Re: Question on EPR and arXiv:0705.2568

On May 28, 10:20 am, Benjamin <Benjamin_Sch...@xxxxxx> wrote:
a student wrote:
A very quick readthrough appears to give a contradiction in their
model. Look at Eq. (13), defining a set of joint probabilities P'.
The righthand side of this equation, summed over the + and - symbols
clearly sums to 1

Sorry, but I do not get 1!
At least when I put this in mathematica....

Why use mathematica? In equations (6) and (7) of the eprint (http://
arxiv.org/abs/0705.2568), probabilities P^A_(+/-), P^B_(+/-) are
defined such that (suppressing explicit angle dependence):
P^A_(+) + P^A(-) = 1 = P^B_(+) + P^B_(-) . (*)
Now, for convenience, define the joint probability distribution by
Q_(+/-, +/-) = P^A_(+/-) P^B(+/-) . (**)
It follows immediately from (*) that
Q_(+,+) + Q_(+,-) + Q_(-,+) + Q_(-,-) = 1. (***)

Noting (**), equation (13) of the eprint can be rewritten as
P'(+/-,+/-) = < Q_(+/-, +/-) >,
where < > denotes a particular average related to one of the angular
variables. It follows immediately from (***) that
P'_(+,+) + P'_(+,-) + P'_(-,+) + P'_(-,-) = < 1 > = 1. (****)

Finally, the authors of the eprint assert that the quantity in their
equation (14), i.e.,
P(+/-,+/-) = 2 P'(+/-,+/-) ,
is a joint probability distribution! This clearly contradicts
(****) ! It further means that their equation (15) is wrong by a
factor of 1/2, and should read
E = (1/2) cos (a,b).
This means that one obtains sqrt(2) instead of 2sqrt(2) in the
corresponding Bell equation, which is well within the classical HV
upper bound of 2.

I imagine the other papers are similarly flawed.
The results of Nelson are from a well respected probability theorist at
princeton:

Yes, you are right, I have read two of his books and several papers,
and certainly expect that the one you mention is all above board - my
apologies for tarring him with the same brush as the eprint.

.