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JesseM
JesseM is offline
#13
Jun10-10, 09:50 PM
Sci Advisor
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Quote Quote by JenniT View Post
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?
beables represent local hidden variables that are supposed to explain correlations seen in observables, and observables are just facts we can actually measure, like whether a particle gives result "spin-up" or "spin-down" when passed through a Stern-Gerlach device oriented at some angle. Take a look at my scratch lotto card analogy in this post (beginning with the paragraph that starts 'Suppose we have a machine that generates pairs...')--the observables would be the cherries or lemons that Alice and Bob actually see when they pick a single square to scratch, the beables would be the complete set of hidden fruits behind all three squares, which are used to explain why it is that they always find the same fruit whenever they scratch the same box (the assumption being that on each trial, the two cards have the same set of hidden fruits).
Quote Quote by JenniT
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?
I don't know much about relativistic quantum theory which is where I think "spinors" appear--my question here would be, are spinors actually local variables associated with a single point in spacetime, or are they defined in some more abstract "space" like Hilbert space?
Quote Quote by JenniT
You seem to require that we would know a priori which of that infinite set satisfied this subset aG conditional?
Not clear what you mean by "this subset aG conditional", can you elaborate?
Quote Quote by JenniT
3. Beside which, if aG were implicit in your lambda
What do you mean by "implicit in"? Do you mean that the measurement a and the result G can be determined from the value of lambda? If so, I'm not sure why you think that, the measurement can be random and I told you in post #82 on this thread that the probabilities of different outcomes may be other than 0 or 1 in a probabilistic local realist theory.
Quote Quote by JenniT
Note that you seem to require lambda to be an undefined infinite set
Nothing "undefined" about it, as I said to billschnieder:
In any well-defined local realist fundamental theory, the complete set of possible physical facts that obtain at a given point in spacetime should be well-defined, no? If your fundamental theory involves M different fields and N different particles and nothing else, then by specifying the value of all M fields at a given point along with which (if any) of the N particles occupies that point, then you have specified every possible physical fact at that spacetime point. As long as there is some fundamental theory of physics and it is a local realist one, then the theory itself gives a precise definition of the sample space of distinct physical possibilities that can obtain at any given point in spacetime--do you disagree?
Quote Quote by JenniT
4. As with the ether experiments and their outcome, don't Bell-tests show that Bell's supposition re Bell's lambda is false?
Like I said to billschnieder in the last post, the basic logic of Bell's argument is a proof-by-contradiction. He starts only by assuming that the universe obeys local realist laws, and then shows that they produce predictions about the statistics of Aspect-type experiments that contradict the predictions (and experimental results) of QM, and so concludes that QM is incompatible with local realism (so if QM's predictions hold up to experimental tests, our own universe must not obey local realist laws).