
diagram[/color]):
A ["complete"
stochastic] theory will be said to be "locally causal" if:
The 'probabilities' 'attached' to 'values' of "local beables" in a spacetime region 1 are
unaltered by 'specification' of 'values' of "local beables" in a
spacelike separated region 2,
when what happens in the backward light cone of 1 is
already sufficiently 'specified', for example by a
full 'specification' of ['values' of] "local beables" in a spacetime region 3.
Now here comes the 'catch':
... what sort of 'existence' do these "local" 'beables' have?
These "local beables"
belong to a 'realm' regarding which
the principle of "separability" applies.
________
For example, the following four quantities are
all construed (by Bell) as being "local beables":
a ≡ Alice's setting ,
b ≡ Bob's setting ,
A ≡ Alice's outcome ,
B ≡ Bob's outcome .
________
So ... "separability" as applied to (these) "local beables" (in this context of Alice and Bob) would (seem to) mean (among other things (something like this)):
The 'real' "state of Alice's instrument" and the 'real' "state of Bob's instrument" 'exist' independently of one another.
This then is (supposed) to imply that in any theory in which a notion of "state" is 'assigned' to the "instruments" of Alice and Bob, the following
two conditions will hold:
1) The "state of Alice's instrument" and the "state of Bob's instrument" can be 'specified' independently of one another;
and
2) A 'specification' of the "joint state of Alice's instrument and Bob's instrument" is equivalent to a joint 'specification' of the "state of Alice's instrument" and the "state of Bob's instrument".
_____________________
DrChinese said:
I believe it is correct to see the conjunction of assumptions in Bell: locality + realism.
Eye_in_the_Sky said:
In connection with "stage 2" of Bell's argument, I agree with you. But in connection with "stage 1" I do not see it.
Okay, now I see it. That is, what I am
now seeing regarding "stage 1" (in terms of a conjunction of assumptions) in Bell is very much along the lines of what you had put as:
locality + realism .
(After quite some thought ... I think) I would (like to) put it like this:
Bell's "local causality" criterion ↔
"causally local" 'reality' Λ "existentially separable" 'macro-apparatus-world' .
... Does this make sense to you?