Juso wrote:
Nice picture! You told the place but not the year. It would be interesting to know the year.
gill1109 wrote:
Einstein implicitly confirms that according to quantum mechanics, it does hold under a quantum mechanical state.
John S. Bell wrote:
[von Neumann's] essential assumption is: Any real linear combination of expectation values ... is the expectation value of the combination. This is true for quantum mechanical states; it is required by von Neumann of the hypothetical dispersion free states also. ... But for a dispersion free state (which has no statistical character) the expectation value of an observable must equal one of its eigenvalues. ... The essential assumption [of von Neumann] can be criticized as follows. ... (from Section 3 of Chapter 1 of Bell's book).
Joy Christian wrote:gill1109 wrote:
Einstein implicitly confirms that according to quantum mechanics, it does hold under a quantum mechanical state.
It is universally agreed, by all parties involved, past and present, that the additivity of expectation values holds within quantum mechanics. But it does not hold for dispersion-free states:John S. Bell wrote:
[von Neumann's] essential assumption is: Any real linear combination of expectation values ... is the expectation value of the combination. This is true for quantum mechanical states; it is required by von Neumann of the hypothetical dispersion free states also. ... But for a dispersion free state (which has no statistical character) the expectation value of an observable must equal one of its eigenvalues. ... The essential assumption [of von Neumann] can be criticized as follows. ... (from Section 3 of Chapter 1 of Bell's book).
Evidently, you have not understood the Einstein-Bell argument against the additivity of expectation values within hidden variable theories. I also doubt that you have read my linked paper.
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gill1109 wrote:
I understand Einstein’s argument. You still have not answered mine. There is no contradiction. My argument used only the additivity within quantum mechanics. Which Einstein agreed with. Please think carefully about the argument I gave; don’t jump to conclusions.
gill1109 wrote:
Consider three observables A, B and C such that C = A + B. Suppose none commute with one another. There are three separate experiments which allow one to experimentally determine <A>, <B>, and <C>, each by averaging many measurements of A, B or C on systems prepared in the same state rho. One will discover that <C> = <A> + <B>.
This is because <A> = trace(rho A), <B> = trace(rho B), <C> = trace(rho C), “trace” is linear.
A hidden variable model for these experiments is a classical probability space with three random variables X, Y and Z defined on it, such that the probability distributions of the three random variables exactly reproduce the probability distributions of the outcomes of measurements of the three observables. In particular, their mean values are the same. Hence E(X) = <A>, E(Y) = <B>, E(Z) = <C>. Hence E(X) + E(Y) = E(Z).
The additivity follows from the linearity of the trace operator. The hidden variable model by definition mimics observable features of the quantum model (probabilities, expectation values...).
John S. Bell wrote:
[von Neumann's] essential assumption is: Any real linear combination of expectation values ... is the expectation value of the combination. This is true for quantum mechanical states; it is required by von Neumann of the hypothetical dispersion free states also. ... But for a dispersion free state (which has no statistical character) the expectation value of an observable must equal one of its eigenvalues. ... The essential assumption [of von Neumann] can be criticized as follows. ... (from Section 3 of Chapter 1 of Bell's book).
Joy Christian wrote:.
I have received a decision email from a journal concerning my paper I have liked above: https://arxiv.org/pdf/1704.02876.pdf.
The paper has been rejected based on two reviewer reports. The first reviewer recommends outright rejection based on an argument identical to the one Justo has put forward in this forum. I do not agree with that argument and might consider fighting back.
The second reviewer has enthusiastically recommended the paper for publication with very positive comments: "The manuscript by Joy Christian is a virtuoso performance and tells us much about the possible analogies and failures of von Neuman's and Bell's no-go proofs. I find Christian's logic convincing and definitely recommend that this work be published." The report then goes on to make some minor criticisms and concludes: "Besides all these minor criticisms, Christian's paper is excellent and definitely should be published."
The paper is nevertheless rejected on the grounds that the journal's "current publication program is not well suited for it, and must regretfully decline your offer to let us publish it."
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Justo wrote:
If your paper is published, I am willing to write a comment on it explaining why I believe is incorrect. But it would not be for personal reasons, it would be just to discuss ideas.
Joy Christian wrote:.
I have received a decision email from a journal concerning my paper I have liked above: https://arxiv.org/pdf/1704.02876.pdf.
The paper has been rejected based on two reviewer reports. The first reviewer recommends outright rejection based on an argument identical to the one Justo has put forward in this forum. I do not agree with that argument and might consider fighting back.
