I Determinism, realism, hidden variables

[DrChinese]

Counterfactual definiteness is not an assumption, but derived from the EPR argument.

This is not a fair statement. CFD is derived by EPR ONLY by in turn making assumptions. Specifically, they assume that all elements of reality (per their definition) are simultaneously real. That rules out CFD per se.

 

[Ilja]

This is not a fair statement. CFD is derived by EPR ONLY by in turn making assumptions. Specifically, they assume that all elements of reality (per their definition) are simultaneously real. That rules out CFD per se.

I don't understand.

If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity.

Given the Bell state and Einstein causality, we can do this for all directions. Choose the direction, measure, compare, see the 100% correlation. Fine. Thus, the results are real, predefined, for all directions. This is how the EPR criterion is formulated: "we can", not "we do".

There are, clearly, additional assumptions: Einstein causality does not follow from the EPR criterion, and the quantum statistics of the Bell state are assumed too. But this is nonetheless the EPR argument.

 

[DrChinese]

Giving up realism means giving up any idea of explanation completely. There is no longer any reality outside, all this is a dream or fantasy or so. There would be no point of doing science, if not for the purpose of studying objective reality.

This is not a description of non-realism. It is a gross distortion and ignores much which has been written on the subject.

 

[DrChinese]

I don't understand. ... Given the Bell state and Einstein causality, we can do this for all directions. Choose the direction, measure, compare, see the 100% correlation. Fine. Thus, the results are real, predefined, for all directions.

That leap is by assumption. EPR simply rejects any other viewpoint as unreasonable. As obviously you do. Nonetheless, it is circular reasoning to assume CFD and then say you have proved it. See the last 2 paragraphs of EPR.

 

[stevendaryl]

This is not a fair statement. CFD is derived by EPR ONLY by in turn making assumptions. Specifically, they assume that all elements of reality (per their definition) are simultaneously real. That rules out CFD per se.

I'm not sure what you mean by that. The way that I see it is that E, P, and R were assuming a particular sort of theory, whereby the results of an experiment depend only on local facts. So, as Bell formulated this, that means that Alice's result depends only on facts about her device and facts about her particle, and similarly for Bob. This implies Bell's assumed form for the joint probability distribution:

P(A, B | \alpha, \beta, \lambda) = P(A|\alpha, \lambda) P(B|\beta, \lambda)

where A represent's Alice's result (assumed to be a boolean), B represents Bob's result, \alpha represents facts about Alice's detector, \beta represents facts about Bob's detector, and \lambda represents facts about the twin pair creation event.

This form seems at first to allow for the possibility that the results are nondeterministic. But if you impose perfect anti-correlations, then that implies:

P(A|\alpha, \lambda) P(B|\alpha, \lambda) = 0 (It is impossible for them to both get spin-up with the same detector settings.)
(1-P(A|\alpha, \lambda))(1 - P(B|\alpha, \lambda)) = 0 (It is also impossible for them to both get spin-down)

These two facts imply that P(A|\alpha, \lambda) = 0 or 1 and P(B|\beta, \lambda) = 0 or 1.

So Bell's factorizability assumption implies that the outcomes are deterministic functions of \lambda and the detector settings, which implies contrafactual definiteness (in the sense that the assumed model implies that there is a definite answer to the question: What would Bob's result have been if he chose a different detector setting?)

 

[Ilja]

That leap is by assumption. EPR simply rejects any other viewpoint as unreasonable. As obviously you do. Nonetheless, it is circular reasoning to assume CFD and then say you have proved it. See the last 2 paragraphs of EPR.

It is certainly nothing circular here, because the EPR criterion is clearly different from CFD. In particular, there are EPR-realistic interpretations of QT like dBB theory, but CFD does not hold in dBB. So CFD is clearly a stronger assumption.

Of course, other viewpoints are possible. But rejecting the EPR criterion means simply rejecting reality and may be classified as mysticism.

 

[DrChinese]

I'm not sure what you mean by that. ...

So Bell's factorizability assumption implies that the outcomes are deterministic functions of \lambda and the detector settings, which implies contrafactual definiteness (in the sense that the assumed model implies that there is a definite answer to the question: What would Bob's result have been if he chose a different detector setting?)

I am talking about Ilja's (incorrect) statement that EPR "proves" CFD. Bell essentially (and usefully) makes it an assumption (along with locality) and shows that those 2 assumptions (together) do not fit with QM. So one or both must be wrong.

EPR says: "One could object to this conclusion on the grounds that our criterion of reality is not sufficiently restrictive. Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted. On this point of view, since either one or the other, but not both simultaneously, of the quantities P and Q can be predicted, they are not simultaneously real. This makes the reality of P and Q depend upon the process of measurement carried out on the first system, which does not disturb the second system in any way. No reasonable definition of reality could be expected to permit this."

Clearly, CFD is inconsistent with the more restrictive requirement. EPR takes the less restrictive view (assuming CFD) and then concludes any other perspective is unreasonable. Well, that places a lot of physicists in the unreasonable camp. Who really thinks that particles have simultaneously well defined P and Q?

 

[DrChinese]

It is certainly nothing circular here, because the EPR criterion is clearly different from CFD.

Not in any way I can see. And if you were correct, every physicist would be a Bohmian.

 

[PeterDonis]

Thread closed for moderation.

Edit: The thread appears to have run its course and will remain closed.