QM Assumptions Regarding Entanglement Properties

[stevendaryl]

A hidden variables theory, should one be developed, will accept all experimental results and will be just as good, if not better, than existing quantum theories at predicting those results.

Right. That's the type of theory that Bell was interested in---one that made exactly the same predictions as QM (at least for experiments where QM proved to be correct). That's the type of theory that his proof is about.

 

[zonde]

Your analogies might be OK for the situations you describe but I don't think they're necessarily relevant to the point I'm trying to make.

So you agree that sometimes we can say something can't be true even when we don't know all the details about the situation, right? Say if I claim that I have made many small purchases and the money spent together is more than I had initially, would you say I got it wrong somewhere even without asking what exactly where those small purchases and how much I spent on every purchase?

Then what type of argument would convince you that particular assumptions give us enough information to conclude that any such a theory is impossible? Well, we have to make some inferences from assumptions that we make. How many steps would be acceptable for you? Say we can examine every step for some length so that you can be certain there are no holes in that particular step.

 

[Dadface]

Right. That's the type of theory that Bell was interested in---one that made exactly the same predictions as QM (at least for experiments where QM proved to be correct). That's the type of theory that his proof is about.

Sorry I don't understand this. You say that Bell was interested in a theory that made the same predictions as QM but the theory that was tested had observations that did not make the same predictions as QM. It cannot be described as a theory. I think what Bell and the experimenters did was to show that a theory, as they interpret(ed) it, was a failure because it predicted results that were not borne out by experiment. As I said before, to be classified as a theory a hidden variables theory must, among other things, conform to the observations. Bell and others did not analyse and test a hidden variable theory .They tested what they thought might be a hidden variable theory and then went on to prove it wasn't a theory at all because it did not meet the necessary criteria. None of that means to say that a proper hidden variable theory will not appear in the future.

In a rush and have to go now.

 

[DrChinese]

While EPR is talking about reality Bell's argument talks about theories. It says: "This [non-local structure] is charateristic, according to the results to be proved here, of any such theory which reproduces exactly quantum mechanical predictions."

Bell used EPR's elements of reality as the basis for his paper. No, he did not label it as such except by the title of the paper.

And the statement you quote simple is a restatement of the idea that the only hidden variable theories that are viable are ones in which the setting of Alice influences the outcome for Bob, however remote. Clearly, the realism assumption can be dropped and then that is not an issue. With the current evidence, I am not sure how it makes sense to say the non-commuting observables have definite values at all times. Which was essentially the assertion of EPR (that a more "compete" theory was possible).

 

[zonde]

Bell used EPR's elements of reality as the basis for his paper. No, he did not label it as such except by the title of the paper.

And the statement you quote simple is a restatement of the idea that the only hidden variable theories that are viable are ones in which the setting of Alice influences the outcome for Bob, however remote. Clearly, the realism assumption can be dropped and then that is not an issue. With the current evidence, I am not sure how it makes sense to say the non-commuting observables have definite values at all times. Which was essentially the assertion of EPR (that a more "compete" theory was possible).

Well, yes Bell is using EPR argument to conclude there can be more complete theory if we assume locality.
"Since we can predict in advance [assuming locality] the result of measuring any chosen component of σ2, by previously measuring the same component of σ1, it follows that the result of any such measurement must actually be predetermined. Since the initial quantum mechanical wave function does not determine the result of an individual measurement, this predetermination implies the possibility of a more complete specification of the state."
Your objection as I understand is that this "any" is applied to the same initial configuration in the quoted text from Bell paper.
So if we drop "any" from above have we got rid of that EPR assumption? Is this modified inference correct without relaying on that EPR assumption:
"Since we can predict in advance [assuming locality] the result of measuring chosen component of σ2, by previously measuring the same component of σ1, it follows that the result of that measurement must actually be predetermined. Since the initial quantum mechanical wave function does not determine the result of an individual measurement, this predetermination implies the possibility of a more complete specification of the state for that component of σ2."

 

[zonde]

Sorry I don't understand this. You say that Bell was interested in a theory that made the same predictions as QM but the theory that was tested had observations that did not make the same predictions as QM. It cannot be described as a theory.

Bell considered two predictions of QM:
#1 perfect correlations when measurement angles are the same
#2 imperfect correlations when measurement angles are not the same
He considered all the theories of certain type that satisfied QM prediction #1 and then demonstrated that there is no way how these theories could make QM prediction #2.

 

[PeterDonis]

Thread closed for moderation.

 

[PeterDonis]

The thread has run its course and will remain closed.