Thread: Understanding Bell's logic View Single Post
P: 375
 Quote by JesseM No, it's not equivalent to saying G and G' are not correlated in a general sense, it just means that if you already know λ then learning G will give you no further information about the probability of G'. For example, if G and G' are correlated, but this correlation is explained entirely by a common cause that lies in the region where the past light cones of the two measurements overlap (the common cause might be that the two particles sent to either experimenter are always created with an identical set of hidden variables by the source), then if you already have the information about the common cause contained in λ (which could detail the set of hidden variables associated with each particle, for example) then in this case it will be true that learning G won't change your estimate of the probability of G'. This is precisely the sort of physical logic that Bell was using, and my argument in which λ was made to stand for all facts in the past light cones of the measurement events was an attempt to make this a bit more rigorous.

Thank you JesseM. I appreciate this detail. I have some basic questions.

1. Could you define for me (briefly) and distinguish Bell's use of the words observable and beable? Is Bell's lambda an observable or a beable or something else -- like what? What size set might it be?

2. If Bell's lambda were an infinite set of spinors (because we want a realistic general "Bell" vector that applies to both bosons and fermions), then wouldn't we need aG to define the infinite subset of spinors that were relevant to the applicable conditional? You seem to require that we would know a priori which of that infinite set satisfied this subset aG conditional? This a priori subset being the lambda you would require here?

3. Beside which, if aG were implicit in your lambda, its restatement/extraction by me would be superfluous and not change the outcome that attaches to the disputed conditional? Note that you seem to require lambda to be an undefined infinite set, perhaps not recognizing that it is an infinite subset (selected by the condition aG, out of your undefined infinite set) which is relevant here?

4. As with the ether experiments and their outcome, don't Bell-tests show that Bell's supposition re Bell's lambda is false?

Thank you.