The second reviewer has enthusiastically recommended the paper for publication with very positive comments: "The manuscript by Joy Christian is a virtuoso performance and tells us much about the possible analogies and failures of von Neuman's and Bell's no-go proofs. I find Christian's logic convincing and definitely recommend that this work be published." The report then goes on to make some minor criticisms and concludes: "Besides all these minor criticisms, Christian's paper is excellent and definitely should be published."
The paper is nevertheless rejected on the grounds that the journal's "current publication program is not well suited for it, and must regretfully decline your offer to let us publish it."
.
minkwe wrote:Joy Christian wrote:.
I have received a decision email from a journal concerning my paper I have liked above: https://arxiv.org/pdf/1704.02876.pdf.
The paper has been rejected based on two reviewer reports. The first reviewer recommends outright rejection based on an argument identical to the one Justo has put forward in this forum. I do not agree with that argument and might consider fighting back.
The second reviewer has enthusiastically recommended the paper for publication with very positive comments: "The manuscript by Joy Christian is a virtuoso performance and tells us much about the possible analogies and failures of von Neuman's and Bell's no-go proofs. I find Christian's logic convincing and definitely recommend that this work be published." The report then goes on to make some minor criticisms and concludes: "Besides all these minor criticisms, Christian's paper is excellent and definitely should be published."
The paper is nevertheless rejected on the grounds that the journal's "current publication program is not well suited for it, and must regretfully decline your offer to let us publish it."
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Why did they send it out for review if it wasn't well suited for the Journal. This is highly unusual. The editor should reject it outright if that is the case.
minkwe wrote:
Are the review reports confidential or can you post it here for us to shred?
Joy Christian wrote:Review reports are always confidential. By posting the information that I have posted is already a violation of some unwritten rules of publication ethics. Moreover, I have decided to appeal the decision because I do not agree with the comments by the first reviewer. It is worth addressing them if only to refute the argument head-on. So, for now, I cannot post the reports here.
Joy Christian wrote:gill1109 wrote:
I understand Einstein’s argument. You still have not answered mine. There is no contradiction. My argument used only the additivity within quantum mechanics. Which Einstein agreed with. Please think carefully about the argument I gave; don’t jump to conclusions.
Ok. Let me respond to Gill's argument in more detail. Here is his argument, which I reproduce from the other thread:gill1109 wrote:
Consider three observables A, B and C such that C = A + B. Suppose none commute with one another. There are three separate experiments which allow one to experimentally determine <A>, <B>, and <C>, each by averaging many measurements of A, B or C on systems prepared in the same state rho. One will discover that <C> = <A> + <B>.
This is because <A> = trace(rho A), <B> = trace(rho B), <C> = trace(rho C), “trace” is linear.
A hidden variable model for these experiments is a classical probability space with three random variables X, Y and Z defined on it, such that the probability distributions of the three random variables exactly reproduce the probability distributions of the outcomes of measurements of the three observables. In particular, their mean values are the same. Hence E(X) = <A>, E(Y) = <B>, E(Z) = <C>. Hence E(X) + E(Y) = E(Z).
The additivity follows from the linearity of the trace operator. The hidden variable model by definition mimics observable features of the quantum model (probabilities, expectation values...).
The mistake in the above argument is obvious, and, as I noted in the other thread, it is precisely the one that was pointed out by Einstein in the mid-1930s, and later by Bell and others.
The mistake is that, while C = A + B by construction, Z is not equal to X + Y, if X, Y, and Z are the eigenvalues of A, B, and C, respectively, as they must be in any hidden variable theory:John S. Bell wrote:
[von Neumann's] essential assumption is: Any real linear combination of expectation values ... is the expectation value of the combination. This is true for quantum mechanical states; it is required by von Neumann of the hypothetical dispersion free states also. ... But for a dispersion free state (which has no statistical character) the expectation value of an observable must equal one of its eigenvalues. ... The essential assumption [of von Neumann] can be criticized as follows. ... (from Section 3 of Chapter 1 of Bell's book).
gill1109 wrote:
There is no reason for X + Y = Z to hold in the presumed underlying dispersion-free states in a possibly contextual hidden variables theory.
It was not the objective measurable predictions of quantum mechanics which ruled out hidden variables. It was the arbitrary assumption of a particular (and impossible) relation between the results of incompatible measurements either of which might be made on a given occasion but only one of which can in fact be made.
gill1109 wrote:The key word is “dispersion-free”. Bell means, to use statistical language, conditional on the values of the underlying hidden variables.
minkwe wrote:gill1109 wrote:The key word is “dispersion-free”. Bell means, to use statistical language, conditional on the values of the underlying hidden variables.
By dispersion-free, Bell simply means deterministic.
gill1109 wrote:He means more than deterministic. He means that after you have conditioned on the values taken by the hidden variables in any particular case, everything else becomes deterministic.
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