.
JesseM said:
So can you please address my point that the formulas in Table 1 are clearly incompatible with those in Table 2, ...
Based on earlier responses from me, and more detail below: I trust this perceived "incompatibility" is now resolved?
There is NO incompatibility. Are we now in agreement on this point?
JesseM said:
as shown by my numerical example in [post=3159151]post 71[/post] (which you never responded to, ...
As I recall: Your post #71 came in on the day JenniT was urgently to go bush. JenniT had delayed her departure to address some earlier matters, and planned to reply to #71 before she left. Vanesch then pointed out that she'd written 0.732 for 0.0732, so at that she went bush ...
... having realized her mistake in responding to posts while in meetings, and under other pressures, in an effort to keep her (perceived) responsibility to this thread moving ... to a helpful conclusion.
Post #78 refers [
https://www.physicsforums.com/showpost.php?p=3159608&postcount=78]
Then, on her return: Most outstanding matters were cleared up in PDF2: With its complete derivation, via L*R, of every relevant EPRB probability. All in full accord with QM. That is: In full accord with the point of view repeatedly emphasized here; as one with QM.
JesseM said:
... and you also didn't respond to my specific request to address this in post 90)?
Sorry: I thought that Post #91 responded to the matters raised in your post #90?
Please bring forward any outstanding matters that remain unresolved between us -- taking PDF2 into account, please.
JesseM said:
More generally, your formulas in Table 1 [sic] are simply the ones predicted by QM, ... [GW emphasis and "sic" added.]
I suspect this is a typo and should read ...
More generally, your formulas in Table 2 are simply the ones predicted by QM,
YES, but they are wholly derived from within L*R; so that "simply" of yours would be better written as "in full accord with".
So, with these understandings, we'd then have:
Your formulas in Table 2 are [STRIKE]simply[/STRIKE] in full accord with the ones predicted by QM.
My response would then be:
Yes, because that QM-ACCORD was a boundary condition on the model and on its submission for discussion here.
NB: I am not in dispute with QM. I am in dispute with Bell's theorem ... in the same way that QM is in dispute with Bell's theorem:
BT cannot be formulated from within QM, nor from within the local realism of L*R. That's the point here.
JesseM said:
... there is no possible way you could ever come up with a list of probabilities P1-P8 that reproduce the QM probabilities, based simply on the argument on the Bell inequality page[/url] which you have never really addressed: ...
Sorry, I thought that PDF2 made it clear: Regarding "Zakurai's Bell Inequality page" -- I accepted his 8 equivalence classes (ECs) as valid (+++ –––, etc.), then derived the relevant P1-P8 (the RHS of Table 1 in PDF2)
that are applicable under L*R.
That is: Going beyond Zakurai and QM: I give specific values for every probability; not some generalized notion that such (in some form) exist, under some form of local realism (perhaps of the naive variety, for all I know).
So:
PDF2, Table 1, shows the normalized distribution of all 8 ECs: under the local realism of L*R.
JesseM said:
1. According to the predetermined results given on the table, it must be true that:
P(a+, b+|ab) = P3 + P4
P(a+, c+|ac) = P2 + P4
P(c+, b+|cb) = P3 + P7
From PDF2, using the notation therein (which is wholly equivalent to yours above), with the PDF2 equation numbers in Appendix A:
(A0a) P(ab++|ab) = [P(ab++|
a) + P(ab++|
b)]/2 = Sab/2.
(A0b) P(ab++|abc) = [P(ab++|
a) + P(ab++|
b) + P(ab++|
c)]/3 = [2P(ab++|ab) + P(ab++|
c)]/3.
(A0c) ∴ P(ab++|ab) = [3P(ab++|abc) – P(ab++|
c)]/2 = Sab/2.
Note that you write:
(1X) P(a+, b+|ab) = P3 + P4. X
(2X) P(a+, c+|ac) = P2 + P4. X
(3X) P(c+, b+|cb) = P3 + P7. X
But these are all incorrect: The conditioning space is NOT variously
ab, ac, cb (respectively), as you have written; but
abc for all. That is, retaining your notation here for comparison, but correcting the conditioning space:
(1) P(a+, b+|abc) = P3 + P4.
(2) P(a+, c+|abc) = P2 + P4.
(3) P(c+, b+|abc) = P3 + P7.
Then:
Since these are Normalized Probabilities from L*R (and NOT from QM), they must be
reduced to deliver the corresponding QM Normalized Probabilities.
The result is shown in PDF2, Table 2; with every calculation detailed in Appendix A: IN FULL ACCORD WITH QM.
Please check your P(a+, b+|ab), P(a+, c+|ac), P(c+, b+|cb) there, in Table 2.
NB: The need for
reduction arises because L*R does what many evidently believe QM cannot do; i.e., L*R goes beyond what many evidently believe to be QM's limit. [A diversionary point not addressed here because QM is not under attack here. It's a point for another day.] That is, and importantly: The reduction DOES NOT arise from any dispute with QM!
JesseM said:
2. Since all the probabilities P1-P8 are real and non-negative, it must be true that:
P3 + P4 ≤ P3 + P4 + P2 + P7
This is NO MORE true in L*R than it is in QM! It is a nonsense in both.
JesseM said:
3. Substituting the formulas from 1. into 2. gives:
P(a+, b+|ab) ≤ P(a+, c+|ac) + P(c+, b+|cb)
Therefore, any theory that gives probabilities for P1-P8 and agrees with the formulas in 1. must satisfy this inequality
Clearly, this is not the case; this is just not so: Let us see, in your notation --
P(a+, b+|ab) = Sab/2.
P(a+, c+|ac) = Sac/2.
P(c+, b+|cb) = Scb/2.
The inequality -- that you insist must exist -- CANNOT be formulated.
As in QM, so on L*R: Bell Inequalities cannot be formulated; BT
non est in both!
Reason: In part due to critical analysis; in part because L*R supplies a physically-significant, local-realistic, specific-valued, normalized distribution that sums to unity: And not some unspecified (perhaps misunderstood) non-specific Probabilities; perhaps attaching to a naive view of local realism? -- which is not relevant (at this time) to our discussions here.
JesseM said:
4. But the QM predictions can violate the inequality in 3. for specific angles a,b,c like a=45, b=22.5 and c=0. So, no theory giving probabilities for P1-P8 can replicate the QM predictions, which are just those given in your Table 2.
As stated above: The inequality cannot be constructed in L*R; just as it cannot be constructed in QM.
Please: Such a result should not be held against L*R; no more than it is held against QM.
In your words: The QM predictions can violate the inequality in 3.
In my words: Agreeing with QM, the L*R predictions can violate the inequality in 3.
JesseM said:
Is there some part of this argument you don't understand? If you understand it but think the logic is flawed, can you tell me which of these points 1-4 you disagree with? Also, please note here that the angles are considered to be defined relative to some fixed coordinate system, so there can be no notion that any of the probabilities P(a+, b+|ab), P(a+, c+|ac), P(c+, b+|cb) are defined as "averages" of different pairs in P1-P8 as opposed to the simple formulas in 1. If you want to dispute this point and continue to talk about "bi-angles", "reference frames" and other such nonsense, please reread my post #88, and respond to this section in post #92:
In haste, trusting these matters are clarified by PDF2 and the above.
JesseM said:
Please respond to that question at the end ("Will you agree to this..."): this should take precedence over all other responses to questions in my post. I really, really, don't want to continue to hear arguments involving "bi-angles", using different "reference frames" on different trials which label the three possible orientations with different angles, and so forth; if you cannot restate your argument in terms of a fixed coordinate system, then clearly what you are talking about has nothing to do with refuting Bell's own argument since he (and every other physicist who uses the same type of notation) was assuming a fixed coordinate system where the angles associated with each of the three physical orientations are constant from trial to trial.
Now resolved, understood, and agreed between us: I trust?
With thanks again,
GW